:: GLIB_003 semantic presentation

REAL is non empty non trivial non finite V60() V61() V62() V66() set
NAT is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal V60() V61() V62() V63() V64() V65() V66() Element of K32(REAL)
K32(REAL) is non trivial non finite set
COMPLEX is non empty non trivial non finite V60() V66() set
RAT is non empty non trivial non finite V60() V61() V62() V63() V66() set
INT is non empty non trivial non finite V60() V61() V62() V63() V64() V66() set
K33(COMPLEX,COMPLEX) is non trivial Relation-like non finite complex-valued set
K32(K33(COMPLEX,COMPLEX)) is non trivial non finite set
K33(K33(COMPLEX,COMPLEX),COMPLEX) is non trivial Relation-like non finite complex-valued set
K32(K33(K33(COMPLEX,COMPLEX),COMPLEX)) is non trivial non finite set
K33(REAL,REAL) is non trivial Relation-like non finite complex-valued ext-real-valued real-valued set
K32(K33(REAL,REAL)) is non trivial non finite set
K33(K33(REAL,REAL),REAL) is non trivial Relation-like non finite complex-valued ext-real-valued real-valued set
K32(K33(K33(REAL,REAL),REAL)) is non trivial non finite set
K33(RAT,RAT) is non trivial Relation-like RAT -valued non finite complex-valued ext-real-valued real-valued set
K32(K33(RAT,RAT)) is non trivial non finite set
K33(K33(RAT,RAT),RAT) is non trivial Relation-like RAT -valued non finite complex-valued ext-real-valued real-valued set
K32(K33(K33(RAT,RAT),RAT)) is non trivial non finite set
K33(INT,INT) is non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued set
K32(K33(INT,INT)) is non trivial non finite set
K33(K33(INT,INT),INT) is non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued set
K32(K33(K33(INT,INT),INT)) is non trivial non finite set
K33(NAT,NAT) is non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
K33(K33(NAT,NAT),NAT) is non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
K32(K33(K33(NAT,NAT),NAT)) is non trivial non finite set
NAT is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal V60() V61() V62() V63() V64() V65() V66() set
K32(NAT) is non trivial non finite set
K32(NAT) is non trivial non finite set
K195(NAT) is V35() set
K363() is set
K32(K363()) is set
K32(K32(K363())) is set
K371() is Element of K32(K32(K363()))
Real>=0 is set
{} is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() set
1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
2 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
3 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
_GraphSelectors is non empty V60() V61() V62() V63() V64() V65() Element of K32(NAT)
VertexSelector is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
EdgeSelector is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
SourceSelector is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
TargetSelector is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
4 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
{VertexSelector,EdgeSelector,SourceSelector,TargetSelector} is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
card {} is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() set
7 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
5 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
6 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
9 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
8 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
0 is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() V31() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of NAT
Real>=0 is V60() V61() V62() Element of K32(REAL)
{ b₁ where b₁ is V21() real ext-real Element of REAL : 0 <= b₁ } is set
<*> REAL is empty Relation-like non-empty empty-yielding NAT -defined REAL -valued Function-like one-to-one constant functional V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() FinSequence of REAL
Sum (<*> REAL) is V21() real ext-real Element of REAL
K168() is Relation-like K33(REAL,REAL) -defined REAL -valued Function-like total V18(K33(REAL,REAL), REAL ) complex-valued ext-real-valued real-valued Element of K32(K33(K33(REAL,REAL),REAL))
K221(REAL,(<*> REAL),K168()) is V21() real ext-real Element of REAL
G is set
v is Relation-like NAT -defined G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of G
K32(v) is finite V40() set
x is Relation-like NAT -defined G -valued Function-like finite FinSubsequence-like Element of K32(v)
Seq x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
val is set
rng (Seq x) is finite set
dom (Seq x) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
Gn is set
(Seq x) . Gn is set
dom v is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
ENext is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
rng v is finite Element of K32(G)
K32(G) is set
x is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
v . x is set
10 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
G is set
<*G*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
v is set
<*v*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
<*G*> ^ <*v*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like set
1 + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
x is set
<*x*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
(<*G*> ^ <*v*>) ^ <*x*> is non empty Relation-like NAT -defined Function-like finite (1 + 1) + 1 -element FinSequence-like FinSubsequence-like set
(1 + 1) + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
val is set
<*val*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
((<*G*> ^ <*v*>) ^ <*x*>) ^ <*val*> is non empty Relation-like NAT -defined Function-like finite ((1 + 1) + 1) + 1 -element FinSequence-like FinSubsequence-like set
((1 + 1) + 1) + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
Gn is set
<*Gn*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
(((<*G*> ^ <*v*>) ^ <*x*>) ^ <*val*>) ^ <*Gn*> is non empty Relation-like NAT -defined Function-like finite (((1 + 1) + 1) + 1) + 1 -element FinSequence-like FinSubsequence-like set
(((1 + 1) + 1) + 1) + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
ENext is set
<*ENext*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
((((<*G*> ^ <*v*>) ^ <*x*>) ^ <*val*>) ^ <*Gn*>) ^ <*ENext*> is non empty Relation-like NAT -defined Function-like finite ((((1 + 1) + 1) + 1) + 1) + 1 -element FinSequence-like FinSubsequence-like set
((((1 + 1) + 1) + 1) + 1) + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
x is set
<*x*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
(((((<*G*> ^ <*v*>) ^ <*x*>) ^ <*val*>) ^ <*Gn*>) ^ <*ENext*>) ^ <*x*> is non empty Relation-like NAT -defined Function-like finite (((((1 + 1) + 1) + 1) + 1) + 1) + 1 -element FinSequence-like FinSubsequence-like set
(((((1 + 1) + 1) + 1) + 1) + 1) + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
n is set
<*n*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
((((((<*G*> ^ <*v*>) ^ <*x*>) ^ <*val*>) ^ <*Gn*>) ^ <*ENext*>) ^ <*x*>) ^ <*n*> is non empty Relation-like NAT -defined Function-like finite ((((((1 + 1) + 1) + 1) + 1) + 1) + 1) + 1 -element FinSequence-like FinSubsequence-like set
((((((1 + 1) + 1) + 1) + 1) + 1) + 1) + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
y is set
<*y*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
(((((((<*G*> ^ <*v*>) ^ <*x*>) ^ <*val*>) ^ <*Gn*>) ^ <*ENext*>) ^ <*x*>) ^ <*n*>) ^ <*y*> is non empty Relation-like NAT -defined Function-like finite (((((((1 + 1) + 1) + 1) + 1) + 1) + 1) + 1) + 1 -element FinSequence-like FinSubsequence-like set
(((((((1 + 1) + 1) + 1) + 1) + 1) + 1) + 1) + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
x is set
<*x*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
((((((((<*G*> ^ <*v*>) ^ <*x*>) ^ <*val*>) ^ <*Gn*>) ^ <*ENext*>) ^ <*x*>) ^ <*n*>) ^ <*y*>) ^ <*x*> is non empty Relation-like NAT -defined Function-like finite ((((((((1 + 1) + 1) + 1) + 1) + 1) + 1) + 1) + 1) + 1 -element FinSequence-like FinSubsequence-like set
((((((((1 + 1) + 1) + 1) + 1) + 1) + 1) + 1) + 1) + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
c₁₁ is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len c₁₁ is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
c₁₁ . 1 is set
c₁₁ . 2 is set
c₁₁ . 3 is set
c₁₁ . 4 is set
c₁₁ . 5 is set
c₁₁ . 6 is set
c₁₁ . 7 is set
c₁₁ . 8 is set
c₁₁ . 9 is set
c₁₁ . 10 is set
((((((((<*G*> ^ <*v*>) ^ <*x*>) ^ <*val*>) ^ <*Gn*>) ^ <*ENext*>) ^ <*x*>) ^ <*n*>) ^ <*y*>) . 1 is set
((((((((<*G*> ^ <*v*>) ^ <*x*>) ^ <*val*>) ^ <*Gn*>) ^ <*ENext*>) ^ <*x*>) ^ <*n*>) ^ <*y*>) . 2 is set
((((((((<*G*> ^ <*v*>) ^ <*x*>) ^ <*val*>) ^ <*Gn*>) ^ <*ENext*>) ^ <*x*>) ^ <*n*>) ^ <*y*>) . 5 is set
((((((((<*G*> ^ <*v*>) ^ <*x*>) ^ <*val*>) ^ <*Gn*>) ^ <*ENext*>) ^ <*x*>) ^ <*n*>) ^ <*y*>) . 6 is set
((((((((<*G*> ^ <*v*>) ^ <*x*>) ^ <*val*>) ^ <*Gn*>) ^ <*ENext*>) ^ <*x*>) ^ <*n*>) ^ <*y*>) . 7 is set
((((((((<*G*> ^ <*v*>) ^ <*x*>) ^ <*val*>) ^ <*Gn*>) ^ <*ENext*>) ^ <*x*>) ^ <*n*>) ^ <*y*>) . 8 is set
len ((((((((<*G*> ^ <*v*>) ^ <*x*>) ^ <*val*>) ^ <*Gn*>) ^ <*ENext*>) ^ <*x*>) ^ <*n*>) ^ <*y*>) is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
dom ((((((((<*G*> ^ <*v*>) ^ <*x*>) ^ <*val*>) ^ <*Gn*>) ^ <*ENext*>) ^ <*x*>) ^ <*n*>) ^ <*y*>) is non empty finite (((((((1 + 1) + 1) + 1) + 1) + 1) + 1) + 1) + 1 -element V60() V61() V62() V63() V64() V65() Element of K32(NAT)
Seg 9 is non empty finite 9 -element V60() V61() V62() V63() V64() V65() Element of K32(NAT)
((((((((<*G*> ^ <*v*>) ^ <*x*>) ^ <*val*>) ^ <*Gn*>) ^ <*ENext*>) ^ <*x*>) ^ <*n*>) ^ <*y*>) . 9 is set
len <*x*> is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(len ((((((((<*G*> ^ <*v*>) ^ <*x*>) ^ <*val*>) ^ <*Gn*>) ^ <*ENext*>) ^ <*x*>) ^ <*n*>) ^ <*y*>)) + (len <*x*>) is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
9 + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
((((((((<*G*> ^ <*v*>) ^ <*x*>) ^ <*val*>) ^ <*Gn*>) ^ <*ENext*>) ^ <*x*>) ^ <*n*>) ^ <*y*>) . 3 is set
((((((((<*G*> ^ <*v*>) ^ <*x*>) ^ <*val*>) ^ <*Gn*>) ^ <*ENext*>) ^ <*x*>) ^ <*n*>) ^ <*y*>) . 4 is set
(len ((((((((<*G*> ^ <*v*>) ^ <*x*>) ^ <*val*>) ^ <*Gn*>) ^ <*ENext*>) ^ <*x*>) ^ <*n*>) ^ <*y*>)) + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
c₁₁ . ((len ((((((((<*G*> ^ <*v*>) ^ <*x*>) ^ <*val*>) ^ <*Gn*>) ^ <*ENext*>) ^ <*x*>) ^ <*n*>) ^ <*y*>)) + 1) is set
G is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K32(G) is finite V40() set
dom G is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
Sum G is V21() real ext-real Element of REAL
K221(REAL,G,K168()) is V21() real ext-real Element of REAL
v is Relation-like NAT -defined REAL -valued Function-like finite FinSubsequence-like complex-valued ext-real-valued real-valued Element of K32(G)
(REAL,G,v) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (REAL,G,v) is V21() real ext-real Element of REAL
K221(REAL,(REAL,G,v),K168()) is V21() real ext-real Element of REAL
len (REAL,G,v) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
x is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
val is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K32(val) is finite V40() set
dom val is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
Gn is Relation-like NAT -defined REAL -valued Function-like finite FinSubsequence-like complex-valued ext-real-valued real-valued Element of K32(val)
(REAL,val,Gn) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len (REAL,val,Gn) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
x + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
ENext is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
x is V21() real ext-real Element of REAL
<*x*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant finite 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued V54() decreasing non-decreasing non-increasing FinSequence of REAL
ENext ^ <*x*> is non empty Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
card Gn is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
dom Gn is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
n is set
y is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
Seg y is finite y -element V60() V61() V62() V63() V64() V65() Element of K32(NAT)
x is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
x is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
c₁₁ is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
val . c₁₁ is V21() real ext-real Element of REAL
len ENext is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
len <*x*> is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(len ENext) + (len <*x*>) is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(len ENext) + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
Sgm (dom Gn) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
dom (REAL,val,Gn) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
card (dom Gn) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
len (Sgm (dom Gn)) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(Sgm (dom Gn)) . (len (Sgm (dom Gn))) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(Sgm (dom Gn)) . (len (REAL,val,Gn)) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
dom (Sgm (dom Gn)) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
rng (Sgm (dom Gn)) is finite V60() V61() V62() V63() V64() V65() Element of K32(REAL)
G3 is set
(Sgm (dom Gn)) . G3 is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
G3 is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
G3 is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(REAL,val,Gn) . (len (REAL,val,Gn)) is V21() real ext-real Element of REAL
(Sgm (dom Gn)) * Gn is Relation-like NAT -defined REAL -valued Function-like finite complex-valued ext-real-valued real-valued set
Gn . ((Sgm (dom Gn)) . (len (REAL,val,Gn))) is V21() real ext-real Element of REAL
[c₁₁,x] is set
Sum (REAL,val,Gn) is V21() real ext-real Element of REAL
K221(REAL,(REAL,val,Gn),K168()) is V21() real ext-real Element of REAL
Sum ENext is V21() real ext-real Element of REAL
K221(REAL,ENext,K168()) is V21() real ext-real Element of REAL
(val . c₁₁) + (Sum ENext) is V21() real ext-real set
len val is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
VL9 is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
c₁₁ + VL9 is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
c₁₁ - 1 is V21() real V30() ext-real set
VL9 is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
Seg VL9 is finite VL9 -element V60() V61() V62() V63() V64() V65() Element of K32(NAT)
Gn | (Seg VL9) is Relation-like NAT -defined Seg VL9 -defined NAT -defined REAL -valued Function-like finite FinSubsequence-like complex-valued ext-real-valued real-valued set
G3 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len G3 is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
G3 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len G3 is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
G3 ^ G3 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
VL9 + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
fsA is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len fsA is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
fsB is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len fsB is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
fsA ^ fsB is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
dom G3 is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
G3 . c₁₁ is V21() real ext-real Element of REAL
fssq is set
G3 is Relation-like NAT -defined REAL -valued Function-like finite FinSubsequence-like complex-valued ext-real-valued real-valued Element of K32(val)
i is set
x1 is set
[i,x1] is set
x2 is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
dom fsA is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
val . x2 is V21() real ext-real Element of REAL
x2 + 0 is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
G3 . x2 is V21() real ext-real Element of REAL
fsA . x2 is V21() real ext-real Element of REAL
K32(fsA) is finite V40() set
i is set
[c₁₁,(val . c₁₁)] is set
{[c₁₁,(val . c₁₁)]} is non empty trivial Relation-like Function-like constant finite 1 -element set
Gn . c₁₁ is V21() real ext-real Element of REAL
[c₁₁,(Gn . c₁₁)] is set
i is set
fssq is Relation-like NAT -defined REAL -valued Function-like finite FinSubsequence-like complex-valued ext-real-valued real-valued Element of K32(fsA)
x1 is set
x2 is set
[x1,x2] is set
z is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
[z,x2] is set
Gn \ {[c₁₁,(val . c₁₁)]} is Relation-like NAT -defined REAL -valued Function-like finite FinSubsequence-like complex-valued ext-real-valued real-valued Element of K32(val)
x1 is set
x2 is set
[x1,x2] is set
z is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
z + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
(z + 1) - 1 is V21() real V30() ext-real set
i is set
Gn . i is V21() real ext-real Element of REAL
[i,(Gn . i)] is set
x1 is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
{c₁₁} is non empty trivial finite V40() 1 -element V60() V61() V62() V63() V64() V65() set
dom fssq is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(dom fssq) \/ {c₁₁} is non empty finite V60() V61() V62() V63() V64() V65() set
fssq . i is V21() real ext-real Element of REAL
[i,(fssq . i)] is set
i is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
x1 is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
fssq . i is V21() real ext-real Element of REAL
[i,(fssq . i)] is Element of K33(NAT,REAL)
K33(NAT,REAL) is non trivial Relation-like non finite complex-valued ext-real-valued real-valued set
card fssq is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
card {[c₁₁,(val . c₁₁)]} is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(card Gn) - (card {[c₁₁,(val . c₁₁)]}) is V21() real V30() ext-real set
(x + 1) - 1 is V21() real V30() ext-real set
(REAL,fsA,fssq) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len (REAL,fsA,fssq) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
i is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
(Sgm (dom Gn)) . i is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
Sgm (dom fssq) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
(Sgm (dom fssq)) . i is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
dom ENext is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
ENext . i is V21() real ext-real Element of REAL
(REAL,val,Gn) . i is V21() real ext-real Element of REAL
len (Sgm (dom fssq)) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
card (dom fssq) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
z is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
Seg z is finite z -element V60() V61() V62() V63() V64() V65() Element of K32(NAT)
dom (Sgm (dom fssq)) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
rng (Sgm (dom fssq)) is finite V60() V61() V62() V63() V64() V65() Element of K32(REAL)
z is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
Seg z is finite z -element V60() V61() V62() V63() V64() V65() Element of K32(NAT)
fssq . ((Sgm (dom fssq)) . i) is V21() real ext-real Element of REAL
[((Sgm (dom fssq)) . i),(fssq . ((Sgm (dom fssq)) . i))] is Element of K33(NAT,REAL)
Gn . ((Sgm (dom fssq)) . i) is V21() real ext-real Element of REAL
Gn . ((Sgm (dom Gn)) . i) is V21() real ext-real Element of REAL
(Sgm (dom fssq)) * fssq is Relation-like NAT -defined REAL -valued Function-like finite complex-valued ext-real-valued real-valued set
dom (REAL,fsA,fssq) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(REAL,fsA,fssq) . i is V21() real ext-real Element of REAL
z is set
Seg (len val) is finite len val -element V60() V61() V62() V63() V64() V65() Element of K32(NAT)
Sgm {c₁₁} is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
(Sgm (dom fssq)) ^ (Sgm {c₁₁}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
z is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
Seg z is finite z -element V60() V61() V62() V63() V64() V65() Element of K32(NAT)
i is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
fsA . i is V21() real ext-real Element of REAL
G3 . i is V21() real ext-real Element of REAL
val . i is V21() real ext-real Element of REAL
Sum fsA is V21() real ext-real Element of REAL
K221(REAL,fsA,K168()) is V21() real ext-real Element of REAL
(Sum (REAL,val,Gn)) + (Sum ENext) is V21() real ext-real set
((val . c₁₁) + (Sum ENext)) + (Sum fsA) is V21() real ext-real set
(val . c₁₁) + (Sum fsA) is V21() real ext-real set
((val . c₁₁) + (Sum fsA)) + (Sum ENext) is V21() real ext-real set
(Sum fsA) + (val . c₁₁) is V21() real ext-real set
i is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
dom G3 is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
c₁₁ + i is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
val . (c₁₁ + i) is V21() real ext-real Element of REAL
G3 . i is V21() real ext-real Element of REAL
Sum G3 is V21() real ext-real Element of REAL
K221(REAL,G3,K168()) is V21() real ext-real Element of REAL
dom fsB is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
fsB . 1 is V21() real ext-real Element of REAL
<*(val . c₁₁)*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant finite 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued V54() decreasing non-decreasing non-increasing FinSequence of REAL
Sum val is V21() real ext-real Element of REAL
K221(REAL,val,K168()) is V21() real ext-real Element of REAL
Sum G3 is V21() real ext-real Element of REAL
K221(REAL,G3,K168()) is V21() real ext-real Element of REAL
(Sum G3) + (Sum G3) is V21() real ext-real set
Sum <*(val . c₁₁)*> is V21() real ext-real Element of REAL
K221(REAL,<*(val . c₁₁)*>,K168()) is V21() real ext-real Element of REAL
(Sum fsA) + (Sum <*(val . c₁₁)*>) is V21() real ext-real set
((Sum fsA) + (Sum <*(val . c₁₁)*>)) + (Sum G3) is V21() real ext-real set
((Sum fsA) + (val . c₁₁)) + (Sum G3) is V21() real ext-real set
((Sum fsA) + (val . c₁₁)) + 0 is V21() real ext-real set
val is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K32(val) is finite V40() set
x is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
dom val is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
Gn is Relation-like NAT -defined REAL -valued Function-like finite FinSubsequence-like complex-valued ext-real-valued real-valued Element of K32(val)
(REAL,val,Gn) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len (REAL,val,Gn) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
x + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
Sum (REAL,val,Gn) is V21() real ext-real Element of REAL
K221(REAL,(REAL,val,Gn),K168()) is V21() real ext-real Element of REAL
Sum val is V21() real ext-real Element of REAL
K221(REAL,val,K168()) is V21() real ext-real Element of REAL
x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K32(x) is finite V40() set
dom x is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
val is Relation-like NAT -defined REAL -valued Function-like finite FinSubsequence-like complex-valued ext-real-valued real-valued Element of K32(x)
(REAL,x,val) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len (REAL,x,val) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
Gn is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
x . Gn is V21() real ext-real Element of REAL
Sum (REAL,x,val) is V21() real ext-real Element of REAL
K221(REAL,(REAL,x,val),K168()) is V21() real ext-real Element of REAL
Sum x is V21() real ext-real Element of REAL
K221(REAL,x,K168()) is V21() real ext-real Element of REAL
x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K32(x) is finite V40() set
dom x is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
val is Relation-like NAT -defined REAL -valued Function-like finite FinSubsequence-like complex-valued ext-real-valued real-valued Element of K32(x)
(REAL,x,val) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len (REAL,x,val) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
Sum (REAL,x,val) is V21() real ext-real Element of REAL
K221(REAL,(REAL,x,val),K168()) is V21() real ext-real Element of REAL
Sum x is V21() real ext-real Element of REAL
K221(REAL,x,K168()) is V21() real ext-real Element of REAL
() is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
() is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
() is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
{1} is non empty trivial finite V40() 1 -element V60() V61() V62() V63() V64() V65() Element of K32(NAT)
K33({},{1}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
K32(K33({},{1})) is finite V40() set
the empty Relation-like non-empty empty-yielding {} -defined {1} -valued Function-like one-to-one constant functional total V18( {} ,{1}) V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33({},{1})) is empty Relation-like non-empty empty-yielding {} -defined {1} -valued Function-like one-to-one constant functional total V18( {} ,{1}) V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33({},{1}))
the empty Relation-like non-empty empty-yielding {} -defined RAT -valued Function-like one-to-one constant functional total V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() set is empty Relation-like non-empty empty-yielding {} -defined RAT -valued Function-like one-to-one constant functional total V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() set
K33({},REAL) is Relation-like complex-valued ext-real-valued real-valued set
K32(K33({},REAL)) is set
the empty Relation-like non-empty empty-yielding {} -defined REAL -valued Function-like one-to-one constant functional total V18( {} , REAL ) V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33({},REAL)) is empty Relation-like non-empty empty-yielding {} -defined REAL -valued Function-like one-to-one constant functional total V18( {} , REAL ) V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33({},REAL))
K33({1},REAL) is non trivial Relation-like non finite complex-valued ext-real-valued real-valued set
K32(K33({1},REAL)) is non trivial non finite set
the Relation-like {1} -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33({1},REAL)) is Relation-like {1} -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33({1},REAL))
<*{1}*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
<*{}*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
<*{1}*> ^ <*{}*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like set
1 + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
<* the empty Relation-like non-empty empty-yielding {} -defined {1} -valued Function-like one-to-one constant functional total V18( {} ,{1}) V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33({},{1}))*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
(<*{1}*> ^ <*{}*>) ^ <* the empty Relation-like non-empty empty-yielding {} -defined {1} -valued Function-like one-to-one constant functional total V18( {} ,{1}) V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33({},{1}))*> is non empty Relation-like NAT -defined Function-like finite (1 + 1) + 1 -element FinSequence-like FinSubsequence-like set
(1 + 1) + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
((<*{1}*> ^ <*{}*>) ^ <* the empty Relation-like non-empty empty-yielding {} -defined {1} -valued Function-like one-to-one constant functional total V18( {} ,{1}) V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33({},{1}))*>) ^ <* the empty Relation-like non-empty empty-yielding {} -defined {1} -valued Function-like one-to-one constant functional total V18( {} ,{1}) V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33({},{1}))*> is non empty Relation-like NAT -defined Function-like finite ((1 + 1) + 1) + 1 -element FinSequence-like FinSubsequence-like set
((1 + 1) + 1) + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
<* the empty Relation-like non-empty empty-yielding {} -defined RAT -valued Function-like one-to-one constant functional total V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() set *> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
(((<*{1}*> ^ <*{}*>) ^ <* the empty Relation-like non-empty empty-yielding {} -defined {1} -valued Function-like one-to-one constant functional total V18( {} ,{1}) V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33({},{1}))*>) ^ <* the empty Relation-like non-empty empty-yielding {} -defined {1} -valued Function-like one-to-one constant functional total V18( {} ,{1}) V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33({},{1}))*>) ^ <* the empty Relation-like non-empty empty-yielding {} -defined RAT -valued Function-like one-to-one constant functional total V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() set *> is non empty Relation-like NAT -defined Function-like finite (((1 + 1) + 1) + 1) + 1 -element FinSequence-like FinSubsequence-like set
(((1 + 1) + 1) + 1) + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
<* the empty Relation-like non-empty empty-yielding {} -defined REAL -valued Function-like one-to-one constant functional total V18( {} , REAL ) V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33({},REAL))*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
((((<*{1}*> ^ <*{}*>) ^ <* the empty Relation-like non-empty empty-yielding {} -defined {1} -valued Function-like one-to-one constant functional total V18( {} ,{1}) V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33({},{1}))*>) ^ <* the empty Relation-like non-empty empty-yielding {} -defined {1} -valued Function-like one-to-one constant functional total V18( {} ,{1}) V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33({},{1}))*>) ^ <* the empty Relation-like non-empty empty-yielding {} -defined RAT -valued Function-like one-to-one constant functional total V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() set *>) ^ <* the empty Relation-like non-empty empty-yielding {} -defined REAL -valued Function-like one-to-one constant functional total V18( {} , REAL ) V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33({},REAL))*> is non empty Relation-like NAT -defined Function-like finite ((((1 + 1) + 1) + 1) + 1) + 1 -element FinSequence-like FinSubsequence-like set
((((1 + 1) + 1) + 1) + 1) + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
<* the Relation-like {1} -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33({1},REAL))*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
(((((<*{1}*> ^ <*{}*>) ^ <* the empty Relation-like non-empty empty-yielding {} -defined {1} -valued Function-like one-to-one constant functional total V18( {} ,{1}) V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33({},{1}))*>) ^ <* the empty Relation-like non-empty empty-yielding {} -defined {1} -valued Function-like one-to-one constant functional total V18( {} ,{1}) V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33({},{1}))*>) ^ <* the empty Relation-like non-empty empty-yielding {} -defined RAT -valued Function-like one-to-one constant functional total V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() set *>) ^ <* the empty Relation-like non-empty empty-yielding {} -defined REAL -valued Function-like one-to-one constant functional total V18( {} , REAL ) V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33({},REAL))*>) ^ <* the Relation-like {1} -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33({1},REAL))*> is non empty Relation-like NAT -defined Function-like finite (((((1 + 1) + 1) + 1) + 1) + 1) + 1 -element FinSequence-like FinSubsequence-like set
(((((1 + 1) + 1) + 1) + 1) + 1) + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
dom the Relation-like {1} -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33({1},REAL)) is finite V40() V60() V61() V62() V63() V64() V65() Element of K32({1})
K32({1}) is finite V40() set
len ((((((<*{1}*> ^ <*{}*>) ^ <* the empty Relation-like non-empty empty-yielding {} -defined {1} -valued Function-like one-to-one constant functional total V18( {} ,{1}) V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33({},{1}))*>) ^ <* the empty Relation-like non-empty empty-yielding {} -defined {1} -valued Function-like one-to-one constant functional total V18( {} ,{1}) V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33({},{1}))*>) ^ <* the empty Relation-like non-empty empty-yielding {} -defined RAT -valued Function-like one-to-one constant functional total V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() set *>) ^ <* the empty Relation-like non-empty empty-yielding {} -defined REAL -valued Function-like one-to-one constant functional total V18( {} , REAL ) V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33({},REAL))*>) ^ <* the Relation-like {1} -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33({1},REAL))*>) is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
n is Relation-like NAT -defined Function-like finite set
dom n is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
Seg 7 is non empty finite 7 -element V60() V61() V62() V63() V64() V65() Element of K32(NAT)
n . () is set
n . () is set
the_Vertices_of n is set
n . VertexSelector is set
the_Edges_of n is set
n . EdgeSelector is set
the_Source_of n is set
n . SourceSelector is set
the_Target_of n is set
n . TargetSelector is set
n . () is set
dom the empty Relation-like non-empty empty-yielding {} -defined REAL -valued Function-like one-to-one constant functional total V18( {} , REAL ) V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33({},REAL)) is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(NAT)
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
G . () is set
the_Edges_of G is set
G . EdgeSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
G . () is set
the_Edges_of G is set
G . EdgeSelector is set
v is Relation-like Function-like set
dom v is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
G . () is set
the_Vertices_of G is non empty set
G . VertexSelector is set
v is Relation-like Function-like set
dom v is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
the_Edges_of G is set
G . EdgeSelector is set
v is Relation-like Function-like set
dom v is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
the_Vertices_of G is non empty set
G . VertexSelector is set
v is Relation-like Function-like set
dom v is set
G is Relation-like NAT -defined Function-like finite [Graph-like] set
v is set
G .set ((),v) is Relation-like NAT -defined Function-like finite set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} is non empty trivial finite V40() 1 -element V60() V61() V62() V63() V64() V65() set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
{v} is non empty trivial finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G .set ((),v) is Relation-like NAT -defined Function-like finite set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} is non empty trivial finite V40() 1 -element V60() V61() V62() V63() V64() V65() set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G .set ((),v) is Relation-like NAT -defined Function-like finite set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} is non empty trivial finite V40() 1 -element V60() V61() V62() V63() V64() V65() set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
v is Relation-like NAT -defined Function-like finite [Graph-like] set
x is set
v .set ((),x) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> x is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> x is non empty Relation-like {()} -defined {x} -valued Function-like constant total V18({()},{x}) finite Element of K32(K33({()},{x}))
{x} is non empty trivial finite 1 -element set
K33({()},{x}) is Relation-like finite set
K32(K33({()},{x})) is finite V40() set
v +* (() .--> x) is Relation-like Function-like finite set
v .set ((),x) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> x is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> x is non empty Relation-like {()} -defined {x} -valued Function-like constant total V18({()},{x}) finite Element of K32(K33({()},{x}))
K33({()},{x}) is Relation-like finite set
K32(K33({()},{x})) is finite V40() set
v +* (() .--> x) is Relation-like Function-like finite set
v .set ((),x) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> x is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> x is non empty Relation-like {()} -defined {x} -valued Function-like constant total V18({()},{x}) finite Element of K32(K33({()},{x}))
K33({()},{x}) is Relation-like finite set
K32(K33({()},{x})) is finite V40() set
v +* (() .--> x) is Relation-like Function-like finite set
the_Edges_of (v .set ((),x)) is set
(v .set ((),x)) . EdgeSelector is set
the_Vertices_of (v .set ((),x)) is non empty set
(v .set ((),x)) . VertexSelector is set
the_Edges_of v is set
v . EdgeSelector is set
the_Vertices_of v is non empty set
v . VertexSelector is set
the_Source_of (v .set ((),x)) is Relation-like the_Edges_of (v .set ((),x)) -defined the_Vertices_of (v .set ((),x)) -valued Function-like total V18( the_Edges_of (v .set ((),x)), the_Vertices_of (v .set ((),x))) Element of K32(K33((the_Edges_of (v .set ((),x))),(the_Vertices_of (v .set ((),x)))))
K33((the_Edges_of (v .set ((),x))),(the_Vertices_of (v .set ((),x)))) is Relation-like set
K32(K33((the_Edges_of (v .set ((),x))),(the_Vertices_of (v .set ((),x))))) is set
(v .set ((),x)) . SourceSelector is set
the_Source_of v is Relation-like the_Edges_of v -defined the_Vertices_of v -valued Function-like total V18( the_Edges_of v, the_Vertices_of v) Element of K32(K33((the_Edges_of v),(the_Vertices_of v)))
K33((the_Edges_of v),(the_Vertices_of v)) is Relation-like set
K32(K33((the_Edges_of v),(the_Vertices_of v))) is set
v . SourceSelector is set
the_Target_of (v .set ((),x)) is Relation-like the_Edges_of (v .set ((),x)) -defined the_Vertices_of (v .set ((),x)) -valued Function-like total V18( the_Edges_of (v .set ((),x)), the_Vertices_of (v .set ((),x))) Element of K32(K33((the_Edges_of (v .set ((),x))),(the_Vertices_of (v .set ((),x)))))
(v .set ((),x)) . TargetSelector is set
the_Target_of v is Relation-like the_Edges_of v -defined the_Vertices_of v -valued Function-like total V18( the_Edges_of v, the_Vertices_of v) Element of K32(K33((the_Edges_of v),(the_Vertices_of v)))
v . TargetSelector is set
the_Edges_of (v .set ((),x)) is set
(v .set ((),x)) . EdgeSelector is set
the_Vertices_of (v .set ((),x)) is non empty set
(v .set ((),x)) . VertexSelector is set
the_Source_of (v .set ((),x)) is Relation-like the_Edges_of (v .set ((),x)) -defined the_Vertices_of (v .set ((),x)) -valued Function-like total V18( the_Edges_of (v .set ((),x)), the_Vertices_of (v .set ((),x))) Element of K32(K33((the_Edges_of (v .set ((),x))),(the_Vertices_of (v .set ((),x)))))
K33((the_Edges_of (v .set ((),x))),(the_Vertices_of (v .set ((),x)))) is Relation-like set
K32(K33((the_Edges_of (v .set ((),x))),(the_Vertices_of (v .set ((),x))))) is set
(v .set ((),x)) . SourceSelector is set
the_Target_of (v .set ((),x)) is Relation-like the_Edges_of (v .set ((),x)) -defined the_Vertices_of (v .set ((),x)) -valued Function-like total V18( the_Edges_of (v .set ((),x)), the_Vertices_of (v .set ((),x))) Element of K32(K33((the_Edges_of (v .set ((),x))),(the_Vertices_of (v .set ((),x)))))
(v .set ((),x)) . TargetSelector is set
the_Edges_of (v .set ((),x)) is set
(v .set ((),x)) . EdgeSelector is set
the_Vertices_of (v .set ((),x)) is non empty set
(v .set ((),x)) . VertexSelector is set
the_Source_of (v .set ((),x)) is Relation-like the_Edges_of (v .set ((),x)) -defined the_Vertices_of (v .set ((),x)) -valued Function-like total V18( the_Edges_of (v .set ((),x)), the_Vertices_of (v .set ((),x))) Element of K32(K33((the_Edges_of (v .set ((),x))),(the_Vertices_of (v .set ((),x)))))
K33((the_Edges_of (v .set ((),x))),(the_Vertices_of (v .set ((),x)))) is Relation-like set
K32(K33((the_Edges_of (v .set ((),x))),(the_Vertices_of (v .set ((),x))))) is set
(v .set ((),x)) . SourceSelector is set
the_Target_of (v .set ((),x)) is Relation-like the_Edges_of (v .set ((),x)) -defined the_Vertices_of (v .set ((),x)) -valued Function-like total V18( the_Edges_of (v .set ((),x)), the_Vertices_of (v .set ((),x))) Element of K32(K33((the_Edges_of (v .set ((),x))),(the_Vertices_of (v .set ((),x)))))
(v .set ((),x)) . TargetSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] finite set
v is set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
{v} is non empty trivial finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G is Relation-like NAT -defined Function-like finite [Graph-like] loopless set
v is set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
{v} is non empty trivial finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G is Relation-like NAT -defined Function-like finite [Graph-like] trivial connected set
v is set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
{v} is non empty trivial finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G is Relation-like NAT -defined Function-like finite [Graph-like] non trivial set
v is set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
{v} is non empty trivial finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G is Relation-like NAT -defined Function-like finite [Graph-like] non-multi non-Dmulti set
v is set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
{v} is non empty trivial finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G is Relation-like NAT -defined Function-like finite [Graph-like] non-Dmulti set
v is set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
{v} is non empty trivial finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G is Relation-like NAT -defined Function-like finite [Graph-like] connected set
v is set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
{v} is non empty trivial finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G is Relation-like NAT -defined Function-like finite [Graph-like] loopless non-multi non-Dmulti simple Dsimple acyclic set
v is set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] loopless non-multi non-Dmulti simple Dsimple set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
{v} is non empty trivial finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] loopless non-multi non-Dmulti simple Dsimple set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] loopless non-multi non-Dmulti simple Dsimple set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
v is set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
{v} is non empty trivial finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
dom G is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
dom (G .set ((),v)) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(G .set ((),v)) . () is set
the_Edges_of (G .set ((),v)) is set
(G .set ((),v)) . EdgeSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Relation-like the_Edges_of G -defined Function-like total set
G . () is set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
dom G is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
dom (G .set ((),v)) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(G .set ((),v)) . () is set
the_Edges_of (G .set ((),v)) is set
(G .set ((),v)) . EdgeSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Relation-like the_Edges_of G -defined Function-like total set
G . () is set
G is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Edges_of G is set
G . EdgeSelector is set
v is Relation-like the_Edges_of G -defined Function-like total set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Function-yielding V125() Element of K32(K33({()},{v}))
{v} is non empty trivial functional finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
dom (G .set ((),v)) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
dom G is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
{()} is non empty trivial finite V40() 1 -element V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(dom G) \/ {()} is non empty finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(G .set ((),v)) . () is set
the_Edges_of (G .set ((),v)) is set
(G .set ((),v)) . EdgeSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Edges_of G is set
G . EdgeSelector is set
v is non empty set
K33((the_Edges_of G),v) is Relation-like set
K32(K33((the_Edges_of G),v)) is set
x is Relation-like the_Edges_of G -defined v -valued Function-like total V18( the_Edges_of G,v) Element of K32(K33((the_Edges_of G),v))
G .set ((),x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> x is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> x is non empty Relation-like {()} -defined {x} -valued Function-like constant total V18({()},{x}) finite Function-yielding V125() Element of K32(K33({()},{x}))
{x} is non empty trivial functional finite 1 -element set
K33({()},{x}) is Relation-like finite set
K32(K33({()},{x})) is finite V40() set
G +* (() .--> x) is Relation-like Function-like finite set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
v is set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
{v} is non empty trivial finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
dom G is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
dom (G .set ((),v)) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(G .set ((),v)) . () is set
the_Edges_of (G .set ((),v)) is set
(G .set ((),v)) . EdgeSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
dom G is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
dom (G .set ((),v)) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(G .set ((),v)) . () is set
the_Edges_of (G .set ((),v)) is set
(G .set ((),v)) . EdgeSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
G is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Edges_of G is set
G . EdgeSelector is set
v is set
K33((the_Edges_of G),v) is Relation-like set
K32(K33((the_Edges_of G),v)) is set
x is Relation-like the_Edges_of G -defined v -valued Function-like Element of K32(K33((the_Edges_of G),v))
G .set ((),x) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> x is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> x is non empty Relation-like {()} -defined {x} -valued Function-like constant total V18({()},{x}) finite Function-yielding V125() Element of K32(K33({()},{x}))
{x} is non empty trivial functional finite 1 -element set
K33({()},{x}) is Relation-like finite set
K32(K33({()},{x})) is finite V40() set
G +* (() .--> x) is Relation-like Function-like finite set
dom (G .set ((),x)) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
dom G is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
{()} is non empty trivial finite V40() 1 -element V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(dom G) \/ {()} is non empty finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(G .set ((),x)) . () is set
the_Edges_of (G .set ((),x)) is set
(G .set ((),x)) . EdgeSelector is set
dom x is Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is set
G is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Edges_of G is set
G . EdgeSelector is set
v is Relation-like the_Edges_of G -defined Function-like total set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Function-yielding V125() Element of K32(K33({()},{v}))
{v} is non empty trivial functional finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
dom (G .set ((),v)) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
dom G is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
{()} is non empty trivial finite V40() 1 -element V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(dom G) \/ {()} is non empty finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(G .set ((),v)) . () is set
the_Edges_of (G .set ((),v)) is set
(G .set ((),v)) . EdgeSelector is set
dom v is Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
v is set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
{v} is non empty trivial finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
dom G is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
dom (G .set ((),v)) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(G .set ((),v)) . () is set
the_Vertices_of (G .set ((),v)) is non empty set
(G .set ((),v)) . VertexSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
dom G is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
dom (G .set ((),v)) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(G .set ((),v)) . () is set
the_Vertices_of (G .set ((),v)) is non empty set
(G .set ((),v)) . VertexSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
G is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G is non empty set
G . VertexSelector is set
v is set
K33((the_Vertices_of G),v) is Relation-like set
K32(K33((the_Vertices_of G),v)) is set
x is Relation-like the_Vertices_of G -defined v -valued Function-like Element of K32(K33((the_Vertices_of G),v))
G .set ((),x) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> x is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> x is non empty Relation-like {()} -defined {x} -valued Function-like constant total V18({()},{x}) finite Function-yielding V125() Element of K32(K33({()},{x}))
{x} is non empty trivial functional finite 1 -element set
K33({()},{x}) is Relation-like finite set
K32(K33({()},{x})) is finite V40() set
G +* (() .--> x) is Relation-like Function-like finite set
dom (G .set ((),x)) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
dom G is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
{()} is non empty trivial finite V40() 1 -element V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(dom G) \/ {()} is non empty finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(G .set ((),x)) . () is set
the_Vertices_of (G .set ((),x)) is non empty set
(G .set ((),x)) . VertexSelector is set
dom x is Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is set
G is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G is non empty set
G . VertexSelector is set
v is Relation-like the_Vertices_of G -defined Function-like total set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Function-yielding V125() Element of K32(K33({()},{v}))
{v} is non empty trivial functional finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
dom (G .set ((),v)) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
dom G is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
{()} is non empty trivial finite V40() 1 -element V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(dom G) \/ {()} is non empty finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(G .set ((),v)) . () is set
the_Vertices_of (G .set ((),v)) is non empty set
(G .set ((),v)) . VertexSelector is set
dom v is Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is set
G is Relation-like NAT -defined Function-like finite [Graph-like] set
G .set ((),{}) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> {} is Relation-like NAT -defined {()} -defined RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued Function-yielding V125() set
{()} --> {} is non empty Relation-like {()} -defined RAT -valued INT -valued {{}} -valued Function-like constant total V18({()},{{}}) finite complex-valued ext-real-valued real-valued natural-valued Function-yielding V125() Element of K32(K33({()},{{}}))
{{}} is non empty trivial functional finite V40() 1 -element V60() V61() V62() V63() V64() V65() set
K33({()},{{}}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
K32(K33({()},{{}})) is finite V40() set
G +* (() .--> {}) is Relation-like Function-like finite set
the_Edges_of G is set
G . EdgeSelector is set
K33((the_Edges_of G),{}) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K32(K33((the_Edges_of G),{})) is set
v is empty Relation-like non-empty empty-yielding the_Edges_of G -defined {} -valued Function-like one-to-one constant functional V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33((the_Edges_of G),{}))
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> v is Relation-like NAT -defined {()} -defined RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued Function-yielding V125() set
{()} --> v is non empty Relation-like {()} -defined RAT -valued INT -valued {v} -valued Function-like constant total V18({()},{v}) finite complex-valued ext-real-valued real-valued natural-valued Function-yielding V125() Element of K32(K33({()},{v}))
{v} is non empty trivial functional finite V40() 1 -element V60() V61() V62() V63() V64() V65() set
K33({()},{v}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G .set ((),{}) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> {} is Relation-like NAT -defined {()} -defined RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued Function-yielding V125() set
{()} --> {} is non empty Relation-like {()} -defined RAT -valued INT -valued {{}} -valued Function-like constant total V18({()},{{}}) finite complex-valued ext-real-valued real-valued natural-valued Function-yielding V125() Element of K32(K33({()},{{}}))
K33({()},{{}}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
K32(K33({()},{{}})) is finite V40() set
G +* (() .--> {}) is Relation-like Function-like finite set
the_Vertices_of G is non empty set
G . VertexSelector is set
K33((the_Vertices_of G),{}) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K32(K33((the_Vertices_of G),{})) is set
v is empty Relation-like non-empty empty-yielding the_Vertices_of G -defined {} -valued Function-like one-to-one constant functional non total V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33((the_Vertices_of G),{}))
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> v is Relation-like NAT -defined {()} -defined RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued Function-yielding V125() set
{()} --> v is non empty Relation-like {()} -defined RAT -valued INT -valued {v} -valued Function-like constant total V18({()},{v}) finite complex-valued ext-real-valued real-valued natural-valued Function-yielding V125() Element of K32(K33({()},{v}))
{v} is non empty trivial functional finite V40() 1 -element V60() V61() V62() V63() V64() V65() set
K33({()},{v}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Edges_of G is set
G . EdgeSelector is set
the Relation-like the_Edges_of G -defined Function-like total set is Relation-like the_Edges_of G -defined Function-like total set
G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> the Relation-like the_Edges_of G -defined Function-like total set is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> the Relation-like the_Edges_of G -defined Function-like total set is non empty Relation-like {()} -defined { the Relation-like the_Edges_of G -defined Function-like total set } -valued Function-like constant total V18({()},{ the Relation-like the_Edges_of G -defined Function-like total set }) finite Function-yielding V125() Element of K32(K33({()},{ the Relation-like the_Edges_of G -defined Function-like total set }))
{ the Relation-like the_Edges_of G -defined Function-like total set } is non empty trivial functional finite 1 -element set
K33({()},{ the Relation-like the_Edges_of G -defined Function-like total set }) is Relation-like finite set
K32(K33({()},{ the Relation-like the_Edges_of G -defined Function-like total set })) is finite V40() set
G +* (() .--> the Relation-like the_Edges_of G -defined Function-like total set ) is Relation-like Function-like finite set
the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) is set
(G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) . EdgeSelector is set
K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)) is set
the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)) is Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))
(G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
() .--> the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)) is non empty Relation-like {()} -defined { the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))} -valued Function-like constant total V18({()},{ the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))}) finite Function-yielding V125() Element of K32(K33({()},{ the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))}))
{ the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))} is non empty trivial functional finite 1 -element set
K33({()},{ the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))}) is Relation-like finite set
K32(K33({()},{ the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))})) is finite V40() set
(G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) +* (() .--> the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))) is Relation-like Function-like finite set
the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) is non empty set
((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) . VertexSelector is set
K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL) is non trivial Relation-like non finite complex-valued ext-real-valued real-valued set
K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL)) is non trivial non finite set
the Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL)) is Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL))
((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) .set ((), the Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL))) is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
() .--> the Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> the Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL)) is non empty Relation-like {()} -defined { the Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL))} -valued Function-like constant total V18({()},{ the Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL))}) finite Function-yielding V125() Element of K32(K33({()},{ the Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL))}))
{ the Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL))} is non empty trivial functional finite 1 -element set
K33({()},{ the Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL))}) is Relation-like finite set
K32(K33({()},{ the Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL))})) is finite V40() set
((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) +* (() .--> the Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL))) is Relation-like Function-like finite set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
v is Relation-like NAT -defined Function-like finite [Graph-like] () Subgraph of G
(G) is Relation-like the_Edges_of G -defined Function-like total set
the_Edges_of G is set
G . EdgeSelector is set
G . () is set
(G) | (the_Edges_of G) is Relation-like the_Edges_of G -defined the_Edges_of G -defined Function-like set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
v is Relation-like NAT -defined Function-like finite [Graph-like] () Subgraph of G
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
the_Edges_of G is set
G . EdgeSelector is set
(v) is Relation-like Function-like set
v . () is set
(G) | (the_Edges_of G) is Relation-like Function-like set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
v is Relation-like NAT -defined Function-like finite [Graph-like] () Subgraph of G
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
the_Vertices_of G is non empty set
G . VertexSelector is set
(v) is Relation-like Function-like set
v . () is set
(G) | (the_Vertices_of G) is Relation-like Function-like set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
v is Relation-like NAT -defined Function-like finite [Graph-like] () () Subgraph of G
(G) is Relation-like the_Edges_of G -defined Function-like total set
the_Edges_of G is set
G . EdgeSelector is set
G . () is set
(G) | (the_Edges_of G) is Relation-like the_Edges_of G -defined the_Edges_of G -defined Function-like set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
(v) is Relation-like Function-like set
v . () is set
(G) | (the_Edges_of G) is Relation-like Function-like set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
v is Relation-like NAT -defined Function-like finite [Graph-like] () () Subgraph of G
(G) is Relation-like the_Edges_of G -defined Function-like total set
the_Edges_of G is set
G . EdgeSelector is set
G . () is set
(G) | (the_Edges_of G) is Relation-like the_Edges_of G -defined the_Edges_of G -defined Function-like set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
the_Vertices_of G is non empty set
G . VertexSelector is set
(v) is Relation-like Function-like set
v . () is set
(G) | (the_Vertices_of G) is Relation-like Function-like set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
v is Relation-like NAT -defined Function-like finite [Graph-like] () () Subgraph of G
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
the_Edges_of G is set
G . EdgeSelector is set
(v) is Relation-like Function-like set
v . () is set
(G) | (the_Edges_of G) is Relation-like Function-like set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
the_Vertices_of G is non empty set
G . VertexSelector is set
(v) is Relation-like Function-like set
v . () is set
(G) | (the_Vertices_of G) is Relation-like Function-like set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
v is Relation-like NAT -defined Function-like finite [Graph-like] () () () Subgraph of G
(G) is Relation-like the_Edges_of G -defined Function-like total set
the_Edges_of G is set
G . EdgeSelector is set
G . () is set
(G) | (the_Edges_of G) is Relation-like the_Edges_of G -defined the_Edges_of G -defined Function-like set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
(v) is Relation-like Function-like set
v . () is set
(G) | (the_Edges_of G) is Relation-like Function-like set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
the_Vertices_of G is non empty set
G . VertexSelector is set
(v) is Relation-like Function-like set
v . () is set
(G) | (the_Vertices_of G) is Relation-like Function-like set
G is Relation-like NAT -defined Function-like finite [Graph-like] set
v is set
x is set
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x is Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x
the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x is Element of K32((the_Edges_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x . EdgeSelector is set
the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set is Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set
the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set is non empty Relation-like {()} -defined { the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set } -valued Function-like constant total V18({()},{ the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set }) finite Function-yielding V125() Element of K32(K33({()},{ the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set }))
{ the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set } is non empty trivial functional finite 1 -element set
K33({()},{ the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set }) is Relation-like finite set
K32(K33({()},{ the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set })) is finite V40() set
the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x +* (() .--> the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ) is Relation-like Function-like finite set
the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) is set
( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) . EdgeSelector is set
K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL)) is set
the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL)) is Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL))
( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL))) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
() .--> the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL)) is non empty Relation-like {()} -defined { the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL))} -valued Function-like constant total V18({()},{ the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL))}) finite Function-yielding V125() Element of K32(K33({()},{ the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL))}))
{ the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL))} is non empty trivial functional finite 1 -element set
K33({()},{ the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL))}) is Relation-like finite set
K32(K33({()},{ the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL))})) is finite V40() set
( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) +* (() .--> the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL))) is Relation-like Function-like finite set
the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL)))) is non empty set
(( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL)))) . VertexSelector is set
K33((the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL))))),REAL) is non trivial Relation-like non finite complex-valued ext-real-valued real-valued set
K32(K33((the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL))))),REAL)) is non trivial non finite set
the Relation-like the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL))))),REAL)) is Relation-like the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL))))),REAL))
(( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL)))) .set ((), the Relation-like the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL))))),REAL))) is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
() .--> the Relation-like the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL))))),REAL)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> the Relation-like the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL))))),REAL)) is non empty Relation-like {()} -defined { the Relation-like the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL))))),REAL))} -valued Function-like constant total V18({()},{ the Relation-like the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL))))),REAL))}) finite Function-yielding V125() Element of K32(K33({()},{ the Relation-like the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL))))),REAL))}))
{ the Relation-like the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL))))),REAL))} is non empty trivial functional finite 1 -element set
K33({()},{ the Relation-like the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL))))),REAL))}) is Relation-like finite set
K32(K33({()},{ the Relation-like the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL))))),REAL))})) is finite V40() set
(( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL)))) +* (() .--> the Relation-like the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) .set ((), the Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x .set ((), the Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x -defined Function-like total set ))),REAL))))),REAL))) is Relation-like Function-like finite set
c₁₁ is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G
the_Edges_of c₁₁ is Element of K32((the_Edges_of G))
c₁₁ . EdgeSelector is set
the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x is non empty Element of K32((the_Vertices_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x . VertexSelector is set
the_Vertices_of c₁₁ is non empty Element of K32((the_Vertices_of G))
c₁₁ . VertexSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
the Relation-like the_Edges_of G -defined Function-like total set is Relation-like the_Edges_of G -defined Function-like total set
G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> the Relation-like the_Edges_of G -defined Function-like total set is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> the Relation-like the_Edges_of G -defined Function-like total set is non empty Relation-like {()} -defined { the Relation-like the_Edges_of G -defined Function-like total set } -valued Function-like constant total V18({()},{ the Relation-like the_Edges_of G -defined Function-like total set }) finite Function-yielding V125() Element of K32(K33({()},{ the Relation-like the_Edges_of G -defined Function-like total set }))
{ the Relation-like the_Edges_of G -defined Function-like total set } is non empty trivial functional finite 1 -element set
K33({()},{ the Relation-like the_Edges_of G -defined Function-like total set }) is Relation-like finite set
K32(K33({()},{ the Relation-like the_Edges_of G -defined Function-like total set })) is finite V40() set
G +* (() .--> the Relation-like the_Edges_of G -defined Function-like total set ) is Relation-like Function-like finite set
the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) is set
(G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) . EdgeSelector is set
K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)) is set
the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)) is Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))
(G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
() .--> the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)) is non empty Relation-like {()} -defined { the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))} -valued Function-like constant total V18({()},{ the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))}) finite Function-yielding V125() Element of K32(K33({()},{ the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))}))
{ the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))} is non empty trivial functional finite 1 -element set
K33({()},{ the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))}) is Relation-like finite set
K32(K33({()},{ the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))})) is finite V40() set
(G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) +* (() .--> the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))) is Relation-like Function-like finite set
the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) is non empty set
((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) . VertexSelector is set
K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL) is non trivial Relation-like non finite complex-valued ext-real-valued real-valued set
K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL)) is non trivial non finite set
the Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL)) is Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL))
((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) .set ((), the Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL))) is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
() .--> the Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> the Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL)) is non empty Relation-like {()} -defined { the Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL))} -valued Function-like constant total V18({()},{ the Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL))}) finite Function-yielding V125() Element of K32(K33({()},{ the Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL))}))
{ the Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL))} is non empty trivial functional finite 1 -element set
K33({()},{ the Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL))}) is Relation-like finite set
K32(K33({()},{ the Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL))})) is finite V40() set
((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) +* (() .--> the Relation-like the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of ((G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) .set ((), the Relation-like the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set )) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (G .set ((), the Relation-like the_Edges_of G -defined Function-like total set ))),REAL))))),REAL))) is Relation-like Function-like finite set
x is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
val is Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G,v,x
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
v is set
x is set
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x is Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x
(G) is Relation-like the_Edges_of G -defined Function-like total set
G . () is set
the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x is Element of K32((the_Edges_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x . EdgeSelector is set
(G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x) is Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x -defined the_Edges_of G -defined Function-like set
dom (G) is Element of K32((the_Edges_of G))
dom ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x)) is Element of K32((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x))
K32((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x)) is set
ENext is Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x -defined Function-like total set
the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x .set ((),ENext) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> ENext is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ENext is non empty Relation-like {()} -defined {ENext} -valued Function-like constant total V18({()},{ENext}) finite Function-yielding V125() Element of K32(K33({()},{ENext}))
{ENext} is non empty trivial functional finite 1 -element set
K33({()},{ENext}) is Relation-like finite set
K32(K33({()},{ENext})) is finite V40() set
the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x +* (() .--> ENext) is Relation-like Function-like finite set
n is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G
the_Vertices_of n is non empty Element of K32((the_Vertices_of G))
n . VertexSelector is set
the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x is non empty Element of K32((the_Vertices_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x . VertexSelector is set
the_Edges_of n is Element of K32((the_Edges_of G))
n . EdgeSelector is set
y is Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x
x is Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x
(x) is Relation-like the_Edges_of x -defined Function-like total set
the_Edges_of x is set
x . EdgeSelector is set
x . () is set
the_Edges_of x is Element of K32((the_Edges_of G))
(G) | (the_Edges_of x) is Relation-like the_Edges_of x -defined the_Edges_of G -defined Function-like set
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
val is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G
Gn is Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x
(G) is Relation-like the_Edges_of G -defined Function-like total set
G . () is set
(G) | (the_Edges_of G) is Relation-like the_Edges_of G -defined the_Edges_of G -defined Function-like set
ENext is Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
val is Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
v is set
x is set
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x is Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x
(G) is Relation-like Function-like set
G . () is set
the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x is Element of K32((the_Edges_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x . EdgeSelector is set
(G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x) is Relation-like Function-like set
dom ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x)) is set
rng ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x)) is set
K33((dom ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x))),(rng ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x)))) is Relation-like set
K32(K33((dom ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x))),(rng ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x))))) is set
K33((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x),(rng ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x)))) is Relation-like set
K32(K33((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x),(rng ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x))))) is set
ENext is Relation-like dom ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x)) -defined rng ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x)) -valued Function-like Element of K32(K33((dom ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x))),(rng ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x)))))
x is Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x -defined rng ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x)) -valued Function-like Element of K32(K33((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x),(rng ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x)))))
the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x .set ((),x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> x is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> x is non empty Relation-like {()} -defined {x} -valued Function-like constant total V18({()},{x}) finite Function-yielding V125() Element of K32(K33({()},{x}))
{x} is non empty trivial functional finite 1 -element set
K33({()},{x}) is Relation-like finite set
K32(K33({()},{x})) is finite V40() set
the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x +* (() .--> x) is Relation-like Function-like finite set
y is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G
the_Vertices_of y is non empty Element of K32((the_Vertices_of G))
y . VertexSelector is set
the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x is non empty Element of K32((the_Vertices_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x . VertexSelector is set
the_Edges_of y is Element of K32((the_Edges_of G))
y . EdgeSelector is set
x is Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x
c₁₁ is Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x
(c₁₁) is Relation-like Function-like set
c₁₁ . () is set
the_Edges_of c₁₁ is Element of K32((the_Edges_of G))
c₁₁ . EdgeSelector is set
(G) | (the_Edges_of c₁₁) is Relation-like Function-like set
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
val is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G
Gn is Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
(G) | (the_Edges_of G) is Relation-like Function-like set
ENext is Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
val is Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
v is set
x is set
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x is Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x
(G) is Relation-like Function-like set
G . () is set
the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x is non empty Element of K32((the_Vertices_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x . VertexSelector is set
(G) | (the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x) is Relation-like Function-like set
dom ((G) | (the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x)) is set
rng ((G) | (the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x)) is set
K33((dom ((G) | (the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x))),(rng ((G) | (the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x)))) is Relation-like set
K32(K33((dom ((G) | (the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x))),(rng ((G) | (the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x))))) is set
K33((the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x),(rng ((G) | (the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x)))) is Relation-like set
K32(K33((the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x),(rng ((G) | (the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x))))) is set
ENext is Relation-like dom ((G) | (the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x)) -defined rng ((G) | (the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x)) -valued Function-like Element of K32(K33((dom ((G) | (the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x))),(rng ((G) | (the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x)))))
x is Relation-like the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x -defined rng ((G) | (the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x)) -valued Function-like Element of K32(K33((the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x),(rng ((G) | (the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x)))))
the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x .set ((),x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> x is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> x is non empty Relation-like {()} -defined {x} -valued Function-like constant total V18({()},{x}) finite Function-yielding V125() Element of K32(K33({()},{x}))
{x} is non empty trivial functional finite 1 -element set
K33({()},{x}) is Relation-like finite set
K32(K33({()},{x})) is finite V40() set
the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x +* (() .--> x) is Relation-like Function-like finite set
y is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G
the_Vertices_of y is non empty Element of K32((the_Vertices_of G))
y . VertexSelector is set
the_Edges_of y is Element of K32((the_Edges_of G))
y . EdgeSelector is set
the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x is Element of K32((the_Edges_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x . EdgeSelector is set
x is Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x
c₁₁ is Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x
(c₁₁) is Relation-like Function-like set
c₁₁ . () is set
the_Vertices_of c₁₁ is non empty Element of K32((the_Vertices_of G))
c₁₁ . VertexSelector is set
(G) | (the_Vertices_of c₁₁) is Relation-like Function-like set
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
val is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G
Gn is Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
(G) | (the_Vertices_of G) is Relation-like Function-like set
ENext is Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
val is Relation-like NAT -defined Function-like finite [Graph-like] () inducedSubgraph of G,v,x
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
v is set
x is set
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x is Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x
(G) is Relation-like the_Edges_of G -defined Function-like total set
G . () is set
the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x is Element of K32((the_Edges_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x . EdgeSelector is set
(G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x) is Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x -defined the_Edges_of G -defined Function-like set
dom (G) is Element of K32((the_Edges_of G))
dom ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x)) is Element of K32((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x))
K32((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x)) is set
ENext is Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x -defined Function-like total set
the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
() .--> ENext is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ENext is non empty Relation-like {()} -defined {ENext} -valued Function-like constant total V18({()},{ENext}) finite Function-yielding V125() Element of K32(K33({()},{ENext}))
{ENext} is non empty trivial functional finite 1 -element set
K33({()},{ENext}) is Relation-like finite set
K32(K33({()},{ENext})) is finite V40() set
the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x +* (() .--> ENext) is Relation-like Function-like finite set
(G) is Relation-like Function-like set
G . () is set
the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)) is set
( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)) . EdgeSelector is set
(G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext))) is Relation-like Function-like set
dom ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)))) is set
rng ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)))) is set
K33((dom ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext))))),(rng ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)))))) is Relation-like set
K32(K33((dom ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext))))),(rng ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext))))))) is set
K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext))),(rng ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)))))) is Relation-like set
K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext))),(rng ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext))))))) is set
y is Relation-like dom ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)))) -defined rng ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)))) -valued Function-like Element of K32(K33((dom ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext))))),(rng ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)))))))
x is Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)) -defined rng ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)))) -valued Function-like Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext))),(rng ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)))))))
( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
() .--> x is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> x is non empty Relation-like {()} -defined {x} -valued Function-like constant total V18({()},{x}) finite Function-yielding V125() Element of K32(K33({()},{x}))
{x} is non empty trivial functional finite 1 -element set
K33({()},{x}) is Relation-like finite set
K32(K33({()},{x})) is finite V40() set
( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)) +* (() .--> x) is Relation-like Function-like finite set
VL is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G
the_Vertices_of VL is non empty Element of K32((the_Vertices_of G))
VL . VertexSelector is set
the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x is non empty Element of K32((the_Vertices_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x . VertexSelector is set
the_Edges_of VL is Element of K32((the_Edges_of G))
VL . EdgeSelector is set
VL9 is Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x
VL9 is Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x
(VL9) is Relation-like the_Edges_of VL9 -defined Function-like total set
the_Edges_of VL9 is set
VL9 . EdgeSelector is set
VL9 . () is set
( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)) . () is set
the_Edges_of VL9 is Element of K32((the_Edges_of G))
(G) | (the_Edges_of VL9) is Relation-like the_Edges_of VL9 -defined the_Edges_of G -defined Function-like set
(VL9) is Relation-like Function-like set
VL9 . () is set
(G) | (the_Edges_of VL9) is Relation-like Function-like set
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
val is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G
Gn is Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x
(G) is Relation-like the_Edges_of G -defined Function-like total set
G . () is set
(G) | (the_Edges_of G) is Relation-like the_Edges_of G -defined the_Edges_of G -defined Function-like set
ENext is Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
(G) | (the_Edges_of G) is Relation-like Function-like set
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
val is Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
v is set
x is set
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x is Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x
(G) is Relation-like the_Edges_of G -defined Function-like total set
G . () is set
the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x is Element of K32((the_Edges_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x . EdgeSelector is set
(G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x) is Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x -defined the_Edges_of G -defined Function-like set
dom (G) is Element of K32((the_Edges_of G))
dom ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x)) is Element of K32((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x))
K32((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x)) is set
ENext is Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x -defined Function-like total set
the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
() .--> ENext is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ENext is non empty Relation-like {()} -defined {ENext} -valued Function-like constant total V18({()},{ENext}) finite Function-yielding V125() Element of K32(K33({()},{ENext}))
{ENext} is non empty trivial functional finite 1 -element set
K33({()},{ENext}) is Relation-like finite set
K32(K33({()},{ENext})) is finite V40() set
the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x +* (() .--> ENext) is Relation-like Function-like finite set
(G) is Relation-like Function-like set
G . () is set
the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)) is non empty set
( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)) . VertexSelector is set
(G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext))) is Relation-like Function-like set
dom ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)))) is set
rng ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)))) is set
K33((dom ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext))))),(rng ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)))))) is Relation-like set
K32(K33((dom ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext))))),(rng ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext))))))) is set
K33((the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext))),(rng ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)))))) is Relation-like set
K32(K33((the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext))),(rng ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext))))))) is set
y is Relation-like dom ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)))) -defined rng ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)))) -valued Function-like Element of K32(K33((dom ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext))))),(rng ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)))))))
x is Relation-like the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)) -defined rng ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)))) -valued Function-like Element of K32(K33((the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext))),(rng ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)))))))
( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
() .--> x is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> x is non empty Relation-like {()} -defined {x} -valued Function-like constant total V18({()},{x}) finite Function-yielding V125() Element of K32(K33({()},{x}))
{x} is non empty trivial functional finite 1 -element set
K33({()},{x}) is Relation-like finite set
K32(K33({()},{x})) is finite V40() set
( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)) +* (() .--> x) is Relation-like Function-like finite set
VL is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G
the_Vertices_of VL is non empty Element of K32((the_Vertices_of G))
VL . VertexSelector is set
the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x is non empty Element of K32((the_Vertices_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x . VertexSelector is set
the_Edges_of VL is Element of K32((the_Edges_of G))
VL . EdgeSelector is set
VL9 is Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x
VL9 is Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x
(VL9) is Relation-like the_Edges_of VL9 -defined Function-like total set
the_Edges_of VL9 is set
VL9 . EdgeSelector is set
VL9 . () is set
( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),ENext)) . () is set
the_Edges_of VL9 is Element of K32((the_Edges_of G))
(G) | (the_Edges_of VL9) is Relation-like the_Edges_of VL9 -defined the_Edges_of G -defined Function-like set
(VL9) is Relation-like Function-like set
VL9 . () is set
the_Vertices_of VL9 is non empty Element of K32((the_Vertices_of G))
VL9 . VertexSelector is set
(G) | (the_Vertices_of VL9) is Relation-like Function-like set
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
val is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G
Gn is Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x
(G) is Relation-like the_Edges_of G -defined Function-like total set
G . () is set
(G) | (the_Edges_of G) is Relation-like the_Edges_of G -defined the_Edges_of G -defined Function-like set
ENext is Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
(G) | (the_Vertices_of G) is Relation-like Function-like set
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
val is Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
v is set
x is set
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x is Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x
(G) is Relation-like Function-like set
G . () is set
the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x is Element of K32((the_Edges_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x . EdgeSelector is set
(G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x) is Relation-like Function-like set
dom ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x)) is set
rng ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x)) is set
K33((dom ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x))),(rng ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x)))) is Relation-like set
K32(K33((dom ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x))),(rng ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x))))) is set
K33((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x),(rng ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x)))) is Relation-like set
K32(K33((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x),(rng ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x))))) is set
ENext is Relation-like dom ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x)) -defined rng ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x)) -valued Function-like Element of K32(K33((dom ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x))),(rng ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x)))))
x is Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x -defined rng ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x)) -valued Function-like Element of K32(K33((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x),(rng ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x)))))
the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
() .--> x is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> x is non empty Relation-like {()} -defined {x} -valued Function-like constant total V18({()},{x}) finite Function-yielding V125() Element of K32(K33({()},{x}))
{x} is non empty trivial functional finite 1 -element set
K33({()},{x}) is Relation-like finite set
K32(K33({()},{x})) is finite V40() set
the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x +* (() .--> x) is Relation-like Function-like finite set
(G) is Relation-like Function-like set
G . () is set
the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x)) is non empty set
( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x)) . VertexSelector is set
(G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x))) is Relation-like Function-like set
dom ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x)))) is set
rng ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x)))) is set
K33((dom ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x))))),(rng ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x)))))) is Relation-like set
K32(K33((dom ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x))))),(rng ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x))))))) is set
K33((the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x))),(rng ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x)))))) is Relation-like set
K32(K33((the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x))),(rng ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x))))))) is set
x is Relation-like dom ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x)))) -defined rng ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x)))) -valued Function-like Element of K32(K33((dom ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x))))),(rng ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x)))))))
c₁₁ is Relation-like the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x)) -defined rng ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x)))) -valued Function-like Element of K32(K33((the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x))),(rng ((G) | (the_Vertices_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x)))))))
( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x)) .set ((),c₁₁) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
() .--> c₁₁ is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> c₁₁ is non empty Relation-like {()} -defined {c₁₁} -valued Function-like constant total V18({()},{c₁₁}) finite Function-yielding V125() Element of K32(K33({()},{c₁₁}))
{c₁₁} is non empty trivial functional finite 1 -element set
K33({()},{c₁₁}) is Relation-like finite set
K32(K33({()},{c₁₁})) is finite V40() set
( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x)) +* (() .--> c₁₁) is Relation-like Function-like finite set
VL9 is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G
the_Vertices_of VL9 is non empty Element of K32((the_Vertices_of G))
VL9 . VertexSelector is set
the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x is non empty Element of K32((the_Vertices_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x . VertexSelector is set
the_Edges_of VL9 is Element of K32((the_Edges_of G))
VL9 . EdgeSelector is set
VL9 is Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x
G3 is Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x
(G3) is Relation-like Function-like set
G3 . () is set
( the Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x .set ((),x)) . () is set
the_Edges_of G3 is Element of K32((the_Edges_of G))
G3 . EdgeSelector is set
(G) | (the_Edges_of G3) is Relation-like Function-like set
(G3) is Relation-like Function-like set
G3 . () is set
the_Vertices_of G3 is non empty Element of K32((the_Vertices_of G))
G3 . VertexSelector is set
(G) | (the_Vertices_of G3) is Relation-like Function-like set
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
val is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G
Gn is Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
(G) | (the_Edges_of G) is Relation-like Function-like set
ENext is Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
(G) | (the_Vertices_of G) is Relation-like Function-like set
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
val is Relation-like NAT -defined Function-like finite [Graph-like] () () inducedSubgraph of G,v,x
G is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
v is set
x is set
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x is Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x
(G) is Relation-like the_Edges_of G -defined Function-like total set
G . () is set
the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x is Element of K32((the_Edges_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x . EdgeSelector is set
(G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x) is Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x -defined the_Edges_of G -defined Function-like set
dom (G) is Element of K32((the_Edges_of G))
dom ((G) | (the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x)) is Element of K32((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x))
K32((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x)) is set
ENext is Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x -defined Function-like total set
the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext) is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
() .--> ENext is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ENext is non empty Relation-like {()} -defined {ENext} -valued Function-like constant total V18({()},{ENext}) finite Function-yielding V125() Element of K32(K33({()},{ENext}))
{ENext} is non empty trivial functional finite 1 -element set
K33({()},{ENext}) is Relation-like finite set
K32(K33({()},{ENext})) is finite V40() set
the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x +* (() .--> ENext) is Relation-like Function-like finite set
(G) is Relation-like Function-like set
G . () is set
the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) is set
( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) . EdgeSelector is set
(G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext))) is Relation-like Function-like set
dom ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)))) is set
rng ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)))) is set
K33((dom ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext))))),(rng ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)))))) is Relation-like set
K32(K33((dom ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext))))),(rng ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext))))))) is set
K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext))),(rng ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)))))) is Relation-like set
K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext))),(rng ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext))))))) is set
y is Relation-like dom ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)))) -defined rng ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)))) -valued Function-like Element of K32(K33((dom ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext))))),(rng ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)))))))
x is Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) -defined rng ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)))) -valued Function-like Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext))),(rng ((G) | (the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)))))))
( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x) is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
() .--> x is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> x is non empty Relation-like {()} -defined {x} -valued Function-like constant total V18({()},{x}) finite Function-yielding V125() Element of K32(K33({()},{x}))
{x} is non empty trivial functional finite 1 -element set
K33({()},{x}) is Relation-like finite set
K32(K33({()},{x})) is finite V40() set
( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) +* (() .--> x) is Relation-like Function-like finite set
(G) is Relation-like Function-like set
G . () is set
the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x)) is non empty set
(( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x)) . VertexSelector is set
(G) | (the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x))) is Relation-like Function-like set
dom ((G) | (the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x)))) is set
rng ((G) | (the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x)))) is set
K33((dom ((G) | (the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x))))),(rng ((G) | (the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x)))))) is Relation-like set
K32(K33((dom ((G) | (the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x))))),(rng ((G) | (the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x))))))) is set
K33((the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x))),(rng ((G) | (the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x)))))) is Relation-like set
K32(K33((the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x))),(rng ((G) | (the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x))))))) is set
VL9 is Relation-like dom ((G) | (the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x)))) -defined rng ((G) | (the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x)))) -valued Function-like Element of K32(K33((dom ((G) | (the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x))))),(rng ((G) | (the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x)))))))
VL9 is Relation-like the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x)) -defined rng ((G) | (the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x)))) -valued Function-like Element of K32(K33((the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x))),(rng ((G) | (the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x)))))))
(( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x)) .set ((),VL9) is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
() .--> VL9 is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> VL9 is non empty Relation-like {()} -defined {VL9} -valued Function-like constant total V18({()},{VL9}) finite Function-yielding V125() Element of K32(K33({()},{VL9}))
{VL9} is non empty trivial functional finite 1 -element set
K33({()},{VL9}) is Relation-like finite set
K32(K33({()},{VL9})) is finite V40() set
(( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x)) +* (() .--> VL9) is Relation-like Function-like finite set
G3 is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G
the_Vertices_of G3 is non empty Element of K32((the_Vertices_of G))
G3 . VertexSelector is set
the_Vertices_of the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x is non empty Element of K32((the_Vertices_of G))
the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x . VertexSelector is set
the_Edges_of G3 is Element of K32((the_Edges_of G))
G3 . EdgeSelector is set
G3 is Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x
G3 is Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x
(G3) is Relation-like the_Edges_of G3 -defined Function-like total set
the_Edges_of G3 is set
G3 . EdgeSelector is set
G3 . () is set
(( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x)) . () is set
( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) . () is set
the_Edges_of G3 is Element of K32((the_Edges_of G))
(G) | (the_Edges_of G3) is Relation-like the_Edges_of G3 -defined the_Edges_of G -defined Function-like set
(G3) is Relation-like Function-like set
G3 . () is set
(( the Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x .set ((),ENext)) .set ((),x)) . () is set
(G) | (the_Edges_of G3) is Relation-like Function-like set
(G3) is Relation-like Function-like set
G3 . () is set
the_Vertices_of G3 is non empty Element of K32((the_Vertices_of G))
G3 . VertexSelector is set
(G) | (the_Vertices_of G3) is Relation-like Function-like set
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
val is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G
Gn is Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x
(G) is Relation-like the_Edges_of G -defined Function-like total set
G . () is set
(G) | (the_Edges_of G) is Relation-like the_Edges_of G -defined the_Edges_of G -defined Function-like set
ENext is Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
(G) | (the_Edges_of G) is Relation-like Function-like set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
(G) | (the_Vertices_of G) is Relation-like Function-like set
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G .edgesBetween v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
G .edgesInto v is Element of K32((the_Edges_of G))
G .edgesOutOf v is Element of K32((the_Edges_of G))
(G .edgesInto v) /\ (G .edgesOutOf v) is Element of K32((the_Edges_of G))
val is Relation-like NAT -defined Function-like finite [Graph-like] () () () inducedSubgraph of G,v,x
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
(G) is Relation-like the_Edges_of G -defined Function-like total set
the_Edges_of G is set
G . EdgeSelector is set
G . () is set
rng (G) is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
G is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Edges_of G is set
G . EdgeSelector is set
K33((the_Edges_of G),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K32(K33((the_Edges_of G),REAL)) is set
v is Relation-like the_Edges_of G -defined REAL -valued Function-like total V18( the_Edges_of G, REAL ) complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of G),REAL))
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Function-yielding V125() Element of K32(K33({()},{v}))
{v} is non empty trivial functional finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
((G .set ((),v))) is Relation-like the_Edges_of (G .set ((),v)) -defined Function-like total set
the_Edges_of (G .set ((),v)) is set
(G .set ((),v)) . EdgeSelector is set
(G .set ((),v)) . () is set
G is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Edges_of G is set
G . EdgeSelector is set
K33((the_Edges_of G),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K32(K33((the_Edges_of G),REAL)) is set
v is Relation-like the_Edges_of G -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of G),REAL))
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Function-yielding V125() Element of K32(K33({()},{v}))
{v} is non empty trivial functional finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
((G .set ((),v))) is Relation-like Function-like set
(G .set ((),v)) . () is set
G is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Edges_of G is set
G . EdgeSelector is set
v is Relation-like the_Edges_of G -defined Function-like total complex-valued ext-real-valued real-valued set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Function-yielding V125() Element of K32(K33({()},{v}))
{v} is non empty trivial functional finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
((G .set ((),v))) is Relation-like Function-like set
(G .set ((),v)) . () is set
G is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G is non empty set
G . VertexSelector is set
K33((the_Vertices_of G),REAL) is non trivial Relation-like non finite complex-valued ext-real-valued real-valued set
K32(K33((the_Vertices_of G),REAL)) is non trivial non finite set
v is Relation-like the_Vertices_of G -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of G),REAL))
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Function-yielding V125() Element of K32(K33({()},{v}))
{v} is non empty trivial functional finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
((G .set ((),v))) is Relation-like Function-like set
(G .set ((),v)) . () is set
G is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G is non empty set
G . VertexSelector is set
v is Relation-like the_Vertices_of G -defined Function-like total complex-valued ext-real-valued real-valued set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Function-yielding V125() Element of K32(K33({()},{v}))
{v} is non empty trivial functional finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
((G .set ((),v))) is Relation-like Function-like set
(G .set ((),v)) . () is set
G is Relation-like NAT -defined Function-like finite [Graph-like] set
G .set ((),{}) is Relation-like NAT -defined Function-like finite [Graph-like] () set
G +* (() .--> {}) is Relation-like Function-like finite set
the_Edges_of G is set
G . EdgeSelector is set
K33((the_Edges_of G),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K32(K33((the_Edges_of G),REAL)) is set
v is Relation-like the_Edges_of G -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of G),REAL))
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Function-yielding V125() Element of K32(K33({()},{v}))
{v} is non empty trivial functional finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G .set ((),{}) is Relation-like NAT -defined Function-like finite [Graph-like] () set
G +* (() .--> {}) is Relation-like Function-like finite set
the_Vertices_of G is non empty set
G . VertexSelector is set
K33((the_Vertices_of G),REAL) is non trivial Relation-like non finite complex-valued ext-real-valued real-valued set
K32(K33((the_Vertices_of G),REAL)) is non trivial non finite set
v is Relation-like the_Vertices_of G -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of G),REAL))
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Function-yielding V125() Element of K32(K33({()},{v}))
{v} is non empty trivial functional finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
G is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G is non empty set
G . VertexSelector is set
v is Element of the_Vertices_of G
x is V21() real ext-real set
v .--> x is Relation-like the_Vertices_of G -defined {v} -defined Function-like one-to-one finite complex-valued ext-real-valued real-valued set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite complex-valued ext-real-valued real-valued Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element V60() V61() V62() set
K33({v},{x}) is Relation-like finite complex-valued ext-real-valued real-valued set
K32(K33({v},{x})) is finite V40() set
G .set ((),(v .--> x)) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> (v .--> x) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> (v .--> x) is non empty Relation-like {()} -defined {(v .--> x)} -valued Function-like constant total V18({()},{(v .--> x)}) finite Function-yielding V125() Element of K32(K33({()},{(v .--> x)}))
{(v .--> x)} is non empty trivial functional finite V40() 1 -element set
K33({()},{(v .--> x)}) is Relation-like finite set
K32(K33({()},{(v .--> x)})) is finite V40() set
G +* (() .--> (v .--> x)) is Relation-like Function-like finite set
{v} is non empty trivial finite 1 -element Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is set
K33({v},{x}) is Relation-like finite complex-valued ext-real-valued real-valued set
K32(K33({v},{x})) is finite V40() set
dom (v .--> x) is finite Element of K32({v})
K32({v}) is finite V40() set
K33((the_Vertices_of G),{x}) is Relation-like complex-valued ext-real-valued real-valued set
K32(K33((the_Vertices_of G),{x})) is set
val is Relation-like {v} -defined {x} -valued Function-like finite complex-valued ext-real-valued real-valued Element of K32(K33({v},{x}))
rng (v .--> x) is finite V60() V61() V62() Element of K32(REAL)
K33((the_Vertices_of G),REAL) is non trivial Relation-like non finite complex-valued ext-real-valued real-valued set
K32(K33((the_Vertices_of G),REAL)) is non trivial non finite set
Gn is Relation-like the_Vertices_of G -defined {x} -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of G),{x}))
ENext is Relation-like the_Vertices_of G -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of G),REAL))
G .set ((),ENext) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
() .--> ENext is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ENext is non empty Relation-like {()} -defined {ENext} -valued Function-like constant total V18({()},{ENext}) finite Function-yielding V125() Element of K32(K33({()},{ENext}))
{ENext} is non empty trivial functional finite 1 -element set
K33({()},{ENext}) is Relation-like finite set
K32(K33({()},{ENext})) is finite V40() set
G +* (() .--> ENext) is Relation-like Function-like finite set
G is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G is non empty set
G . VertexSelector is set
v is Element of the_Vertices_of G
x is V21() real ext-real set
v .--> x is Relation-like the_Vertices_of G -defined {v} -defined Function-like one-to-one finite complex-valued ext-real-valued real-valued set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite complex-valued ext-real-valued real-valued Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element V60() V61() V62() set
K33({v},{x}) is Relation-like finite complex-valued ext-real-valued real-valued set
K32(K33({v},{x})) is finite V40() set
G .set ((),(v .--> x)) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> (v .--> x) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> (v .--> x) is non empty Relation-like {()} -defined {(v .--> x)} -valued Function-like constant total V18({()},{(v .--> x)}) finite Function-yielding V125() Element of K32(K33({()},{(v .--> x)}))
{(v .--> x)} is non empty trivial functional finite V40() 1 -element set
K33({()},{(v .--> x)}) is Relation-like finite set
K32(K33({()},{(v .--> x)})) is finite V40() set
G +* (() .--> (v .--> x)) is Relation-like Function-like finite set
{v} is non empty trivial finite 1 -element Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is set
K33({v},{x}) is Relation-like finite complex-valued ext-real-valued real-valued set
K32(K33({v},{x})) is finite V40() set
dom (v .--> x) is finite Element of K32({v})
K32({v}) is finite V40() set
K33((the_Vertices_of G),{x}) is Relation-like complex-valued ext-real-valued real-valued set
K32(K33((the_Vertices_of G),{x})) is set
val is Relation-like {v} -defined {x} -valued Function-like finite complex-valued ext-real-valued real-valued Element of K32(K33({v},{x}))
ENext is set
K33((the_Vertices_of G),REAL) is non trivial Relation-like non finite complex-valued ext-real-valued real-valued set
K32(K33((the_Vertices_of G),REAL)) is non trivial non finite set
Gn is Relation-like the_Vertices_of G -defined {x} -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of G),{x}))
ENext is Relation-like the_Vertices_of G -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of G),REAL))
G .set ((),ENext) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
() .--> ENext is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ENext is non empty Relation-like {()} -defined {ENext} -valued Function-like constant total V18({()},{ENext}) finite Function-yielding V125() Element of K32(K33({()},{ENext}))
{ENext} is non empty trivial functional finite 1 -element set
K33({()},{ENext}) is Relation-like finite set
K32(K33({()},{ENext})) is finite V40() set
G +* (() .--> ENext) is Relation-like Function-like finite set
{1} is non empty trivial finite V40() 1 -element V60() V61() V62() V63() V64() V65() Element of K32(NAT)
K33({},{1}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
K32(K33({},{1})) is finite V40() set
x is empty Relation-like non-empty empty-yielding {} -defined {1} -valued Function-like one-to-one constant functional total V18( {} ,{1}) V21() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real V30() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non negative complex-valued ext-real-valued real-valued natural-valued V60() V61() V62() V63() V64() V65() V66() Function-yielding V125() Element of K32(K33({},{1}))
createGraph ({1},{},x,x) is Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set
the_Edges_of (createGraph ({1},{},x,x)) is finite set
(createGraph ({1},{},x,x)) . EdgeSelector is set
K33((the_Edges_of (createGraph ({1},{},x,x))),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)) is set
the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)) is Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))
(createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))) is Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () set
() .--> the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)) is non empty Relation-like {()} -defined { the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))} -valued Function-like constant total V18({()},{ the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))}) finite Function-yielding V125() Element of K32(K33({()},{ the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))}))
{ the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))} is non empty trivial functional finite V40() 1 -element set
K33({()},{ the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))}) is Relation-like finite set
K32(K33({()},{ the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))})) is finite V40() set
(createGraph ({1},{},x,x)) +* (() .--> the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))) is Relation-like Function-like finite set
the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) is finite set
((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) . EdgeSelector is set
K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)) is set
the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)) is Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))
((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))) is Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () set
() .--> the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)) is non empty Relation-like {()} -defined { the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))} -valued Function-like constant total V18({()},{ the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))}) finite Function-yielding V125() Element of K32(K33({()},{ the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))}))
{ the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))} is non empty trivial functional finite 1 -element set
K33({()},{ the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))}) is Relation-like finite set
K32(K33({()},{ the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))})) is finite V40() set
((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) +* (() .--> the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))) is Relation-like Function-like finite set
the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) is non empty finite set
(((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) . VertexSelector is set
K33((the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))))),REAL) is non trivial Relation-like non finite complex-valued ext-real-valued real-valued set
K32(K33((the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))))),REAL)) is non trivial non finite set
the Relation-like the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))))),REAL)) is Relation-like the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))))),REAL))
(((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) .set ((), the Relation-like the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))))),REAL))) is Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () () set
() .--> the Relation-like the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))))),REAL)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> the Relation-like the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))))),REAL)) is non empty Relation-like {()} -defined { the Relation-like the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))))),REAL))} -valued Function-like constant total V18({()},{ the Relation-like the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))))),REAL))}) finite Function-yielding V125() Element of K32(K33({()},{ the Relation-like the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))))),REAL))}))
{ the Relation-like the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))))),REAL))} is non empty trivial functional finite 1 -element set
K33({()},{ the Relation-like the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))))),REAL))}) is Relation-like finite set
K32(K33({()},{ the Relation-like the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))))),REAL))})) is finite V40() set
(((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) +* (() .--> the Relation-like the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))))),REAL))) is Relation-like Function-like finite set
(((((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) .set ((), the Relation-like the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))))),REAL))))) is Relation-like the_Edges_of ((((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) .set ((), the Relation-like the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))))),REAL)))) -defined Function-like total set
the_Edges_of ((((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) .set ((), the Relation-like the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))))),REAL)))) is finite set
((((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) .set ((), the Relation-like the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))))),REAL)))) . EdgeSelector is set
((((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) .set ((), the Relation-like the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))))),REAL)))) . () is set
(((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) . () is set
((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) . () is set
rng (((((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) .set ((), the Relation-like the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))))),REAL))))) is set
(((((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) .set ((), the Relation-like the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))))),REAL))))) is Relation-like Function-like set
((((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) .set ((), the Relation-like the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL))))),REAL)))) . () is set
(((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) .set ((), the Relation-like the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL)))) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ((createGraph ({1},{},x,x)) .set ((), the Relation-like the_Edges_of (createGraph ({1},{},x,x)) -defined REAL -valued Function-like total V18( the_Edges_of (createGraph ({1},{},x,x)), REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of (createGraph ({1},{},x,x))),REAL))))),REAL)))) . () is set
the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set is Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set
the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set is finite set
the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set . EdgeSelector is set
(the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set ) --> 0 is Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set -defined NAT -valued RAT -valued INT -valued Function-like constant total V18( the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set , NAT ) finite complex-valued ext-real-valued real-valued natural-valued Function-yielding V125() Element of K32(K33((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set ),NAT))
K33((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set ),NAT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K32(K33((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set ),NAT)) is set
{0} is non empty trivial functional finite V40() 1 -element V60() V61() V62() V63() V64() V65() set
K33((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set ),{0}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
dom ((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set ) --> 0) is finite Element of K32((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set ))
K32((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set )) is finite V40() set
rng ((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set ) --> 0) is trivial finite V60() V61() V62() V63() V64() V65() Element of K32(REAL)
{0} is non empty trivial functional finite V40() 1 -element V60() V61() V62() V63() V64() V65() Element of K32(NAT)
K33((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set ),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K32(K33((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set ),REAL)) is set
x is Relation-like the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set -defined REAL -valued Function-like total V18( the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set , REAL ) finite complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set ),REAL))
the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x) is Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () set
() .--> x is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> x is non empty Relation-like {()} -defined {x} -valued Function-like constant total V18({()},{x}) finite Function-yielding V125() Element of K32(K33({()},{x}))
{x} is non empty trivial functional finite V40() 1 -element set
K33({()},{x}) is Relation-like finite set
K32(K33({()},{x})) is finite V40() set
the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set +* (() .--> x) is Relation-like Function-like finite set
the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x)) is finite set
( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x)) . EdgeSelector is set
K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x))),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x))),REAL)) is set
Gn is Relation-like the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x)) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of ( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x))),REAL))
( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x)) .set ((),Gn) is Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () set
() .--> Gn is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> Gn is non empty Relation-like {()} -defined {Gn} -valued Function-like constant total V18({()},{Gn}) finite Function-yielding V125() Element of K32(K33({()},{Gn}))
{Gn} is non empty trivial functional finite 1 -element set
K33({()},{Gn}) is Relation-like finite set
K32(K33({()},{Gn})) is finite V40() set
( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x)) +* (() .--> Gn) is Relation-like Function-like finite set
the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x)) .set ((),Gn)) is non empty finite set
(( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x)) .set ((),Gn)) . VertexSelector is set
K33((the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x)) .set ((),Gn))),REAL) is non trivial Relation-like non finite complex-valued ext-real-valued real-valued set
K32(K33((the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x)) .set ((),Gn))),REAL)) is non trivial non finite set
x is Relation-like the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x)) .set ((),Gn)) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of (( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x)) .set ((),Gn))),REAL))
(( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x)) .set ((),Gn)) .set ((),x) is Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () () set
() .--> x is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> x is non empty Relation-like {()} -defined {x} -valued Function-like constant total V18({()},{x}) finite Function-yielding V125() Element of K32(K33({()},{x}))
{x} is non empty trivial functional finite 1 -element set
K33({()},{x}) is Relation-like finite set
K32(K33({()},{x})) is finite V40() set
(( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x)) .set ((),Gn)) +* (() .--> x) is Relation-like Function-like finite set
(((( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x)) .set ((),Gn)) .set ((),x))) is Relation-like the_Edges_of ((( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x)) .set ((),Gn)) .set ((),x)) -defined Function-like total set
the_Edges_of ((( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x)) .set ((),Gn)) .set ((),x)) is finite set
((( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x)) .set ((),Gn)) .set ((),x)) . EdgeSelector is set
((( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x)) .set ((),Gn)) .set ((),x)) . () is set
(( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x)) .set ((),Gn)) . () is set
( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x)) . () is set
y is set
rng x is finite V60() V61() V62() Element of K32(REAL)
(((( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x)) .set ((),Gn)) .set ((),x))) is Relation-like Function-like set
((( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x)) .set ((),Gn)) .set ((),x)) . () is set
(( the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless non trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like set .set ((),x)) .set ((),Gn)) . () is set
G is Relation-like NAT -defined Function-like finite [Graph-like] finite () set
(G) is Relation-like the_Edges_of G -defined Function-like total set
the_Edges_of G is finite set
G . EdgeSelector is set
G . () is set
dom (G) is finite Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is finite V40() set
rng (G) is set
G is Relation-like NAT -defined Function-like finite [Graph-like] finite () set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
the_Edges_of G is finite set
G . EdgeSelector is set
rng (G) is set
G is Relation-like NAT -defined Function-like finite [Graph-like] finite () set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
rng (G) is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
(G) is Relation-like the_Edges_of G -defined Function-like total set
the_Edges_of G is set
G . EdgeSelector is set
G . () is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
(G) is Relation-like Function-like set
G . () is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
(G) is Relation-like Function-like set
G . () is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
v is set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
{v} is non empty trivial finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
((G .set ((),v))) is Relation-like the_Edges_of (G .set ((),v)) -defined Function-like total set
the_Edges_of (G .set ((),v)) is set
(G .set ((),v)) . EdgeSelector is set
(G .set ((),v)) . () is set
(G) is Relation-like the_Edges_of G -defined Function-like total complex-valued ext-real-valued real-valued set
the_Edges_of G is set
G . EdgeSelector is set
G . () is set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
((G .set ((),v))) is Relation-like the_Edges_of (G .set ((),v)) -defined Function-like total set
the_Edges_of (G .set ((),v)) is set
(G .set ((),v)) . EdgeSelector is set
(G .set ((),v)) . () is set
(G) is Relation-like the_Edges_of G -defined Function-like total complex-valued ext-real-valued real-valued set
the_Edges_of G is set
G . EdgeSelector is set
G . () is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
v is set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
{v} is non empty trivial finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
((G .set ((),v))) is Relation-like the_Edges_of (G .set ((),v)) -defined Function-like total complex-valued ext-real-valued real-valued set
the_Edges_of (G .set ((),v)) is set
(G .set ((),v)) . EdgeSelector is set
(G .set ((),v)) . () is set
(G) is Relation-like the_Edges_of G -defined Function-like total complex-valued ext-real-valued real-valued set
the_Edges_of G is set
G . EdgeSelector is set
G . () is set
rng (G) is V60() V61() V62() Element of K32(REAL)
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
((G .set ((),v))) is Relation-like the_Edges_of (G .set ((),v)) -defined Function-like total complex-valued ext-real-valued real-valued set
the_Edges_of (G .set ((),v)) is set
(G .set ((),v)) . EdgeSelector is set
(G .set ((),v)) . () is set
(G) is Relation-like the_Edges_of G -defined Function-like total complex-valued ext-real-valued real-valued set
the_Edges_of G is set
G . EdgeSelector is set
G . () is set
rng (G) is V60() V61() V62() Element of K32(REAL)
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
v is set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
{v} is non empty trivial finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
((G .set ((),v))) is Relation-like Function-like set
(G .set ((),v)) . () is set
(G) is Relation-like Function-like complex-valued ext-real-valued real-valued set
G . () is set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
((G .set ((),v))) is Relation-like Function-like set
(G .set ((),v)) . () is set
(G) is Relation-like Function-like complex-valued ext-real-valued real-valued set
G . () is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
v is set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
{v} is non empty trivial finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
((G .set ((),v))) is Relation-like Function-like set
(G .set ((),v)) . () is set
(G) is Relation-like Function-like complex-valued ext-real-valued real-valued set
G . () is set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
((G .set ((),v))) is Relation-like Function-like set
(G .set ((),v)) . () is set
(G) is Relation-like Function-like complex-valued ext-real-valued real-valued set
G . () is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
v is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
v .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like EdgeSeq of G
len (v .edgeSeq()) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(G) is Relation-like the_Edges_of G -defined Function-like total set
G . () is set
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len x is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
dom x is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
val is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
x . val is set
(v .edgeSeq()) . val is set
(G) . ((v .edgeSeq()) . val) is set
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len x is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
val is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len val is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
Gn is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
x . Gn is set
(v .edgeSeq()) . Gn is set
(G) . ((v .edgeSeq()) . Gn) is set
val . Gn is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
v is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
(G,v) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
x is set
rng (G,v) is finite set
dom (G,v) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
val is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
(G,v) . val is set
len (G,v) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(G) is Relation-like the_Edges_of G -defined Function-like total complex-valued ext-real-valued real-valued set
G . () is set
v .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like EdgeSeq of G
(v .edgeSeq()) . val is set
(G) . ((v .edgeSeq()) . val) is V21() real ext-real Element of REAL
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
v is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
(G,v) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (G,v) is V21() real ext-real Element of REAL
K221(REAL,(G,v),K168()) is V21() real ext-real Element of REAL
x is set
val is set
K33(x,val) is Relation-like set
K32(K33(x,val)) is set
G is set
v is set
G .--> v is Relation-like {G} -defined Function-like one-to-one finite set
{G} is non empty trivial finite 1 -element set
{G} --> v is non empty Relation-like {G} -defined {v} -valued Function-like constant total V18({G},{v}) finite Element of K32(K33({G},{v}))
{v} is non empty trivial finite 1 -element set
K33({G},{v}) is Relation-like finite set
K32(K33({G},{v})) is finite V40() set
Gn is Relation-like x -defined val -valued Function-like Element of K32(K33(x,val))
Gn +* (G .--> v) is Relation-like Function-like set
rng (Gn +* (G .--> v)) is set
rng Gn is Element of K32(val)
K32(val) is set
rng (G .--> v) is finite set
(rng Gn) \/ (rng (G .--> v)) is set
x is set
dom (Gn +* (G .--> v)) is set
K33((dom (Gn +* (G .--> v))),val) is Relation-like set
K32(K33((dom (Gn +* (G .--> v))),val)) is set
n is set
x is Relation-like dom (Gn +* (G .--> v)) -defined val -valued Function-like Element of K32(K33((dom (Gn +* (G .--> v))),val))
dom x is Element of K32((dom (Gn +* (G .--> v))))
K32((dom (Gn +* (G .--> v)))) is set
dom Gn is Element of K32(x)
K32(x) is set
dom (G .--> v) is finite Element of K32({G})
K32({G}) is finite V40() set
(dom Gn) \/ (dom (G .--> v)) is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
v is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Relation-like Function-like set
G . () is set
x is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Edges_of (G .set ((),((G) +* (v .--> x)))) is set
(G .set ((),((G) +* (v .--> x)))) . EdgeSelector is set
dom ((G) +* (v .--> x)) is set
dom (G) is set
dom (v .--> x) is finite Element of K32({v})
K32({v}) is finite V40() set
(dom (G)) \/ (dom (v .--> x)) is set
(dom (G)) \/ {v} is non empty set
ENext is set
(G .set ((),((G) +* (v .--> x)))) . () is set
dom G is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
dom (G .set ((),((G) +* (v .--> x)))) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
G is Relation-like NAT -defined Function-like finite [Graph-like] finite () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Edges_of G is finite set
G . EdgeSelector is set
(G) is Relation-like Function-like finite set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like finite set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] finite set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite V40() 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Edges_of G is finite set
G . EdgeSelector is set
the_Edges_of G is finite set
G . EdgeSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] loopless () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] loopless set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Edges_of G is set
G . EdgeSelector is set
the_Edges_of G is set
G . EdgeSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] trivial connected () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] trivial connected set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Edges_of G is set
G . EdgeSelector is set
the_Edges_of G is set
G . EdgeSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] non trivial () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] non trivial set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Edges_of G is set
G . EdgeSelector is set
the_Edges_of G is set
G . EdgeSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] non-multi non-Dmulti () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] non-multi non-Dmulti set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Edges_of G is set
G . EdgeSelector is set
the_Edges_of G is set
G . EdgeSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] non-Dmulti () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] non-Dmulti set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Edges_of G is set
G . EdgeSelector is set
the_Edges_of G is set
G . EdgeSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] connected () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] connected set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Edges_of G is set
G . EdgeSelector is set
the_Edges_of G is set
G . EdgeSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] loopless non-multi non-Dmulti simple Dsimple acyclic () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] loopless non-multi non-Dmulti simple Dsimple () set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] loopless non-multi non-Dmulti simple Dsimple acyclic set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Edges_of G is set
G . EdgeSelector is set
the_Edges_of G is set
G . EdgeSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Edges_of G is set
G . EdgeSelector is set
the_Edges_of G is set
G . EdgeSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Edges_of G is set
G . EdgeSelector is set
the_Edges_of G is set
G . EdgeSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Edges_of G is set
G . EdgeSelector is set
the_Edges_of G is set
G . EdgeSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () () () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Edges_of G is set
G . EdgeSelector is set
the_Edges_of G is set
G . EdgeSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
v is set
x is V21() real ext-real Element of REAL
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Relation-like Function-like complex-valued ext-real-valued real-valued set
G . () is set
v .--> x is Relation-like {v} -defined REAL -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined REAL -valued {x} -valued Function-like constant total V18({v},{x}) finite complex-valued ext-real-valued real-valued Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element V60() V61() V62() set
K33({v},{x}) is Relation-like finite complex-valued ext-real-valued real-valued set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like complex-valued ext-real-valued real-valued set
rng (G) is V60() V61() V62() Element of K32(REAL)
dom (G) is set
K33((dom (G)),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K32(K33((dom (G)),REAL)) is set
K33((the_Edges_of G),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K32(K33((the_Edges_of G),REAL)) is set
Gn is Relation-like the_Edges_of G -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Edges_of G),REAL))
G .set ((),Gn) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
() .--> Gn is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> Gn is non empty Relation-like {()} -defined {Gn} -valued Function-like constant total V18({()},{Gn}) finite Function-yielding V125() Element of K32(K33({()},{Gn}))
{Gn} is non empty trivial functional finite 1 -element set
K33({()},{Gn}) is Relation-like finite set
K32(K33({()},{Gn})) is finite V40() set
G +* (() .--> Gn) is Relation-like Function-like finite set
the_Edges_of G is set
G . EdgeSelector is set
the_Edges_of G is set
G . EdgeSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Edges_of G is set
G . EdgeSelector is set
the_Edges_of G is set
G . EdgeSelector is set
v is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty set
G . VertexSelector is set
(G) is Relation-like Function-like set
G . () is set
x is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
dom ((G) +* (v .--> x)) is set
dom (G) is set
dom (v .--> x) is finite Element of K32({v})
K32({v}) is finite V40() set
(dom (G)) \/ (dom (v .--> x)) is set
ENext is set
rng ((G) +* (v .--> x)) is set
K33((the_Vertices_of G),(rng ((G) +* (v .--> x)))) is Relation-like set
K32(K33((the_Vertices_of G),(rng ((G) +* (v .--> x))))) is set
ENext is Relation-like the_Vertices_of G -defined rng ((G) +* (v .--> x)) -valued Function-like Element of K32(K33((the_Vertices_of G),(rng ((G) +* (v .--> x)))))
G .set ((),ENext) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> ENext is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ENext is non empty Relation-like {()} -defined {ENext} -valued Function-like constant total V18({()},{ENext}) finite Function-yielding V125() Element of K32(K33({()},{ENext}))
{ENext} is non empty trivial functional finite 1 -element set
K33({()},{ENext}) is Relation-like finite set
K32(K33({()},{ENext})) is finite V40() set
G +* (() .--> ENext) is Relation-like Function-like finite set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
G is Relation-like NAT -defined Function-like finite [Graph-like] finite () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
(G) is Relation-like Function-like finite set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like finite set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] finite set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite V40() 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] loopless () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty set
G . VertexSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] loopless set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] trivial connected () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] trivial connected set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] non trivial () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty set
G . VertexSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] non trivial set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] non-multi non-Dmulti () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty set
G . VertexSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] non-multi non-Dmulti set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] non-Dmulti () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty set
G . VertexSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] non-Dmulti set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] connected () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty set
G . VertexSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] connected set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] loopless non-multi non-Dmulti simple Dsimple acyclic () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] loopless non-multi non-Dmulti simple Dsimple () set
the_Vertices_of G is non empty set
G . VertexSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] loopless non-multi non-Dmulti simple Dsimple acyclic set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty set
G . VertexSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty set
G . VertexSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
the_Vertices_of G is non empty set
G . VertexSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () () () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
the_Vertices_of G is non empty set
G . VertexSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
the_Vertices_of G is non empty set
G . VertexSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
v is set
x is V21() real ext-real Element of REAL
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty set
G . VertexSelector is set
(G) is Relation-like Function-like complex-valued ext-real-valued real-valued set
G . () is set
v .--> x is Relation-like {v} -defined REAL -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined REAL -valued {x} -valued Function-like constant total V18({v},{x}) finite complex-valued ext-real-valued real-valued Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element V60() V61() V62() set
K33({v},{x}) is Relation-like finite complex-valued ext-real-valued real-valued set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like complex-valued ext-real-valued real-valued set
rng (G) is V60() V61() V62() Element of K32(REAL)
dom (G) is set
K33((dom (G)),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K32(K33((dom (G)),REAL)) is set
K33((the_Vertices_of G),REAL) is non trivial Relation-like non finite complex-valued ext-real-valued real-valued set
K32(K33((the_Vertices_of G),REAL)) is non trivial non finite set
Gn is Relation-like the_Vertices_of G -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K32(K33((the_Vertices_of G),REAL))
G .set ((),Gn) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
() .--> Gn is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> Gn is non empty Relation-like {()} -defined {Gn} -valued Function-like constant total V18({()},{Gn}) finite Function-yielding V125() Element of K32(K33({()},{Gn}))
{Gn} is non empty trivial functional finite 1 -element set
K33({()},{Gn}) is Relation-like finite set
K32(K33({()},{Gn})) is finite V40() set
G +* (() .--> Gn) is Relation-like Function-like finite set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
v is Relation-like NAT -defined Function-like finite [Graph-like] () (G) Subgraph of G
(G) is Relation-like the_Edges_of G -defined Function-like total complex-valued ext-real-valued real-valued set
the_Edges_of G is set
G . EdgeSelector is set
G . () is set
the_Edges_of v is Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is set
v . EdgeSelector is set
(G) | (the_Edges_of v) is Relation-like the_Edges_of v -defined the_Edges_of G -defined Function-like complex-valued ext-real-valued real-valued set
(v) is Relation-like the_Edges_of v -defined Function-like total set
the_Edges_of v is set
v . () is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
v is Relation-like NAT -defined Function-like finite [Graph-like] () (G) () Subgraph of G
(G) is Relation-like the_Edges_of G -defined Function-like total complex-valued ext-real-valued real-valued set
the_Edges_of G is set
G . EdgeSelector is set
G . () is set
rng (G) is V60() V61() V62() Element of K32(REAL)
x is set
(v) is Relation-like the_Edges_of v -defined Function-like total complex-valued ext-real-valued real-valued set
the_Edges_of v is set
v . EdgeSelector is set
v . () is set
rng (v) is V60() V61() V62() Element of K32(REAL)
the_Edges_of v is Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is set
(G) | (the_Edges_of v) is Relation-like the_Edges_of v -defined the_Edges_of G -defined Function-like complex-valued ext-real-valued real-valued set
rng ((G) | (the_Edges_of v)) is V60() V61() V62() Element of K32(REAL)
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
v is Relation-like NAT -defined Function-like finite [Graph-like] () (G) Subgraph of G
(v) is Relation-like Function-like set
v . () is set
(G) is Relation-like Function-like complex-valued ext-real-valued real-valued set
G . () is set
the_Edges_of v is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
v . EdgeSelector is set
(G) | (the_Edges_of v) is Relation-like Function-like complex-valued ext-real-valued real-valued set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
v is Relation-like NAT -defined Function-like finite [Graph-like] () (G) Subgraph of G
(v) is Relation-like Function-like set
v . () is set
(G) is Relation-like Function-like complex-valued ext-real-valued real-valued set
G . () is set
the_Vertices_of v is non empty Element of K32((the_Vertices_of G))
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
v . VertexSelector is set
(G) | (the_Vertices_of v) is Relation-like Function-like complex-valued ext-real-valued real-valued set
the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () () () () () () set is Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () () () () () () set
NAT --> the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () () () () () () set is non empty Relation-like NAT -defined { the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () () () () () () set } -valued Function-like constant total V18( NAT ,{ the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () () () () () () set }) T-Sequence-like Function-yielding V125() Element of K32(K33(NAT,{ the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () () () () () () set }))
{ the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () () () () () () set } is non empty trivial functional finite V40() 1 -element set
K33(NAT,{ the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () () () () () () set }) is non trivial Relation-like non finite set
K32(K33(NAT,{ the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () () () () () () set })) is non trivial non finite set
dom (NAT --> the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () () () () () () set ) is non empty epsilon-transitive epsilon-connected ordinal V60() V61() V62() V63() V64() V65() Element of K32(NAT)
val is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
x is Relation-like NAT -defined Function-like total set
x . val is set
rng x is set
val is Relation-like NAT -defined Function-like total Graph-yielding set
Gn is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
val . Gn is Relation-like NAT -defined Function-like finite [Graph-like] set
rng val is set
G is Relation-like NAT -defined Function-like total Graph-yielding () set
v is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
G . v is Relation-like NAT -defined Function-like finite [Graph-like] set
x is Relation-like NAT -defined Function-like finite [Graph-like] set
G is Relation-like NAT -defined Function-like total Graph-yielding () set
v is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
G . v is Relation-like NAT -defined Function-like finite [Graph-like] set
x is Relation-like NAT -defined Function-like finite [Graph-like] set
G is Relation-like NAT -defined Function-like total Graph-yielding () set
v is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
G . v is Relation-like NAT -defined Function-like finite [Graph-like] set
x is Relation-like NAT -defined Function-like finite [Graph-like] set
G is Relation-like NAT -defined Function-like total Graph-yielding () () () set
v is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
G . v is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
x is Relation-like NAT -defined Function-like finite [Graph-like] () () () () () () () set
v is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
G . v is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
x is Relation-like NAT -defined Function-like finite [Graph-like] () () () () () () () set
v is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
G . v is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
x is Relation-like NAT -defined Function-like finite [Graph-like] () () () () () () () set
G is Relation-like NAT -defined Function-like total Graph-yielding () () () set
v is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
G . v is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
x is Relation-like NAT -defined Function-like finite [Graph-like] () () () () () () () set
the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () () () () () () set is Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () () () () () () set
NAT --> the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () () () () () () set is non empty Relation-like NAT -defined { the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () () () () () () set } -valued Function-like constant total V18( NAT ,{ the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () () () () () () set }) T-Sequence-like Function-yielding V125() Element of K32(K33(NAT,{ the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () () () () () () set }))
{ the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () () () () () () set } is non empty trivial functional finite V40() 1 -element set
K33(NAT,{ the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () () () () () () set }) is non trivial Relation-like non finite set
K32(K33(NAT,{ the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () () () () () () set })) is non trivial non finite set
dom (NAT --> the Relation-like NAT -defined Function-like finite [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple connected acyclic Tree-like () () () () () () () () set ) is non empty epsilon-transitive epsilon-connected ordinal V60() V61() V62() V63() V64() V65() Element of K32(NAT)
val is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
x is Relation-like NAT -defined Function-like total set
x . val is set
rng x is set
Gn is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
val is Relation-like NAT -defined Function-like total Graph-yielding set
val . Gn is Relation-like NAT -defined Function-like finite [Graph-like] set
rng val is set
Gn is Relation-like NAT -defined Function-like total Graph-yielding () () () set
1 + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
Gn . (1 + 1) is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
rng Gn is set
Gn . 1 is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
ENext is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
Gn . ENext is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
G is Relation-like NAT -defined Function-like total Graph-yielding () () set
v is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
G . v is Relation-like NAT -defined Function-like finite [Graph-like] () set
x is Relation-like NAT -defined Function-like finite [Graph-like] () set
G is Relation-like NAT -defined Function-like total Graph-yielding () () set
v is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
G . v is Relation-like NAT -defined Function-like finite [Graph-like] () set
x is Relation-like NAT -defined Function-like finite [Graph-like] () set
G is Relation-like NAT -defined Function-like total Graph-yielding () () set
v is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
G . v is Relation-like NAT -defined Function-like finite [Graph-like] () set
x is Relation-like NAT -defined Function-like finite [Graph-like] () set
G is Relation-like NAT -defined Function-like total Graph-yielding () () set
v is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
G . v is Relation-like NAT -defined Function-like finite [Graph-like] () set
x is Relation-like NAT -defined Function-like finite [Graph-like] () set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
(G) is Relation-like the_Edges_of G -defined Function-like total set
the_Edges_of G is set
G . EdgeSelector is set
G . () is set
v is Relation-like NAT -defined Function-like finite [Graph-like] () set
(v) is Relation-like Function-like set
v . () is set
x is Relation-like NAT -defined Function-like finite [Graph-like] () set
(x) is Relation-like Function-like set
x . () is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
the_Edges_of G is set
G . EdgeSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
the_Vertices_of G is non empty set
G . VertexSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] set
v is set
G .set ((),v) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> v is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> v is non empty Relation-like {()} -defined {v} -valued Function-like constant total V18({()},{v}) finite Element of K32(K33({()},{v}))
{v} is non empty trivial finite 1 -element set
K33({()},{v}) is Relation-like finite set
K32(K33({()},{v})) is finite V40() set
G +* (() .--> v) is Relation-like Function-like finite set
x is Relation-like NAT -defined Function-like finite [Graph-like] set
val is set
x .set ((),val) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> val is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> val is non empty Relation-like {()} -defined {val} -valued Function-like constant total V18({()},{val}) finite Element of K32(K33({()},{val}))
{val} is non empty trivial finite 1 -element set
K33({()},{val}) is Relation-like finite set
K32(K33({()},{val})) is finite V40() set
x +* (() .--> val) is Relation-like Function-like finite set
Gn is Relation-like NAT -defined Function-like finite [Graph-like] set
ENext is set
Gn .set ((),ENext) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> ENext is Relation-like NAT -defined {()} -defined Function-like one-to-one finite set
{()} --> ENext is non empty Relation-like {()} -defined {ENext} -valued Function-like constant total V18({()},{ENext}) finite Element of K32(K33({()},{ENext}))
{ENext} is non empty trivial finite 1 -element set
K33({()},{ENext}) is Relation-like finite set
K32(K33({()},{ENext})) is finite V40() set
Gn +* (() .--> ENext) is Relation-like Function-like finite set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
v is Relation-like NAT -defined Function-like finite [Graph-like] () set
(G) is Relation-like the_Edges_of G -defined Function-like total set
the_Edges_of G is set
G . EdgeSelector is set
G . () is set
(v) is Relation-like the_Edges_of v -defined Function-like total set
the_Edges_of v is set
v . EdgeSelector is set
v . () is set
x is Relation-like NAT -defined Function-like finite [Graph-like] () set
(x) is Relation-like the_Edges_of x -defined Function-like total set
the_Edges_of x is set
x . EdgeSelector is set
x . () is set
(x) | (the_Edges_of v) is Relation-like the_Edges_of v -defined the_Edges_of x -defined Function-like set
val is Relation-like NAT -defined Function-like finite [Graph-like] () Subgraph of x
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
v is Relation-like NAT -defined Function-like finite [Graph-like] () (G) Subgraph of G
x is Relation-like NAT -defined Function-like finite [Graph-like] () (v) Subgraph of v
(x) is Relation-like the_Edges_of x -defined Function-like total set
the_Edges_of x is set
x . EdgeSelector is set
x . () is set
(v) is Relation-like the_Edges_of v -defined Function-like total set
the_Edges_of v is set
v . EdgeSelector is set
v . () is set
the_Edges_of x is Element of K32((the_Edges_of v))
K32((the_Edges_of v)) is set
(v) | (the_Edges_of x) is Relation-like the_Edges_of x -defined the_Edges_of v -defined Function-like set
(G) is Relation-like the_Edges_of G -defined Function-like total set
the_Edges_of G is set
G . EdgeSelector is set
G . () is set
the_Edges_of v is Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is set
(G) | (the_Edges_of v) is Relation-like the_Edges_of v -defined the_Edges_of G -defined Function-like set
((G) | (the_Edges_of v)) | (the_Edges_of x) is Relation-like the_Edges_of x -defined the_Edges_of G -defined Function-like set
(G) | (the_Edges_of x) is Relation-like the_Edges_of x -defined the_Edges_of G -defined Function-like set
val is Relation-like NAT -defined Function-like finite [Graph-like] () Subgraph of G
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
v is Relation-like NAT -defined Function-like finite [Graph-like] () set
(G) is Relation-like the_Edges_of G -defined Function-like total set
the_Edges_of G is set
G . EdgeSelector is set
G . () is set
(v) is Relation-like the_Edges_of v -defined Function-like total set
the_Edges_of v is set
v . EdgeSelector is set
v . () is set
x is Relation-like NAT -defined Function-like finite [Graph-like] () (G) Subgraph of G
(x) is Relation-like the_Edges_of x -defined Function-like total set
the_Edges_of x is set
x . EdgeSelector is set
x . () is set
the_Edges_of x is Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is set
(v) | (the_Edges_of x) is Relation-like the_Edges_of x -defined the_Edges_of v -defined Function-like set
val is Relation-like NAT -defined Function-like finite [Graph-like] () Subgraph of v
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
(G) is Relation-like the_Edges_of G -defined Function-like total set
the_Edges_of G is set
G . EdgeSelector is set
G . () is set
v is Relation-like NAT -defined Function-like finite [Graph-like] () (G) Subgraph of G
the_Edges_of v is Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is set
v . EdgeSelector is set
(v) is Relation-like the_Edges_of v -defined Function-like total set
the_Edges_of v is set
v . () is set
x is set
(v) . x is set
(G) . x is set
dom (v) is Element of K32((the_Edges_of v))
K32((the_Edges_of v)) is set
(G) | (the_Edges_of v) is Relation-like the_Edges_of v -defined the_Edges_of G -defined Function-like set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
v is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
(G,v) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
v .length() is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
v .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like EdgeSeq of G
len (v .edgeSeq()) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
len (G,v) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
v is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
(G,v) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (G,v) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
v .length() is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
v .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like EdgeSeq of G
len (v .edgeSeq()) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
(G) is Relation-like the_Edges_of G -defined Function-like total set
the_Edges_of G is set
G . EdgeSelector is set
G . () is set
v is set
x is set
val is set
G .walkOf (v,val,x) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
the_Vertices_of G is non empty set
G . VertexSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
(G,(G .walkOf (v,val,x))) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(G) . val is set
<*((G) . val)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
(G .walkOf (v,val,x)) .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like EdgeSeq of G
<*val*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
len ((G .walkOf (v,val,x)) .edgeSeq()) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
len (G,(G .walkOf (v,val,x))) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
ENext is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
(G,(G .walkOf (v,val,x))) . ENext is set
<*val*> . 1 is set
(G) . (<*val*> . 1) is set
<*((G) . val)*> . ENext is set
len <*((G) . val)*> is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
v is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
v .reverse() is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
(G,(v .reverse())) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(G,v) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
Rev (G,v) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (v .reverse()) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
len v is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(v .reverse()) .length() is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
v .length() is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(v .reverse()) .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like EdgeSeq of G
len ((v .reverse()) .edgeSeq()) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
v .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like EdgeSeq of G
len (v .edgeSeq()) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
len (G,(v .reverse())) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
len (G,v) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
Gn is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
dom (v .edgeSeq()) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(len (G,v)) - Gn is V21() real V30() ext-real set
((len (G,v)) - Gn) + 1 is V21() real V30() ext-real set
Seg (len (G,v)) is finite len (G,v) -element V60() V61() V62() V63() V64() V65() Element of K32(NAT)
x is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(G,(v .reverse())) . Gn is set
(G) is Relation-like the_Edges_of G -defined Function-like total set
G . () is set
((v .reverse()) .edgeSeq()) . Gn is set
(G) . (((v .reverse()) .edgeSeq()) . Gn) is set
Rev (v .edgeSeq()) is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the_Edges_of G
(Rev (v .edgeSeq())) . Gn is set
(G) . ((Rev (v .edgeSeq())) . Gn) is set
(len (v .edgeSeq())) - Gn is V21() real V30() ext-real set
((len (v .edgeSeq())) - Gn) + 1 is V21() real V30() ext-real set
(v .edgeSeq()) . (((len (v .edgeSeq())) - Gn) + 1) is set
(G) . ((v .edgeSeq()) . (((len (v .edgeSeq())) - Gn) + 1)) is set
dom (G,v) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(Rev (G,v)) . Gn is set
(G,v) . x is set
(v .edgeSeq()) . x is set
(G) . ((v .edgeSeq()) . x) is set
len (Rev (G,v)) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
v is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
v .last() is Element of the_Vertices_of G
x is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
x .first() is Element of the_Vertices_of G
v .append x is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
(G,(v .append x)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(G,v) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(G,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(G,v) ^ (G,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(v .append x) .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like EdgeSeq of G
v .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like EdgeSeq of G
x .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like EdgeSeq of G
(v .edgeSeq()) ^ (x .edgeSeq()) is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the_Edges_of G
len ((v .append x) .edgeSeq()) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
len (v .edgeSeq()) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
len (x .edgeSeq()) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(len (v .edgeSeq())) + (len (x .edgeSeq())) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
len (G,(v .append x)) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
len (G,v) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(len (G,v)) + (len (x .edgeSeq())) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
len (G,x) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(len (G,v)) + (len (G,x)) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
len ((G,v) ^ (G,x)) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
ENext is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
(G,(v .append x)) . ENext is set
(G) is Relation-like the_Edges_of G -defined Function-like total set
G . () is set
((v .append x) .edgeSeq()) . ENext is set
(G) . (((v .append x) .edgeSeq()) . ENext) is set
((v .edgeSeq()) ^ (x .edgeSeq())) . ENext is set
(G) . (((v .edgeSeq()) ^ (x .edgeSeq())) . ENext) is set
dom ((G,v) ^ (G,x)) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
dom (G,v) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
dom (v .edgeSeq()) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
((G,v) ^ (G,x)) . ENext is set
(G,v) . ENext is set
(v .edgeSeq()) . ENext is set
(G) . ((v .edgeSeq()) . ENext) is set
dom (G,x) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
x is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
(len (G,v)) + x is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
x is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
(len (G,v)) + x is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
dom (x .edgeSeq()) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(len (v .edgeSeq())) + x is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
((G,v) ^ (G,x)) . ENext is set
(G,x) . x is set
(x .edgeSeq()) . x is set
(G) . ((x .edgeSeq()) . x) is set
dom (G,v) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
dom (G,x) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
((G,v) ^ (G,x)) . ENext is set
((G,v) ^ (G,x)) . ENext is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
(G) is Relation-like the_Edges_of G -defined Function-like total set
G . () is set
v is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
v .last() is Element of the_Vertices_of G
(v .last()) .edgesInOut() is Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is set
{(v .last())} is non empty trivial finite 1 -element Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is set
G .edgesInOut {(v .last())} is Element of K32((the_Edges_of G))
G .edgesInto {(v .last())} is Element of K32((the_Edges_of G))
G .edgesOutOf {(v .last())} is Element of K32((the_Edges_of G))
(G .edgesInto {(v .last())}) \/ (G .edgesOutOf {(v .last())}) is Element of K32((the_Edges_of G))
(G,v) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
x is set
v .addEdge x is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
(G,(v .addEdge x)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(G) . x is set
<*((G) . x)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
(G,v) ^ <*((G) . x)*> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(v .last()) .adj x is Element of the_Vertices_of G
G .walkOf ((v .last()),x,((v .last()) .adj x)) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
v .append (G .walkOf ((v .last()),x,((v .last()) .adj x))) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
(G .walkOf ((v .last()),x,((v .last()) .adj x))) .first() is Element of the_Vertices_of G
(G,(G .walkOf ((v .last()),x,((v .last()) .adj x)))) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(G,v) ^ (G,(G .walkOf ((v .last()),x,((v .last()) .adj x)))) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
v is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
(G,v) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K32((G,v)) is finite V40() set
x is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Subwalk of v
(G,x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
v .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like EdgeSeq of G
K32((v .edgeSeq())) is finite V40() set
x .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like EdgeSeq of G
val is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSubsequence-like Element of K32((v .edgeSeq()))
((the_Edges_of G),(v .edgeSeq()),val) is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the_Edges_of G
(G) is Relation-like the_Edges_of G -defined Function-like total complex-valued ext-real-valued real-valued set
G . () is set
dom val is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
Gn is Relation-like Function-like set
dom Gn is set
x is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
Seg x is finite x -element V60() V61() V62() V63() V64() V65() Element of K32(NAT)
x is set
ENext is Relation-like NAT -defined Function-like FinSubsequence-like set
n is set
y is set
[n,y] is set
val . n is set
[n,(val . n)] is set
dom (v .edgeSeq()) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
ENext . n is set
x is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
len (v .edgeSeq()) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
len (G,v) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(G,v) . x is V21() real ext-real Element of REAL
(v .edgeSeq()) . x is set
(G) . ((v .edgeSeq()) . x) is V21() real ext-real Element of REAL
dom (G,v) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
[x,((G,v) . x)] is Element of K33(NAT,REAL)
K33(NAT,REAL) is non trivial Relation-like non finite complex-valued ext-real-valued real-valued set
val . x is set
(G) . (val . x) is V21() real ext-real Element of REAL
x is Relation-like NAT -defined REAL -valued Function-like finite FinSubsequence-like complex-valued ext-real-valued real-valued Element of K32((G,v))
(REAL,(G,v),x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len ((the_Edges_of G),(v .edgeSeq()),val) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
card val is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
dom x is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
card (dom x) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
card x is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
len (REAL,(G,v),x) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
len (G,x) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
Sgm (dom val) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
rng (Sgm (dom val)) is finite V60() V61() V62() V63() V64() V65() Element of K32(REAL)
n is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
Seg n is finite n -element V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(Sgm (dom val)) * x is Relation-like NAT -defined REAL -valued Function-like finite complex-valued ext-real-valued real-valued set
n is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
(Sgm (dom val)) * val is Relation-like NAT -defined the_Edges_of G -valued Function-like finite set
dom ((the_Edges_of G),(v .edgeSeq()),val) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
dom (REAL,(G,v),x) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
dom (Sgm (dom val)) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(Sgm (dom val)) . n is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(REAL,(G,v),x) . n is V21() real ext-real Element of REAL
x . ((Sgm (dom val)) . n) is V21() real ext-real Element of REAL
val . ((Sgm (dom val)) . n) is set
(G) . (val . ((Sgm (dom val)) . n)) is V21() real ext-real Element of REAL
((the_Edges_of G),(v .edgeSeq()),val) . n is set
(G) . (((the_Edges_of G),(v .edgeSeq()),val) . n) is V21() real ext-real Element of REAL
(G,x) . n is V21() real ext-real Element of REAL
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
v is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of v is non empty set
v . VertexSelector is set
the_Edges_of v is set
v . EdgeSelector is set
(the_Vertices_of v) \/ (the_Edges_of v) is non empty set
(G) is Relation-like the_Edges_of G -defined Function-like total set
G . () is set
(v) is Relation-like the_Edges_of v -defined Function-like total set
v . () is set
x is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
(G,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
val is Relation-like NAT -defined (the_Vertices_of v) \/ (the_Edges_of v) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of v
(v,val) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
x .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like EdgeSeq of G
val .edgeSeq() is Relation-like NAT -defined the_Edges_of v -valued Function-like finite FinSequence-like FinSubsequence-like EdgeSeq of v
len (G,x) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
len (v,val) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
len (x .edgeSeq()) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
x is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
dom (G,x) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(v,val) . x is set
(val .edgeSeq()) . x is set
(v) . ((val .edgeSeq()) . x) is set
(x .edgeSeq()) . x is set
(G) . ((x .edgeSeq()) . x) is set
(G,x) . x is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
v is Relation-like NAT -defined Function-like finite [Graph-like] () (G) Subgraph of G
the_Vertices_of v is non empty set
v . VertexSelector is set
the_Edges_of v is set
v . EdgeSelector is set
(the_Vertices_of v) \/ (the_Edges_of v) is non empty set
x is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
(G,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
val is Relation-like NAT -defined (the_Vertices_of v) \/ (the_Edges_of v) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of v
(v,val) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
x .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like EdgeSeq of G
val .edgeSeq() is Relation-like NAT -defined the_Edges_of v -valued Function-like finite FinSequence-like FinSubsequence-like EdgeSeq of v
len (G,x) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
len (v,val) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
len (x .edgeSeq()) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
x is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
dom (G,x) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
len (val .edgeSeq()) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
dom (val .edgeSeq()) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(v,val) . x is set
(v) is Relation-like the_Edges_of v -defined Function-like total set
v . () is set
(val .edgeSeq()) . x is set
(v) . ((val .edgeSeq()) . x) is set
(G) is Relation-like the_Edges_of G -defined Function-like total set
G . () is set
the_Edges_of v is Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is set
(G) | (the_Edges_of v) is Relation-like the_Edges_of v -defined the_Edges_of G -defined Function-like set
((G) | (the_Edges_of v)) . ((val .edgeSeq()) . x) is set
(x .edgeSeq()) . x is set
(G) . ((x .edgeSeq()) . x) is set
(G,x) . x is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
v is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
(G,v) is V21() real ext-real Element of REAL
(G,v) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (G,v) is V21() real ext-real Element of REAL
K221(REAL,(G,v),K168()) is V21() real ext-real Element of REAL
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
the_Vertices_of G is non empty set
G . VertexSelector is set
(G) is Relation-like the_Edges_of G -defined Function-like total complex-valued ext-real-valued real-valued set
the_Edges_of G is set
G . EdgeSelector is set
G . () is set
v is Element of the_Vertices_of G
x is Element of the_Vertices_of G
val is set
G .walkOf (v,val,x) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
(G,(G .walkOf (v,val,x))) is V21() real ext-real Element of REAL
(G,(G .walkOf (v,val,x))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (G,(G .walkOf (v,val,x))) is V21() real ext-real Element of REAL
K221(REAL,(G,(G .walkOf (v,val,x))),K168()) is V21() real ext-real Element of REAL
(G) . val is V21() real ext-real Element of REAL
<*((G) . val)*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant finite 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued V54() decreasing non-decreasing non-increasing FinSequence of REAL
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
v is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
(G,v) is V21() real ext-real Element of REAL
(G,v) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (G,v) is V21() real ext-real Element of REAL
K221(REAL,(G,v),K168()) is V21() real ext-real Element of REAL
v .reverse() is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
(G,(v .reverse())) is V21() real ext-real Element of REAL
(G,(v .reverse())) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (G,(v .reverse())) is V21() real ext-real Element of REAL
K221(REAL,(G,(v .reverse())),K168()) is V21() real ext-real Element of REAL
Rev (G,v) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (Rev (G,v)) is V21() real ext-real Element of REAL
K221(REAL,(Rev (G,v)),K168()) is V21() real ext-real Element of REAL
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
v is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
v .last() is Element of the_Vertices_of G
x is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
x .first() is Element of the_Vertices_of G
v .append x is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
(G,(v .append x)) is V21() real ext-real Element of REAL
(G,(v .append x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (G,(v .append x)) is V21() real ext-real Element of REAL
K221(REAL,(G,(v .append x)),K168()) is V21() real ext-real Element of REAL
(G,v) is V21() real ext-real Element of REAL
(G,v) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (G,v) is V21() real ext-real Element of REAL
K221(REAL,(G,v),K168()) is V21() real ext-real Element of REAL
(G,x) is V21() real ext-real Element of REAL
(G,x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (G,x) is V21() real ext-real Element of REAL
K221(REAL,(G,x),K168()) is V21() real ext-real Element of REAL
(G,v) + (G,x) is V21() real ext-real set
(G,v) ^ (G,x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
(G) is Relation-like the_Edges_of G -defined Function-like total complex-valued ext-real-valued real-valued set
G . () is set
v is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
v .last() is Element of the_Vertices_of G
(v .last()) .edgesInOut() is Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is set
{(v .last())} is non empty trivial finite 1 -element Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is set
G .edgesInOut {(v .last())} is Element of K32((the_Edges_of G))
G .edgesInto {(v .last())} is Element of K32((the_Edges_of G))
G .edgesOutOf {(v .last())} is Element of K32((the_Edges_of G))
(G .edgesInto {(v .last())}) \/ (G .edgesOutOf {(v .last())}) is Element of K32((the_Edges_of G))
(G,v) is V21() real ext-real Element of REAL
(G,v) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (G,v) is V21() real ext-real Element of REAL
K221(REAL,(G,v),K168()) is V21() real ext-real Element of REAL
x is set
v .addEdge x is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
(G,(v .addEdge x)) is V21() real ext-real Element of REAL
(G,(v .addEdge x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (G,(v .addEdge x)) is V21() real ext-real Element of REAL
K221(REAL,(G,(v .addEdge x)),K168()) is V21() real ext-real Element of REAL
(G) . x is V21() real ext-real Element of REAL
(G,v) + ((G) . x) is V21() real ext-real set
<*((G) . x)*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant finite 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued V54() decreasing non-decreasing non-increasing FinSequence of REAL
(G,v) ^ <*((G) . x)*> is non empty Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum <*((G) . x)*> is V21() real ext-real Element of REAL
K221(REAL,<*((G) . x)*>,K168()) is V21() real ext-real Element of REAL
(Sum (G,v)) + (Sum <*((G) . x)*>) is V21() real ext-real set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
v is Relation-like NAT -defined Function-like finite [Graph-like] () () set
the_Vertices_of v is non empty set
v . VertexSelector is set
the_Edges_of v is set
v . EdgeSelector is set
(the_Vertices_of v) \/ (the_Edges_of v) is non empty set
x is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
val is Relation-like NAT -defined (the_Vertices_of v) \/ (the_Edges_of v) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of v
(G) is Relation-like the_Edges_of G -defined Function-like total complex-valued ext-real-valued real-valued set
G . () is set
(v) is Relation-like the_Edges_of v -defined Function-like total complex-valued ext-real-valued real-valued set
v . () is set
(G,x) is V21() real ext-real Element of REAL
(G,x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (G,x) is V21() real ext-real Element of REAL
K221(REAL,(G,x),K168()) is V21() real ext-real Element of REAL
(v,val) is V21() real ext-real Element of REAL
(v,val) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (v,val) is V21() real ext-real Element of REAL
K221(REAL,(v,val),K168()) is V21() real ext-real Element of REAL
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
v is Relation-like NAT -defined Function-like finite [Graph-like] () (G) () Subgraph of G
the_Vertices_of v is non empty set
v . VertexSelector is set
the_Edges_of v is set
v . EdgeSelector is set
(the_Vertices_of v) \/ (the_Edges_of v) is non empty set
x is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
val is Relation-like NAT -defined (the_Vertices_of v) \/ (the_Edges_of v) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of v
(G,x) is V21() real ext-real Element of REAL
(G,x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (G,x) is V21() real ext-real Element of REAL
K221(REAL,(G,x),K168()) is V21() real ext-real Element of REAL
(v,val) is V21() real ext-real Element of REAL
(v,val) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (v,val) is V21() real ext-real Element of REAL
K221(REAL,(v,val),K168()) is V21() real ext-real Element of REAL
G is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
v is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
(G,v) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
dom (G,v) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
x is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(G,v) . x is V21() real ext-real Element of REAL
len (G,v) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
v .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like EdgeSeq of G
len (v .edgeSeq()) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(G) is Relation-like the_Edges_of G -defined Function-like total complex-valued ext-real-valued real-valued set
G . () is set
dom (G) is Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is set
dom (v .edgeSeq()) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
(v .edgeSeq()) . x is set
(G) . ((v .edgeSeq()) . x) is V21() real ext-real Element of REAL
rng (G) is V60() V61() V62() Element of K32(REAL)
Gn is V21() real ext-real Element of REAL
G is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
v is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
(G,v) is V21() real ext-real Element of REAL
(G,v) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (G,v) is V21() real ext-real Element of REAL
K221(REAL,(G,v),K168()) is V21() real ext-real Element of REAL
dom (G,v) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
x is V21() epsilon-transitive epsilon-connected ordinal natural real V30() finite cardinal ext-real non negative set
(G,v) . x is V21() real ext-real Element of REAL
G is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Edges_of G is set
G . EdgeSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
v is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Walk of G
(G,v) is V21() real ext-real Element of REAL
(G,v) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (G,v) is V21() real ext-real Element of REAL
K221(REAL,(G,v),K168()) is V21() real ext-real Element of REAL
x is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like Subwalk of v
(G,x) is V21() real ext-real Element of REAL
(G,x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (G,x) is V21() real ext-real Element of REAL
K221(REAL,(G,x),K168()) is V21() real ext-real Element of REAL
K32((G,v)) is finite V40() set
dom (G,v) is finite V60() V61() V62() V63() V64() V65() Element of K32(NAT)
val is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(G,v) . val is V21() real ext-real Element of REAL
val is Relation-like NAT -defined REAL -valued Function-like finite FinSubsequence-like complex-valued ext-real-valued real-valued Element of K32((G,v))
(REAL,(G,v),val) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
G is Relation-like NAT -defined Function-like finite [Graph-like] () () () set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Relation-like the_Edges_of G -defined Function-like total complex-valued ext-real-valued real-valued set
G . () is set
v is set
(G) . v is V21() real ext-real Element of REAL
dom (G) is Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is set
rng (G) is V60() V61() V62() Element of K32(REAL)
x is V21() real ext-real Element of REAL
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Relation-like Function-like set
G . () is set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
((G,v,x)) is Relation-like Function-like set
(G,v,x) . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
(G .set ((),((G) +* (v .--> x)))) . () is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Edges_of G is set
G . EdgeSelector is set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
((G,v,x)) is Relation-like Function-like set
(G,v,x) . () is set
((G,v,x)) . v is set
{v} is non empty trivial finite 1 -element set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
dom (v .--> x) is finite Element of K32({v})
K32({v}) is finite V40() set
(G) is Relation-like Function-like set
G . () is set
(G) +* (v .--> x) is Relation-like Function-like set
(v .--> x) . v is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Edges_of (G,v,x) is set
(G,v,x) . EdgeSelector is set
the_Vertices_of (G,v,x) is non empty set
(G,v,x) . VertexSelector is set
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is set
G . SourceSelector is set
the_Source_of (G,v,x) is Relation-like the_Edges_of (G,v,x) -defined the_Vertices_of (G,v,x) -valued Function-like total V18( the_Edges_of (G,v,x), the_Vertices_of (G,v,x)) Element of K32(K33((the_Edges_of (G,v,x)),(the_Vertices_of (G,v,x))))
K33((the_Edges_of (G,v,x)),(the_Vertices_of (G,v,x))) is Relation-like set
K32(K33((the_Edges_of (G,v,x)),(the_Vertices_of (G,v,x)))) is set
(G,v,x) . SourceSelector is set
the_Target_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
G . TargetSelector is set
the_Target_of (G,v,x) is Relation-like the_Edges_of (G,v,x) -defined the_Vertices_of (G,v,x) -valued Function-like total V18( the_Edges_of (G,v,x), the_Vertices_of (G,v,x)) Element of K32(K33((the_Edges_of (G,v,x)),(the_Vertices_of (G,v,x))))
(G,v,x) . TargetSelector is set
the_Edges_of G is set
G . EdgeSelector is set
the_Edges_of G is set
G . EdgeSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
(G) is Relation-like the_Edges_of G -defined Function-like total set
the_Edges_of G is set
G . EdgeSelector is set
G . () is set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
((G,v,x)) is Relation-like the_Edges_of (G,v,x) -defined Function-like total set
the_Edges_of (G,v,x) is set
(G,v,x) . EdgeSelector is set
(G,v,x) . () is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
(G) is Relation-like Function-like set
G . () is set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
((G,v,x)) is Relation-like Function-like set
(G,v,x) . () is set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Edges_of G is set
G . EdgeSelector is set
the_Edges_of G is set
G . EdgeSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
(G) is Relation-like Function-like set
G . () is set
v is set
x is set
val is set
(G,v,val) is Relation-like NAT -defined Function-like finite [Graph-like] () set
((G,v,val)) is Relation-like Function-like set
(G,v,val) . () is set
((G,v,val)) . x is set
(G) . x is set
the_Edges_of G is set
G . EdgeSelector is set
{v} is non empty trivial finite 1 -element set
v .--> val is Relation-like {v} -defined Function-like one-to-one finite set
{v} --> val is non empty Relation-like {v} -defined {val} -valued Function-like constant total V18({v},{val}) finite Element of K32(K33({v},{val}))
{val} is non empty trivial finite 1 -element set
K33({v},{val}) is Relation-like finite set
K32(K33({v},{val})) is finite V40() set
dom (v .--> val) is finite Element of K32({v})
K32({v}) is finite V40() set
(G) +* (v .--> val) is Relation-like Function-like set
the_Edges_of G is set
G . EdgeSelector is set
the_Edges_of G is set
G . EdgeSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty set
G . VertexSelector is set
(G) is Relation-like Function-like set
G . () is set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
((G,v,x)) is Relation-like Function-like set
(G,v,x) . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
(G .set ((),((G) +* (v .--> x)))) . () is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty set
G . VertexSelector is set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
((G,v,x)) is Relation-like Function-like set
(G,v,x) . () is set
((G,v,x)) . v is set
{v} is non empty trivial finite 1 -element set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
dom (v .--> x) is finite Element of K32({v})
K32({v}) is finite V40() set
(G) is Relation-like Function-like set
G . () is set
(G) +* (v .--> x) is Relation-like Function-like set
(v .--> x) . v is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty set
G . VertexSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Edges_of G is set
G . EdgeSelector is set
the_Edges_of (G,v,x) is set
(G,v,x) . EdgeSelector is set
the_Vertices_of (G,v,x) is non empty set
(G,v,x) . VertexSelector is set
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is set
G . SourceSelector is set
the_Source_of (G,v,x) is Relation-like the_Edges_of (G,v,x) -defined the_Vertices_of (G,v,x) -valued Function-like total V18( the_Edges_of (G,v,x), the_Vertices_of (G,v,x)) Element of K32(K33((the_Edges_of (G,v,x)),(the_Vertices_of (G,v,x))))
K33((the_Edges_of (G,v,x)),(the_Vertices_of (G,v,x))) is Relation-like set
K32(K33((the_Edges_of (G,v,x)),(the_Vertices_of (G,v,x)))) is set
(G,v,x) . SourceSelector is set
the_Target_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
G . TargetSelector is set
the_Target_of (G,v,x) is Relation-like the_Edges_of (G,v,x) -defined the_Vertices_of (G,v,x) -valued Function-like total V18( the_Edges_of (G,v,x), the_Vertices_of (G,v,x)) Element of K32(K33((the_Edges_of (G,v,x)),(the_Vertices_of (G,v,x))))
(G,v,x) . TargetSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
(G) is Relation-like the_Edges_of G -defined Function-like total set
the_Edges_of G is set
G . EdgeSelector is set
G . () is set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
((G,v,x)) is Relation-like the_Edges_of (G,v,x) -defined Function-like total set
the_Edges_of (G,v,x) is set
(G,v,x) . EdgeSelector is set
(G,v,x) . () is set
the_Vertices_of G is non empty set
G . VertexSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
(G) is Relation-like Function-like set
G . () is set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
((G,v,x)) is Relation-like Function-like set
(G,v,x) . () is set
the_Vertices_of G is non empty set
G . VertexSelector is set
(G) is Relation-like Function-like set
G . () is set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
G .set ((),((G) +* (v .--> x))) is Relation-like NAT -defined Function-like finite [Graph-like] () set
() .--> ((G) +* (v .--> x)) is Relation-like NAT -defined {()} -defined Function-like one-to-one finite Function-yielding V125() set
{()} --> ((G) +* (v .--> x)) is non empty Relation-like {()} -defined {((G) +* (v .--> x))} -valued Function-like constant total V18({()},{((G) +* (v .--> x))}) finite Function-yielding V125() Element of K32(K33({()},{((G) +* (v .--> x))}))
{((G) +* (v .--> x))} is non empty trivial functional finite 1 -element set
K33({()},{((G) +* (v .--> x))}) is Relation-like finite set
K32(K33({()},{((G) +* (v .--> x))})) is finite V40() set
G +* (() .--> ((G) +* (v .--> x))) is Relation-like Function-like finite set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
(G) is Relation-like Function-like set
G . () is set
v is set
x is set
val is set
(G,v,val) is Relation-like NAT -defined Function-like finite [Graph-like] () set
((G,v,val)) is Relation-like Function-like set
(G,v,val) . () is set
((G,v,val)) . x is set
(G) . x is set
the_Vertices_of G is non empty set
G . VertexSelector is set
{v} is non empty trivial finite 1 -element set
v .--> val is Relation-like {v} -defined Function-like one-to-one finite set
{v} --> val is non empty Relation-like {v} -defined {val} -valued Function-like constant total V18({v},{val}) finite Element of K32(K33({v},{val}))
{val} is non empty trivial finite 1 -element set
K33({v},{val}) is Relation-like finite set
K32(K33({v},{val})) is finite V40() set
dom (v .--> val) is finite Element of K32({v})
K32({v}) is finite V40() set
(G) +* (v .--> val) is Relation-like Function-like set
the_Vertices_of G is non empty set
G . VertexSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
(G) is Relation-like Function-like set
G . () is set
v is Relation-like NAT -defined Function-like finite [Graph-like] () set
(v) is Relation-like Function-like set
v . () is set
(G) is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
dom (G) is set
(v) is Element of K32((the_Edges_of v))
the_Edges_of v is set
v . EdgeSelector is set
K32((the_Edges_of v)) is set
dom (v) is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
((G,v,x)) is Element of K32((the_Edges_of (G,v,x)))
the_Edges_of (G,v,x) is set
(G,v,x) . EdgeSelector is set
K32((the_Edges_of (G,v,x))) is set
((G,v,x)) is Relation-like Function-like set
(G,v,x) . () is set
dom ((G,v,x)) is set
{v} is non empty trivial finite 1 -element set
(G) \/ {v} is non empty set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
dom (v .--> x) is finite Element of K32({v})
K32({v}) is finite V40() set
(dom (G)) \/ (dom (v .--> x)) is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Edges_of G is set
G . EdgeSelector is set
(G) is Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
((G,v,x)) is Element of K32((the_Edges_of (G,v,x)))
the_Edges_of (G,v,x) is set
(G,v,x) . EdgeSelector is set
K32((the_Edges_of (G,v,x))) is set
((G,v,x)) is Relation-like Function-like set
(G,v,x) . () is set
dom ((G,v,x)) is set
{v} is non empty trivial finite 1 -element set
(G) \/ {v} is non empty set
G is Relation-like NAT -defined Function-like finite [Graph-like] finite () set
the_Edges_of G is finite set
G . EdgeSelector is set
(G) is finite Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is finite V40() set
(G) is Relation-like Function-like finite set
G . () is set
dom (G) is finite set
card (G) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(card (G)) + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] finite () set
((G,v,x)) is finite Element of K32((the_Edges_of (G,v,x)))
the_Edges_of (G,v,x) is finite set
(G,v,x) . EdgeSelector is set
K32((the_Edges_of (G,v,x))) is finite V40() set
((G,v,x)) is Relation-like Function-like finite set
(G,v,x) . () is set
dom ((G,v,x)) is finite set
card ((G,v,x)) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
{v} is non empty trivial finite 1 -element set
(dom (G)) \/ {v} is non empty finite set
card ((dom (G)) \/ {v}) is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
card (dom (G)) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(card (dom (G))) + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like finite set
dom (v .--> x) is finite Element of K32({v})
K32({v}) is finite V40() set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
(G) is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
x is set
v is set
val is set
(G,v,val) is Relation-like NAT -defined Function-like finite [Graph-like] () set
((G,v,val)) is Element of K32((the_Edges_of (G,v,val)))
the_Edges_of (G,v,val) is set
(G,v,val) . EdgeSelector is set
K32((the_Edges_of (G,v,val))) is set
((G,v,val)) is Relation-like Function-like set
(G,v,val) . () is set
dom ((G,v,val)) is set
v .--> val is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> val is non empty Relation-like {v} -defined {val} -valued Function-like constant total V18({v},{val}) finite Element of K32(K33({v},{val}))
{val} is non empty trivial finite 1 -element set
K33({v},{val}) is Relation-like finite set
K32(K33({v},{val})) is finite V40() set
(G) +* (v .--> val) is Relation-like Function-like set
dom (v .--> val) is finite Element of K32({v})
K32({v}) is finite V40() set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
(G) is Element of K32((the_Edges_of G))
the_Edges_of G is set
G . EdgeSelector is set
K32((the_Edges_of G)) is set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
((G,v,x)) is Element of K32((the_Edges_of (G,v,x)))
the_Edges_of (G,v,x) is set
(G,v,x) . EdgeSelector is set
K32((the_Edges_of (G,v,x))) is set
((G,v,x)) is Relation-like Function-like set
(G,v,x) . () is set
dom ((G,v,x)) is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Edges_of G is set
G . EdgeSelector is set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
((G,v,x)) is Element of K32((the_Edges_of (G,v,x)))
the_Edges_of (G,v,x) is set
(G,v,x) . EdgeSelector is set
K32((the_Edges_of (G,v,x))) is set
((G,v,x)) is Relation-like Function-like set
(G,v,x) . () is set
dom ((G,v,x)) is set
(G) is Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
{v} is non empty trivial finite 1 -element set
(G) \/ {v} is non empty set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
(G) is Relation-like Function-like set
G . () is set
v is Relation-like NAT -defined Function-like finite [Graph-like] () set
(v) is Relation-like Function-like set
v . () is set
(G) is Element of K32((the_Vertices_of G))
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
dom (G) is set
(v) is Element of K32((the_Vertices_of v))
the_Vertices_of v is non empty set
v . VertexSelector is set
K32((the_Vertices_of v)) is set
dom (v) is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty set
G . VertexSelector is set
(G) is Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
((G,v,x)) is Element of K32((the_Vertices_of (G,v,x)))
the_Vertices_of (G,v,x) is non empty set
(G,v,x) . VertexSelector is set
K32((the_Vertices_of (G,v,x))) is set
((G,v,x)) is Relation-like Function-like set
(G,v,x) . () is set
dom ((G,v,x)) is set
{v} is non empty trivial finite 1 -element set
(G) \/ {v} is non empty set
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like set
dom (v .--> x) is finite Element of K32({v})
K32({v}) is finite V40() set
(dom (G)) \/ (dom (v .--> x)) is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty set
G . VertexSelector is set
(G) is Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
((G,v,x)) is Element of K32((the_Vertices_of (G,v,x)))
the_Vertices_of (G,v,x) is non empty set
(G,v,x) . VertexSelector is set
K32((the_Vertices_of (G,v,x))) is set
((G,v,x)) is Relation-like Function-like set
(G,v,x) . () is set
dom ((G,v,x)) is set
{v} is non empty trivial finite 1 -element set
(G) \/ {v} is non empty set
G is Relation-like NAT -defined Function-like finite [Graph-like] finite () set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
(G) is finite Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is finite V40() set
(G) is Relation-like Function-like finite set
G . () is set
dom (G) is finite set
card (G) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(card (G)) + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] finite () set
((G,v,x)) is finite Element of K32((the_Vertices_of (G,v,x)))
the_Vertices_of (G,v,x) is non empty finite set
(G,v,x) . VertexSelector is set
K32((the_Vertices_of (G,v,x))) is finite V40() set
((G,v,x)) is Relation-like Function-like finite set
(G,v,x) . () is set
dom ((G,v,x)) is finite set
card ((G,v,x)) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
{v} is non empty trivial finite 1 -element set
(dom (G)) \/ {v} is non empty finite set
card ((dom (G)) \/ {v}) is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
card (dom (G)) is V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real non negative V60() V61() V62() V63() V64() V65() Element of NAT
(card (dom (G))) + 1 is non empty V21() epsilon-transitive epsilon-connected ordinal natural real V30() V31() finite cardinal ext-real positive non negative V60() V61() V62() V63() V64() V65() Element of NAT
v .--> x is Relation-like {v} -defined Function-like one-to-one finite set
{v} --> x is non empty Relation-like {v} -defined {x} -valued Function-like constant total V18({v},{x}) finite Element of K32(K33({v},{x}))
{x} is non empty trivial finite 1 -element set
K33({v},{x}) is Relation-like finite set
K32(K33({v},{x})) is finite V40() set
(G) +* (v .--> x) is Relation-like Function-like finite set
dom (v .--> x) is finite Element of K32({v})
K32({v}) is finite V40() set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
(G) is Element of K32((the_Vertices_of G))
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
x is set
v is set
val is set
(G,v,val) is Relation-like NAT -defined Function-like finite [Graph-like] () set
((G,v,val)) is Element of K32((the_Vertices_of (G,v,val)))
the_Vertices_of (G,v,val) is non empty set
(G,v,val) . VertexSelector is set
K32((the_Vertices_of (G,v,val))) is set
((G,v,val)) is Relation-like Function-like set
(G,v,val) . () is set
dom ((G,v,val)) is set
v .--> val is Relation-like {v} -defined Function-like one-to-one finite set
{v} is non empty trivial finite 1 -element set
{v} --> val is non empty Relation-like {v} -defined {val} -valued Function-like constant total V18({v},{val}) finite Element of K32(K33({v},{val}))
{val} is non empty trivial finite 1 -element set
K33({v},{val}) is Relation-like finite set
K32(K33({v},{val})) is finite V40() set
(G) +* (v .--> val) is Relation-like Function-like set
dom (v .--> val) is finite Element of K32({v})
K32({v}) is finite V40() set
G is Relation-like NAT -defined Function-like finite [Graph-like] () () set
(G) is Element of K32((the_Vertices_of G))
the_Vertices_of G is non empty set
G . VertexSelector is set
K32((the_Vertices_of G)) is set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
v is set
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () () set
((G,v,x)) is Element of K32((the_Vertices_of (G,v,x)))
the_Vertices_of (G,v,x) is non empty set
(G,v,x) . VertexSelector is set
K32((the_Vertices_of (G,v,x))) is set
((G,v,x)) is Relation-like Function-like set
(G,v,x) . () is set
dom ((G,v,x)) is set
G is Relation-like NAT -defined Function-like finite [Graph-like] () set
the_Vertices_of G is non empty set
G . VertexSelector is set
v is Element of the_Vertices_of G
x is set
(G,v,x) is Relation-like NAT -defined Function-like finite [Graph-like] () set
((G,v,x)) is Element of K32((the_Vertices_of (G,v,x)))
the_Vertices_of (G,v,x) is non empty set
(G,v,x) . VertexSelector is set
K32((the_Vertices_of (G,v,x))) is set
((G,v,x)) is Relation-like Function-like set
(G,v,x) . () is set
dom ((G,v,x)) is set
(G) is Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is set
(G) is Relation-like Function-like set
G . () is set
dom (G) is set
{v} is non empty trivial finite 1 -element Element of K32((the_Vertices_of G))
(G) \/ {v} is non empty Element of K32((the_Vertices_of G))