REAL is complex-membered ext-real-membered real-membered V30() V33() V34() V36() set
NAT is non empty non trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V30() V31() V33() epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal Element of bool REAL
bool REAL is non empty cup-closed diff-closed preBoolean set
NAT is non empty non trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V30() V31() V33() epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal set
bool NAT is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
bool NAT is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
COMPLEX is complex-membered V30() set
RAT is complex-membered ext-real-membered real-membered rational-membered V30() set
INT is complex-membered ext-real-membered real-membered rational-membered integer-membered V30() set
{} is empty Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V30() V33() V34() V35() V36() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V55() real V57() complex-valued ext-real-valued real-valued natural-valued FinSequence-yielding finite-support Function-yielding V264() set
2 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
[:NAT,REAL:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:NAT,REAL:] is non empty cup-closed diff-closed preBoolean set
1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
K216(1,NAT) is M10( NAT )
{{},1} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered set
3 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
_GraphSelectors is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V33() Element of bool NAT
VertexSelector is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
EdgeSelector is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
SourceSelector is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
TargetSelector is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
4 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
{VertexSelector,EdgeSelector,SourceSelector,TargetSelector} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite Element of bool NAT
card {} is empty Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V30() V33() V34() V35() V36() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V55() real V57() complex-valued ext-real-valued real-valued natural-valued FinSequence-yielding finite-support Function-yielding V264() set
0 is empty Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V30() V33() V34() V35() V36() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V55() real V57() V59() complex-valued ext-real-valued real-valued natural-valued FinSequence-yielding finite-support Function-yielding V264() Element of NAT
proj1 {} is empty Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V30() V33() V34() V35() V36() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V55() real V57() complex-valued ext-real-valued real-valued natural-valued FinSequence-yielding finite-support Function-yielding V264() set
proj2 {} is empty trivial Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V30() V33() V34() V35() V36() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V55() real V57() complex-valued ext-real-valued real-valued natural-valued V72() decreasing non-decreasing non-increasing FinSequence-yielding finite-support V224() Function-yielding V264() set
6 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
5 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like Function-like set
proj1 G is set
L is set
V is set
L .--> V is Relation-like {L} -defined Function-like one-to-one finite finite-support set
{L} is non empty trivial finite 1 -element set
{L} --> V is non empty Relation-like {L} -defined {V} -valued Function-like constant total quasi_total finite finite-support Element of bool [:{L},{V}:]
{V} is non empty trivial finite 1 -element set
[:{L},{V}:] is non empty Relation-like finite set
bool [:{L},{V}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
G +* (L .--> V) is Relation-like Function-like set
proj1 (G +* (L .--> V)) is set
(proj1 G) \/ {L} is non empty set
dom (L .--> V) is trivial finite Element of bool {L}
bool {L} is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(proj1 G) \/ (dom (L .--> V)) is set
G is Relation-like Function-like one-to-one set
L is set
V is set
G | L is Relation-like Function-like set
(G | L) " is Relation-like Function-like set
proj1 ((G | L) ") is set
G | V is Relation-like Function-like set
(G | V) " is Relation-like Function-like set
(G | L) ~ is Relation-like set
(G | V) ~ is Relation-like set
a is set
((G | L) ") . a is set
((G | V) ") . a is set
G is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G + L is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V is non empty set
[:NAT,V:] is non empty non trivial Relation-like non finite set
bool [:NAT,V:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
a is Relation-like NAT -defined V -valued Function-like quasi_total Element of bool [:NAT,V:]
{ (a . b1) where b1 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT : ( G <= b1 & b1 <= G + L ) } is set
card { (a . b1) where b1 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT : ( G <= b1 & b1 <= G + L ) } is epsilon-transitive epsilon-connected ordinal cardinal set
{ (a . b1) where b1 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT : ( G <= b1 & b1 <= G + a1 ) } is set
card { (a . b1) where b1 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT : ( G <= b1 & b1 <= G + a1 ) } is epsilon-transitive epsilon-connected ordinal cardinal set
dom a is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool NAT
b is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G + b is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
{ (a . b1) where b1 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT : ( G <= b1 & b1 <= G + b ) } is set
card { (a . b1) where b1 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT : ( G <= b1 & b1 <= G + b ) } is epsilon-transitive epsilon-connected ordinal cardinal set
b + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G + (b + 1) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
{ (a . b1) where b1 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT : ( G <= b1 & b1 <= G + (b + 1) ) } is set
card { (a . b1) where b1 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT : ( G <= b1 & b1 <= G + (b + 1) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
(b + 1) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G + b) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
{ (a . b1) where b1 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT : ( G <= b1 & b1 <= (G + b) + 1 ) } is set
vc is set
P is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a . P is Element of V
a . ((G + b) + 1) is Element of V
{(a . ((G + b) + 1))} is non empty trivial finite 1 -element Element of bool V
bool V is non empty cup-closed diff-closed preBoolean V225() set
va is finite set
va \/ {(a . ((G + b) + 1))} is non empty finite set
va is finite set
a . ((G + b) + 1) is Element of V
{(a . ((G + b) + 1))} is non empty trivial finite 1 -element Element of bool V
bool V is non empty cup-closed diff-closed preBoolean V225() set
va \/ {(a . ((G + b) + 1))} is non empty finite set
va is finite set
a . ((G + b) + 1) is Element of V
{(a . ((G + b) + 1))} is non empty trivial finite 1 -element Element of bool V
bool V is non empty cup-closed diff-closed preBoolean V225() set
va \/ {(a . ((G + b) + 1))} is non empty finite set
va is finite set
a . ((G + b) + 1) is Element of V
{(a . ((G + b) + 1))} is non empty trivial finite 1 -element Element of bool V
bool V is non empty cup-closed diff-closed preBoolean V225() set
va \/ {(a . ((G + b) + 1))} is non empty finite set
P is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a . P is Element of V
{ (a . b2) where b1 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT : ( G <= b2 & b2 <= (G + b) + 1 ) } is set
{ (a . b2) where b1 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT : ( G <= b2 & b2 <= (G + b) + 1 ) } is set
{ (a . b2) where b1 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT : ( G <= b2 & b2 <= (G + b) + 1 ) } is set
vc is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a . vc is Element of V
card (va \/ {(a . ((G + b) + 1))}) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
b is set
G + 0 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
{ (a . b1) where b1 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT : ( G <= b1 & b1 <= G + 0 ) } is set
c is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a . c is Element of V
a . G is Element of V
{(a . G)} is non empty trivial finite 1 -element Element of bool V
bool V is non empty cup-closed diff-closed preBoolean V225() set
card { (a . b1) where b1 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT : ( G <= b1 & b1 <= G + 0 ) } is epsilon-transitive epsilon-connected ordinal cardinal set
0 + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L is ext-real V55() real set
G is ext-real V55() real set
V is ext-real V55() real set
V - G is ext-real V55() real set
(V - G) + 1 is ext-real V55() real set
V - L is ext-real V55() real set
(V - L) + 1 is ext-real V55() real set
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
G is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V -' G is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V -' L is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V - G is ext-real V55() real V57() set
V - L is ext-real V55() real V57() set
bool (bool NAT) is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
{1} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element Element of bool NAT
{{1}} is non empty trivial finite finite-membered 1 -element Element of bool (bool NAT)
L is Element of bool (bool NAT)
G is Relation-like Function-like set
proj1 G is set
L is Relation-like Function-like set
proj1 L is set
(proj1 G) \/ (proj1 L) is set
a is set
G . a is set
L . a is set
(G . a) \/ (L . a) is set
a is Relation-like Function-like set
proj1 a is set
a is Relation-like Function-like set
proj1 a is set
b is set
a . b is set
G . b is set
L . b is set
(G . b) \/ (L . b) is set
V is Relation-like Function-like set
proj1 V is set
a is Relation-like Function-like set
proj1 a is set
b is set
V . b is set
G . b is set
L . b is set
(G . b) \/ (L . b) is set
a . b is set
G is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
Seg V is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite V -element Element of bool NAT
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V -' L is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
Seg (V -' L) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite V -' L -element Element of bool NAT
(Seg V) \ (Seg (V -' L)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
0 + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
Seg L is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite L -element Element of bool NAT
L -' G is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
Seg (L -' G) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite L -' G -element Element of bool NAT
(Seg L) \ (Seg (L -' G)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
L -' V is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
Seg (L -' V) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite L -' V -element Element of bool NAT
(Seg L) \ (Seg (L -' V)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
a is set
a is set
b is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
G is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
Seg L is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite L -element Element of bool NAT
L -' G is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
Seg (L -' G) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite L -' G -element Element of bool NAT
(Seg L) \ (Seg (L -' G)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
{(L -' G)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element Element of bool NAT
((Seg L) \ (Seg (L -' G))) \/ {(L -' G)} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite Element of bool NAT
G + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L -' (G + 1) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
Seg (L -' (G + 1)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite L -' (G + 1) -element Element of bool NAT
(Seg L) \ (Seg (L -' (G + 1))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
b is set
c is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
b is set
c is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(L -' (G + 1)) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
NAT --> {} is non empty Relation-like NAT -defined RAT -valued INT -valued {{}} -valued Function-like constant total quasi_total T-Sequence-like complex-valued ext-real-valued real-valued natural-valued Function-yielding V264() Element of bool [:NAT,{{}}:]
{{}} is non empty trivial functional complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:NAT,{{}}:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:NAT,{{}}:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
rng (NAT --> {}) is non empty trivial functional complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element Element of bool {{}}
bool {{}} is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
L is set
L is set
G is Relation-like Function-like finite-yielding () set
L is set
G . L is finite set
proj1 G is set
proj2 G is finite-membered set
proj1 G is set
proj1 G is set
G is epsilon-transitive epsilon-connected ordinal set
bool G is non empty cup-closed diff-closed preBoolean set
L is finite Element of bool G
V is finite Element of bool G
(L,1) -bag is Relation-like G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags G
Bags G is non empty set
Bags G is non empty functional Element of bool (Bags G)
bool (Bags G) is non empty cup-closed diff-closed preBoolean V225() set
(V,1) -bag is Relation-like G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags G
a is set
((V,1) -bag) . a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
proj1 G is set
L is set
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
L /\ (proj1 G) is set
a is Relation-like Function-like set
proj1 a is set
b is set
proj2 a is set
c is set
a . c is set
G . c is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G . c) + V is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G +* a is Relation-like Function-like set
proj2 (G +* a) is set
rng G is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool RAT
bool RAT is non empty cup-closed diff-closed preBoolean set
(rng G) \/ (proj2 a) is set
b is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
proj1 b is set
(proj1 G) \/ (L /\ (proj1 G)) is set
c is set
b . c is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a . c is set
G . c is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G . c) + V is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
c is set
b . c is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G . c is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G . c) + V is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
va is set
b . va is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G . va is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
proj1 a is set
b is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
proj1 b is set
c is set
a . c is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G . c is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G . c) + V is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
b . c is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a . c is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G . c is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
b . c is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is epsilon-transitive epsilon-connected ordinal set
Bags G is non empty functional Element of bool (Bags G)
Bags G is non empty set
bool (Bags G) is non empty cup-closed diff-closed preBoolean V225() set
[:(Bags G),(Bags G):] is non empty Relation-like set
bool [:(Bags G),(Bags G):] is non empty cup-closed diff-closed preBoolean V225() set
bool (Bags G) is non empty cup-closed diff-closed preBoolean V225() set
V is non empty functional finite Element of bool (Bags G)
L is Relation-like Bags G -defined Bags G -valued total reflexive antisymmetric connected transitive Element of bool [:(Bags G),(Bags G):]
a is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
proj2 a is finite set
len a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
dom a is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
b is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
b + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a . (b + 1) is set
va is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
a . va is set
vb is Relation-like G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
va is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
a . va is set
vb is Relation-like G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
c is Relation-like G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
max (vb,c,L) is Relation-like G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
a . P is set
e1 is Relation-like G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
a . P is set
e1 is Relation-like G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
a . 1 is set
c is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
a . c is set
va is Relation-like G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
b is Relation-like G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
b is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
a . b is set
c is Relation-like G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
va is Relation-like G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
vb is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
a . vb is set
va is Relation-like G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
a is Relation-like G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
b is Relation-like G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
G is epsilon-transitive epsilon-connected ordinal set
InvLexOrder G is Relation-like Bags G -defined Bags G -valued total reflexive antisymmetric transitive admissible Element of bool [:(Bags G),(Bags G):]
Bags G is non empty functional Element of bool (Bags G)
Bags G is non empty set
bool (Bags G) is non empty cup-closed diff-closed preBoolean V225() set
[:(Bags G),(Bags G):] is non empty Relation-like set
bool [:(Bags G),(Bags G):] is non empty cup-closed diff-closed preBoolean V225() set
G is Relation-like NAT -defined Function-like finite finite-support [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
L is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
L .last() is Element of the_Vertices_of G
len L is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
L . (len L) is set
L .length() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support EdgeSeq of G
len (L .edgeSeq()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(L .length()) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a is set
V is set
L .addEdge V is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
(L .last()) .adj V is Element of the_Vertices_of G
G .walkOf ((L .last()),V,((L .last()) .adj V)) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
L .append (G .walkOf ((L .last()),V,((L .last()) .adj V))) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
(L .addEdge V) .length() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(L .addEdge V) .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support EdgeSeq of G
len ((L .addEdge V) .edgeSeq()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
<*V*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support set
(L .edgeSeq()) ^ <*V*> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
len <*V*> is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [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
L is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
L .length() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support EdgeSeq of G
len (L .edgeSeq()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L .reverse() is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
(L .reverse()) .length() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(L .reverse()) .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support EdgeSeq of G
len ((L .reverse()) .edgeSeq()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
len L is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
2 * (L .length()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() even Element of NAT
(2 * (L .length())) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
len (L .reverse()) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
((2 * (L .length())) + 1) - 1 is ext-real V55() real V57() even set
2 * ((L .reverse()) .length()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() even Element of NAT
(2 * ((L .reverse()) .length())) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
((2 * ((L .reverse()) .length())) + 1) - 1 is ext-real V55() real V57() even set
G is Relation-like NAT -defined Function-like finite finite-support [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
L is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
L .last() is Element of the_Vertices_of G
len L is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
L . (len L) is set
dom L is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
a is set
V is set
L .addEdge V is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
(L .last()) .adj V is Element of the_Vertices_of G
G .walkOf ((L .last()),V,((L .last()) .adj V)) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
L .append (G .walkOf ((L .last()),V,((L .last()) .adj V))) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
dom (L .addEdge V) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
b is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(L .addEdge V) . b is set
L . b is set
(len L) + 2 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
len (L .addEdge V) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
NAT --> 1 is non empty Relation-like non-zero NAT -defined NAT -valued RAT -valued INT -valued Function-like constant total quasi_total T-Sequence-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:NAT,NAT:]
[:NAT,NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:NAT,NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
{1} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:NAT,{1}:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
L is Relation-like NAT -defined Function-like total set
L . 0 is set
0 + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . (0 + 1) is set
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
L . V is set
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
L . a is set
V + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . (V + 1) is set
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . (a + 1) is set
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
L . V is set
G is Relation-like NAT -defined Function-like total set
G .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G . (G .Lifespan()) is set
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G .Lifespan()) + V is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G . ((G .Lifespan()) + V) is set
V + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .Lifespan()) + (V + 1) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G . ((G .Lifespan()) + (V + 1)) is set
(G .Lifespan()) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G . ((G .Lifespan()) + 1) is set
((G .Lifespan()) + V) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G . (((G .Lifespan()) + V) + 1) is set
(G .Lifespan()) + 0 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G . ((G .Lifespan()) + 0) is set
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
G . V is set
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G .Lifespan()) + a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like total set
G is Relation-like NAT -defined Function-like total set
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
G . L is set
L + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G . (L + 1) is set
G is Relation-like NAT -defined Function-like total set
G is Relation-like NAT -defined Function-like total halting () () set
G .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G . (G .Lifespan()) is set
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
G . V is set
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G .Lifespan()) + a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G . ((G .Lifespan()) + a) is set
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .Lifespan()) + (a + 1) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G . ((G .Lifespan()) + (a + 1)) is set
(G .Lifespan()) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G . ((G .Lifespan()) + 1) is set
((G .Lifespan()) + a) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G . (((G .Lifespan()) + a) + 1) is set
(G .Lifespan()) + 0 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G . ((G .Lifespan()) + 0) is set
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G .Lifespan()) + a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like total halting () () set
G .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
G . V is set
G . L is set
G . (G .Lifespan()) is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
L is Relation-like NAT -defined Function-like total set
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
L . V is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
L is Relation-like NAT -defined Function-like total (G)
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
L . V is set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
card (the_Vertices_of G) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
canFS (the_Vertices_of G) is non empty Relation-like NAT -defined the_Vertices_of G -valued Function-like one-to-one onto finite FinSequence-like FinSubsequence-like finite-support FinSequence of the_Vertices_of G
[:NAT,NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:NAT,NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
a is Relation-like NAT -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of bool [:NAT,NAT:]
b is set
c is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
Seg c is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite c -element Element of bool NAT
(canFS (the_Vertices_of G)) | (Seg c) is Relation-like NAT -defined Seg c -defined NAT -defined the_Vertices_of G -valued Function-like finite FinSubsequence-like finite-support Element of bool [:NAT,(the_Vertices_of G):]
[:NAT,(the_Vertices_of G):] is non empty non trivial Relation-like non finite set
bool [:NAT,(the_Vertices_of G):] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
((canFS (the_Vertices_of G)) | (Seg c)) " is Relation-like Function-like set
(((canFS (the_Vertices_of G)) | (Seg c)) ") * a is Relation-like NAT -valued RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
b is Relation-like NAT -defined Function-like total set
c is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
b . c is set
Seg c is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite c -element Element of bool NAT
(canFS (the_Vertices_of G)) | (Seg c) is Relation-like NAT -defined Seg c -defined NAT -defined the_Vertices_of G -valued Function-like finite FinSubsequence-like finite-support Element of bool [:NAT,(the_Vertices_of G):]
[:NAT,(the_Vertices_of G):] is non empty non trivial Relation-like non finite set
bool [:NAT,(the_Vertices_of G):] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
((canFS (the_Vertices_of G)) | (Seg c)) " is Relation-like Function-like set
(((canFS (the_Vertices_of G)) | (Seg c)) ") * a is Relation-like NAT -valued RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
va is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
Seg va is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite va -element Element of bool NAT
(canFS (the_Vertices_of G)) | (Seg va) is Relation-like NAT -defined Seg va -defined NAT -defined the_Vertices_of G -valued Function-like finite FinSubsequence-like finite-support Element of bool [:NAT,(the_Vertices_of G):]
((canFS (the_Vertices_of G)) | (Seg va)) " is Relation-like Function-like set
(((canFS (the_Vertices_of G)) | (Seg va)) ") * a is Relation-like NAT -valued RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
len (canFS (the_Vertices_of G)) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(canFS (the_Vertices_of G)) " is Relation-like Function-like one-to-one set
((canFS (the_Vertices_of G)) ") * a is Relation-like NAT -valued RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
dom (canFS (the_Vertices_of G)) is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite Element of bool NAT
Seg (len (canFS (the_Vertices_of G))) is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite len (canFS (the_Vertices_of G)) -element Element of bool NAT
c is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
b . c is set
Seg c is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite c -element Element of bool NAT
(canFS (the_Vertices_of G)) | (Seg c) is Relation-like NAT -defined Seg c -defined NAT -defined the_Vertices_of G -valued Function-like finite FinSubsequence-like finite-support Element of bool [:NAT,(the_Vertices_of G):]
[:NAT,(the_Vertices_of G):] is non empty non trivial Relation-like non finite set
bool [:NAT,(the_Vertices_of G):] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
c is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
Seg c is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite c -element Element of bool NAT
(canFS (the_Vertices_of G)) | (Seg c) is Relation-like NAT -defined Seg c -defined NAT -defined the_Vertices_of G -valued Function-like finite FinSubsequence-like finite-support Element of bool [:NAT,(the_Vertices_of G):]
[:NAT,(the_Vertices_of G):] is non empty non trivial Relation-like non finite set
bool [:NAT,(the_Vertices_of G):] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
((canFS (the_Vertices_of G)) | (Seg c)) " is Relation-like Function-like set
(((canFS (the_Vertices_of G)) | (Seg c)) ") * a is Relation-like NAT -valued RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
vb is set
rng ((((canFS (the_Vertices_of G)) | (Seg c)) ") * a) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool RAT
bool RAT is non empty cup-closed diff-closed preBoolean set
rng a is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool NAT
((canFS (the_Vertices_of G)) | (Seg c)) ~ is Relation-like the_Vertices_of G -defined NAT -valued complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
vb is set
proj1 ((((canFS (the_Vertices_of G)) | (Seg c)) ") * a) is set
proj1 (((canFS (the_Vertices_of G)) | (Seg c)) ") is set
rng ((canFS (the_Vertices_of G)) | (Seg c)) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
b . c is set
dom a is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool NAT
c is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
b . c is set
card (b . c) is epsilon-transitive epsilon-connected ordinal cardinal set
Seg c is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite c -element Element of bool NAT
Seg (len (canFS (the_Vertices_of G))) is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite len (canFS (the_Vertices_of G)) -element Element of bool NAT
(canFS (the_Vertices_of G)) | (Seg c) is Relation-like NAT -defined Seg c -defined NAT -defined the_Vertices_of G -valued Function-like finite FinSubsequence-like finite-support Element of bool [:NAT,(the_Vertices_of G):]
((canFS (the_Vertices_of G)) | (Seg c)) " is Relation-like Function-like set
(((canFS (the_Vertices_of G)) | (Seg c)) ") * a is Relation-like NAT -valued RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
card (Seg c) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
dom (canFS (the_Vertices_of G)) is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite Element of bool NAT
dom ((canFS (the_Vertices_of G)) | (Seg c)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
proj2 (((canFS (the_Vertices_of G)) | (Seg c)) ") is set
proj1 ((((canFS (the_Vertices_of G)) | (Seg c)) ") * a) is set
proj1 (((canFS (the_Vertices_of G)) | (Seg c)) ") is set
rng ((canFS (the_Vertices_of G)) | (Seg c)) is finite Element of bool (the_Vertices_of G)
card (proj1 ((((canFS (the_Vertices_of G)) | (Seg c)) ") * a)) is epsilon-transitive epsilon-connected ordinal cardinal set
c is Relation-like NAT -defined Function-like total (G)
vb is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
va is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,c,va) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,c,vb) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
va + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,c,(va + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
vb + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,c,(vb + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
card (G,c,vb) is epsilon-transitive epsilon-connected ordinal cardinal set
proj2 ((canFS (the_Vertices_of G)) ") is set
vc is set
(canFS (the_Vertices_of G)) ~ is Relation-like Function-like set
proj2 ((canFS (the_Vertices_of G)) ~) is set
dom (canFS (the_Vertices_of G)) is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite Element of bool NAT
card (G,c,vb) is epsilon-transitive epsilon-connected ordinal cardinal set
dom (G,c,vb) is finite Element of bool (the_Vertices_of G)
card (dom (G,c,vb)) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
proj1 ((canFS (the_Vertices_of G)) ") is set
card (proj1 ((canFS (the_Vertices_of G)) ")) is epsilon-transitive epsilon-connected ordinal cardinal set
rng (canFS (the_Vertices_of G)) is non empty finite Element of bool (the_Vertices_of G)
card (rng (canFS (the_Vertices_of G))) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
dom (canFS (the_Vertices_of G)) is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite Element of bool NAT
card (dom (canFS (the_Vertices_of G))) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
va is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
c . va is set
vb is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
c . vb is set
va + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
c . (va + 1) is set
vb + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
c . (vb + 1) is set
(G,c,va) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,c,vb) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,c,(va + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,c,(vb + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,c,(va + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,c,(vb + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
va is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
va + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,c,va) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,c,(va + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
vb is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,c,vb) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
vb + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,c,(vb + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
card (G,c,(vb + 1)) is epsilon-transitive epsilon-connected ordinal cardinal set
c .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
vb is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
vb + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(canFS (the_Vertices_of G)) . (vb + 1) is set
0 + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
dom (canFS (the_Vertices_of G)) is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite Element of bool NAT
rng (canFS (the_Vertices_of G)) is non empty finite Element of bool (the_Vertices_of G)
P is Element of the_Vertices_of G
Seg vb is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite vb -element Element of bool NAT
(canFS (the_Vertices_of G)) | (Seg vb) is Relation-like NAT -defined Seg vb -defined NAT -defined the_Vertices_of G -valued Function-like finite FinSubsequence-like finite-support Element of bool [:NAT,(the_Vertices_of G):]
e1 is Element of the_Vertices_of G
(G,c,vb) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
dom (G,c,vb) is finite Element of bool (the_Vertices_of G)
((canFS (the_Vertices_of G)) | (Seg vb)) " is Relation-like Function-like set
(((canFS (the_Vertices_of G)) | (Seg vb)) ") * a is Relation-like NAT -valued RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
proj1 ((((canFS (the_Vertices_of G)) | (Seg vb)) ") * a) is set
proj1 (((canFS (the_Vertices_of G)) | (Seg vb)) ") is set
rng ((canFS (the_Vertices_of G)) | (Seg vb)) is finite Element of bool (the_Vertices_of G)
dom ((canFS (the_Vertices_of G)) | (Seg vb)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
e2 is set
((canFS (the_Vertices_of G)) | (Seg vb)) . e2 is set
(canFS (the_Vertices_of G)) . e2 is set
j is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
Seg (vb + 1) is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite vb + 1 -element vb + 1 -element Element of bool NAT
(canFS (the_Vertices_of G)) | (Seg (vb + 1)) is Relation-like NAT -defined Seg (vb + 1) -defined NAT -defined the_Vertices_of G -valued Function-like finite FinSubsequence-like finite-support Element of bool [:NAT,(the_Vertices_of G):]
e2 is set
(G,c,(vb + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
dom (G,c,(vb + 1)) is finite Element of bool (the_Vertices_of G)
((canFS (the_Vertices_of G)) | (Seg (vb + 1))) " is Relation-like Function-like set
(((canFS (the_Vertices_of G)) | (Seg (vb + 1))) ") * a is Relation-like NAT -valued RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
proj1 ((((canFS (the_Vertices_of G)) | (Seg (vb + 1))) ") * a) is set
proj1 (((canFS (the_Vertices_of G)) | (Seg (vb + 1))) ") is set
rng ((canFS (the_Vertices_of G)) | (Seg (vb + 1))) is finite Element of bool (the_Vertices_of G)
dom ((canFS (the_Vertices_of G)) | (Seg (vb + 1))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
j is set
((canFS (the_Vertices_of G)) | (Seg (vb + 1))) . j is set
(c .Lifespan()) -' vb is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
e1 .--> ((c .Lifespan()) -' vb) is Relation-like the_Vertices_of G -defined {e1} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{e1} is non empty trivial finite 1 -element set
{e1} --> ((c .Lifespan()) -' vb) is non empty Relation-like {e1} -defined NAT -valued RAT -valued INT -valued {((c .Lifespan()) -' vb)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{e1},{((c .Lifespan()) -' vb)}:]
{((c .Lifespan()) -' vb)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{e1},{((c .Lifespan()) -' vb)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{e1},{((c .Lifespan()) -' vb)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(G,c,vb) +* (e1 .--> ((c .Lifespan()) -' vb)) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
proj1 ((G,c,vb) +* (e1 .--> ((c .Lifespan()) -' vb))) is set
dom (e1 .--> ((c .Lifespan()) -' vb)) is trivial finite Element of bool {e1}
bool {e1} is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(dom (G,c,vb)) \/ (dom (e1 .--> ((c .Lifespan()) -' vb))) is finite set
k is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
((canFS (the_Vertices_of G)) | (Seg vb)) . k is set
(canFS (the_Vertices_of G)) . k is set
(((canFS (the_Vertices_of G)) | (Seg vb)) ") . e2 is set
(((canFS (the_Vertices_of G)) | (Seg vb)) ") . e2 is set
(((canFS (the_Vertices_of G)) | (Seg (vb + 1))) ") . e2 is set
proj2 (((canFS (the_Vertices_of G)) | (Seg (vb + 1))) ") is set
(((canFS (the_Vertices_of G)) | (Seg (vb + 1))) ") . e2 is set
e2 is set
j is set
((canFS (the_Vertices_of G)) | (Seg vb)) . j is set
k is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(canFS (the_Vertices_of G)) . k is set
(G,c,(vb + 1)) . e2 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(((canFS (the_Vertices_of G)) | (Seg (vb + 1))) ") . e2 is set
a . ((((canFS (the_Vertices_of G)) | (Seg (vb + 1))) ") . e2) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(((canFS (the_Vertices_of G)) | (Seg vb)) ") . e2 is set
a . ((((canFS (the_Vertices_of G)) | (Seg vb)) ") . e2) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,c,vb) . e2 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((G,c,vb) +* (e1 .--> ((c .Lifespan()) -' vb))) . e2 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((canFS (the_Vertices_of G)) | (Seg (vb + 1))) . (vb + 1) is set
((G,c,vb) +* (e1 .--> ((c .Lifespan()) -' vb))) . e2 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(e1 .--> ((c .Lifespan()) -' vb)) . e2 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,c,(vb + 1)) . e2 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((((canFS (the_Vertices_of G)) | (Seg (vb + 1))) ") * a) . e2 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(((canFS (the_Vertices_of G)) | (Seg (vb + 1))) ") . e2 is set
a . ((((canFS (the_Vertices_of G)) | (Seg (vb + 1))) ") . e2) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a . (vb + 1) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
va -' (vb + 1) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(va -' (vb + 1)) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
va - (vb + 1) is ext-real V55() real V57() set
(va - (vb + 1)) + 1 is ext-real V55() real V57() set
va - vb is ext-real V55() real V57() set
(G,c,0) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
card (G,c,0) is epsilon-transitive epsilon-connected ordinal cardinal set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
L is Relation-like NAT -defined Function-like total (G)
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
L is Relation-like NAT -defined Function-like total halting () () (G) (G)
L .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
choose (the_Vertices_of G) is Element of the_Vertices_of G
(G,L,V) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
dom (G,L,V) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
V + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,(V + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(L .Lifespan()) -' V is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a is Element of the_Vertices_of G
a .--> ((L .Lifespan()) -' V) is Relation-like the_Vertices_of G -defined {a} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{a} is non empty trivial finite 1 -element set
{a} --> ((L .Lifespan()) -' V) is non empty Relation-like {a} -defined NAT -valued RAT -valued INT -valued {((L .Lifespan()) -' V)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{a},{((L .Lifespan()) -' V)}:]
{((L .Lifespan()) -' V)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{a},{((L .Lifespan()) -' V)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{a},{((L .Lifespan()) -' V)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(G,L,V) +* (a .--> ((L .Lifespan()) -' V)) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
c is set
va is set
c .--> ((L .Lifespan()) -' V) is Relation-like {c} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{c} is non empty trivial finite 1 -element set
{c} --> ((L .Lifespan()) -' V) is non empty Relation-like {c} -defined NAT -valued RAT -valued INT -valued {((L .Lifespan()) -' V)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{c},{((L .Lifespan()) -' V)}:]
{((L .Lifespan()) -' V)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{c},{((L .Lifespan()) -' V)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{c},{((L .Lifespan()) -' V)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(G,L,V) +* (c .--> ((L .Lifespan()) -' V)) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
va .--> ((L .Lifespan()) -' V) is Relation-like {va} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{va} is non empty trivial finite 1 -element set
{va} --> ((L .Lifespan()) -' V) is non empty Relation-like {va} -defined NAT -valued RAT -valued INT -valued {((L .Lifespan()) -' V)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{va},{((L .Lifespan()) -' V)}:]
[:{va},{((L .Lifespan()) -' V)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{va},{((L .Lifespan()) -' V)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(G,L,V) +* (va .--> ((L .Lifespan()) -' V)) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
dom (va .--> ((L .Lifespan()) -' V)) is trivial finite Element of bool {va}
bool {va} is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
dom (G,L,(V + 1)) is finite Element of bool (the_Vertices_of G)
(dom (G,L,V)) \/ {va} is non empty finite set
dom (c .--> ((L .Lifespan()) -' V)) is trivial finite Element of bool {c}
bool {c} is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(dom (G,L,V)) \/ {c} is non empty finite set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
L is Relation-like NAT -defined Function-like total halting () () (G) (G)
L .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,V) is set
V + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,(V + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
dom (G,L,(V + 1)) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(G,L,V) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
dom (G,L,V) is finite Element of bool (the_Vertices_of G)
{(G,L,V)} is non empty trivial finite 1 -element set
(dom (G,L,V)) \/ {(G,L,V)} is non empty finite set
(L .Lifespan()) -' V is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,V) .--> ((L .Lifespan()) -' V) is Relation-like {(G,L,V)} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(G,L,V)} --> ((L .Lifespan()) -' V) is non empty Relation-like {(G,L,V)} -defined NAT -valued RAT -valued INT -valued {((L .Lifespan()) -' V)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{(G,L,V)},{((L .Lifespan()) -' V)}:]
{((L .Lifespan()) -' V)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{(G,L,V)},{((L .Lifespan()) -' V)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{(G,L,V)},{((L .Lifespan()) -' V)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
dom ((G,L,V) .--> ((L .Lifespan()) -' V)) is trivial finite Element of bool {(G,L,V)}
bool {(G,L,V)} is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(G,L,V) +* ((G,L,V) .--> ((L .Lifespan()) -' V)) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
L is Relation-like NAT -defined Function-like total halting () () (G) (G)
L .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,(V + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
the_Vertices_of G is non empty finite set
G . VertexSelector is set
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
(G,L,V) is set
(G,L,(V + 1)) . (G,L,V) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(L .Lifespan()) -' V is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,V) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,L,V) .--> ((L .Lifespan()) -' V) is Relation-like {(G,L,V)} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(G,L,V)} is non empty trivial finite 1 -element set
{(G,L,V)} --> ((L .Lifespan()) -' V) is non empty Relation-like {(G,L,V)} -defined NAT -valued RAT -valued INT -valued {((L .Lifespan()) -' V)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{(G,L,V)},{((L .Lifespan()) -' V)}:]
{((L .Lifespan()) -' V)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{(G,L,V)},{((L .Lifespan()) -' V)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{(G,L,V)},{((L .Lifespan()) -' V)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
((G,L,V) .--> ((L .Lifespan()) -' V)) . (G,L,V) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
dom ((G,L,V) .--> ((L .Lifespan()) -' V)) is trivial finite Element of bool {(G,L,V)}
bool {(G,L,V)} is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(G,L,V) +* ((G,L,V) .--> ((L .Lifespan()) -' V)) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
L is Relation-like NAT -defined Function-like total halting () () (G) (G)
L .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,V) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
dom (G,L,V) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
card (dom (G,L,V)) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,a) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
dom (G,L,a) is finite Element of bool (the_Vertices_of G)
card (dom (G,L,a)) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,(a + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
dom (G,L,(a + 1)) is finite Element of bool (the_Vertices_of G)
card (dom (G,L,(a + 1))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,a) is set
(L .Lifespan()) -' a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,a) .--> ((L .Lifespan()) -' a) is Relation-like {(G,L,a)} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(G,L,a)} is non empty trivial finite 1 -element set
{(G,L,a)} --> ((L .Lifespan()) -' a) is non empty Relation-like {(G,L,a)} -defined NAT -valued RAT -valued INT -valued {((L .Lifespan()) -' a)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{(G,L,a)},{((L .Lifespan()) -' a)}:]
{((L .Lifespan()) -' a)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{(G,L,a)},{((L .Lifespan()) -' a)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{(G,L,a)},{((L .Lifespan()) -' a)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
dom ((G,L,a) .--> ((L .Lifespan()) -' a)) is trivial finite Element of bool {(G,L,a)}
bool {(G,L,a)} is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(G,L,a) +* ((G,L,a) .--> ((L .Lifespan()) -' a)) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
(dom (G,L,a)) \/ {(G,L,a)} is non empty finite set
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,a) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
dom (G,L,a) is finite Element of bool (the_Vertices_of G)
card (dom (G,L,a)) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,(a + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
dom (G,L,(a + 1)) is finite Element of bool (the_Vertices_of G)
card (dom (G,L,(a + 1))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,0) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
dom (G,L,0) is finite Element of bool (the_Vertices_of G)
card (dom (G,L,0)) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
L is Relation-like NAT -defined Function-like total halting () () (G) (G)
L .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
Seg (L .Lifespan()) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite L .Lifespan() -element Element of bool NAT
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,V) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
the_Vertices_of G is non empty finite set
G . VertexSelector is set
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
rng (G,L,V) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool NAT
(L .Lifespan()) -' V is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
Seg ((L .Lifespan()) -' V) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite (L .Lifespan()) -' V -element Element of bool NAT
(Seg (L .Lifespan())) \ (Seg ((L .Lifespan()) -' V)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(G,L,(L .Lifespan())) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
va is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,va) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
rng (G,L,va) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool NAT
(L .Lifespan()) -' va is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
Seg ((L .Lifespan()) -' va) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite (L .Lifespan()) -' va -element Element of bool NAT
(Seg (L .Lifespan())) \ (Seg ((L .Lifespan()) -' va)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
va + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,(va + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
rng (G,L,(va + 1)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool NAT
(L .Lifespan()) -' (va + 1) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
Seg ((L .Lifespan()) -' (va + 1)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite (L .Lifespan()) -' (va + 1) -element Element of bool NAT
(Seg (L .Lifespan())) \ (Seg ((L .Lifespan()) -' (va + 1))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(G,L,va) is set
(G,L,va) .--> ((L .Lifespan()) -' va) is Relation-like {(G,L,va)} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(G,L,va)} is non empty trivial finite 1 -element set
{(G,L,va)} --> ((L .Lifespan()) -' va) is non empty Relation-like {(G,L,va)} -defined NAT -valued RAT -valued INT -valued {((L .Lifespan()) -' va)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{(G,L,va)},{((L .Lifespan()) -' va)}:]
{((L .Lifespan()) -' va)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{(G,L,va)},{((L .Lifespan()) -' va)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{(G,L,va)},{((L .Lifespan()) -' va)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
dom ((G,L,va) .--> ((L .Lifespan()) -' va)) is trivial finite Element of bool {(G,L,va)}
bool {(G,L,va)} is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
dom (G,L,va) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
rng ((G,L,va) .--> ((L .Lifespan()) -' va)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool RAT
bool RAT is non empty cup-closed diff-closed preBoolean set
{((L .Lifespan()) -' va)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element Element of bool NAT
(G,L,va) +* ((G,L,va) .--> ((L .Lifespan()) -' va)) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
(rng (G,L,va)) \/ {((L .Lifespan()) -' va)} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V33() Element of bool NAT
(G,L,0) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
rng (G,L,0) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool NAT
(L .Lifespan()) -' 0 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
Seg ((L .Lifespan()) -' 0) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite (L .Lifespan()) -' 0 -element Element of bool NAT
(Seg (L .Lifespan())) \ (Seg ((L .Lifespan()) -' 0)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(L .Lifespan()) - 0 is ext-real non negative V55() real V57() set
V - V is ext-real V55() real V57() set
(L .Lifespan()) - V is ext-real V55() real V57() set
(L .Lifespan()) -' (L .Lifespan()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
L is Relation-like NAT -defined Function-like total halting () () (G) (G)
L .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,V) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
dom (G,L,V) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
a is set
(G,L,V) . a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
rng (G,L,V) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool NAT
Seg (L .Lifespan()) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite L .Lifespan() -element Element of bool NAT
(L .Lifespan()) -' V is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
Seg ((L .Lifespan()) -' V) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite (L .Lifespan()) -' V -element Element of bool NAT
(Seg (L .Lifespan())) \ (Seg ((L .Lifespan()) -' V)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
rng (G,L,V) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool NAT
Seg (L .Lifespan()) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite L .Lifespan() -element Element of bool NAT
(L .Lifespan()) -' V is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
Seg ((L .Lifespan()) -' V) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite (L .Lifespan()) -' V -element Element of bool NAT
(Seg (L .Lifespan())) \ (Seg ((L .Lifespan()) -' V)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
0 + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
L is Relation-like NAT -defined Function-like total halting () () (G) (G)
L .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(L .Lifespan()) -' V is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,V) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
dom (G,L,V) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
Seg (L .Lifespan()) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite L .Lifespan() -element Element of bool NAT
Seg ((L .Lifespan()) -' V) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite (L .Lifespan()) -' V -element Element of bool NAT
(Seg (L .Lifespan())) \ (Seg ((L .Lifespan()) -' V)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
rng (G,L,V) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool NAT
va is set
(G,L,V) . va is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
L is Relation-like NAT -defined Function-like total halting () () (G) (G)
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,V) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
(G,L,a) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
va is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,va) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
va + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,(va + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
L .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,va) is set
(L .Lifespan()) -' va is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,va) .--> ((L .Lifespan()) -' va) is Relation-like {(G,L,va)} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(G,L,va)} is non empty trivial finite 1 -element set
{(G,L,va)} --> ((L .Lifespan()) -' va) is non empty Relation-like {(G,L,va)} -defined NAT -valued RAT -valued INT -valued {((L .Lifespan()) -' va)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{(G,L,va)},{((L .Lifespan()) -' va)}:]
{((L .Lifespan()) -' va)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{(G,L,va)},{((L .Lifespan()) -' va)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{(G,L,va)},{((L .Lifespan()) -' va)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
dom ((G,L,va) .--> ((L .Lifespan()) -' va)) is trivial finite Element of bool {(G,L,va)}
bool {(G,L,va)} is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
dom (G,L,va) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(G,L,va) +* ((G,L,va) .--> ((L .Lifespan()) -' va)) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
L .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
va is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V + va is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,(V + va)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
va + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V + (va + 1) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,(V + (va + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(V + va) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,((V + va) + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
V + 0 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,(V + 0)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
va is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V + va is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
L is Relation-like NAT -defined Function-like total halting () () (G) (G)
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,V) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
the_Vertices_of G is non empty finite set
G . VertexSelector is set
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
L .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
b is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,b) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
b + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,(b + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,L,b) is set
(L .Lifespan()) -' b is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,b) .--> ((L .Lifespan()) -' b) is Relation-like {(G,L,b)} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(G,L,b)} is non empty trivial finite 1 -element set
{(G,L,b)} --> ((L .Lifespan()) -' b) is non empty Relation-like {(G,L,b)} -defined NAT -valued RAT -valued INT -valued {((L .Lifespan()) -' b)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{(G,L,b)},{((L .Lifespan()) -' b)}:]
{((L .Lifespan()) -' b)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{(G,L,b)},{((L .Lifespan()) -' b)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{(G,L,b)},{((L .Lifespan()) -' b)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
rng (G,L,b) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool NAT
Seg (L .Lifespan()) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite L .Lifespan() -element Element of bool NAT
Seg ((L .Lifespan()) -' b) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite (L .Lifespan()) -' b -element Element of bool NAT
(Seg (L .Lifespan())) \ (Seg ((L .Lifespan()) -' b)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
rng ((G,L,b) .--> ((L .Lifespan()) -' b)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool RAT
bool RAT is non empty cup-closed diff-closed preBoolean set
{((L .Lifespan()) -' b)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element Element of bool NAT
(G,L,b) +* ((G,L,b) .--> ((L .Lifespan()) -' b)) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
(G,L,0) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
L is Relation-like NAT -defined Function-like total halting () () (G) (G)
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,V) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
dom (G,L,V) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,a) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
dom (G,L,a) is finite Element of bool (the_Vertices_of G)
b is set
(G,L,V) . b is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,a) . b is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
[b,((G,L,V) . b)] is V1() set
{b,((G,L,V) . b)} is non empty finite set
{b} is non empty trivial finite 1 -element set
{{b,((G,L,V) . b)},{b}} is non empty finite finite-membered set
[b,((G,L,a) . b)] is V1() set
{b,((G,L,a) . b)} is non empty finite set
{{b,((G,L,a) . b)},{b}} is non empty finite finite-membered set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
L is Relation-like NAT -defined Function-like total halting () () (G) (G)
L .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,V) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
dom (G,L,V) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(L .Lifespan()) -' a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,((L .Lifespan()) -' a)) is set
b is set
(G,L,V) . b is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((L .Lifespan()) -' a) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,(((L .Lifespan()) -' a) + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(L .Lifespan()) - a is ext-real V55() real V57() set
(L .Lifespan()) -' ((L .Lifespan()) -' a) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(L .Lifespan()) - ((L .Lifespan()) - a) is ext-real V55() real V57() set
(G,L,(((L .Lifespan()) -' a) + 1)) . (G,L,((L .Lifespan()) -' a)) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
dom (G,L,(((L .Lifespan()) -' a) + 1)) is finite Element of bool (the_Vertices_of G)
V + a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
((L .Lifespan()) - a) + a is ext-real V55() real V57() set
a + V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(a + V) - V is ext-real V55() real V57() set
(L .Lifespan()) - V is ext-real V55() real V57() set
rng (G,L,V) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool NAT
Seg (L .Lifespan()) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite L .Lifespan() -element Element of bool NAT
(L .Lifespan()) -' V is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
Seg ((L .Lifespan()) -' V) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite (L .Lifespan()) -' V -element Element of bool NAT
(Seg (L .Lifespan())) \ (Seg ((L .Lifespan()) -' V)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
[(G,L,((L .Lifespan()) -' a)),a] is V1() set
{(G,L,((L .Lifespan()) -' a)),a} is non empty finite set
{(G,L,((L .Lifespan()) -' a))} is non empty trivial finite 1 -element set
{{(G,L,((L .Lifespan()) -' a)),a},{(G,L,((L .Lifespan()) -' a))}} is non empty finite finite-membered set
(G,L,V) . (G,L,((L .Lifespan()) -' a)) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
L is Relation-like NAT -defined Function-like total halting () () (G) (G)
L .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,a) is set
(G,L,V) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
dom (G,L,V) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(G,L,V) . (G,L,a) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(L .Lifespan()) -' a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,(a + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,L,(a + 1)) . (G,L,a) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
dom (G,L,(a + 1)) is finite Element of bool (the_Vertices_of G)
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
L is Relation-like NAT -defined Function-like total halting () () (G) (G)
L .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,V) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
dom (G,L,V) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(L .Lifespan()) -' V is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a is set
(G,L,V) . a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(L .Lifespan()) -' ((G,L,V) . a) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,((L .Lifespan()) -' ((G,L,V) . a))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,L,((L .Lifespan()) -' ((G,L,V) . a))) is set
(L .Lifespan()) - ((G,L,V) . a) is ext-real V55() real V57() set
dom (G,L,((L .Lifespan()) -' ((G,L,V) . a))) is finite Element of bool (the_Vertices_of G)
(L .Lifespan()) - V is ext-real V55() real V57() set
V + ((G,L,V) . a) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((L .Lifespan()) - ((G,L,V) . a)) + ((G,L,V) . a) is ext-real V55() real V57() set
((G,L,V) . a) + V is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(((G,L,V) . a) + V) - V is ext-real V55() real V57() set
(L .Lifespan()) - V is ext-real V55() real V57() set
(L .Lifespan()) - V is ext-real V55() real V57() set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
L is Relation-like NAT -defined Function-like total halting () () (G) (G)
L .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,V) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
dom (G,L,V) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
a is set
b is set
(G,L,V) . b is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,V) . a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(L .Lifespan()) -' ((G,L,V) . a) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,((L .Lifespan()) -' ((G,L,V) . a))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
dom (G,L,((L .Lifespan()) -' ((G,L,V) . a))) is finite Element of bool (the_Vertices_of G)
(L .Lifespan()) - ((G,L,V) . a) is ext-real V55() real V57() set
(L .Lifespan()) -' ((L .Lifespan()) -' ((G,L,V) . a)) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(L .Lifespan()) - ((L .Lifespan()) - ((G,L,V) . a)) is ext-real V55() real V57() set
e2 is Element of the_Vertices_of G
(G,L,((L .Lifespan()) -' ((G,L,V) . a))) . e2 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,((L .Lifespan()) -' ((G,L,V) . a))) is set
[e2,((G,L,V) . b)] is V1() Element of [:(the_Vertices_of G),NAT:]
{e2,((G,L,V) . b)} is non empty finite set
{e2} is non empty trivial finite 1 -element set
{{e2,((G,L,V) . b)},{e2}} is non empty finite finite-membered set
(G,L,V) . e2 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
L is Relation-like NAT -defined Function-like total halting () () (G) (G)
L .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,V) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
dom (G,L,V) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
a is set
b is set
(G,L,V) . b is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,V) . a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(L .Lifespan()) -' ((G,L,V) . b) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,((L .Lifespan()) -' ((G,L,V) . b))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
dom (G,L,((L .Lifespan()) -' ((G,L,V) . b))) is finite Element of bool (the_Vertices_of G)
(L .Lifespan()) -' ((G,L,V) . a) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(L .Lifespan()) - ((G,L,V) . a) is ext-real V55() real V57() set
(G,L,((L .Lifespan()) -' ((G,L,V) . a))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(L .Lifespan()) - ((G,L,V) . b) is ext-real V55() real V57() set
dom (G,L,((L .Lifespan()) -' ((G,L,V) . a))) is finite Element of bool (the_Vertices_of G)
(G,L,((L .Lifespan()) -' ((G,L,V) . a))) is set
G is set
L is set
PFuncs (G,L) is non empty functional M38(G,L)
V is non empty set
[:(PFuncs (G,L)),V:] is non empty Relation-like set
a is Element of [:(PFuncs (G,L)),V:]
a `1 is set
G is non empty set
V is set
L is non empty set
Funcs (V,L) is non empty FUNCTION_DOMAIN of V,L
[:G,(Funcs (V,L)):] is non empty Relation-like set
a is Element of [:G,(Funcs (V,L)):]
a `2 is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Fin NAT is non empty cup-closed diff-closed preBoolean set
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
L is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total Element of Funcs ((the_Vertices_of G),(Fin NAT))
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] set
the_Vertices_of G is non empty set
G . VertexSelector is set
(the_Vertices_of G) --> {} is non empty Relation-like the_Vertices_of G -defined RAT -valued INT -valued {{}} -valued Function-like constant total quasi_total complex-valued ext-real-valued real-valued natural-valued Function-yielding V264() Element of bool [:(the_Vertices_of G),{{}}:]
{{}} is non empty trivial functional complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:(the_Vertices_of G),{{}}:] is non empty Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),{{}}:] is non empty cup-closed diff-closed preBoolean V225() set
[{},((the_Vertices_of G) --> {})] is V1() set
{{},((the_Vertices_of G) --> {})} is non empty functional finite set
{{{},((the_Vertices_of G) --> {})},{{}}} is non empty finite finite-membered set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
rng {} is empty trivial Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V30() V33() V34() V35() V36() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V55() real V57() complex-valued ext-real-valued real-valued natural-valued V72() decreasing non-decreasing non-increasing FinSequence-yielding finite-support V224() Function-yielding V264() Element of bool RAT
bool RAT is non empty cup-closed diff-closed preBoolean set
rng ((the_Vertices_of G) --> {}) is non empty trivial functional complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element Element of bool {{}}
bool {{}} is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
dom ((the_Vertices_of G) --> {}) is non empty Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty cup-closed diff-closed preBoolean V225() set
dom {} is empty proper Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V30() V33() V34() V35() V36() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V55() real V57() complex-valued ext-real-valued real-valued natural-valued FinSequence-yielding finite-support Function-yielding V264() Element of bool NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
L is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
choose (the_Vertices_of G) is Element of the_Vertices_of G
Bags NAT is non empty functional Element of bool (Bags NAT)
Bags NAT is non empty set
bool (Bags NAT) is non empty cup-closed diff-closed preBoolean V225() set
bool (Bags NAT) is non empty cup-closed diff-closed preBoolean V225() set
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
(the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)) is finite Element of bool (the_Vertices_of G)
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) | ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) is Relation-like the_Vertices_of G -defined (the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)) -defined the_Vertices_of G -defined Fin NAT -valued Function-like finite finite-support Element of bool [:(the_Vertices_of G),(Fin NAT):]
[:(the_Vertices_of G),(Fin NAT):] is non empty Relation-like set
bool [:(the_Vertices_of G),(Fin NAT):] is non empty cup-closed diff-closed preBoolean V225() set
InvLexOrder NAT is Relation-like Bags NAT -defined Bags NAT -valued total reflexive antisymmetric connected transitive admissible Element of bool [:(Bags NAT),(Bags NAT):]
[:(Bags NAT),(Bags NAT):] is non empty Relation-like set
bool [:(Bags NAT),(Bags NAT):] is non empty cup-closed diff-closed preBoolean V225() set
rng (((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) | ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)))) is finite Element of bool (Fin NAT)
bool (Fin NAT) is non empty cup-closed diff-closed preBoolean V225() set
dom (((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) | ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)))) is finite Element of bool ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)))
bool ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) is non empty finite finite-membered cup-closed diff-closed preBoolean set
dom ((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) is finite Element of bool (the_Vertices_of G)
(dom ((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L)) /\ ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) is finite Element of bool (the_Vertices_of G)
(the_Vertices_of G) /\ (the_Vertices_of G) is finite set
((the_Vertices_of G) /\ (the_Vertices_of G)) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)) is finite Element of bool ((the_Vertices_of G) /\ (the_Vertices_of G))
bool ((the_Vertices_of G) /\ (the_Vertices_of G)) is non empty finite finite-membered cup-closed diff-closed preBoolean set
vb is Relation-like Function-like set
proj1 vb is set
proj2 vb is set
vb is set
rng ((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) is finite Element of bool (Fin NAT)
vb is set
vb is set
vb is set
vb is non empty finite finite-membered Element of bool (bool NAT)
{ H1(b1) where b1 is finite Element of vb : b1 in vb } is set
P is set
e1 is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(e1,1) -bag is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags NAT
e2 is set
j is finite Element of vb
(j,1) -bag is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags NAT
e2 is non empty functional finite Element of bool (Bags NAT)
j is set
k is finite Element of vb
(k,1) -bag is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags NAT
(NAT,(InvLexOrder NAT),e2) is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
k is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(k,1) -bag is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags NAT
support (NAT,(InvLexOrder NAT),e2) is finite set
{(support (NAT,(InvLexOrder NAT),e2))} is non empty trivial finite finite-membered 1 -element set
(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) | ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)))) " {(support (NAT,(InvLexOrder NAT),e2))} is finite Element of bool (the_Vertices_of G)
choose ((((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) | ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)))) " {(support (NAT,(InvLexOrder NAT),e2))}) is Element of (((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) | ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)))) " {(support (NAT,(InvLexOrder NAT),e2))}
R is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(R,1) -bag is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags NAT
D is Element of the_Vertices_of G
R is non empty finite Element of bool (bool NAT)
ir is Relation-like Function-like set
proj2 ir is set
i is non empty functional finite Element of bool (Bags NAT)
(NAT,(InvLexOrder NAT),i) is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
support (NAT,(InvLexOrder NAT),i) is finite set
{(support (NAT,(InvLexOrder NAT),i))} is non empty trivial finite finite-membered 1 -element set
ir " {(support (NAT,(InvLexOrder NAT),i))} is set
choose (ir " {(support (NAT,(InvLexOrder NAT),i))}) is Element of ir " {(support (NAT,(InvLexOrder NAT),i))}
V is Element of the_Vertices_of G
a is Element of the_Vertices_of G
vb is non empty finite Element of bool (bool NAT)
P is Relation-like Function-like set
proj2 P is set
vc is non empty functional finite Element of bool (Bags NAT)
(NAT,(InvLexOrder NAT),vc) is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
support (NAT,(InvLexOrder NAT),vc) is finite set
{(support (NAT,(InvLexOrder NAT),vc))} is non empty trivial finite finite-membered 1 -element set
P " {(support (NAT,(InvLexOrder NAT),vc))} is set
choose (P " {(support (NAT,(InvLexOrder NAT),vc))}) is Element of P " {(support (NAT,(InvLexOrder NAT),vc))}
vb is non empty finite Element of bool (bool NAT)
P is Relation-like Function-like set
proj2 P is set
vc is non empty functional finite Element of bool (Bags NAT)
(NAT,(InvLexOrder NAT),vc) is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
support (NAT,(InvLexOrder NAT),vc) is finite set
{(support (NAT,(InvLexOrder NAT),vc))} is non empty trivial finite finite-membered 1 -element set
P " {(support (NAT,(InvLexOrder NAT),vc))} is set
choose (P " {(support (NAT,(InvLexOrder NAT),vc))}) is Element of P " {(support (NAT,(InvLexOrder NAT),vc))}
e1 is non empty finite Element of bool (bool NAT)
j is Relation-like Function-like set
proj2 j is set
e2 is non empty functional finite Element of bool (Bags NAT)
(NAT,(InvLexOrder NAT),e2) is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
support (NAT,(InvLexOrder NAT),e2) is finite set
{(support (NAT,(InvLexOrder NAT),e2))} is non empty trivial finite finite-membered 1 -element set
j " {(support (NAT,(InvLexOrder NAT),e2))} is set
choose (j " {(support (NAT,(InvLexOrder NAT),e2))}) is Element of j " {(support (NAT,(InvLexOrder NAT),e2))}
e1 is non empty finite Element of bool (bool NAT)
j is Relation-like Function-like set
proj2 j is set
e2 is non empty functional finite Element of bool (Bags NAT)
(NAT,(InvLexOrder NAT),e2) is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
support (NAT,(InvLexOrder NAT),e2) is finite set
{(support (NAT,(InvLexOrder NAT),e2))} is non empty trivial finite finite-membered 1 -element set
j " {(support (NAT,(InvLexOrder NAT),e2))} is set
choose (j " {(support (NAT,(InvLexOrder NAT),e2))}) is Element of j " {(support (NAT,(InvLexOrder NAT),e2))}
k is set
e is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(e,1) -bag is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags NAT
k is set
e is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(e,1) -bag is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
L is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
V is Element of the_Vertices_of G
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G .order()) -' a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V .--> ((G .order()) -' a) is Relation-like the_Vertices_of G -defined {V} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{V} is non empty trivial finite 1 -element set
{V} --> ((G .order()) -' a) is non empty Relation-like {V} -defined NAT -valued RAT -valued INT -valued {((G .order()) -' a)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{V},{((G .order()) -' a)}:]
{((G .order()) -' a)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{V},{((G .order()) -' a)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{V},{((G .order()) -' a)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' a)) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
{V} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
G .AdjacentSet {V} is finite Element of bool (the_Vertices_of G)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) is finite Element of bool (the_Vertices_of G)
(G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)) is finite Element of bool (the_Vertices_of G)
{((G .order()) -' a)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element Element of bool NAT
((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' a)} is Relation-like non-zero the_Vertices_of G -defined (G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)) -defined bool NAT -valued Function-like constant total Element of PFuncs ((the_Vertices_of G),(bool NAT))
PFuncs ((the_Vertices_of G),(bool NAT)) is non empty functional M38( the_Vertices_of G, bool NAT)
{{((G .order()) -' a)}} is non empty trivial finite finite-membered 1 -element set
[:((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))),{{((G .order()) -' a)}}:] is Relation-like finite set
(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' a)})) is Relation-like Function-like set
[(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' a))),(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' a)}))] is V1() set
{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' a))),(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' a)}))} is non empty functional finite set
{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' a)))} is non empty trivial functional finite finite-membered 1 -element set
{{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' a))),(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' a)}))},{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' a)))}} is non empty finite finite-membered set
dom (V .--> ((G .order()) -' a)) is trivial finite Element of bool {V}
bool {V} is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
rng (V .--> ((G .order()) -' a)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool RAT
bool RAT is non empty cup-closed diff-closed preBoolean set
rng ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(rng ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)) \/ (rng (V .--> ((G .order()) -' a))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite set
rng (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' a))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool RAT
proj1 (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' a))) is finite set
(dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)) \/ (dom (V .--> ((G .order()) -' a))) is finite set
c is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
{c} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element Element of bool NAT
{{c}} is non empty trivial finite finite-membered 1 -element Element of bool (bool NAT)
P is Relation-like Function-like set
proj1 P is set
proj2 P is set
rng (((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' a)}) is trivial finite V224() Element of bool (bool NAT)
proj1 (((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' a)})) is set
dom (((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' a)}) is finite Element of bool ((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)))
bool ((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) is non empty finite finite-membered cup-closed diff-closed preBoolean set
(proj1 P) \/ (dom (((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' a)})) is set
proj2 (((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' a)})) is set
e1 is set
e2 is set
(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' a)})) . e2 is set
P . e2 is set
(((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' a)}) . e2 is set
(P . e2) \/ ((((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' a)}) . e2) is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
L is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
V is Element of the_Vertices_of G
{V} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
G .AdjacentSet {V} is finite Element of bool (the_Vertices_of G)
a is set
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) . a is set
b is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,V,b) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G .order()) -' b is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V .--> ((G .order()) -' b) is Relation-like the_Vertices_of G -defined {V} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{V} is non empty trivial finite 1 -element set
{V} --> ((G .order()) -' b) is non empty Relation-like {V} -defined NAT -valued RAT -valued INT -valued {((G .order()) -' b)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{V},{((G .order()) -' b)}:]
{((G .order()) -' b)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{V},{((G .order()) -' b)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{V},{((G .order()) -' b)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' b)) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) is finite Element of bool (the_Vertices_of G)
(G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)) is finite Element of bool (the_Vertices_of G)
{((G .order()) -' b)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element Element of bool NAT
((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)} is Relation-like non-zero the_Vertices_of G -defined (G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)) -defined bool NAT -valued Function-like constant total Element of PFuncs ((the_Vertices_of G),(bool NAT))
PFuncs ((the_Vertices_of G),(bool NAT)) is non empty functional M38( the_Vertices_of G, bool NAT)
{{((G .order()) -' b)}} is non empty trivial finite finite-membered 1 -element set
[:((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))),{{((G .order()) -' b)}}:] is Relation-like finite set
(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)})) is Relation-like Function-like set
[(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' b))),(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)}))] is V1() set
{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' b))),(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)}))} is non empty functional finite set
{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' b)))} is non empty trivial functional finite finite-membered 1 -element set
{{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' b))),(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)}))},{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' b)))}} is non empty finite finite-membered set
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,L,V,b)) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,L,V,b)) . a is set
dom (((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)}) is finite Element of bool ((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)))
bool ((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) is non empty finite finite-membered cup-closed diff-closed preBoolean set
(((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)}) . a is set
dom ((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) is finite Element of bool (the_Vertices_of G)
(dom ((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L)) \/ (dom (((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)})) is finite set
(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) . a) \/ ((((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)}) . a) is set
dom ((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) is finite Element of bool (the_Vertices_of G)
(dom ((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L)) \/ (dom (((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)})) is finite set
dom ((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,L,V,b)) is finite Element of bool (the_Vertices_of G)
dom ((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) is finite Element of bool (the_Vertices_of G)
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
L is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
V is Element of the_Vertices_of G
a is set
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) . a is set
b is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,V,b) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G .order()) -' b is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V .--> ((G .order()) -' b) is Relation-like the_Vertices_of G -defined {V} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{V} is non empty trivial finite 1 -element set
{V} --> ((G .order()) -' b) is non empty Relation-like {V} -defined NAT -valued RAT -valued INT -valued {((G .order()) -' b)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{V},{((G .order()) -' b)}:]
{((G .order()) -' b)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{V},{((G .order()) -' b)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{V},{((G .order()) -' b)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' b)) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{V} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
G .AdjacentSet {V} is finite Element of bool (the_Vertices_of G)
(G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)) is finite Element of bool (the_Vertices_of G)
{((G .order()) -' b)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element Element of bool NAT
((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)} is Relation-like non-zero the_Vertices_of G -defined (G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)) -defined bool NAT -valued Function-like constant total Element of PFuncs ((the_Vertices_of G),(bool NAT))
PFuncs ((the_Vertices_of G),(bool NAT)) is non empty functional M38( the_Vertices_of G, bool NAT)
{{((G .order()) -' b)}} is non empty trivial finite finite-membered 1 -element set
[:((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))),{{((G .order()) -' b)}}:] is Relation-like finite set
(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)})) is Relation-like Function-like set
[(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' b))),(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)}))] is V1() set
{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' b))),(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)}))} is non empty functional finite set
{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' b)))} is non empty trivial functional finite finite-membered 1 -element set
{{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' b))),(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)}))},{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' b)))}} is non empty finite finite-membered set
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,L,V,b)) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,L,V,b)) . a is set
dom (((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)}) is finite Element of bool ((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)))
bool ((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) is non empty finite finite-membered cup-closed diff-closed preBoolean set
(((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)}) . a is set
dom ((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) is finite Element of bool (the_Vertices_of G)
(dom ((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L)) \/ (dom (((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)})) is finite set
(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) . a) \/ ((((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)}) . a) is set
dom ((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) is finite Element of bool (the_Vertices_of G)
(dom ((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L)) \/ (dom (((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)})) is finite set
dom ((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,L,V,b)) is finite Element of bool (the_Vertices_of G)
dom ((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) is finite Element of bool (the_Vertices_of G)
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
L is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
V is Element of the_Vertices_of G
{V} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
G .AdjacentSet {V} is finite Element of bool (the_Vertices_of G)
a is set
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) . a is set
b is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,V,b) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G .order()) -' b is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V .--> ((G .order()) -' b) is Relation-like the_Vertices_of G -defined {V} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{V} is non empty trivial finite 1 -element set
{V} --> ((G .order()) -' b) is non empty Relation-like {V} -defined NAT -valued RAT -valued INT -valued {((G .order()) -' b)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{V},{((G .order()) -' b)}:]
{((G .order()) -' b)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{V},{((G .order()) -' b)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{V},{((G .order()) -' b)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' b)) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)) is finite Element of bool (the_Vertices_of G)
{((G .order()) -' b)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element Element of bool NAT
((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)} is Relation-like non-zero the_Vertices_of G -defined (G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)) -defined bool NAT -valued Function-like constant total Element of PFuncs ((the_Vertices_of G),(bool NAT))
PFuncs ((the_Vertices_of G),(bool NAT)) is non empty functional M38( the_Vertices_of G, bool NAT)
{{((G .order()) -' b)}} is non empty trivial finite finite-membered 1 -element set
[:((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))),{{((G .order()) -' b)}}:] is Relation-like finite set
(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)})) is Relation-like Function-like set
[(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' b))),(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)}))] is V1() set
{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' b))),(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)}))} is non empty functional finite set
{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' b)))} is non empty trivial functional finite finite-membered 1 -element set
{{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' b))),(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)}))},{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* (V .--> ((G .order()) -' b)))}} is non empty finite finite-membered set
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,L,V,b)) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,L,V,b)) . a is set
(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) . a) \/ {((G .order()) -' b)} is non empty set
dom (((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)}) is finite Element of bool ((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)))
bool ((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) is non empty finite finite-membered cup-closed diff-closed preBoolean set
dom ((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) is finite Element of bool (the_Vertices_of G)
(dom ((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L)) \/ (dom (((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)})) is finite set
(((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' b)}) . a is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
L is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L) is Element of the_Vertices_of G
(G,L,(G,L),(card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)))) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)))) is Relation-like the_Vertices_of G -defined {(G,L)} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(G,L)} is non empty trivial finite 1 -element set
{(G,L)} --> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)))) is non empty Relation-like {(G,L)} -defined NAT -valued RAT -valued INT -valued {((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))))} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{(G,L)},{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))))}:]
{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))))} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{(G,L)},{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))))}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{(G,L)},{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))))}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* ((G,L) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))))) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
{(G,L)} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
G .AdjacentSet {(G,L)} is finite Element of bool (the_Vertices_of G)
(G .AdjacentSet {(G,L)}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)) is finite Element of bool (the_Vertices_of G)
{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))))} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element Element of bool NAT
((G .AdjacentSet {(G,L)}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))))} is Relation-like non-zero the_Vertices_of G -defined (G .AdjacentSet {(G,L)}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)) -defined bool NAT -valued Function-like constant total Element of PFuncs ((the_Vertices_of G),(bool NAT))
PFuncs ((the_Vertices_of G),(bool NAT)) is non empty functional M38( the_Vertices_of G, bool NAT)
{{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))))}} is non empty trivial finite finite-membered 1 -element set
[:((G .AdjacentSet {(G,L)}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))),{{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))))}}:] is Relation-like finite set
(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(((G .AdjacentSet {(G,L)}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))))})) is Relation-like Function-like set
[(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* ((G,L) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)))))),(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(((G .AdjacentSet {(G,L)}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))))}))] is V1() set
{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* ((G,L) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)))))),(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(((G .AdjacentSet {(G,L)}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))))}))} is non empty functional finite set
{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* ((G,L) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))))))} is non empty trivial functional finite finite-membered 1 -element set
{{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* ((G,L) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)))))),(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(((G .AdjacentSet {(G,L)}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) --> {((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))))}))},{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) +* ((G,L) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))))))}} is non empty finite finite-membered set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] set
the_Vertices_of G is non empty set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
the Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
V is Relation-like NAT -defined Function-like total set
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V . a is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] set
L is Relation-like NAT -defined Function-like total (G)
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
L . V is set
the_Vertices_of G is non empty set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] set
L is Relation-like NAT -defined Function-like total (G)
L .Result() is set
L .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . (L .Lifespan()) is set
the_Vertices_of G is non empty set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
L is Relation-like NAT -defined Function-like total (G)
V is Relation-like NAT -defined Function-like total set
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V . a is set
(G,L,a) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,L,a)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
a is Relation-like NAT -defined Function-like total (G)
b is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,a,b) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,L,b) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,L,b)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
V is Relation-like NAT -defined Function-like total (G)
a is Relation-like NAT -defined Function-like total (G)
b is set
V . b is set
c is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,c) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,L,c)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
a . b is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
(G) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
(the_Vertices_of G) --> {} is non empty Relation-like the_Vertices_of G -defined RAT -valued INT -valued {{}} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Function-yielding V264() Element of bool [:(the_Vertices_of G),{{}}:]
[:(the_Vertices_of G),{{}}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),{{}}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
[{},((the_Vertices_of G) --> {})] is V1() set
{{},((the_Vertices_of G) --> {})} is non empty functional finite finite-membered set
{{{},((the_Vertices_of G) --> {})},{{}}} is non empty finite finite-membered set
V is set
a is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G,a) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
L is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V is set
L is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V is set
L is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V is set
b is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
a is set
(G,b) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
V is set
L is Relation-like Function-like set
proj1 L is set
L . 0 is set
V is Relation-like NAT -defined Function-like total set
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V . a is set
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V . (a + 1) is set
b is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G,b) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
V . 0 is set
a is Relation-like NAT -defined Function-like total (G)
(G,a,0) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
b is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
b + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,a,(b + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G,a,b) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G,(G,a,b)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
c is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G,c) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
L is Relation-like NAT -defined Function-like total (G)
(G,L,0) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
V is Relation-like NAT -defined Function-like total (G)
(G,V,0) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,a) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G,V,a) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,(a + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G,(G,V,a)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G,V,(a + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,a) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G,V,a) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,(a + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G,V,(a + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
a is set
L . a is set
V . a is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
(G) is Relation-like NAT -defined Function-like total (G)
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G) . V is set
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G) . a is set
V + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G) . (V + 1) is set
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G) . (a + 1) is set
(G,(G),V) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
(G,(G),a) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G,(G),(V + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G,(G,(G),V)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G,(G),(a + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
(G) is Relation-like NAT -defined Function-like total (G)
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] set
the_Vertices_of G is non empty set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
(G) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
(the_Vertices_of G) --> {} is non empty Relation-like the_Vertices_of G -defined RAT -valued INT -valued {{}} -valued Function-like constant total quasi_total complex-valued ext-real-valued real-valued natural-valued Function-yielding V264() Element of bool [:(the_Vertices_of G),{{}}:]
[:(the_Vertices_of G),{{}}:] is non empty Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),{{}}:] is non empty cup-closed diff-closed preBoolean V225() set
[{},((the_Vertices_of G) --> {})] is V1() set
{{},((the_Vertices_of G) --> {})} is non empty functional finite set
{{{},((the_Vertices_of G) --> {})},{{}}} is non empty finite finite-membered set
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G)) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total Element of Funcs ((the_Vertices_of G),(Fin NAT))
dom ((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G)) is Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty cup-closed diff-closed preBoolean V225() set
L is set
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G)) . L is set
b is set
dom ((the_Vertices_of G) --> {}) is non empty Element of bool (the_Vertices_of G)
((the_Vertices_of G) --> {}) . b is Relation-like Function-like ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() finite-support Element of NAT
b is set
dom ((the_Vertices_of G) --> {}) is non empty Element of bool (the_Vertices_of G)
((the_Vertices_of G) --> {}) . b is Relation-like Function-like ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() finite-support Element of NAT
b is set
dom ((the_Vertices_of G) --> {}) is non empty Element of bool (the_Vertices_of G)
G is set
L is set
Fin L is non empty cup-closed diff-closed preBoolean set
[:G,(Fin L):] is Relation-like set
bool [:G,(Fin L):] is non empty cup-closed diff-closed preBoolean set
V is Relation-like G -defined Fin L -valued Function-like quasi_total Element of bool [:G,(Fin L):]
a is set
V . a is set
bool L is non empty cup-closed diff-closed preBoolean set
dom V is Element of bool G
bool G is non empty cup-closed diff-closed preBoolean set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
L is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
(G,L) is Element of the_Vertices_of G
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(G,L)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),(G,L)),1) -bag is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags NAT
V is set
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),V) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L),V),1) -bag is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags NAT
(the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)) is finite Element of bool (the_Vertices_of G)
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) | ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) is Relation-like the_Vertices_of G -defined (the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)) -defined the_Vertices_of G -defined Fin NAT -valued Function-like finite finite-support Element of bool [:(the_Vertices_of G),(Fin NAT):]
[:(the_Vertices_of G),(Fin NAT):] is non empty Relation-like set
bool [:(the_Vertices_of G),(Fin NAT):] is non empty cup-closed diff-closed preBoolean V225() set
vb is non empty finite Element of bool (bool NAT)
P is Relation-like Function-like set
proj2 P is set
vc is non empty functional finite Element of bool (Bags NAT)
(NAT,(InvLexOrder NAT),vc) is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
support (NAT,(InvLexOrder NAT),vc) is finite set
{(support (NAT,(InvLexOrder NAT),vc))} is non empty trivial finite finite-membered 1 -element set
P " {(support (NAT,(InvLexOrder NAT),vc))} is set
choose (P " {(support (NAT,(InvLexOrder NAT),vc))}) is Element of P " {(support (NAT,(InvLexOrder NAT),vc))}
proj1 P is set
dom ((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) is finite Element of bool (the_Vertices_of G)
(dom ((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L)) /\ ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) is finite Element of bool (the_Vertices_of G)
e2 is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(e2,1) -bag is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags NAT
P . (G,L) is set
P . V is set
EmptyBag NAT is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
L is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(G,L) is Element of the_Vertices_of G
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
(the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)) is finite Element of bool (the_Vertices_of G)
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) | ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) is Relation-like the_Vertices_of G -defined (the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L)) -defined the_Vertices_of G -defined Fin NAT -valued Function-like finite finite-support Element of bool [:(the_Vertices_of G),(Fin NAT):]
[:(the_Vertices_of G),(Fin NAT):] is non empty Relation-like set
bool [:(the_Vertices_of G),(Fin NAT):] is non empty cup-closed diff-closed preBoolean V225() set
va is non empty finite Element of bool (bool NAT)
vc is Relation-like Function-like set
proj2 vc is set
vb is non empty functional finite Element of bool (Bags NAT)
(NAT,(InvLexOrder NAT),vb) is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
support (NAT,(InvLexOrder NAT),vb) is finite set
{(support (NAT,(InvLexOrder NAT),vb))} is non empty trivial finite finite-membered 1 -element set
vc " {(support (NAT,(InvLexOrder NAT),vb))} is set
choose (vc " {(support (NAT,(InvLexOrder NAT),vb))}) is Element of vc " {(support (NAT,(InvLexOrder NAT),vb))}
e1 is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(e1,1) -bag is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags NAT
proj1 vc is set
dom ((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L) is finite Element of bool (the_Vertices_of G)
(dom ((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),L)) /\ ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),L))) is finite Element of bool (the_Vertices_of G)
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
the_Vertices_of G is non empty finite set
G . VertexSelector is set
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
(G) is Relation-like NAT -defined Function-like total () (G)
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(L + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(L + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
(G,(G,(G),L)) is Element of the_Vertices_of G
(G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G),L)) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L))))) is Relation-like the_Vertices_of G -defined {(G,(G,(G),L))} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(G,(G,(G),L))} is non empty trivial finite 1 -element set
{(G,(G,(G),L))} --> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L))))) is non empty Relation-like {(G,(G,(G),L))} -defined NAT -valued RAT -valued INT -valued {((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))))} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{(G,(G,(G),L))},{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))))}:]
{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))))} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{(G,(G,(G),L))},{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))))}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{(G,(G,(G),L))},{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))))}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))))) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(G,(G,(G),L)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G,(G,(G),L),(G,(G,(G),L)),(card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L))))) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
{(G,(G,(G),L))} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
G .AdjacentSet {(G,(G,(G),L))} is finite Element of bool (the_Vertices_of G)
(G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L))) is finite Element of bool (the_Vertices_of G)
{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))))} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element Element of bool NAT
((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))) --> {((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))))} is Relation-like non-zero the_Vertices_of G -defined (G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L))) -defined bool NAT -valued Function-like constant total Element of PFuncs ((the_Vertices_of G),(bool NAT))
PFuncs ((the_Vertices_of G),(bool NAT)) is non empty functional M38( the_Vertices_of G, bool NAT)
{{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))))}} is non empty trivial finite finite-membered 1 -element set
[:((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))),{{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))))}}:] is Relation-like finite set
(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)),(((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))) --> {((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))))})) is Relation-like Function-like set
[(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L))))))),(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)),(((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))) --> {((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))))}))] is V1() set
{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L))))))),(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)),(((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))) --> {((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))))}))} is non empty functional finite set
{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))))))} is non empty trivial functional finite finite-membered 1 -element set
{{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L))))))),(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)),(((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))) --> {((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))))}))},{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))))))}} is non empty finite finite-membered set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
the_Vertices_of G is non empty finite set
G . VertexSelector is set
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
(G) is Relation-like NAT -defined Function-like total () (G)
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),a) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),a)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),a)) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),a))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(a + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(a + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(a + 1))) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(a + 1)))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G),a)) is Element of the_Vertices_of G
(G .order()) -' a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G),a)) .--> ((G .order()) -' a) is Relation-like the_Vertices_of G -defined {(G,(G,(G),a))} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(G,(G,(G),a))} is non empty trivial finite 1 -element set
{(G,(G,(G),a))} --> ((G .order()) -' a) is non empty Relation-like {(G,(G,(G),a))} -defined NAT -valued RAT -valued INT -valued {((G .order()) -' a)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{(G,(G,(G),a))},{((G .order()) -' a)}:]
{((G .order()) -' a)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{(G,(G,(G),a))},{((G .order()) -' a)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{(G,(G,(G),a))},{((G .order()) -' a)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
dom ((G,(G,(G),a)) .--> ((G .order()) -' a)) is trivial finite Element of bool {(G,(G,(G),a))}
bool {(G,(G,(G),a))} is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
{(G,(G,(G),a))} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),a)) +* ((G,(G,(G),a)) .--> ((G .order()) -' a)) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),a))) \/ {(G,(G,(G),a))} is non empty finite Element of bool (the_Vertices_of G)
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),a) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),a)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),a)) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),a))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(a + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(a + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(a + 1))) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(a + 1)))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),0) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(the_Vertices_of G) --> {} is non empty Relation-like the_Vertices_of G -defined RAT -valued INT -valued {{}} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Function-yielding V264() Element of bool [:(the_Vertices_of G),{{}}:]
[:(the_Vertices_of G),{{}}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),{{}}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
[{},((the_Vertices_of G) --> {})] is V1() set
{{},((the_Vertices_of G) --> {})} is non empty functional finite finite-membered set
{{{},((the_Vertices_of G) --> {})},{{}}} is non empty finite finite-membered set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),0)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),0)) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),0))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
the_Vertices_of G is non empty finite set
G . VertexSelector is set
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G) is Relation-like NAT -defined Function-like total () (G)
(G,(G),(G .order())) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G .order()) + a is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),((G .order()) + a)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((G .order()) + a))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((G .order()) + a))) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((G .order()) + a)))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .order()) + (a + 1) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),((G .order()) + (a + 1))) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((G .order()) + (a + 1)))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((G .order()) + (a + 1)))) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((G .order()) + (a + 1))))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((G .order()) + a) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(((G .order()) + a) + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G,(G,(G),((G .order()) + a))) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G .order()) + 0 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),((G .order()) + 0)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((G .order()) + 0))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((G .order()) + 0))) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((G .order()) + 0)))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G .order()) + a is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),((G .order()) + a)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .order()) + (a + 1) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),((G .order()) + (a + 1))) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((G .order()) + a) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(((G .order()) + a) + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((G .order()) + a))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
(G,(G,(G),((G .order()) + a))) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((G .order()) + a))) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((G .order()) + a)))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G .order()) + a is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
the_Vertices_of G is non empty finite set
G . VertexSelector is set
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G) is Relation-like NAT -defined Function-like total () (G)
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
(G,(G),V) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G,(G),(G .order())) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
(G) is Relation-like NAT -defined Function-like total () (G)
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
the_Vertices_of G is non empty finite set
G . VertexSelector is set
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G) . (G .order()) is set
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G) . L is set
(G,(G),(G .order())) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
(G) is Relation-like NAT -defined Function-like total () (G)
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
(G) is Relation-like NAT -defined Function-like total halting () () (G)
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(G,(G),(G .order())) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(G .order()))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(G .order()))) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(G .order())))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
(G) is Relation-like NAT -defined Function-like total halting () () (G)
(G) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
the_Vertices_of G is non empty finite set
G . VertexSelector is set
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),V) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
V + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(V + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G,(G,(G),V)) is Element of the_Vertices_of G
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(V + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),V)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),V)) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),V))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),V)))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G),V)) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),V))))) is Relation-like the_Vertices_of G -defined {(G,(G,(G),V))} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(G,(G,(G),V))} is non empty trivial finite 1 -element set
{(G,(G,(G),V))} --> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),V))))) is non empty Relation-like {(G,(G,(G),V))} -defined NAT -valued RAT -valued INT -valued {((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),V)))))} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{(G,(G,(G),V))},{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),V)))))}:]
{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),V)))))} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{(G,(G,(G),V))},{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),V)))))}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{(G,(G,(G),V))},{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),V)))))}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),V)) +* ((G,(G,(G),V)) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),V)))))) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom ((G,(G,(G),V)) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),V)))))) is trivial finite Element of bool {(G,(G,(G),V))}
bool {(G,(G,(G),V))} is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
{(G,(G,(G),V))} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(V + 1))) is finite Element of bool (the_Vertices_of G)
(dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),V))) \/ {(G,(G,(G),V))} is non empty finite Element of bool (the_Vertices_of G)
(G .order()) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(G .order())) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
(G,(G),((G .order()) + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
(G) is Relation-like NAT -defined Function-like total halting () () (G)
(G,(G)) is Relation-like NAT -defined Function-like total (G)
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),a) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
b is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
c is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G,(G)),b) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
(G,(G),b) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),b)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
(G,(G),c) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),c)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
(G,(G,(G)),c) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G,(G)),a) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
(G) is Relation-like NAT -defined Function-like total halting () () (G)
(G,(G)) is Relation-like NAT -defined Function-like total (G)
(G,(G)) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
the_Vertices_of G is non empty finite set
G . VertexSelector is set
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
(G .order()) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),((G .order()) + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((G .order()) + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
(G,(G,(G)),((G .order()) + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
b is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G,(G)),b) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
b + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G)),(b + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,(G),(b + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(b + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(b + 1))) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(b + 1)))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),b) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),b)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),b)) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),b))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(G .order())) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(G .order()))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
(G,(G,(G)),(G .order())) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
(G) is Relation-like NAT -defined Function-like total halting () () (G)
(G,(G)) is Relation-like NAT -defined Function-like total (G)
(G,(G)) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G)),0) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
the_Vertices_of G is non empty finite set
G . VertexSelector is set
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
(G,(G),0) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),0)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
(G) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(the_Vertices_of G) --> {} is non empty Relation-like the_Vertices_of G -defined RAT -valued INT -valued {{}} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Function-yielding V264() Element of bool [:(the_Vertices_of G),{{}}:]
[:(the_Vertices_of G),{{}}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),{{}}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
[{},((the_Vertices_of G) --> {})] is V1() set
{{},((the_Vertices_of G) --> {})} is non empty functional finite finite-membered set
{{{},((the_Vertices_of G) --> {})},{{}}} is non empty finite finite-membered set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G,(G)),a) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
b is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G,(G)),b) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G)),(a + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,(G),(a + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(a + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
(G,(G),a) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),a)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
b + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G)),(b + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,(G),(b + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(b + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
(G,(G),b) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),b)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),b)) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),b))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(G .order())) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(G .order()))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(G .order()))) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(G .order())))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),a)) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),a))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(G .order())) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(G .order()))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(G .order()))) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(G .order())))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),b)) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),b))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(G .order())) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(G .order()))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G,(G)),a) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
dom (G,(G,(G)),a) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G)),(a + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
((G,(G)) .Lifespan()) -' a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),a) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G,(G,(G),a)) is Element of the_Vertices_of G
b is Element of the_Vertices_of G
b .--> (((G,(G)) .Lifespan()) -' a) is Relation-like the_Vertices_of G -defined {b} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{b} is non empty trivial finite 1 -element set
{b} --> (((G,(G)) .Lifespan()) -' a) is non empty Relation-like {b} -defined NAT -valued RAT -valued INT -valued {(((G,(G)) .Lifespan()) -' a)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{b},{(((G,(G)) .Lifespan()) -' a)}:]
{(((G,(G)) .Lifespan()) -' a)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{b},{(((G,(G)) .Lifespan()) -' a)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{b},{(((G,(G)) .Lifespan()) -' a)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(G,(G,(G)),a) +* (b .--> (((G,(G)) .Lifespan()) -' a)) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),a)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),a)) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),a))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(a + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(a + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
(G) is Relation-like NAT -defined Function-like total halting () () (G)
(G,(G)) is Relation-like NAT -defined Function-like total halting () () (G) (G)
(G,(G)) .Result() is set
(G,(G)) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G)) . ((G,(G)) .Lifespan()) is set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
(G,(G)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
(G) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G) . ((G) .Lifespan()) is set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
(G,(G,(G)),((G) .Lifespan())) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
the_Vertices_of G is non empty finite set
G . VertexSelector is set
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G) is Relation-like NAT -defined Function-like total halting () () (G)
(G,(G)) is Relation-like NAT -defined Function-like total halting () () (G) (G)
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G,(G)),L) is set
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
(G,(G,(G),L)) is Element of the_Vertices_of G
L + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(L + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(L + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
(G) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((G) .Lifespan()) -' L is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G),L)) .--> (((G) .Lifespan()) -' L) is Relation-like the_Vertices_of G -defined {(G,(G,(G),L))} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(G,(G,(G),L))} is non empty trivial finite 1 -element set
{(G,(G,(G),L))} --> (((G) .Lifespan()) -' L) is non empty Relation-like {(G,(G,(G),L))} -defined NAT -valued RAT -valued INT -valued {(((G) .Lifespan()) -' L)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{(G,(G,(G),L))},{(((G) .Lifespan()) -' L)}:]
{(((G) .Lifespan()) -' L)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{(G,(G,(G),L))},{(((G) .Lifespan()) -' L)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{(G,(G,(G),L))},{(((G) .Lifespan()) -' L)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
dom ((G,(G,(G),L)) .--> (((G) .Lifespan()) -' L)) is trivial finite Element of bool {(G,(G,(G),L))}
bool {(G,(G,(G),L))} is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
{(G,(G,(G),L))} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) +* ((G,(G,(G),L)) .--> (((G) .Lifespan()) -' L)) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(L + 1))) is finite Element of bool (the_Vertices_of G)
(dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L))) \/ {(G,(G,(G),L))} is non empty finite Element of bool (the_Vertices_of G)
(G,(G,(G)),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
(G,(G,(G)),L) .--> (((G) .Lifespan()) -' L) is Relation-like {(G,(G,(G)),L)} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(G,(G,(G)),L)} is non empty trivial finite 1 -element set
{(G,(G,(G)),L)} --> (((G) .Lifespan()) -' L) is non empty Relation-like {(G,(G,(G)),L)} -defined NAT -valued RAT -valued INT -valued {(((G) .Lifespan()) -' L)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{(G,(G,(G)),L)},{(((G) .Lifespan()) -' L)}:]
[:{(G,(G,(G)),L)},{(((G) .Lifespan()) -' L)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{(G,(G,(G)),L)},{(((G) .Lifespan()) -' L)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
dom ((G,(G,(G)),L) .--> (((G) .Lifespan()) -' L)) is trivial finite Element of bool {(G,(G,(G)),L)}
bool {(G,(G,(G)),L)} is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(G,(G)) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G)),(L + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) +* ((G,(G,(G)),L) .--> (((G) .Lifespan()) -' L)) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L))) \/ {(G,(G,(G)),L)} is non empty finite set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
the_Vertices_of G is non empty finite set
G . VertexSelector is set
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G) is Relation-like NAT -defined Function-like total halting () () (G)
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
(G,(G,(G),L)) is Element of the_Vertices_of G
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
L + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(L + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(L + 1))) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
(G .order()) -' L is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
{((G .order()) -' L)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element Element of bool NAT
{(G,(G,(G),L))} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
G .AdjacentSet {(G,(G,(G),L))} is finite Element of bool (the_Vertices_of G)
(G,(G,(G),L)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G),L),(G,(G,(G),L)),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G,(G,(G),L)) .--> ((G .order()) -' L) is Relation-like the_Vertices_of G -defined {(G,(G,(G),L))} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(G,(G,(G),L))} is non empty trivial finite 1 -element set
{(G,(G,(G),L))} --> ((G .order()) -' L) is non empty Relation-like {(G,(G,(G),L))} -defined NAT -valued RAT -valued INT -valued {((G .order()) -' L)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{(G,(G,(G),L))},{((G .order()) -' L)}:]
{((G .order()) -' L)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{(G,(G,(G),L))},{((G .order()) -' L)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{(G,(G,(G),L))},{((G .order()) -' L)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' L)) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L))) is finite Element of bool (the_Vertices_of G)
((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))) --> {((G .order()) -' L)} is Relation-like non-zero the_Vertices_of G -defined (G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L))) -defined bool NAT -valued Function-like constant total Element of PFuncs ((the_Vertices_of G),(bool NAT))
PFuncs ((the_Vertices_of G),(bool NAT)) is non empty functional M38( the_Vertices_of G, bool NAT)
{{((G .order()) -' L)}} is non empty trivial finite finite-membered 1 -element set
[:((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))),{{((G .order()) -' L)}}:] is Relation-like finite set
(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)),(((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))) --> {((G .order()) -' L)})) is Relation-like Function-like set
[(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' L))),(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)),(((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))) --> {((G .order()) -' L)}))] is V1() set
{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' L))),(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)),(((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))) --> {((G .order()) -' L)}))} is non empty functional finite set
{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' L)))} is non empty trivial functional finite finite-membered 1 -element set
{{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' L))),(((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)),(((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)))) --> {((G .order()) -' L)}))},{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' L)))}} is non empty finite finite-membered set
P is set
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(L + 1))),P) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)),P) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(L + 1))),P) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)),P) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
P is set
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(L + 1))),P) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)),P) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)),P) \/ {((G .order()) -' L)} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite Element of bool NAT
e1 is set
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(L + 1))),e1) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)),e1) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
(G) is Relation-like NAT -defined Function-like total halting () () (G)
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
Seg (G .order()) is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite G .order() -element Element of bool NAT
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
(G .order()) -' L is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
Seg ((G .order()) -' L) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite (G .order()) -' L -element Element of bool NAT
(Seg (G .order())) \ (Seg ((G .order()) -' L)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
V is set
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)),V) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(G,(G),(G .order())) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(G .order()))) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
vc is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),vc) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),vc)) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),vc)),V) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(G .order()) -' vc is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
Seg ((G .order()) -' vc) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite (G .order()) -' vc -element Element of bool NAT
(Seg (G .order())) \ (Seg ((G .order()) -' vc)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
vc + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(vc + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(vc + 1))) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(vc + 1))),V) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(G .order()) -' (vc + 1) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
Seg ((G .order()) -' (vc + 1)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite (G .order()) -' (vc + 1) -element Element of bool NAT
(Seg (G .order())) \ (Seg ((G .order()) -' (vc + 1))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),vc)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
(G,(G,(G),vc)) is Element of the_Vertices_of G
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),vc)) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
{((G .order()) -' vc)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element Element of bool NAT
e is Element of the_Vertices_of G
{e} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
G .AdjacentSet {e} is finite Element of bool (the_Vertices_of G)
((Seg (G .order())) \ (Seg ((G .order()) -' vc))) \/ {((G .order()) -' vc)} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite Element of bool NAT
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),vc)),V) \/ {((G .order()) -' vc)} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite Element of bool NAT
(G,(G),0) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(the_Vertices_of G) --> {} is non empty Relation-like the_Vertices_of G -defined RAT -valued INT -valued {{}} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Function-yielding V264() Element of bool [:(the_Vertices_of G),{{}}:]
[:(the_Vertices_of G),{{}}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),{{}}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
[{},((the_Vertices_of G) --> {})] is V1() set
{{},((the_Vertices_of G) --> {})} is non empty functional finite finite-membered set
{{{},((the_Vertices_of G) --> {})},{{}}} is non empty finite finite-membered set
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),0)) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),0)),V) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(G .order()) -' 0 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
Seg ((G .order()) -' 0) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite (G .order()) -' 0 -element Element of bool NAT
(Seg (G .order())) \ (Seg ((G .order()) -' 0)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
L - L is ext-real V55() real V57() set
(G .order()) - L is ext-real V55() real V57() set
(G .order()) -' (G .order()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
(G) is Relation-like NAT -defined Function-like total halting () () (G)
L is set
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),V) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),V)) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),V)),L) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(G,(G),a) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),a)) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),a)),L) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
vb is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V + vb is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),(V + vb)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(V + vb))) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(V + vb))),L) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
vb + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V + (vb + 1) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),(V + (vb + 1))) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(V + (vb + 1)))) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(V + (vb + 1)))),L) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(V + vb) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),((V + vb) + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(V + vb))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),((V + vb) + 1))) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G,(G),(V + vb))) is Element of the_Vertices_of G
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(V + vb))) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(G .order()) -' (V + vb) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
{((G .order()) -' (V + vb))} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element Element of bool NAT
k is Element of the_Vertices_of G
{k} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
G .AdjacentSet {k} is finite Element of bool (the_Vertices_of G)
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),((V + vb) + 1))),L) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(V + vb))),L) \/ {((G .order()) -' (V + vb))} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite Element of bool NAT
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V + 0 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),(V + 0)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(V + 0))) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(V + 0))),L) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
vb is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V + vb is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
the_Vertices_of G is non empty finite set
G . VertexSelector is set
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G) is Relation-like NAT -defined Function-like total halting () () (G)
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),V) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
(G,(G,(G),V)) is Element of the_Vertices_of G
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),V)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),V)) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(G .order()) -' V is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
b is set
a is set
{b} is non empty trivial finite 1 -element set
G .AdjacentSet {b} is finite Element of bool (the_Vertices_of G)
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)),a) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
V + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(V + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(V + 1))) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(V + 1))),a) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
{((G .order()) -' V)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element Element of bool NAT
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),V)) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),V)),a) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),V)),a) \/ {((G .order()) -' V)} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite Element of bool NAT
k is Element of the_Vertices_of G
{k} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
G .AdjacentSet {k} is finite Element of bool (the_Vertices_of G)
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
the_Vertices_of G is non empty finite set
G . VertexSelector is set
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
(G) is Relation-like NAT -defined Function-like total halting () () (G)
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G .order()) -' L is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(L + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(L + 1))) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
(G,(G),V) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),V)) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
va is set
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(L + 1))),va) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),V)),va) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
vb is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(L + 1) + vb is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),((L + 1) + vb)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),((L + 1) + vb))) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),((L + 1) + vb))),va) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
vb + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(L + 1) + (vb + 1) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),((L + 1) + (vb + 1))) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),((L + 1) + (vb + 1)))) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),((L + 1) + (vb + 1)))),va) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((L + 1) + vb))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
((L + 1) + vb) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(((L + 1) + vb) + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(((L + 1) + vb) + 1))) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
(G,(G,(G),((L + 1) + vb))) is Element of the_Vertices_of G
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((L + 1) + vb))) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(G .order()) -' ((L + 1) + vb) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
{((G .order()) -' ((L + 1) + vb))} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element Element of bool NAT
k is Element of the_Vertices_of G
{k} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
G .AdjacentSet {k} is finite Element of bool (the_Vertices_of G)
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(((L + 1) + vb) + 1))),va) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),((L + 1) + vb))),va) \/ {((G .order()) -' ((L + 1) + vb))} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite Element of bool NAT
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(((L + 1) + vb) + 1))),va) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(((L + 1) + vb) + 1))),va) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(((L + 1) + vb) + 1))),va) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(((L + 1) + vb) + 1))),va) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(((L + 1) + vb) + 1))),va) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(((L + 1) + vb) + 1))),va) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(L + 1) + 0 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),((L + 1) + 0)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),((L + 1) + 0))) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),((L + 1) + 0))),va) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
vb is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(L + 1) + vb is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
the_Vertices_of G is non empty finite set
G . VertexSelector is set
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
(G) is Relation-like NAT -defined Function-like total halting () () (G)
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G .order()) -' a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),V) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),V)) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
vb is set
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),V)),vb) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)),vb) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(a + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(a + 1))) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(a + 1))),vb) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
(G) is Relation-like NAT -defined Function-like total halting () () (G)
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
(G .order()) -' V is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),((G .order()) -' V)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G,(G,(G),((G .order()) -' V))) is Element of the_Vertices_of G
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((G .order()) -' V))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((G .order()) -' V))) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),((G .order()) -' V))) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
((G .order()) -' V) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(((G .order()) -' V) + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(((G .order()) -' V) + 1))) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
j is Element of the_Vertices_of G
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)),j) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
Seg (G .order()) is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite G .order() -element Element of bool NAT
(G .order()) -' L is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
Seg ((G .order()) -' L) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite (G .order()) -' L -element Element of bool NAT
(Seg (G .order())) \ (Seg ((G .order()) -' L)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(G .order()) - V is ext-real V55() real V57() set
(G .order()) -' ((G .order()) -' V) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .order()) - ((G .order()) - V) is ext-real V55() real V57() set
{V} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
k is Element of the_Vertices_of G
{k} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
G .AdjacentSet {k} is finite Element of bool (the_Vertices_of G)
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),((G .order()) -' V))),j) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
Seg ((G .order()) -' ((G .order()) -' V)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite (G .order()) -' ((G .order()) -' V) -element Element of bool NAT
(Seg (G .order())) \ (Seg ((G .order()) -' ((G .order()) -' V))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(G .order()) - L is ext-real V55() real V57() set
V + L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
((G .order()) - L) + L is ext-real V55() real V57() set
L + V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(L + V) - V is ext-real V55() real V57() set
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),(((G .order()) -' V) + 1))),j) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
(G) is Relation-like NAT -defined Function-like total halting () () (G)
(G,(G)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
(G) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G) . ((G) .Lifespan()) is set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G))) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),(G .order())) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
(G) is Relation-like NAT -defined Function-like total halting () () (G)
(G,(G)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
(G) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G) . ((G) .Lifespan()) is set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G))) " is Relation-like Function-like set
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),(G .order())) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(G .order()))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
(G,(G)) is Relation-like NAT -defined Function-like total halting () () (G) (G)
(G,(G,(G)),(G .order())) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(G .order()))) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(G .order()))) " is Relation-like Function-like set
proj2 (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(G .order()))) ") is set
(G,(G)) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
rng (G,(G,(G)),(G .order())) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool NAT
Seg (G .order()) is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite G .order() -element Element of bool NAT
(G .order()) -' (G .order()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
Seg ((G .order()) -' (G .order())) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite (G .order()) -' (G .order()) -element Element of bool NAT
(Seg (G .order())) \ (Seg ((G .order()) -' (G .order()))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
Seg 0 is empty proper Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V30() V33() V34() V35() V36() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal 0 -element {} -element FinSequence-like FinSubsequence-like FinSequence-membered V55() real V57() complex-valued ext-real-valued real-valued natural-valued FinSequence-yielding finite-support Function-yielding V264() Element of bool NAT
(Seg (G .order())) \ (Seg 0) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
proj1 (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),(G .order()))) ") is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
(G) is Relation-like NAT -defined Function-like total halting () () (G)
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),V) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),V)) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
a is Element of the_Vertices_of G
b is Element of the_Vertices_of G
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) . b is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) . a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) . b) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),V)),a) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),V)),a),1) -bag is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags NAT
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),V)),b) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),V)),b),1) -bag is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags NAT
(G,(G)) is Relation-like NAT -defined Function-like total halting () () (G) (G)
(G,(G,(G)),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
(G,(G,(G)),V) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,(G,(G)),L) . b is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G)) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .order()) -' ((G,(G,(G)),L) . b) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .order()) - ((G,(G,(G)),L) . b) is ext-real V55() real V57() set
(G .order()) -' V is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .order()) - ((G .order()) - ((G,(G,(G)),L) . b)) is ext-real V55() real V57() set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),V)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),V)) is finite Element of bool (the_Vertices_of G)
dom (G,(G,(G)),V) is finite Element of bool (the_Vertices_of G)
(G,(G,(G)),V) . a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G)),V) is set
(G,(G,(G),V)) is Element of the_Vertices_of G
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
(G) is Relation-like NAT -defined Function-like total halting () () (G)
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
a is Element of the_Vertices_of G
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),L)),a) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(G,(G)) is Relation-like NAT -defined Function-like total halting () () (G) (G)
(G,(G,(G)),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G .order()) -' V is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),((G .order()) -' V)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((G .order()) -' V))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
(G) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G)) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G),((G .order()) -' V))) is Element of the_Vertices_of G
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((G .order()) -' V))) is finite Element of bool (the_Vertices_of G)
e1 is Element of the_Vertices_of G
{e1} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
G .AdjacentSet {e1} is finite Element of bool (the_Vertices_of G)
Seg (G .order()) is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite G .order() -element Element of bool NAT
(G .order()) -' L is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
Seg ((G .order()) -' L) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite (G .order()) -' L -element Element of bool NAT
(Seg (G .order())) \ (Seg ((G .order()) -' L)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(G .order()) - V is ext-real V55() real V57() set
(G .order()) - ((G .order()) -' V) is ext-real V55() real V57() set
(G .order()) - ((G .order()) - V) is ext-real V55() real V57() set
(G .order()) - L is ext-real V55() real V57() set
((G .order()) - ((G .order()) -' V)) + L is ext-real V55() real V57() set
((G .order()) - L) + L is ext-real V55() real V57() set
(G .order()) + L is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((G .order()) + L) - ((G .order()) -' V) is ext-real V55() real V57() set
(((G .order()) + L) - ((G .order()) -' V)) + ((G .order()) -' V) is ext-real V55() real V57() set
(G .order()) + ((G .order()) -' V) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L + (G .order()) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(L + (G .order())) - (G .order()) is ext-real V55() real V57() set
((G .order()) -' V) + (G .order()) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(((G .order()) -' V) + (G .order())) - (G .order()) is ext-real V55() real V57() set
(G,(G,(G)),((G .order()) -' V)) is set
(G,(G,(G)),L) . e1 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .order()) -' ((G .order()) -' V) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] set
the_Vertices_of G is non empty set
G . VertexSelector is set
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
(G) is Relation-like NAT -defined Function-like total halting () () (G)
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
(G,(G)) is Relation-like NAT -defined Function-like total halting () () (G) (G)
(G,(G,(G)),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
(G) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G)) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
b is Element of the_Vertices_of G
dom (G,(G,(G)),L) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
c is Element of the_Vertices_of G
va is Element of the_Vertices_of G
(G,(G,(G)),L) . c is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G)),L) . b is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G)),L) . va is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .order()) -' ((G,(G,(G)),L) . va) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .order()) -' ((G,(G,(G)),L) . c) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G)),((G .order()) -' ((G,(G,(G)),L) . va))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,(G),((G .order()) -' ((G,(G,(G)),L) . va))) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G,(G,(G)),((G .order()) -' ((G,(G,(G)),L) . c))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,(G),((G .order()) -' ((G,(G,(G)),L) . c))) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),((G .order()) -' ((G,(G,(G)),L) . c)))) is Relation-like the_Vertices_of G -defined Fin NAT -valued Function-like quasi_total finite finite-support Element of Funcs ((the_Vertices_of G),(Fin NAT))
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),((G .order()) -' ((G,(G,(G)),L) . c)))),c) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
((the_Vertices_of G),NAT,((PFuncs ((the_Vertices_of G),NAT)),(Fin NAT),(the_Vertices_of G),(G,(G),((G .order()) -' ((G,(G,(G)),L) . c)))),b) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
Seg (G .order()) is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite G .order() -element Element of bool NAT
(G .order()) -' ((G .order()) -' ((G,(G,(G)),L) . c)) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
Seg ((G .order()) -' ((G .order()) -' ((G,(G,(G)),L) . c))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite (G .order()) -' ((G .order()) -' ((G,(G,(G)),L) . c)) -element Element of bool NAT
(Seg (G .order())) \ (Seg ((G .order()) -' ((G .order()) -' ((G,(G,(G)),L) . c)))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
k is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((G .order()) -' ((G,(G,(G)),L) . va)))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
e is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
dom (G,(G,(G)),((G .order()) -' ((G,(G,(G)),L) . c))) is finite Element of bool (the_Vertices_of G)
(G .order()) - ((G,(G,(G)),L) . va) is ext-real V55() real V57() set
(G .order()) -' ((G .order()) -' ((G,(G,(G)),L) . va)) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .order()) - ((G .order()) - ((G,(G,(G)),L) . va)) is ext-real V55() real V57() set
rng (G,(G,(G)),((G .order()) -' ((G,(G,(G)),L) . va))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool NAT
Seg ((G .order()) -' ((G .order()) -' ((G,(G,(G)),L) . va))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite (G .order()) -' ((G .order()) -' ((G,(G,(G)),L) . va)) -element Element of bool NAT
(Seg (G .order())) \ (Seg ((G .order()) -' ((G .order()) -' ((G,(G,(G)),L) . va)))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
dom (G,(G,(G)),((G .order()) -' ((G,(G,(G)),L) . va))) is finite Element of bool (the_Vertices_of G)
(G,(G,(G)),((G .order()) -' ((G,(G,(G)),L) . va))) . b is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G)),((G .order()) -' ((G,(G,(G)),L) . va))) is set
(G,(G,(G),((G .order()) -' ((G,(G,(G)),L) . va)))) is Element of the_Vertices_of G
(G,(G,(G)),((G .order()) -' ((G,(G,(G)),L) . c))) . va is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((G .order()) -' ((G,(G,(G)),L) . c)))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
{va} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
G .AdjacentSet {va} is finite Element of bool (the_Vertices_of G)
R is Element of the_Vertices_of G
(G,(G,(G)),((G .order()) -' ((G,(G,(G)),L) . c))) . R is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
{R} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
G .AdjacentSet {R} is finite Element of bool (the_Vertices_of G)
(k,1) -bag is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags NAT
((k,1) -bag) . ((G,(G,(G)),((G .order()) -' ((G,(G,(G)),L) . c))) . va) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(e,1) -bag is Relation-like NAT -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags NAT
((e,1) -bag) . ((G,(G,(G)),((G .order()) -' ((G,(G,(G)),L) . c))) . va) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
[((k,1) -bag),((e,1) -bag)] is V1() Element of [:(Bags NAT),(Bags NAT):]
{((k,1) -bag),((e,1) -bag)} is non empty functional finite set
{((k,1) -bag)} is non empty trivial functional finite 1 -element set
{{((k,1) -bag),((e,1) -bag)},{((k,1) -bag)}} is non empty finite finite-membered set
R is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
((k,1) -bag) . R is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((e,1) -bag) . R is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
i is epsilon-transitive epsilon-connected ordinal set
((k,1) -bag) . i is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((e,1) -bag) . i is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
R is epsilon-transitive epsilon-connected ordinal set
((k,1) -bag) . R is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((e,1) -bag) . R is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
R is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
((k,1) -bag) . R is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((e,1) -bag) . R is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
i is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
ir is epsilon-transitive epsilon-connected ordinal set
ir is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
{ b1 where b1 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT : not ir <= b1 } is set
((k,1) -bag) . ir is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((e,1) -bag) . ir is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
j is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
{ b1 where b1 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT : not i <= b1 } is set
((k,1) -bag) . i is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((G .order()) -' ((G,(G,(G)),L) . c)))) is finite Element of bool (the_Vertices_of G)
ir is Element of the_Vertices_of G
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((G .order()) -' ((G,(G,(G)),L) . c)))) . ir is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
{ir} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
G .AdjacentSet {ir} is finite Element of bool (the_Vertices_of G)
(G,(G,(G)),L) . ir is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .order()) -' ((G,(G,(G)),L) . ir) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .order()) - ((G,(G,(G)),L) . ir) is ext-real V55() real V57() set
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),L)) is finite Element of bool (the_Vertices_of G)
(G .order()) -' ((G .order()) -' ((G,(G,(G)),L) . ir)) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .order()) - ((G .order()) - ((G,(G,(G)),L) . ir)) is ext-real V55() real V57() set
(G,(G,(G)),((G .order()) -' ((G,(G,(G)),L) . ir))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,(G),((G .order()) -' ((G,(G,(G)),L) . ir))) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
(G,(G,(G)),((G .order()) -' ((G,(G,(G)),L) . ir))) is set
(G,(G,(G),((G .order()) -' ((G,(G,(G)),L) . ir)))) is Element of the_Vertices_of G
[ir,i] is V1() Element of [:(the_Vertices_of G),NAT:]
{ir,i} is non empty finite set
{ir} is non empty trivial finite 1 -element set
{{ir,i},{ir}} is non empty finite finite-membered set
[va,((G,(G,(G)),((G .order()) -' ((G,(G,(G)),L) . c))) . va)] is V1() Element of [:(the_Vertices_of G),NAT:]
{va,((G,(G,(G)),((G .order()) -' ((G,(G,(G)),L) . c))) . va)} is non empty finite set
{va} is non empty trivial finite 1 -element set
{{va,((G,(G,(G)),((G .order()) -' ((G,(G,(G)),L) . c))) . va)},{va}} is non empty finite finite-membered set
kr is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
kr is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
rng (G,(G,(G)),((G .order()) -' ((G,(G,(G)),L) . ir))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool NAT
Seg ((G .order()) -' ((G .order()) -' ((G,(G,(G)),L) . ir))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite (G .order()) -' ((G .order()) -' ((G,(G,(G)),L) . ir)) -element Element of bool NAT
(Seg (G .order())) \ (Seg ((G .order()) -' ((G .order()) -' ((G,(G,(G)),L) . ir)))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
dom (G,(G,(G)),((G .order()) -' ((G,(G,(G)),L) . ir))) is finite Element of bool (the_Vertices_of G)
(G,(G,(G)),((G .order()) -' ((G,(G,(G)),L) . ir))) . b is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
kr is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
kr is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G),((G .order()) -' ((G,(G,(G)),L) . ir)))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
R is epsilon-transitive epsilon-connected ordinal set
((k,1) -bag) . R is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((e,1) -bag) . R is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
vb is Element of the_Vertices_of G
(G,(G,(G)),L) . vb is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
vb is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
rng (G,(G,(G)),L) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool NAT
vc is Element of the_Vertices_of G
(G,(G,(G)),L) . vc is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .order()) -' L is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
Seg ((G .order()) -' L) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite (G .order()) -' L -element Element of bool NAT
(Seg (G .order())) \ (Seg ((G .order()) -' L)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
vc is Element of the_Vertices_of G
(G,(G,(G)),L) . vc is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
vb is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
vb is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
vc is Element of the_Vertices_of G
(G,(G,(G)),L) . vc is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
vc is Element of the_Vertices_of G
(G,(G,(G)),L) . vc is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
P is Element of the_Vertices_of G
(G,(G,(G)),L) . P is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite chordal set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
L is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
dom L is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
V is non empty Relation-like NAT -defined the_Vertices_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support VertexScheme of G
V " is Relation-like Function-like set
dom V is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite Element of bool NAT
a is Element of the_Vertices_of G
b is Element of the_Vertices_of G
L . b is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
c is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
va is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V /. c is Element of the_Vertices_of G
V /. va is Element of the_Vertices_of G
V . va is set
V . c is set
the_Edges_of G is finite set
G . EdgeSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty finite set
2 * 1 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() even Element of NAT
(2 * 1) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
2 * 0 is empty Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V30() V33() V34() V35() V36() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V55() real V57() V59() complex-valued ext-real-valued real-valued natural-valued FinSequence-yielding finite-support Function-yielding V264() even Element of NAT
(2 * 0) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
a - 1 is ext-real V55() real V57() set
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(a + 1) - 1 is ext-real V55() real V57() set
b is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
b - 1 is ext-real V55() real V57() set
c is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
c .length() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
c .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support EdgeSeq of G
len (c .edgeSeq()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
va is Element of the_Vertices_of G
len c is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
(len c) - 2 is ext-real V55() real V57() set
c . ((len c) - 2) is set
vb is Element of the_Vertices_of G
c . 3 is set
vc is Element of the_Vertices_of G
c .last() is Element of the_Vertices_of G
c . (len c) is set
P is Element of the_Vertices_of G
c .first() is Element of the_Vertices_of G
c . 1 is set
L . P is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . vc is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . vb is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . va is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
c .vertices() is finite Element of bool (the_Vertices_of G)
c .vertexSeq() is Relation-like NAT -defined the_Vertices_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support VertexSeq of G
rng (c .vertexSeq()) is finite Element of bool (the_Vertices_of G)
c is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
c .length() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
c .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support EdgeSeq of G
len (c .edgeSeq()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
va is Element of the_Vertices_of G
len c is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
(len c) - 2 is ext-real V55() real V57() set
c . ((len c) - 2) is set
vb is Element of the_Vertices_of G
c . 3 is set
vc is Element of the_Vertices_of G
c .last() is Element of the_Vertices_of G
c . (len c) is set
P is Element of the_Vertices_of G
c .first() is Element of the_Vertices_of G
c . 1 is set
L . P is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . vc is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . vb is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . va is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
c .vertices() is finite Element of bool (the_Vertices_of G)
c .vertexSeq() is Relation-like NAT -defined the_Vertices_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support VertexSeq of G
rng (c .vertexSeq()) is finite Element of bool (the_Vertices_of G)
2 * (b - 1) is ext-real V55() real V57() even set
(2 * (b - 1)) + 1 is non empty ext-real V55() real V57() non even set
2 * 4 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() even Element of NAT
2 * b is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() even Element of NAT
8 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
8 - 1 is ext-real V55() real V57() set
(2 * b) - 1 is non empty ext-real V55() real V57() non even set
dom c is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
e1 is set
1 + 2 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
e1 is set
e1 is Element of the_Vertices_of G
L . e1 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
e2 is set
j is Element of the_Vertices_of G
L . j is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
j is set
c .addEdge e2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
(c .last()) .adj e2 is Element of the_Vertices_of G
G .walkOf ((c .last()),e2,((c .last()) .adj e2)) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
c .append (G .walkOf ((c .last()),e2,((c .last()) .adj e2))) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
(c .addEdge e2) .reverse() is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
len ((c .addEdge e2) .reverse()) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
len (c .addEdge e2) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
dom (c .addEdge e2) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(c .addEdge e2) . 3 is set
(len ((c .addEdge e2) .reverse())) - 3 is ext-real V55() real V57() set
((len ((c .addEdge e2) .reverse())) - 3) + 1 is ext-real V55() real V57() set
((c .addEdge e2) .reverse()) . (((len ((c .addEdge e2) .reverse())) - 3) + 1) is set
(c .addEdge e2) .first() is Element of the_Vertices_of G
(c .addEdge e2) . 1 is set
((c .addEdge e2) .reverse()) .last() is Element of the_Vertices_of G
((c .addEdge e2) .reverse()) . (len ((c .addEdge e2) .reverse())) is set
(len c) + 2 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
(len (c .addEdge e2)) - 2 is ext-real V55() real V57() set
(c .addEdge e2) . ((len (c .addEdge e2)) - 2) is set
(len ((c .addEdge e2) .reverse())) - ((len (c .addEdge e2)) - 2) is ext-real V55() real V57() set
((len ((c .addEdge e2) .reverse())) - ((len (c .addEdge e2)) - 2)) + 1 is ext-real V55() real V57() set
((c .addEdge e2) .reverse()) . (((len ((c .addEdge e2) .reverse())) - ((len (c .addEdge e2)) - 2)) + 1) is set
(c .addEdge e2) .last() is Element of the_Vertices_of G
(c .addEdge e2) . (len (c .addEdge e2)) is set
((c .addEdge e2) .reverse()) .first() is Element of the_Vertices_of G
((c .addEdge e2) .reverse()) . 1 is set
(c .addEdge e2) .length() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(c .addEdge e2) .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support EdgeSeq of G
len ((c .addEdge e2) .edgeSeq()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(b - 1) + 1 is ext-real V55() real V57() set
((c .addEdge e2) .reverse()) .length() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((c .addEdge e2) .reverse()) .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support EdgeSeq of G
len (((c .addEdge e2) .reverse()) .edgeSeq()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
b + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(b + 1) - 1 is ext-real V55() real V57() set
e is set
((c .addEdge e2) .reverse()) .vertices() is finite Element of bool (the_Vertices_of G)
((c .addEdge e2) .reverse()) .vertexSeq() is Relation-like NAT -defined the_Vertices_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support VertexSeq of G
rng (((c .addEdge e2) .reverse()) .vertexSeq()) is finite Element of bool (the_Vertices_of G)
(c .addEdge e2) .vertices() is finite Element of bool (the_Vertices_of G)
(c .addEdge e2) .vertexSeq() is Relation-like NAT -defined the_Vertices_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support VertexSeq of G
rng ((c .addEdge e2) .vertexSeq()) is finite Element of bool (the_Vertices_of G)
{e1} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
(c .vertices()) \/ {e1} is non empty finite Element of bool (the_Vertices_of G)
L . e is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . e is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
11 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
11 + (G .order()) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
len V is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V .followSet a is finite Element of bool (the_Vertices_of G)
G .edgesBetween (V .followSet a) is finite Element of bool (the_Edges_of G)
bool (the_Edges_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean set
G .edgesInto (V .followSet a) is finite Element of bool (the_Edges_of G)
G .edgesOutOf (V .followSet a) is finite Element of bool (the_Edges_of G)
(G .edgesInto (V .followSet a)) /\ (G .edgesOutOf (V .followSet a)) is finite Element of bool (the_Edges_of G)
V . a is set
b is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite chordal inducedSubgraph of G,V .followSet a,G .edgesBetween (V .followSet a)
the_Vertices_of b is non empty finite set
b . VertexSelector is set
c is Element of the_Vertices_of b
b is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite chordal inducedSubgraph of G,V .followSet a,G .edgesBetween (V .followSet a)
the_Vertices_of b is non empty finite set
b . VertexSelector is set
c is Element of the_Vertices_of b
va is Element of the_Vertices_of b
vb is Element of the_Vertices_of b
the_Vertices_of b is non empty finite Element of bool (the_Vertices_of G)
P is Element of the_Vertices_of G
L . P is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
e1 is Element of the_Vertices_of G
L . e1 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
e2 is Element of the_Vertices_of G
j is Element of the_Vertices_of G
L . j is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . e2 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
vc is Element of the_Vertices_of G
e2 is Element of the_Vertices_of G
j is Element of the_Vertices_of G
L . j is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . e2 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
vc is Element of the_Vertices_of G
vc is Element of the_Vertices_of G
vc is Element of the_Vertices_of G
e2 is Element of the_Vertices_of G
j is Element of the_Vertices_of G
L . j is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . e2 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
e2 is Element of the_Vertices_of G
j is Element of the_Vertices_of G
L . j is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . e2 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
rng V is non empty finite Element of bool (the_Vertices_of G)
k is set
V . k is set
e is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V /. e is Element of the_Vertices_of G
L . (V /. e) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
k is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V /. k is Element of the_Vertices_of G
L . (V /. k) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
k is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V /. k is Element of the_Vertices_of G
L . (V /. k) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
D is Element of the_Vertices_of G
i is set
V . i is set
ir is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V /. ir is Element of the_Vertices_of G
0 + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
D .. V is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
e is Element of the_Vertices_of G
V /. a is Element of the_Vertices_of G
L . D is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . e is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
R is Element of the_Vertices_of G
4 - 1 is ext-real V55() real V57() set
L . R is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
ir is Element of the_Vertices_of G
L . ir is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
{R,e,D} is non empty finite Element of bool (the_Vertices_of G)
j is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
len j is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
j .length() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
j .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support EdgeSeq of G
len (j .edgeSeq()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
k is set
kr is set
j .edges() is finite Element of bool (the_Edges_of G)
rng (j .edgeSeq()) is finite Element of bool (the_Edges_of G)
{k,kr} is non empty finite set
j .vertices() is finite Element of bool (the_Vertices_of G)
j .vertexSeq() is Relation-like NAT -defined the_Vertices_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support VertexSeq of G
rng (j .vertexSeq()) is finite Element of bool (the_Vertices_of G)
j . 1 is set
j . 3 is set
j . 5 is set
j .last() is Element of the_Vertices_of G
j . (len j) is set
jr is set
j .addEdge jr is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
(j .last()) .adj jr is Element of the_Vertices_of G
G .walkOf ((j .last()),jr,((j .last()) .adj jr)) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
j .append (G .walkOf ((j .last()),jr,((j .last()) .adj jr))) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
(j .addEdge jr) .reverse() is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
(j .addEdge jr) .last() is Element of the_Vertices_of G
len (j .addEdge jr) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
(j .addEdge jr) . (len (j .addEdge jr)) is set
5 + 2 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
dom (j .addEdge jr) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
dom j is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(j .addEdge jr) . 5 is set
7 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
7 - 5 is ext-real V55() real V57() set
(7 - 5) + 1 is ext-real V55() real V57() set
((j .addEdge jr) .reverse()) . ((7 - 5) + 1) is set
7 - 7 is ext-real V55() real V57() set
(7 - 7) + 1 is ext-real V55() real V57() set
((j .addEdge jr) .reverse()) . ((7 - 7) + 1) is set
((j .addEdge jr) .reverse()) .first() is Element of the_Vertices_of G
((j .addEdge jr) .reverse()) . 1 is set
(j .addEdge jr) . 3 is set
(j .addEdge jr) .length() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(j .addEdge jr) .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support EdgeSeq of G
len ((j .addEdge jr) .edgeSeq()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
2 + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((j .addEdge jr) .reverse()) .length() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((j .addEdge jr) .reverse()) .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support EdgeSeq of G
len (((j .addEdge jr) .reverse()) .edgeSeq()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
3 + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(3 + 1) - 1 is ext-real V55() real V57() set
(j .addEdge jr) . 1 is set
(len (j .addEdge jr)) - 1 is ext-real V55() real V57() even set
((len (j .addEdge jr)) - 1) + 1 is non empty ext-real V55() real V57() non even set
((j .addEdge jr) .reverse()) . (((len (j .addEdge jr)) - 1) + 1) is set
((j .addEdge jr) .reverse()) .last() is Element of the_Vertices_of G
len ((j .addEdge jr) .reverse()) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
((j .addEdge jr) .reverse()) . (len ((j .addEdge jr) .reverse())) is set
j .first() is Element of the_Vertices_of G
x is set
L . x is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . x is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . x is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(len j) - 2 is ext-real V55() real V57() set
j . ((len j) - 2) is set
x is set
x is set
((j .addEdge jr) .reverse()) .vertices() is finite Element of bool (the_Vertices_of G)
((j .addEdge jr) .reverse()) .vertexSeq() is Relation-like NAT -defined the_Vertices_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support VertexSeq of G
rng (((j .addEdge jr) .reverse()) .vertexSeq()) is finite Element of bool (the_Vertices_of G)
(j .addEdge jr) .vertices() is finite Element of bool (the_Vertices_of G)
(j .addEdge jr) .vertexSeq() is Relation-like NAT -defined the_Vertices_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support VertexSeq of G
rng ((j .addEdge jr) .vertexSeq()) is finite Element of bool (the_Vertices_of G)
{ir} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
(j .vertices()) \/ {ir} is non empty finite Element of bool (the_Vertices_of G)
L . x is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . x is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
7 - 3 is ext-real V55() real V57() set
(7 - 3) + 1 is ext-real V55() real V57() set
((j .addEdge jr) .reverse()) . ((7 - 3) + 1) is set
(len ((j .addEdge jr) .reverse())) - 2 is ext-real V55() real V57() set
((j .addEdge jr) .reverse()) . ((len ((j .addEdge jr) .reverse())) - 2) is set
(G .order()) + 11 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((G .order()) + 11) - 1 is ext-real V55() real V57() set
ir is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
ir .length() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
ir .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support EdgeSeq of G
len (ir .edgeSeq()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
j is Element of the_Vertices_of G
len ir is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
(len ir) - 2 is ext-real V55() real V57() set
ir . ((len ir) - 2) is set
k is Element of the_Vertices_of G
ir . 3 is set
kr is Element of the_Vertices_of G
ir .last() is Element of the_Vertices_of G
ir . (len ir) is set
jr is Element of the_Vertices_of G
ir .first() is Element of the_Vertices_of G
ir . 1 is set
L . jr is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . kr is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . k is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . j is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
ir .vertices() is finite Element of bool (the_Vertices_of G)
ir .vertexSeq() is Relation-like NAT -defined the_Vertices_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support VertexSeq of G
rng (ir .vertexSeq()) is finite Element of bool (the_Vertices_of G)
ir is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
ir .length() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
ir .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support EdgeSeq of G
len (ir .edgeSeq()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
j is Element of the_Vertices_of G
len ir is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
(len ir) - 2 is ext-real V55() real V57() set
ir . ((len ir) - 2) is set
k is Element of the_Vertices_of G
ir . 3 is set
kr is Element of the_Vertices_of G
ir .last() is Element of the_Vertices_of G
ir . (len ir) is set
jr is Element of the_Vertices_of G
ir .first() is Element of the_Vertices_of G
ir . 1 is set
L . jr is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . kr is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . k is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . j is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
10 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .order()) + 10 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
2 * ((G .order()) + 10) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() even Element of NAT
(2 * ((G .order()) + 10)) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
2 * (G .order()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() even Element of NAT
21 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(2 * (G .order())) + 21 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((2 * (G .order())) + 21) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
ir .vertexSeq() is Relation-like NAT -defined the_Vertices_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support VertexSeq of G
len (ir .vertexSeq()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
2 * (len (ir .vertexSeq())) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() even Element of NAT
(G .order()) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite chordal set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
(G) is Relation-like NAT -defined Function-like total halting () () (G)
(G,(G)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
(G) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G) . ((G) .Lifespan()) is set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G))) " is Relation-like Function-like set
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G))) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(G,(G)) is Relation-like NAT -defined Function-like total halting () () (G) (G)
(G,(G)) .Result() is set
(G,(G)) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G)) . ((G,(G)) .Lifespan()) is set
V is non empty Relation-like NAT -defined the_Vertices_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support VertexScheme of G
V " is Relation-like Function-like set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
(the_Vertices_of G) --> 0 is non empty Relation-like the_Vertices_of G -defined NAT -valued RAT -valued INT -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Function-yielding V264() Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
{0} is non empty trivial functional complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:(the_Vertices_of G),{0}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
[{},((the_Vertices_of G) --> 0)] is V1() set
{{},((the_Vertices_of G) --> 0)} is non empty functional finite finite-membered set
{{{},((the_Vertices_of G) --> 0)},{{}}} is non empty finite finite-membered set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
rng {} is empty trivial Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V30() V33() V34() V35() V36() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V55() real V57() complex-valued ext-real-valued real-valued natural-valued V72() decreasing non-decreasing non-increasing FinSequence-yielding finite-support V224() Function-yielding V264() Element of bool RAT
bool RAT is non empty cup-closed diff-closed preBoolean set
rng ((the_Vertices_of G) --> 0) is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite 1 -element Element of bool RAT
dom ((the_Vertices_of G) --> 0) is non empty finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
dom {} is empty proper Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V30() V33() V34() V35() V36() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V55() real V57() complex-valued ext-real-valued real-valued natural-valued FinSequence-yielding finite-support Function-yielding V264() Element of bool NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
L is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
choose (the_Vertices_of G) is Element of the_Vertices_of G
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
(the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)) is finite Element of bool (the_Vertices_of G)
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) | ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))) is Relation-like the_Vertices_of G -defined (the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)) -defined the_Vertices_of G -defined NAT -valued RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
rng (((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) | ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool RAT
bool RAT is non empty cup-closed diff-closed preBoolean set
dom (((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) | ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)))) is finite Element of bool ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)))
bool ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))) is non empty finite finite-membered cup-closed diff-closed preBoolean set
dom ((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) is finite Element of bool (the_Vertices_of G)
(dom ((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L)) /\ ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))) is finite Element of bool (the_Vertices_of G)
(the_Vertices_of G) /\ (the_Vertices_of G) is finite set
((the_Vertices_of G) /\ (the_Vertices_of G)) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)) is finite Element of bool ((the_Vertices_of G) /\ (the_Vertices_of G))
bool ((the_Vertices_of G) /\ (the_Vertices_of G)) is non empty finite finite-membered cup-closed diff-closed preBoolean set
vb is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite set
max vb is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() set
{(max vb)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) | ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)))) " {(max vb)} is finite Element of bool (the_Vertices_of G)
choose ((((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) | ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)))) " {(max vb)}) is Element of (((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) | ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)))) " {(max vb)}
e1 is Element of the_Vertices_of G
e2 is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite set
j is Relation-like Function-like set
proj2 j is set
max e2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() set
{(max e2)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
j " {(max e2)} is set
choose (j " {(max e2)}) is Element of j " {(max e2)}
V is Element of the_Vertices_of G
a is Element of the_Vertices_of G
va is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite set
vb is Relation-like Function-like set
proj2 vb is set
b is Element of the_Vertices_of G
max va is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() set
{(max va)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
vb " {(max va)} is set
choose (vb " {(max va)}) is Element of vb " {(max va)}
vc is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite set
P is Relation-like Function-like set
proj2 P is set
c is Element of the_Vertices_of G
max vc is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() set
{(max vc)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
P " {(max vc)} is set
choose (P " {(max vc)}) is Element of P " {(max vc)}
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
L is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
V is set
{V} is non empty trivial finite 1 -element set
G .AdjacentSet {V} is finite Element of bool (the_Vertices_of G)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) is finite Element of bool (the_Vertices_of G)
(G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)) is finite Element of bool (the_Vertices_of G)
(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
[((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1)] is V1() set
{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1)} is non empty functional finite set
{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)} is non empty trivial functional finite 1 -element set
{{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1)},{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)}} is non empty finite finite-membered set
va is set
rng (((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool RAT
bool RAT is non empty cup-closed diff-closed preBoolean set
proj1 (((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1) is set
vb is set
(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1) . vb is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
dom ((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) is finite Element of bool (the_Vertices_of G)
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
L is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
V is Element of the_Vertices_of G
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G .order()) -' a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V .--> ((G .order()) -' a) is Relation-like the_Vertices_of G -defined {V} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{V} is non empty trivial finite 1 -element set
{V} --> ((G .order()) -' a) is non empty Relation-like {V} -defined NAT -valued RAT -valued INT -valued {((G .order()) -' a)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{V},{((G .order()) -' a)}:]
{((G .order()) -' a)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{V},{((G .order()) -' a)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{V},{((G .order()) -' a)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) +* (V .--> ((G .order()) -' a)) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
[(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) +* (V .--> ((G .order()) -' a))),((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L)] is V1() set
{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) +* (V .--> ((G .order()) -' a))),((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L)} is non empty functional finite set
{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) +* (V .--> ((G .order()) -' a)))} is non empty trivial functional finite 1 -element set
{{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) +* (V .--> ((G .order()) -' a))),((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L)},{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) +* (V .--> ((G .order()) -' a)))}} is non empty finite finite-membered set
proj1 (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) +* (V .--> ((G .order()) -' a))) is set
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) is finite Element of bool (the_Vertices_of G)
{V} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
(dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)) \/ {V} is non empty finite Element of bool (the_Vertices_of G)
rng (V .--> ((G .order()) -' a)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool RAT
bool RAT is non empty cup-closed diff-closed preBoolean set
{((G .order()) -' a)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element Element of bool NAT
rng ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool NAT
(rng ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)) \/ (rng (V .--> ((G .order()) -' a))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() set
rng (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) +* (V .--> ((G .order()) -' a))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool RAT
va is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G,va,V) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),va) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
G .AdjacentSet {V} is finite Element of bool (the_Vertices_of G)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va) is finite Element of bool (the_Vertices_of G)
(G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va)) is finite Element of bool (the_Vertices_of G)
(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),va),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va))),1) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
[((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),va),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va))),1)] is V1() set
{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),va),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va))),1)} is non empty functional finite set
{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va)} is non empty trivial functional finite 1 -element set
{{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),va),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va))),1)},{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va)}} is non empty finite finite-membered set
va is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
b is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G,va,V) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),va) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
G .AdjacentSet {V} is finite Element of bool (the_Vertices_of G)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va) is finite Element of bool (the_Vertices_of G)
(G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va)) is finite Element of bool (the_Vertices_of G)
(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),va),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va))),1) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
[((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),va),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va))),1)] is V1() set
{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),va),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va))),1)} is non empty functional finite set
{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va)} is non empty trivial functional finite 1 -element set
{{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),va),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va))),1)},{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),va)}} is non empty finite finite-membered set
vb is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
c is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G,vb,V) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),vb) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb) is finite Element of bool (the_Vertices_of G)
(G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb)) is finite Element of bool (the_Vertices_of G)
(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),vb),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb))),1) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
[((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),vb),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb))),1)] is V1() set
{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),vb),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb))),1)} is non empty functional finite set
{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb)} is non empty trivial functional finite 1 -element set
{{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),vb),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb))),1)},{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb)}} is non empty finite finite-membered set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
L is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L) is Element of the_Vertices_of G
(G,L,(G,L),(card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)))) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] set
the_Vertices_of G is non empty set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
the Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
V is Relation-like NAT -defined Function-like total set
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V . a is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] set
L is Relation-like NAT -defined Function-like total (G)
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
L . V is set
the_Vertices_of G is non empty set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] set
L is Relation-like NAT -defined Function-like total (G)
L .Result() is set
L .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . (L .Lifespan()) is set
the_Vertices_of G is non empty set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
L is Relation-like NAT -defined Function-like total (G)
V is Relation-like NAT -defined Function-like total set
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V . a is set
(G,L,a) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,L,a)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
a is Relation-like NAT -defined Function-like total (G)
b is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,a,b) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,L,b) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,L,b)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
V is Relation-like NAT -defined Function-like total (G)
a is Relation-like NAT -defined Function-like total (G)
b is set
V . b is set
c is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,c) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,L,c)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
a . b is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
(G) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
(the_Vertices_of G) --> 0 is non empty Relation-like the_Vertices_of G -defined NAT -valued RAT -valued INT -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Function-yielding V264() Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
[:(the_Vertices_of G),{0}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
[{},((the_Vertices_of G) --> 0)] is V1() set
{{},((the_Vertices_of G) --> 0)} is non empty functional finite finite-membered set
{{{},((the_Vertices_of G) --> 0)},{{}}} is non empty finite finite-membered set
V is set
L is set
a is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G,a) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
b is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
V is set
L is set
V is set
L is set
L is set
V is set
b is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
c is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
a is set
va is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G,c) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
vb is set
V is set
L is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L is Relation-like Function-like set
proj1 L is set
L . 0 is set
V is Relation-like NAT -defined Function-like total set
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V . a is set
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V . (a + 1) is set
b is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
c is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
va is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G,c) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
V . 0 is set
a is Relation-like NAT -defined Function-like total (G)
(G,a,0) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
b is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
b + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,a,(b + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G,a,b) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G,(G,a,b)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
c is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
va is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
vb is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G,va) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
L is Relation-like NAT -defined Function-like total (G)
(G,L,0) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
V is Relation-like NAT -defined Function-like total (G)
(G,V,0) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,L,a) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G,V,a) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,(a + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G,(G,V,a)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G,V,(a + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,a) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G,V,a) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,(a + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G,V,(a + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
a is set
L . a is set
V . a is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
(G) is Relation-like NAT -defined Function-like total (G)
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G) . V is set
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G) . a is set
V + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G) . (V + 1) is set
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G) . (a + 1) is set
(G,(G),(V + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
(G,(G),V) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G,(G,(G),V)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
(G) is Relation-like NAT -defined Function-like total (G)
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
(G) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
(the_Vertices_of G) --> 0 is non empty Relation-like the_Vertices_of G -defined NAT -valued RAT -valued INT -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Function-yielding V264() Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
[:(the_Vertices_of G),{0}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
[{},((the_Vertices_of G) --> 0)] is V1() set
{{},((the_Vertices_of G) --> 0)} is non empty functional finite finite-membered set
{{{},((the_Vertices_of G) --> 0)},{{}}} is non empty finite finite-membered set
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
L is set
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G)) . L is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(the_Vertices_of G) --> {} is non empty Relation-like the_Vertices_of G -defined RAT -valued INT -valued {{}} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Function-yielding V264() Element of bool [:(the_Vertices_of G),{{}}:]
[:(the_Vertices_of G),{{}}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),{{}}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
[{},((the_Vertices_of G) --> {})] is V1() set
{{},((the_Vertices_of G) --> {})} is non empty functional finite finite-membered set
{{{},((the_Vertices_of G) --> {})},{{}}} is non empty finite finite-membered set
[{},((the_Vertices_of G) --> {})] `2 is set
dom ((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G)) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
rng ((the_Vertices_of G) --> {}) is non empty trivial functional complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element Element of bool {{}}
bool {{}} is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
[:(the_Vertices_of G),(rng ((the_Vertices_of G) --> {})):] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),(rng ((the_Vertices_of G) --> {})):] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
b is set
a is Relation-like the_Vertices_of G -defined rng ((the_Vertices_of G) --> {}) -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Function-yielding V264() Element of bool [:(the_Vertices_of G),(rng ((the_Vertices_of G) --> {})):]
dom a is finite Element of bool (the_Vertices_of G)
a . b is Relation-like Function-like ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() finite-support Element of NAT
b is set
a is Relation-like the_Vertices_of G -defined rng ((the_Vertices_of G) --> {}) -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Function-yielding V264() Element of bool [:(the_Vertices_of G),(rng ((the_Vertices_of G) --> {})):]
dom a is finite Element of bool (the_Vertices_of G)
a . b is Relation-like Function-like ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() finite-support Element of NAT
b is set
a is Relation-like the_Vertices_of G -defined rng ((the_Vertices_of G) --> {}) -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Function-yielding V264() Element of bool [:(the_Vertices_of G),(rng ((the_Vertices_of G) --> {})):]
dom a is finite Element of bool (the_Vertices_of G)
a is Relation-like the_Vertices_of G -defined rng ((the_Vertices_of G) --> {}) -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Function-yielding V264() Element of bool [:(the_Vertices_of G),(rng ((the_Vertices_of G) --> {})):]
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
L is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
(G,L) is Element of the_Vertices_of G
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) . (G,L) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V is set
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) . V is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)) is finite Element of bool (the_Vertices_of G)
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) | ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))) is Relation-like the_Vertices_of G -defined (the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)) -defined the_Vertices_of G -defined NAT -valued RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
vb is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite set
vc is Relation-like Function-like set
proj2 vc is set
max vb is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() set
{(max vb)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
vc " {(max vb)} is set
choose (vc " {(max vb)}) is Element of vc " {(max vb)}
proj1 vc is set
dom ((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) is finite Element of bool (the_Vertices_of G)
(dom ((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L)) /\ ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))) is finite Element of bool (the_Vertices_of G)
vc . (G,L) is set
vc . V is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
L is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(G,L) is Element of the_Vertices_of G
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
(the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)) is finite Element of bool (the_Vertices_of G)
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) | ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))) is Relation-like the_Vertices_of G -defined (the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)) -defined the_Vertices_of G -defined NAT -valued RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
va is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite set
vb is Relation-like Function-like set
proj2 vb is set
max va is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() set
{(max va)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
vb " {(max va)} is set
choose (vb " {(max va)}) is Element of vb " {(max va)}
proj1 vb is set
dom ((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) is finite Element of bool (the_Vertices_of G)
(dom ((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L)) /\ ((the_Vertices_of G) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))) is finite Element of bool (the_Vertices_of G)
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
L is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
a is set
V is set
{V} is non empty trivial finite 1 -element set
G .AdjacentSet {V} is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) . a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,L,V) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) is finite Element of bool (the_Vertices_of G)
(G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)) is finite Element of bool (the_Vertices_of G)
(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
[((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1)] is V1() set
{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1)} is non empty functional finite set
{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)} is non empty trivial functional finite 1 -element set
{{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1)},{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)}} is non empty finite finite-membered set
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,L,V)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,L,V)) . a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
[((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1)] `2 is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
L is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
a is set
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) . a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V is set
(G,L,V) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
{V} is non empty trivial finite 1 -element set
G .AdjacentSet {V} is finite Element of bool (the_Vertices_of G)
(G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)) is finite Element of bool (the_Vertices_of G)
(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
[((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1)] is V1() set
{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1)} is non empty functional finite set
{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)} is non empty trivial functional finite 1 -element set
{{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1)},{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)}} is non empty finite finite-membered set
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,L,V)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,L,V)) . a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
[((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1)] `2 is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
L is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
dom ((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) is finite Element of bool (the_Vertices_of G)
a is set
V is set
{V} is non empty trivial finite 1 -element set
G .AdjacentSet {V} is finite Element of bool (the_Vertices_of G)
(G,L,V) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)) is finite Element of bool (the_Vertices_of G)
(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
[((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1)] is V1() set
{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1)} is non empty functional finite set
{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)} is non empty trivial functional finite 1 -element set
{{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1)},{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)}} is non empty finite finite-membered set
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,L,V)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,L,V)) . a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) . a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) . a) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
[((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1)] `2 is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
L is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
dom ((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
V is set
(G,L,V) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
{V} is non empty trivial finite 1 -element set
G .AdjacentSet {V} is finite Element of bool (the_Vertices_of G)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L) is finite Element of bool (the_Vertices_of G)
(G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)) is finite Element of bool (the_Vertices_of G)
(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
[((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1)] is V1() set
{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1)} is non empty functional finite set
{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)} is non empty trivial functional finite 1 -element set
{{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1)},{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L)}} is non empty finite finite-membered set
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,L,V)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
dom ((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,L,V)) is finite Element of bool (the_Vertices_of G)
[((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),L),((G .AdjacentSet {V}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),L))),1)] `2 is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
the_Vertices_of G is non empty finite set
G . VertexSelector is set
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
(G) is Relation-like NAT -defined Function-like total () (G)
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(L + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(L + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
(G,(G,(G),L)) is Element of the_Vertices_of G
(G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G),L)) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L))))) is Relation-like the_Vertices_of G -defined {(G,(G,(G),L))} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(G,(G,(G),L))} is non empty trivial finite 1 -element set
{(G,(G,(G),L))} --> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L))))) is non empty Relation-like {(G,(G,(G),L))} -defined NAT -valued RAT -valued INT -valued {((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)))))} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{(G,(G,(G),L))},{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)))))}:]
{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)))))} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{(G,(G,(G),L))},{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)))))}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{(G,(G,(G),L))},{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)))))}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)))))) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
(G,(G,(G),L)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G,(G,(G),L),(G,(G,(G),L)),(card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L))))) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),L)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
[(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L))))))),((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),L))] is V1() set
{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L))))))),((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),L))} is non empty functional finite set
{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)))))))} is non empty trivial functional finite 1 -element set
{{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L))))))),((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),L))},{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)))))))}} is non empty finite finite-membered set
vb is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G,vb,(G,(G,(G),L))) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),vb) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
G .AdjacentSet {(G,(G,(G),L))} is finite Element of bool (the_Vertices_of G)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb) is finite Element of bool (the_Vertices_of G)
(G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb)) is finite Element of bool (the_Vertices_of G)
(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),vb),((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb))),1) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
[((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),vb),((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb))),1)] is V1() set
{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),vb),((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb))),1)} is non empty functional finite set
{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb)} is non empty trivial functional finite 1 -element set
{{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),vb),((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb))),1)},{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb)}} is non empty finite finite-membered set
{(G,(G,(G),L))} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
G .AdjacentSet {(G,(G,(G),L))} is finite Element of bool (the_Vertices_of G)
(G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb)) is finite Element of bool (the_Vertices_of G)
(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),vb),((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb))),1) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
[((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),vb),((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb))),1)] is V1() set
{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),vb),((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb))),1)} is non empty functional finite set
{{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),vb),((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb))),1)},{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb)}} is non empty finite finite-membered set
[((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),vb),((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),vb))),1)] `1 is set
[(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L))))))),((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),L))] `1 is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
the_Vertices_of G is non empty finite set
G . VertexSelector is set
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
(G) is Relation-like NAT -defined Function-like total () (G)
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),V) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),V)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),V)) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),V))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(V + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(V + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(V + 1))) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(V + 1)))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G),V)) is Element of the_Vertices_of G
(G .order()) -' V is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G),V)) .--> ((G .order()) -' V) is Relation-like the_Vertices_of G -defined {(G,(G,(G),V))} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(G,(G,(G),V))} is non empty trivial finite 1 -element set
{(G,(G,(G),V))} --> ((G .order()) -' V) is non empty Relation-like {(G,(G,(G),V))} -defined NAT -valued RAT -valued INT -valued {((G .order()) -' V)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{(G,(G,(G),V))},{((G .order()) -' V)}:]
{((G .order()) -' V)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{(G,(G,(G),V))},{((G .order()) -' V)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{(G,(G,(G),V))},{((G .order()) -' V)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
dom ((G,(G,(G),V)) .--> ((G .order()) -' V)) is trivial finite Element of bool {(G,(G,(G),V))}
bool {(G,(G,(G),V))} is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
{(G,(G,(G),V))} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),V)) +* ((G,(G,(G),V)) .--> ((G .order()) -' V)) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
(dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),V))) \/ {(G,(G,(G),V))} is non empty finite Element of bool (the_Vertices_of G)
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),V) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),V)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),V)) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),V))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(V + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(V + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(V + 1))) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(V + 1)))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(the_Vertices_of G) --> 0 is non empty Relation-like the_Vertices_of G -defined NAT -valued RAT -valued INT -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Function-yielding V264() Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
[:(the_Vertices_of G),{0}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
[{},((the_Vertices_of G) --> 0)] is V1() set
{{},((the_Vertices_of G) --> 0)} is non empty functional finite finite-membered set
{{{},((the_Vertices_of G) --> 0)},{{}}} is non empty finite finite-membered set
[{},((the_Vertices_of G) --> 0)] `1 is set
(G,(G),0) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),0)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),0)) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),0))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
the_Vertices_of G is non empty finite set
G . VertexSelector is set
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G) is Relation-like NAT -defined Function-like total () (G)
(G,(G),(G .order())) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G .order()) + a is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),((G .order()) + a)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),((G .order()) + a))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),((G .order()) + a))) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),((G .order()) + a)))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .order()) + (a + 1) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),((G .order()) + (a + 1))) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),((G .order()) + (a + 1)))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),((G .order()) + (a + 1)))) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),((G .order()) + (a + 1))))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((G .order()) + a) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(((G .order()) + a) + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G,(G,(G),((G .order()) + a))) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G .order()) + 0 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),((G .order()) + 0)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),((G .order()) + 0))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),((G .order()) + 0))) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),((G .order()) + 0)))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G .order()) + a is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),((G .order()) + a)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .order()) + (a + 1) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),((G .order()) + (a + 1))) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((G .order()) + a) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(((G .order()) + a) + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),((G .order()) + a))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
(G,(G,(G),((G .order()) + a))) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),((G .order()) + a))) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),((G .order()) + a)))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G .order()) + a is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
the_Vertices_of G is non empty finite set
G . VertexSelector is set
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G) is Relation-like NAT -defined Function-like total () (G)
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
(G,(G),V) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G,(G),(G .order())) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
(G) is Relation-like NAT -defined Function-like total () (G)
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
the_Vertices_of G is non empty finite set
G . VertexSelector is set
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G) . (G .order()) is set
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G) . L is set
(G,(G),(G .order())) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
(G) is Relation-like NAT -defined Function-like total () (G)
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
(G) is Relation-like NAT -defined Function-like total halting () () (G)
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(G,(G),(G .order())) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(G .order()))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(G .order()))) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(G .order())))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
(G) is Relation-like NAT -defined Function-like total halting () () (G)
(G) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
the_Vertices_of G is non empty finite set
G . VertexSelector is set
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),V) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
V + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(V + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G,(G,(G),V)) is Element of the_Vertices_of G
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(V + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),V)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),V)) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),V))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),V)))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G),V)) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),V))))) is Relation-like the_Vertices_of G -defined {(G,(G,(G),V))} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(G,(G,(G),V))} is non empty trivial finite 1 -element set
{(G,(G,(G),V))} --> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),V))))) is non empty Relation-like {(G,(G,(G),V))} -defined NAT -valued RAT -valued INT -valued {((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),V)))))} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{(G,(G,(G),V))},{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),V)))))}:]
{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),V)))))} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{(G,(G,(G),V))},{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),V)))))}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{(G,(G,(G),V))},{((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),V)))))}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),V)) +* ((G,(G,(G),V)) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),V)))))) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
dom ((G,(G,(G),V)) .--> ((G .order()) -' (card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),V)))))) is trivial finite Element of bool {(G,(G,(G),V))}
bool {(G,(G,(G),V))} is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
{(G,(G,(G),V))} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(V + 1))) is finite Element of bool (the_Vertices_of G)
(dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),V))) \/ {(G,(G,(G),V))} is non empty finite Element of bool (the_Vertices_of G)
(G .order()) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(G .order())) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
(G,(G),((G .order()) + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
(G) is Relation-like NAT -defined Function-like total halting () () (G)
(G,(G)) is Relation-like NAT -defined Function-like total (G)
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),a) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
b is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
c is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G,(G)),b) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
(G,(G),b) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),b)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
(G,(G),c) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),c)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
(G,(G,(G)),c) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G,(G)),a) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
(G) is Relation-like NAT -defined Function-like total halting () () (G)
(G,(G)) is Relation-like NAT -defined Function-like total (G)
(G,(G)) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
the_Vertices_of G is non empty finite set
G . VertexSelector is set
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
(G .order()) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),((G .order()) + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),((G .order()) + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
(G,(G,(G)),((G .order()) + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
b is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G,(G)),b) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
b + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G)),(b + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,(G),(b + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(b + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(b + 1))) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(b + 1)))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),b) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),b)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),b)) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),b))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(G .order())) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(G .order()))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
(G,(G,(G)),(G .order())) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
(G) is Relation-like NAT -defined Function-like total halting () () (G)
(G,(G)) is Relation-like NAT -defined Function-like total (G)
(G,(G),0) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
the_Vertices_of G is non empty finite set
G . VertexSelector is set
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
(G) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(the_Vertices_of G) --> 0 is non empty Relation-like the_Vertices_of G -defined NAT -valued RAT -valued INT -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Function-yielding V264() Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
[:(the_Vertices_of G),{0}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
[{},((the_Vertices_of G) --> 0)] is V1() set
{{},((the_Vertices_of G) --> 0)} is non empty functional finite finite-membered set
{{{},((the_Vertices_of G) --> 0)},{{}}} is non empty finite finite-membered set
[{},((the_Vertices_of G) --> 0)] `1 is set
(G,(G,(G)),0) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),0)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
(G,(G)) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G,(G)),a) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
b is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G,(G)),b) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G)),(a + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,(G),(a + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(a + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
(G,(G),a) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),a)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
b + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G)),(b + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,(G),(b + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(b + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
(G,(G),b) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),b)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),b)) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),b))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(G .order())) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(G .order()))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(G .order()))) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(G .order())))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),a)) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),a))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(G .order())) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(G .order()))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(G .order()))) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(G .order())))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),b)) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),b))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(G .order())) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(G .order()))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
(G) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G,(G)),a) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
dom (G,(G,(G)),a) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
a + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G)),(a + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
((G,(G)) .Lifespan()) -' a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),a) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G,(G,(G),a)) is Element of the_Vertices_of G
b is Element of the_Vertices_of G
b .--> (((G,(G)) .Lifespan()) -' a) is Relation-like the_Vertices_of G -defined {b} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{b} is non empty trivial finite 1 -element set
{b} --> (((G,(G)) .Lifespan()) -' a) is non empty Relation-like {b} -defined NAT -valued RAT -valued INT -valued {(((G,(G)) .Lifespan()) -' a)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{b},{(((G,(G)) .Lifespan()) -' a)}:]
{(((G,(G)) .Lifespan()) -' a)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{b},{(((G,(G)) .Lifespan()) -' a)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{b},{(((G,(G)) .Lifespan()) -' a)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(G,(G,(G)),a) +* (b .--> (((G,(G)) .Lifespan()) -' a)) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),a)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
(G,(G),(a + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(a + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
card (dom (G,(G,(G)),a)) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
(G) is Relation-like NAT -defined Function-like total halting () () (G)
(G,(G)) is Relation-like NAT -defined Function-like total (G)
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
the_Vertices_of G is non empty finite set
G . VertexSelector is set
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G) is Relation-like NAT -defined Function-like total halting () () (G)
(G,(G)) is Relation-like NAT -defined Function-like total halting () () (G) (G)
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G,(G)),L) is set
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
(G,(G,(G),L)) is Element of the_Vertices_of G
L + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(L + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(L + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
(G) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((G) .Lifespan()) -' L is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G),L)) .--> (((G) .Lifespan()) -' L) is Relation-like the_Vertices_of G -defined {(G,(G,(G),L))} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(G,(G,(G),L))} is non empty trivial finite 1 -element set
{(G,(G,(G),L))} --> (((G) .Lifespan()) -' L) is non empty Relation-like {(G,(G,(G),L))} -defined NAT -valued RAT -valued INT -valued {(((G) .Lifespan()) -' L)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{(G,(G,(G),L))},{(((G) .Lifespan()) -' L)}:]
{(((G) .Lifespan()) -' L)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{(G,(G,(G),L))},{(((G) .Lifespan()) -' L)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{(G,(G,(G),L))},{(((G) .Lifespan()) -' L)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
dom ((G,(G,(G),L)) .--> (((G) .Lifespan()) -' L)) is trivial finite Element of bool {(G,(G,(G),L))}
bool {(G,(G,(G),L))} is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
{(G,(G,(G),L))} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) is finite Element of bool (the_Vertices_of G)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) +* ((G,(G,(G),L)) .--> (((G) .Lifespan()) -' L)) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(L + 1))) is finite Element of bool (the_Vertices_of G)
(dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L))) \/ {(G,(G,(G),L))} is non empty finite Element of bool (the_Vertices_of G)
(G,(G)) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G)),L) .--> (((G) .Lifespan()) -' L) is Relation-like {(G,(G,(G)),L)} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(G,(G,(G)),L)} is non empty trivial finite 1 -element set
{(G,(G,(G)),L)} --> (((G) .Lifespan()) -' L) is non empty Relation-like {(G,(G,(G)),L)} -defined NAT -valued RAT -valued INT -valued {(((G) .Lifespan()) -' L)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{(G,(G,(G)),L)},{(((G) .Lifespan()) -' L)}:]
[:{(G,(G,(G)),L)},{(((G) .Lifespan()) -' L)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{(G,(G,(G)),L)},{(((G) .Lifespan()) -' L)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
dom ((G,(G,(G)),L) .--> (((G) .Lifespan()) -' L)) is trivial finite Element of bool {(G,(G,(G)),L)}
bool {(G,(G,(G)),L)} is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
(G,(G,(G)),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
(G,(G,(G)),(L + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) +* ((G,(G,(G)),L) .--> (((G) .Lifespan()) -' L)) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
(dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L))) \/ {(G,(G,(G)),L)} is non empty finite set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
the_Vertices_of G is non empty finite set
G . VertexSelector is set
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G) is Relation-like NAT -defined Function-like total halting () () (G)
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
(G,(G,(G),L)) is Element of the_Vertices_of G
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
L + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(L + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),(L + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),L)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
card (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .order()) -' L is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G),L)) .--> ((G .order()) -' L) is Relation-like the_Vertices_of G -defined {(G,(G,(G),L))} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(G,(G,(G),L))} is non empty trivial finite 1 -element set
{(G,(G,(G),L))} --> ((G .order()) -' L) is non empty Relation-like {(G,(G,(G),L))} -defined NAT -valued RAT -valued INT -valued {((G .order()) -' L)} -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of bool [:{(G,(G,(G),L))},{((G .order()) -' L)}:]
{((G .order()) -' L)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element set
[:{(G,(G,(G),L))},{((G .order()) -' L)}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:{(G,(G,(G),L))},{((G .order()) -' L)}:] is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' L)) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
[(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' L))),((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),L))] is V1() set
{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' L))),((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),L))} is non empty functional finite set
{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' L)))} is non empty trivial functional finite 1 -element set
{{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' L))),((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),L))},{(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' L)))}} is non empty finite finite-membered set
proj1 (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' L))) is set
{(G,(G,(G),L))} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
(dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L))) \/ {(G,(G,(G),L))} is non empty finite Element of bool (the_Vertices_of G)
rng ((G,(G,(G),L)) .--> ((G .order()) -' L)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool RAT
bool RAT is non empty cup-closed diff-closed preBoolean set
{((G .order()) -' L)} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite finite-membered 1 -element Element of bool NAT
rng ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool NAT
(rng ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L))) \/ (rng ((G,(G,(G),L)) .--> ((G .order()) -' L))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() set
rng (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' L))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool RAT
(G,(G,(G),L)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G,(G,(G),L),(G,(G,(G),L)),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
P is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(G,P,(G,(G,(G),L))) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),P) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),P) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
G .AdjacentSet {(G,(G,(G),L))} is finite Element of bool (the_Vertices_of G)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),P) is finite Element of bool (the_Vertices_of G)
(G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),P)) is finite Element of bool (the_Vertices_of G)
(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),P),((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),P))),1) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
[((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),P),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),P),((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),P))),1)] is V1() set
{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),P),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),P),((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),P))),1)} is non empty functional finite set
{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),P)} is non empty trivial functional finite 1 -element set
{{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),P),(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),P),((G .AdjacentSet {(G,(G,(G),L))}) \ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),P))),1)},{((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),P)}} is non empty finite finite-membered set
G .AdjacentSet {(G,(G,(G),L))} is finite Element of bool (the_Vertices_of G)
[(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' L))),((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),L))] `1 is set
[(((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) +* ((G,(G,(G),L)) .--> ((G .order()) -' L))),((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),L))] `2 is set
e is set
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),(L + 1))) . e is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),L)) . e is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),(L + 1))) . e is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),L)) . e is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
dom ((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),L)) is finite Element of bool (the_Vertices_of G)
e is set
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),(L + 1))) . e is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),L)) . e is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),L)) . e) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
e is set
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),(L + 1))) . e is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),L)) . e is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),L)) . e) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
D is set
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),(L + 1))) . D is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),L)) . D is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
(G) is Relation-like NAT -defined Function-like total halting () () (G)
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) is finite Element of bool (the_Vertices_of G)
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),L)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
b is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),b) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),b)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),b)) is finite Element of bool (the_Vertices_of G)
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),b)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
b + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(b + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(b + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(b + 1))) is finite Element of bool (the_Vertices_of G)
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),(b + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
e2 is set
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),(b + 1))) . e2 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
{e2} is non empty trivial finite 1 -element set
G .AdjacentSet {e2} is finite Element of bool (the_Vertices_of G)
(G .AdjacentSet {e2}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(b + 1)))) is finite Element of bool (the_Vertices_of G)
card ((G .AdjacentSet {e2}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(b + 1))))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G)) is Relation-like NAT -defined Function-like total halting () () (G) (G)
(G) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G)),b) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
(G,(G)) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G)),(b + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
(G,(G,(G),b)) is Element of the_Vertices_of G
j is Element of the_Vertices_of G
{j} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
G .AdjacentSet {j} is finite Element of bool (the_Vertices_of G)
(G,(G,(G)),b) is set
(dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),b))) \/ {j} is non empty finite Element of bool (the_Vertices_of G)
k is set
{k} is non empty trivial finite 1 -element set
G .AdjacentSet {k} is finite Element of bool (the_Vertices_of G)
(G .AdjacentSet {k}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),b))) is finite Element of bool (the_Vertices_of G)
card ((G .AdjacentSet {k}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),b)))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),b)) . k is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .AdjacentSet {k}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(b + 1)))) is finite Element of bool (the_Vertices_of G)
(G .AdjacentSet {k}) /\ {j} is finite Element of bool (the_Vertices_of G)
((G .AdjacentSet {k}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),b)))) \/ ((G .AdjacentSet {k}) /\ {j}) is finite Element of bool (the_Vertices_of G)
((G .AdjacentSet {k}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),b)))) \/ {j} is non empty finite Element of bool (the_Vertices_of G)
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),(b + 1))) . k is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),b)) . k) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card ((G .AdjacentSet {k}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(b + 1))))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .AdjacentSet {k}) /\ {j} is finite Element of bool (the_Vertices_of G)
bool {j} is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
{{},{j}} is non empty finite finite-membered set
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),(b + 1))) . k is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .AdjacentSet {k}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(b + 1)))) is finite Element of bool (the_Vertices_of G)
((G .AdjacentSet {k}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),b)))) \/ ((G .AdjacentSet {k}) /\ {j}) is finite Element of bool (the_Vertices_of G)
((G .AdjacentSet {k}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),b)))) \/ {} is finite set
card ((G .AdjacentSet {k}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(b + 1))))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
k is set
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),(b + 1))) . k is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
{k} is non empty trivial finite 1 -element set
G .AdjacentSet {k} is finite Element of bool (the_Vertices_of G)
(G .AdjacentSet {k}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(b + 1)))) is finite Element of bool (the_Vertices_of G)
card ((G .AdjacentSet {k}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(b + 1))))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),0) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),0)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),0)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
c is set
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),0)) is finite Element of bool (the_Vertices_of G)
(G) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
(the_Vertices_of G) --> 0 is non empty Relation-like the_Vertices_of G -defined NAT -valued RAT -valued INT -valued Function-like constant total quasi_total finite complex-valued ext-real-valued real-valued natural-valued finite-support Function-yielding V264() Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
[:(the_Vertices_of G),{0}:] is non empty Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
[{},((the_Vertices_of G) --> 0)] is V1() set
{{},((the_Vertices_of G) --> 0)} is non empty functional finite finite-membered set
{{{},((the_Vertices_of G) --> 0)},{{}}} is non empty finite finite-membered set
[{},((the_Vertices_of G) --> 0)] `1 is set
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),0)) . c is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
{c} is non empty trivial finite 1 -element set
G .AdjacentSet {c} is finite Element of bool (the_Vertices_of G)
(G .AdjacentSet {c}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),0))) is finite Element of bool (the_Vertices_of G)
card ((G .AdjacentSet {c}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),0)))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
b is set
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),0)) . b is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
{b} is non empty trivial finite 1 -element set
G .AdjacentSet {b} is finite Element of bool (the_Vertices_of G)
(G .AdjacentSet {b}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),0))) is finite Element of bool (the_Vertices_of G)
card ((G .AdjacentSet {b}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),0)))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
b is set
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),L)) . b is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
{b} is non empty trivial finite 1 -element set
G .AdjacentSet {b} is finite Element of bool (the_Vertices_of G)
(G .AdjacentSet {b}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L))) is finite Element of bool (the_Vertices_of G)
card ((G .AdjacentSet {b}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] set
the_Vertices_of G is non empty set
G . VertexSelector is set
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
Funcs ((the_Vertices_of G),NAT) is non empty FUNCTION_DOMAIN of the_Vertices_of G, NAT
(G) is Relation-like NAT -defined Function-like total halting () () (G)
L is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G,(G),L) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):] is non empty Relation-like set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
(G,(G)) is Relation-like NAT -defined Function-like total halting () () (G) (G)
(G) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G)) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G)),L) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
c is Element of the_Vertices_of G
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
va is Element of the_Vertices_of G
vb is Element of the_Vertices_of G
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . c is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . vb is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
(G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va))) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va)))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va)))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like quasi_total complex-valued ext-real-valued real-valued natural-valued Element of Funcs ((the_Vertices_of G),NAT)
{va} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
G .AdjacentSet {va} is finite Element of bool (the_Vertices_of G)
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va)))) is finite Element of bool (the_Vertices_of G)
(G .AdjacentSet {va}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va))))) is finite Element of bool (the_Vertices_of G)
(G,(G,(G)),((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va))) is set
{c} is non empty trivial finite 1 -element Element of bool (the_Vertices_of G)
G .AdjacentSet {c} is finite Element of bool (the_Vertices_of G)
(G,(G,(G)),((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va)))) . c is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .AdjacentSet {c}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va))))) is finite Element of bool (the_Vertices_of G)
card ((G .AdjacentSet {c}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va)))))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G .order()) - (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va) is ext-real V55() real V57() set
(G .order()) - ((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va)) is ext-real V55() real V57() set
(G .order()) -' ((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va)) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va)))) . c is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va)) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G),(((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va)) + 1)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),NAT)):]
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va)) + 1))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of PFuncs ((the_Vertices_of G),NAT)
e is set
D is Element of the_Vertices_of G
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . D is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va)))) . D is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G,(G,(G)),(((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va)) + 1)) is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va)) + 1))) is finite Element of bool (the_Vertices_of G)
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va)) + 1))) . va is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),(((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va)) + 1))) . D is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
rng ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va)))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool NAT
Seg (G .order()) is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite G .order() -element Element of bool NAT
Seg ((G .order()) -' ((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite (G .order()) -' ((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va)) -element Element of bool NAT
(Seg (G .order())) \ (Seg ((G .order()) -' ((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va)))) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
(G,(G,(G),((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va)))) is Element of the_Vertices_of G
((PFuncs ((the_Vertices_of G),NAT)),NAT,(the_Vertices_of G),(G,(G),((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va)))) . va is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card ((G .AdjacentSet {va}) /\ (dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),((G .order()) -' (((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . va)))))) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
vc is Element of the_Vertices_of G
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),NAT)),(G,(G),L)) . vc is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
Funcs ((the_Vertices_of G),(Fin NAT)) is non empty FUNCTION_DOMAIN of the_Vertices_of G, Fin NAT
(G) is Relation-like NAT -defined Function-like total halting () () (G)
(G,(G)) is Element of [:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):]
PFuncs ((the_Vertices_of G),NAT) is non empty functional M38( the_Vertices_of G, NAT )
[:(PFuncs ((the_Vertices_of G),NAT)),(Funcs ((the_Vertices_of G),(Fin NAT))):] is non empty Relation-like set
(G) .Lifespan() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(G) . ((G) .Lifespan()) is set
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G))) is Relation-like the_Vertices_of G -defined NAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of PFuncs ((the_Vertices_of G),NAT)
a is Element of the_Vertices_of G
dom ((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G))) is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
b is Element of the_Vertices_of G
c is Element of the_Vertices_of G
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G))) . b is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G))) . a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G))) . c is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
va is Element of the_Vertices_of G
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G))) . va is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
vb is Element of the_Vertices_of G
((the_Vertices_of G),NAT,(Funcs ((the_Vertices_of G),(Fin NAT))),(G,(G))) . vb is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite chordal set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
[:(the_Vertices_of G),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(the_Vertices_of G),NAT:] is non empty non trivial non finite cup-closed diff-closed preBoolean V225() set
L is Relation-like the_Vertices_of G -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of bool [:(the_Vertices_of G),NAT:]
dom L is finite Element of bool (the_Vertices_of G)
bool (the_Vertices_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean V225() set
the_Edges_of G is finite set
G . EdgeSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty finite set
V is non empty Relation-like NAT -defined the_Vertices_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support VertexScheme of G
V " is Relation-like Function-like set
len V is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
dom V is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite Element of bool NAT
G .order() is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
card (the_Vertices_of G) is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
Seg (G .order()) is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() finite G .order() -element Element of bool NAT
rng L is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() Element of bool NAT
a is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
b is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
len b is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
b .first() is Element of the_Vertices_of G
b . 1 is set
L . (b .first()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
b .last() is Element of the_Vertices_of G
b . (len b) is set
L . (b .last()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
b . 3 is set
L . (b . 3) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
c is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
b is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
len b is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
b .first() is Element of the_Vertices_of G
b . 1 is set
L . (b .first()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
b .last() is Element of the_Vertices_of G
b . (len b) is set
L . (b .last()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
b . 3 is set
L . (b . 3) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
len a is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
a .first() is Element of the_Vertices_of G
a . 1 is set
L . (a .first()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a .last() is Element of the_Vertices_of G
a . (len a) is set
L . (a .last()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
a . 3 is set
L . (a . 3) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
b is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
b is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
c is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
len c is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
c .first() is Element of the_Vertices_of G
c . 1 is set
L . (c .first()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
c .last() is Element of the_Vertices_of G
c . (len c) is set
L . (c .last()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
c . 3 is set
L . (c . 3) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
va is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
c is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
len c is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
c .first() is Element of the_Vertices_of G
c . 1 is set
L . (c .first()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
c .last() is Element of the_Vertices_of G
c . (len c) is set
L . (c .last()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
c . 3 is set
L . (c . 3) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
va is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
2 * 1 is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() even Element of NAT
(2 * 1) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
c .vertexAt ((2 * 1) + 1) is Element of the_Vertices_of G
vb is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
2 * 0 is empty Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V30() V33() V34() V35() V36() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V55() real V57() V59() complex-valued ext-real-valued real-valued natural-valued FinSequence-yielding finite-support Function-yielding V264() even Element of NAT
(2 * 0) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
P is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
1 + 2 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
P is set
e1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
vc is Element of the_Vertices_of G
vb is Element of the_Vertices_of G
P is set
e1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
e2 is set
P is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
va is Element of the_Vertices_of G
P is set
L . vb is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
P is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
P is Element of the_Vertices_of G
L . P is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . vc is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
e1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
e1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
L . va is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
e2 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
c .vertices() is finite Element of bool (the_Vertices_of G)
c .vertexSeq() is Relation-like NAT -defined the_Vertices_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support VertexSeq of G
rng (c .vertexSeq()) is finite Element of bool (the_Vertices_of G)
e2 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
c . e2 is set
j is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
e2 is set
e2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
c . e2 is set
j is set
e2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
c . e2 is set
j is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
c .cut (1,j) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
c . j is set
e is set
e is set
k is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
D is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
len k is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
(len k) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() even Element of NAT
j + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() even Element of NAT
D is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
dom k is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
k . D is set
1 + D is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() even Element of NAT
(1 + D) - 1 is non empty ext-real V55() real V57() non even set
c . ((1 + D) - 1) is set
c . D is set
k . 3 is set
3 + 2 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
(len k) - 2 is ext-real V55() real V57() set
k . ((len k) - 2) is set
D is set
(3 + 2) - 2 is ext-real V55() real V57() set
(len k) - (2 * 1) is non empty ext-real V55() real V57() non even set
R is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
c . R is set
k .last() is Element of the_Vertices_of G
k . (len k) is set
k .vertices() is finite Element of bool (the_Vertices_of G)
k .vertexSeq() is Relation-like NAT -defined the_Vertices_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support VertexSeq of G
rng (k .vertexSeq()) is finite Element of bool (the_Vertices_of G)
k .addEdge e is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
(k .last()) .adj e is Element of the_Vertices_of G
G .walkOf ((k .last()),e,((k .last()) .adj e)) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
k .append (G .walkOf ((k .last()),e,((k .last()) .adj e))) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
D is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
D .reverse() is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
len D is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
(len k) + 2 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
L . (c . j) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . (c . j) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . (c . j) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . (c . j) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
i is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
L . (c . j) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
i is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
i is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
L . (c . j) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . (c . j) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
k .first() is Element of the_Vertices_of G
k . 1 is set
D .first() is Element of the_Vertices_of G
D . 1 is set
R is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
R .last() is Element of the_Vertices_of G
len R is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
R . (len R) is set
D . 3 is set
D .last() is Element of the_Vertices_of G
D . (len D) is set
R .first() is Element of the_Vertices_of G
R . 1 is set
i is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
R . i is set
(len D) - i is ext-real V55() real V57() even set
((len D) - i) + 1 is non empty ext-real V55() real V57() non even set
D . (((len D) - i) + 1) is set
dom R is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
dom D is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
i is non empty ext-real positive non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() non even set
k . i is set
D . i is set
i is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
ir is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
j + (2 * 1) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
j + 2 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
(j + 2) - 2 is ext-real V55() real V57() set
D . i is set
k . j is set
D . ir is set
L . (D . ir) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . (D . i) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
i is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
ir is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
D . i is set
k . i is set
c . i is set
D . ir is set
k . ir is set
c . ir is set
L . (D . i) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . (D . ir) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
i is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
ir is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
D . ir is set
L . (D . ir) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
D . i is set
L . (D . i) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
ir is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
j is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
D . ir is set
L . (D . ir) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
D . j is set
L . (D . j) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
i is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
ir is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
j + (2 * 1) is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
j + 2 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
(j + 2) - 2 is ext-real V55() real V57() set
D . i is set
k . i is set
c . i is set
L . (D . i) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . (D . i) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . (D . i) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . (D . i) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
D . ir is set
L . (D . ir) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
D . ir is set
k . ir is set
c . ir is set
L . (D . ir) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . (D . i) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
i is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
ir is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
D . ir is set
k . ir is set
c . ir is set
D . i is set
k . i is set
c . i is set
L . (D . i) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . (D . ir) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
i is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
ir is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
D . ir is set
L . (D . ir) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
D . i is set
L . (D . i) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
ir is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
j is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
D . ir is set
L . (D . ir) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
D . j is set
L . (D . j) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
i is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
i is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
(len D) - i is ext-real V55() real V57() even set
((len D) - i) + 1 is non empty ext-real V55() real V57() non even set
(len D) - 1 is ext-real V55() real V57() even set
((len D) - 1) + 1 is non empty ext-real V55() real V57() non even set
(len D) - (len D) is ext-real V55() real V57() even set
j is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
k is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
ir is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
(len D) - j is ext-real V55() real V57() even set
((len D) - j) + 1 is non empty ext-real V55() real V57() non even set
R . j is set
D . (((len D) - j) + 1) is set
i + k is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() even Element of NAT
(((len D) - i) + 1) + i is ext-real V55() real V57() even set
(i + k) - k is non empty ext-real V55() real V57() non even set
(len D) + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() even Element of NAT
((len D) + 1) - k is non empty ext-real V55() real V57() non even set
(len D) - k is ext-real V55() real V57() even set
((len D) - k) + 1 is non empty ext-real V55() real V57() non even set
kr is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
D . kr is set
L . (D . kr) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
jr is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
D . jr is set
L . (D . jr) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . (R . j) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
R . k is set
L . (R . k) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
j is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
k is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
(len D) - k is ext-real V55() real V57() even set
((len D) - k) + 1 is non empty ext-real V55() real V57() non even set
R . k is set
D . (((len D) - k) + 1) is set
(len D) - j is ext-real V55() real V57() even set
((len D) - j) + 1 is non empty ext-real V55() real V57() non even set
R . j is set
D . (((len D) - j) + 1) is set
i + j is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() even Element of NAT
((len D) + 1) - j is non empty ext-real V55() real V57() non even set
(i + j) - j is non empty ext-real V55() real V57() non even set
jr is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
kr is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
L . (R . k) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . (R . j) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
0 + 1 is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
j is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
k is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
R . k is set
L . (R . k) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
R . j is set
L . (R . j) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
kr is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
jr is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
R . kr is set
L . (R . kr) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
R . jr is set
L . (R . jr) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
dom R is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() finite Element of bool NAT
R . 3 is set
(len D) - 3 is ext-real V55() real V57() set
((len D) - 3) + 1 is ext-real V55() real V57() set
D . (((len D) - 3) + 1) is set
k . j is set
L . (R .last()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . (R . 3) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
i is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
i is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
ir is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
L " is Relation-like Function-like set
b is Element of the_Vertices_of G
c is Element of the_Vertices_of G
a is Element of the_Vertices_of G
va is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
vb is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
vc is ext-real non negative epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() set
V . va is set
V . vb is set
V . vc is set
L . a is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . c is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V . (L . c) is set
L . b is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
V . (L . b) is set
{c,a,b} is non empty finite Element of bool (the_Vertices_of G)
P is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
len P is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
P .length() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
P .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support EdgeSeq of G
len (P .edgeSeq()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
e1 is set
e2 is set
P .edges() is finite Element of bool (the_Edges_of G)
bool (the_Edges_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean set
rng (P .edgeSeq()) is finite Element of bool (the_Edges_of G)
{e1,e2} is non empty finite set
P .vertices() is finite Element of bool (the_Vertices_of G)
P .vertexSeq() is Relation-like NAT -defined the_Vertices_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support VertexSeq of G
rng (P .vertexSeq()) is finite Element of bool (the_Vertices_of G)
P . 1 is set
P . 3 is set
P . 5 is set
P .first() is Element of the_Vertices_of G
j is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
k is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
P . j is set
L . (P . j) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
P . k is set
L . (P . k) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
j is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
k is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
P . k is set
L . (P . k) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
P . j is set
L . (P . j) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
P .last() is Element of the_Vertices_of G
P . (len P) is set
L . (P .first()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . (P .last()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . (P . 3) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
j is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
{b,a,c} is non empty finite Element of bool (the_Vertices_of G)
P is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
len P is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
P .length() is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
P .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support EdgeSeq of G
len (P .edgeSeq()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
e1 is set
e2 is set
P .edges() is finite Element of bool (the_Edges_of G)
bool (the_Edges_of G) is non empty finite finite-membered cup-closed diff-closed preBoolean set
rng (P .edgeSeq()) is finite Element of bool (the_Edges_of G)
{e1,e2} is non empty finite set
P .vertices() is finite Element of bool (the_Vertices_of G)
P .vertexSeq() is Relation-like NAT -defined the_Vertices_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support VertexSeq of G
rng (P .vertexSeq()) is finite Element of bool (the_Vertices_of G)
P . 1 is set
P . 3 is set
P . 5 is set
P .first() is Element of the_Vertices_of G
j is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
k is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
P . j is set
L . (P . j) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
P . k is set
L . (P . k) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
j is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
k is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT
P . k is set
L . (P . k) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
P . j is set
L . (P . j) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
P .last() is Element of the_Vertices_of G
P . (len P) is set
L . (P .first()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . (P .last()) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
L . (P . 3) is ext-real non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() Element of NAT
j is non empty ext-real positive non negative complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V31() V32() V33() V34() V35() epsilon-transitive epsilon-connected ordinal natural finite cardinal V55() real V57() V59() non even Element of NAT