:: GRAPH_3 semantic presentation

REAL is V100() V101() V102() V106() V109() V110() V112() set
NAT is V6() V7() V8() non empty non trivial non finite cardinal limit_cardinal V100() V101() V102() V103() V104() V105() V106() V107() V109() Element of bool REAL
bool REAL is set
NAT is V6() V7() V8() non empty non trivial non finite cardinal limit_cardinal V100() V101() V102() V103() V104() V105() V106() V107() V109() set
bool NAT is non trivial non finite set
bool NAT is non trivial non finite set
COMPLEX is V100() V106() set
RAT is V100() V101() V102() V103() V106() set
INT is V100() V101() V102() V103() V104() V106() set
{} is Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() set
the Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() set is Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() set
2 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
3 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
0 is Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() V123() Element of NAT
dom {} is Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() set
rng {} is Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() set
card {} is Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() set
{{},1} is non empty finite V32() V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() set
Seg 1 is non empty trivial finite 1 -element V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() Element of bool NAT
G is set
V is functional non empty FinSequence-membered FinSequenceSet of G
bool V is set
E is functional non empty FinSequence-membered Element of bool V
v1 is FinSequence-like Element of E
G is V39() integer even ext-real V122() set
V is V39() integer even ext-real V122() set
G - V is V39() integer ext-real V122() set
E is V39() integer ext-real V122() set
2 * E is V39() integer even ext-real V122() set
v1 is V39() integer ext-real V122() set
2 * v1 is V39() integer even ext-real V122() set
v1 - E is V39() integer ext-real V122() set
2 * (v1 - E) is V39() integer even ext-real V122() set
G is V39() integer ext-real V122() set
V is V39() integer ext-real V122() set
G - V is V39() integer ext-real V122() set
E is V39() integer ext-real V122() set
v1 is V39() integer ext-real V122() set
E - v1 is V39() integer ext-real V122() set
G is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len G is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(V,E) -cut G is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len ((V,E) -cut G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len ((V,E) -cut G)) + V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
((V,E) -cut G) . (v1 + 1) is set
V + v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G . (V + v1) is set
v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
((V,E) -cut G) . (v1 + 1) is set
V + v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G . (V + v1) is set
G is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom G is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(V,E) -cut G is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom ((V,E) -cut G) is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
((V,E) -cut G) . v1 is set
V + v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
len ((V,E) -cut G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
len G is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
0 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
G9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G9 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V + G9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G . E9 is set
E9 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(len ((V,E) -cut G)) + V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V + (len ((V,E) -cut G)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
len G is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
len G is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G is non empty V68() MultiGraphStruct
the carrier of G is non empty set
V is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
E is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
len E is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
len V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len V) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
G is non empty V68() MultiGraphStruct
the carrier' of G is set
V is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G
len V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
V . E is set
v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
V . v1 is set
dom V is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
G is non empty V68() MultiGraphStruct
the carrier' of G is set
V is set
<*V*> is Relation-like NAT -defined Function-like non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
E is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
len E is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v2 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E . v1 is set
E . v2 is set
G is non empty V68() MultiGraphStruct
the carrier' of G is set
V is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G
E is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(E,v1) -cut V is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
len V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
len V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
len v2 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v2 . G9 is set
v2 . E9 is set
dom v2 is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
dom V is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
E + E9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
P9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
V . P9 is set
P9 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
E + G9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
n is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
V . n is set
n + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
len V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G is non empty V68() MultiGraphStruct
the carrier' of G is set
the carrier of G is non empty set
V is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G
rng V is finite set
E is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G
rng E is finite set
V ^ E is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
v1 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
len v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v1 . (len v1) is set
v2 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
v2 . 1 is set
n is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
P9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
len P9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
P9 . n is set
P9 . p9 is set
dom P9 is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
dom V is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
V . n is set
V . p9 is set
dom V is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
dom E is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
len V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
V . n is set
p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
(len V) + p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
(len V) + p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
(len V) + p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E . p is set
vs9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
(len V) + vs9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
dom V is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
dom E is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
len V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
(len V) + p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
(len V) + p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
vs9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
(len V) + vs9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
dom E is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
len V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
(len V) + p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
vs9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
(len V) + vs9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
(len V) + p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
vs9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
(len V) + vs9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
(len V) + p1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
vs9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
(len V) + vs9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E . p is set
E . vs9 is set
dom V is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
dom E is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
len V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G is non empty V68() MultiGraphStruct
V is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
the carrier of G is non empty set
the Element of the carrier of G is Element of the carrier of G
<* the Element of the carrier of G*> is Relation-like NAT -defined the carrier of G -valued Function-like non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of G
<* the Element of the carrier of G*> . 1 is set
len <* the Element of the carrier of G*> is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
<* the Element of the carrier of G*> . (len <* the Element of the carrier of G*>) is set
G is non empty V68() MultiGraphStruct
the carrier' of G is set
V is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G
G is non empty V68() MultiGraphStruct
the carrier' of G is set
V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
V + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
E is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like cyclic Chain of G
len E is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
((V + 1),(len E)) -cut E is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
(1,V) -cut E is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
(((V + 1),(len E)) -cut E) ^ ((1,V) -cut E) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
len ((1,V) -cut E) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len ((1,V) -cut E)) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
0 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
len (((V + 1),(len E)) -cut E) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len (((V + 1),(len E)) -cut E)) + (V + 1) is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(len E) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
the carrier of G is non empty set
P9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
(1,(V + 1)) -cut P9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
len P9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
((V + 1),(len P9)) -cut P9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
(len E) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
p9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
E9 is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G
(len P9) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
n is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
len n is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len n) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(V + 1) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
G9 is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G
len p9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len p9) + (V + 1) is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
1 + (V + 1) is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
p9 ^' n is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
(2,(len n)) -cut n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
p9 ^ ((2,(len n)) -cut n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
E9 ^ G9 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
P9 . (len P9) is set
P9 . 1 is set
n . 1 is set
p9 . (len p9) is set
p is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
p1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
G9 ^ E9 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
rng G9 is finite set
rng E9 is finite set
n . (len n) is set
P9 . (V + 1) is set
p9 . 1 is set
p . 1 is set
len p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p . (len p) is set
vs is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G
G is non empty V68() MultiGraphStruct
the carrier' of G is set
V is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G
dom V is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
len V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
rng V is finite set
E is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
((E + 1),(len V)) -cut V is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
(1,E) -cut V is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
(((E + 1),(len V)) -cut V) ^ ((1,E) -cut V) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
len ((((E + 1),(len V)) -cut V) ^ ((1,E) -cut V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
rng ((((E + 1),(len V)) -cut V) ^ ((1,E) -cut V)) is finite set
((((E + 1),(len V)) -cut V) ^ ((1,E) -cut V)) . 1 is set
V . (E + 1) is set
(len V) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
((1,E) -cut V) ^ (((E + 1),(len V)) -cut V) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
len ((1,E) -cut V) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
len (((E + 1),(len V)) -cut V) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len ((1,E) -cut V)) + (len (((E + 1),(len V)) -cut V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
rng ((1,E) -cut V) is finite set
rng (((E + 1),(len V)) -cut V) is finite set
(rng ((1,E) -cut V)) \/ (rng (((E + 1),(len V)) -cut V)) is finite set
(len (((E + 1),(len V)) -cut V)) + (E + 1) is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
1 + (E + 1) is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
dom (((E + 1),(len V)) -cut V) is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
0 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(((E + 1),(len V)) -cut V) . (0 + 1) is set
(E + 1) + 0 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ((E + 1) + 0) is set
G is non empty V68() MultiGraphStruct
the carrier' of G is set
V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like cyclic Chain of G
dom E is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
E . V is set
len E is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
rng E is finite set
E . 1 is set
1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(V,(len E)) -cut E is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
(1,v1) -cut E is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
((V,(len E)) -cut E) ^ ((1,v1) -cut E) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
v2 is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like cyclic Chain of G
v2 . 1 is set
len v2 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
rng v2 is finite set
G is non empty V68() MultiGraphStruct
the carrier of G is non empty set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
the carrier' of G is set
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
V is set
the Source of G . V is set
the Target of G . V is set
<*V*> is Relation-like NAT -defined Function-like non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
E is Element of the carrier of G
v1 is Element of the carrier of G
<*v1,E*> is Relation-like NAT -defined the carrier of G -valued Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of G
1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
<*v1,E*> /. (1 + 1) is Element of the carrier of G
len <*V*> is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
len <*v1,E*> is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(len <*V*>) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
E9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
<*v1,E*> /. E9 is Element of the carrier of G
E9 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
<*v1,E*> /. (E9 + 1) is Element of the carrier of G
<*V*> . E9 is set
<*V*> . 1 is set
<*v1,E*> /. 1 is Element of the carrier of G
G is non empty V68() MultiGraphStruct
the carrier of G is non empty set
the carrier' of G is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
V is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
E is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
len E is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E . (len E) is set
E . 1 is set
v1 is set
the Source of G . v1 is set
<*v1*> is Relation-like NAT -defined Function-like non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
V ^ <*v1*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
the Target of G . v1 is set
<*( the Source of G . v1),( the Target of G . v1)*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like set
E ^' <*( the Source of G . v1),( the Target of G . v1)*> is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len <*( the Source of G . v1),( the Target of G . v1)*> is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(2,(len <*( the Source of G . v1),( the Target of G . v1)*>)) -cut <*( the Source of G . v1),( the Target of G . v1)*> is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
E ^ ((2,(len <*( the Source of G . v1),( the Target of G . v1)*>)) -cut <*( the Source of G . v1),( the Target of G . v1)*>) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
G9 is Element of the carrier of G
E9 is Element of the carrier of G
<*G9,E9*> is Relation-like NAT -defined the carrier of G -valued Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of G
P9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
v2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
P9 . 1 is set
V ^ v2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
E ^' P9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
len P9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(2,(len P9)) -cut P9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
E ^ ((2,(len P9)) -cut P9) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
p9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
p9 . 1 is set
len p9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p9 . (len p9) is set
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
len V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len V) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
P9 . (len P9) is set
G is non empty V68() MultiGraphStruct
the carrier of G is non empty set
the carrier' of G is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
V is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
E is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
len E is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E . (len E) is set
E . 1 is set
v1 is set
the Target of G . v1 is set
<*v1*> is Relation-like NAT -defined Function-like non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
V ^ <*v1*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
the Source of G . v1 is set
<*( the Target of G . v1),( the Source of G . v1)*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like set
E ^' <*( the Target of G . v1),( the Source of G . v1)*> is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len <*( the Target of G . v1),( the Source of G . v1)*> is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(2,(len <*( the Target of G . v1),( the Source of G . v1)*>)) -cut <*( the Target of G . v1),( the Source of G . v1)*> is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
E ^ ((2,(len <*( the Target of G . v1),( the Source of G . v1)*>)) -cut <*( the Target of G . v1),( the Source of G . v1)*>) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
E9 is Element of the carrier of G
G9 is Element of the carrier of G
<*E9,G9*> is Relation-like NAT -defined the carrier of G -valued Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of G
P9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
v2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
P9 . 1 is set
V ^ v2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
E ^' P9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
len P9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(2,(len P9)) -cut P9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
E ^ ((2,(len P9)) -cut P9) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
p9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
p9 . 1 is set
len p9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p9 . (len p9) is set
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
len V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len V) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
P9 . (len P9) is set
G is non empty V68() MultiGraphStruct
the carrier of G is non empty set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
the carrier' of G is set
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
V is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
len V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
len E is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len V) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
v1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
E . v1 is set
V . v1 is set
the Target of G . (V . v1) is set
E . (v1 + 1) is set
the Source of G . (V . v1) is set
v2 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E . v2 is set
E /. v2 is Element of the carrier of G
v2 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
E . (v2 + 1) is set
E /. (v2 + 1) is Element of the carrier of G
V . v2 is set
G is non empty V68() MultiGraphStruct
the carrier of G is non empty set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
the carrier' of G is set
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
V is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
dom V is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
E is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E . v1 is set
V . v1 is set
the Target of G . (V . v1) is set
v1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
E . (v1 + 1) is set
the Source of G . (V . v1) is set
len V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G is non empty V68() MultiGraphStruct
the carrier of G is non empty set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
the carrier' of G is set
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
V is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
rng V is finite set
E is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
rng E is finite set
v1 is set
the Target of G . v1 is set
the Source of G . v1 is set
v2 is Element of the carrier' of G
G9 is Element of the carrier of G
G -VSet (rng V) is set
{ b₁ where b₁ is Element of the carrier of G : ex b₂ being Element of the carrier' of G st
( b₂ in rng V & ( b₁ = the Source of G . b₂ or b₁ = the Target of G . b₂ ) ) } is set
E9 is Element of the carrier of G
G is non empty V68() MultiGraphStruct
V is set
G -VSet V is set
the carrier of G is non empty set
the carrier' of G is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
{ b₁ where b₁ is Element of the carrier of G : ex b₂ being Element of the carrier' of G st
( b₂ in V & ( b₁ = the Source of G . b₂ or b₁ = the Target of G . b₂ ) ) } is set
bool the carrier of G is set
{ b₁ where b₁ is Element of the carrier of G : S₁[b₁] } is set
G is non empty V68() MultiGraphStruct
(G,{}) is Element of bool the carrier of G
the carrier of G is non empty set
bool the carrier of G is set
the carrier' of G is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
{ b₁ where b₁ is Element of the carrier of G : ex b₂ being Element of the carrier' of G st
( b₂ in {} & ( b₁ = the Source of G . b₂ or b₁ = the Target of G . b₂ ) ) } is set
V is set
E is Element of the carrier of G
v1 is Element of the carrier' of G
the Source of G . v1 is set
the Target of G . v1 is set
G is non empty V68() MultiGraphStruct
the carrier' of G is set
V is set
E is set
(G,E) is Element of bool the carrier of G
the carrier of G is non empty set
bool the carrier of G is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
{ b₁ where b₁ is Element of the carrier of G : ex b₂ being Element of the carrier' of G st
( b₂ in E & ( b₁ = the Source of G . b₂ or b₁ = the Target of G . b₂ ) ) } is set
the Source of G . V is set
v1 is Element of the carrier of G
G is non empty V68() MultiGraphStruct
the carrier of G is non empty set
the carrier' of G is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
G9 is Element of the carrier of G
E9 is Element of the carrier of G
v2 is non empty set
{ b₁ where b₁ is Element of v2 : ( b₁ = G9 or ex b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G ex b₃ being Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G st
( not b₂ is empty & b₃ is_vertex_seq_of b₂ & b₃ . 1 = G9 & b₃ . (len b₃) = b₁ ) ) } is set
v2 \ { b₁ where b₁ is Element of v2 : ( b₁ = G9 or ex b₂ being Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G ex b₃ being Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G st
( not b₂ is empty & b₃ is_vertex_seq_of b₂ & b₃ . 1 = G9 & b₃ . (len b₃) = b₁ ) ) } is Element of bool v2
bool v2 is set
p9 is non empty set
p is Element of the carrier of G
vs9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
p1 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
p1 . 1 is set
len p1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p1 . (len p1) is set
{ b₁ where b₁ is Element of v2 : S₁[b₁] } is set
vs9 is set
dom the Source of G is set
the carrier' of G \ vs9 is Element of bool the carrier' of G
bool the carrier' of G is set
the Source of G | ( the carrier' of G \ vs9) is Relation-like the carrier' of G -defined the carrier' of G \ vs9 -defined the carrier' of G -defined the carrier of G -valued Function-like Element of bool [: the carrier' of G, the carrier of G:]
dom ( the Source of G | ( the carrier' of G \ vs9)) is set
(dom the Source of G) /\ ( the carrier' of G \ vs9) is Element of bool the carrier' of G
rng the Source of G is set
rng ( the Source of G | ( the carrier' of G \ vs9)) is set
p is non empty set
vs is set
vs is set
( the Source of G | ( the carrier' of G \ vs9)) . vs is set
p is Element of the carrier' of G
( the Source of G | ( the carrier' of G \ vs9)) . p is set
the Source of G . p is set
the Target of G . p is set
m is Element of the carrier of G
<*p*> is Relation-like NAT -defined Function-like non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
i is Element of the carrier of G
<*G9,i*> is Relation-like NAT -defined the carrier of G -valued Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of G
t is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
len t is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
t . 1 is set
t . (len t) is set
ep is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
ep is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
t is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
t . 1 is set
len t is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
t . (len t) is set
ep is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
t is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
t . 1 is set
len t is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
t . (len t) is set
<*p*> is Relation-like NAT -defined Function-like non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
ep ^ <*p*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
<*( the Source of G . p),( the Target of G . p)*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like set
t ^' <*( the Source of G . p),( the Target of G . p)*> is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len <*( the Source of G . p),( the Target of G . p)*> is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(2,(len <*( the Source of G . p),( the Target of G . p)*>)) -cut <*( the Source of G . p),( the Target of G . p)*> is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
t ^ ((2,(len <*( the Source of G . p),( the Target of G . p)*>)) -cut <*( the Source of G . p),( the Target of G . p)*>) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
s is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
i is Element of the carrier of G
ts is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
ts . 1 is set
len ts is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ts . (len ts) is set
ep is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
t is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
t . 1 is set
len t is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
t . (len t) is set
the Target of G . p is set
[:( the carrier' of G \ vs9),p:] is Relation-like set
bool [:( the carrier' of G \ vs9),p:] is set
dom the Target of G is set
the Target of G | ( the carrier' of G \ vs9) is Relation-like the carrier' of G -defined the carrier' of G \ vs9 -defined the carrier' of G -defined the carrier of G -valued Function-like Element of bool [: the carrier' of G, the carrier of G:]
dom ( the Target of G | ( the carrier' of G \ vs9)) is set
(dom the Target of G) /\ ( the carrier' of G \ vs9) is Element of bool the carrier' of G
rng the Target of G is set
rng ( the Target of G | ( the carrier' of G \ vs9)) is set
vs is set
p is set
( the Target of G | ( the carrier' of G \ vs9)) . p is set
i is Element of the carrier' of G
( the Target of G | ( the carrier' of G \ vs9)) . i is set
the Target of G . i is set
the Source of G . i is set
ep is Element of the carrier of G
<*i*> is Relation-like NAT -defined Function-like non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
m is Element of the carrier of G
<*G9,m*> is Relation-like NAT -defined the carrier of G -valued Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of G
s is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
len s is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
s . 1 is set
s . (len s) is set
t is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
t is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
s is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
s . 1 is set
len s is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
s . (len s) is set
t is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
s is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
s . 1 is set
len s is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
s . (len s) is set
<*i*> is Relation-like NAT -defined Function-like non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
t ^ <*i*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
<*( the Target of G . i),( the Source of G . i)*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like set
s ^' <*( the Target of G . i),( the Source of G . i)*> is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len <*( the Target of G . i),( the Source of G . i)*> is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(2,(len <*( the Target of G . i),( the Source of G . i)*>)) -cut <*( the Target of G . i),( the Source of G . i)*> is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
s ^ ((2,(len <*( the Target of G . i),( the Source of G . i)*>)) -cut <*( the Target of G . i),( the Source of G . i)*>) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
ts is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
m is Element of the carrier of G
p1 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
p1 . 1 is set
len p1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p1 . (len p1) is set
t is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
s is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
s . 1 is set
len s is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
s . (len s) is set
the Source of G . i is set
p is set
the Target of G | vs9 is Relation-like the carrier' of G -defined vs9 -defined the carrier' of G -defined the carrier of G -valued Function-like Element of bool [: the carrier' of G, the carrier of G:]
dom ( the Target of G | vs9) is set
(dom the Target of G) /\ vs9 is set
the carrier' of G /\ vs9 is set
rng ( the Target of G | vs9) is set
p is set
i is set
( the Target of G | vs9) . i is set
the Target of G . i is set
[:vs9,p9:] is Relation-like set
bool [:vs9,p9:] is set
the Source of G | vs9 is Relation-like the carrier' of G -defined vs9 -defined the carrier' of G -defined the carrier of G -valued Function-like Element of bool [: the carrier' of G, the carrier of G:]
dom ( the Source of G | vs9) is set
(dom the Source of G) /\ vs9 is set
rng ( the Source of G | vs9) is set
i is set
m is set
( the Source of G | vs9) . m is set
the Source of G . m is set
i is Relation-like vs9 -defined p9 -valued Function-like V25(vs9,p9) Element of bool [:vs9,p9:]
p is Relation-like vs9 -defined p9 -valued Function-like V25(vs9,p9) Element of bool [:vs9,p9:]
MultiGraphStruct(# p9,vs9,i,p #) is strict MultiGraphStruct
vs is Relation-like the carrier' of G \ vs9 -defined p -valued Function-like V25( the carrier' of G \ vs9,p) Element of bool [:( the carrier' of G \ vs9),p:]
vs is Relation-like the carrier' of G \ vs9 -defined p -valued Function-like V25( the carrier' of G \ vs9,p) Element of bool [:( the carrier' of G \ vs9),p:]
MultiGraphStruct(# p,( the carrier' of G \ vs9),vs,vs #) is strict MultiGraphStruct
m is non empty V68() MultiGraphStruct
ep is non empty V68() MultiGraphStruct
MultiGraphStruct(# the carrier of G, the carrier' of G, the Source of G, the Target of G #) is strict MultiGraphStruct
the Target of m is Relation-like the carrier' of m -defined the carrier of m -valued Function-like V25( the carrier' of m, the carrier of m) Element of bool [: the carrier' of m, the carrier of m:]
the carrier' of m is set
the carrier of m is non empty set
[: the carrier' of m, the carrier of m:] is Relation-like set
bool [: the carrier' of m, the carrier of m:] is set
the Target of ep is Relation-like the carrier' of ep -defined the carrier of ep -valued Function-like V25( the carrier' of ep, the carrier of ep) Element of bool [: the carrier' of ep, the carrier of ep:]
the carrier' of ep is set
the carrier of ep is non empty set
[: the carrier' of ep, the carrier of ep:] is Relation-like set
bool [: the carrier' of ep, the carrier of ep:] is set
s is set
dom the Target of m is set
dom the Target of ep is set
(dom the Target of m) /\ (dom the Target of ep) is set
the Target of m . s is set
the Target of ep . s is set
the Source of m is Relation-like the carrier' of m -defined the carrier of m -valued Function-like V25( the carrier' of m, the carrier of m) Element of bool [: the carrier' of m, the carrier of m:]
the Source of ep is Relation-like the carrier' of ep -defined the carrier of ep -valued Function-like V25( the carrier' of ep, the carrier of ep) Element of bool [: the carrier' of ep, the carrier of ep:]
m \/ ep is non empty V68() strict MultiGraphStruct
s is set
dom the Source of m is set
dom the Source of ep is set
(dom the Source of m) /\ (dom the Source of ep) is set
the Source of m . s is set
the Source of ep . s is set
t is non empty V68() strict MultiGraphStruct
the Source of t is Relation-like the carrier' of t -defined the carrier of t -valued Function-like V25( the carrier' of t, the carrier of t) Element of bool [: the carrier' of t, the carrier of t:]
the carrier' of t is set
the carrier of t is non empty set
[: the carrier' of t, the carrier of t:] is Relation-like set
bool [: the carrier' of t, the carrier of t:] is set
the Target of t is Relation-like the carrier' of t -defined the carrier of t -valued Function-like V25( the carrier' of t, the carrier of t) Element of bool [: the carrier' of t, the carrier of t:]
s is set
the Source of t . s is set
the Source of m . s is set
the Target of t . s is set
the Target of m . s is set
ts is set
the Source of t . ts is set
the Source of ep . ts is set
the Target of t . ts is set
the Target of ep . ts is set
the carrier of m \/ the carrier of ep is non empty set
the carrier' of m \/ the carrier' of ep is set
v2 is non empty V68() MultiGraphStruct
the carrier of v2 is non empty set
G9 is non empty V68() MultiGraphStruct
the carrier of G9 is non empty set
the Element of the carrier of G9 is Element of the carrier of G9
the Element of the carrier of v2 is Element of the carrier of v2
the Target of G9 is Relation-like the carrier' of G9 -defined the carrier of G9 -valued Function-like V25( the carrier' of G9, the carrier of G9) Element of bool [: the carrier' of G9, the carrier of G9:]
the carrier' of G9 is set
[: the carrier' of G9, the carrier of G9:] is Relation-like set
bool [: the carrier' of G9, the carrier of G9:] is set
the Target of v2 is Relation-like the carrier' of v2 -defined the carrier of v2 -valued Function-like V25( the carrier' of v2, the carrier of v2) Element of bool [: the carrier' of v2, the carrier of v2:]
the carrier' of v2 is set
[: the carrier' of v2, the carrier of v2:] is Relation-like set
bool [: the carrier' of v2, the carrier of v2:] is set
the Source of G9 is Relation-like the carrier' of G9 -defined the carrier of G9 -valued Function-like V25( the carrier' of G9, the carrier of G9) Element of bool [: the carrier' of G9, the carrier of G9:]
the Source of v2 is Relation-like the carrier' of v2 -defined the carrier of v2 -valued Function-like V25( the carrier' of v2, the carrier of v2) Element of bool [: the carrier' of v2, the carrier of v2:]
MultiGraphStruct(# the carrier of G, the carrier' of G, the Source of G, the Target of G #) is strict MultiGraphStruct
v2 \/ G9 is non empty V68() strict MultiGraphStruct
the carrier' of v2 \/ the carrier' of G9 is set
the carrier of MultiGraphStruct(# the carrier of G, the carrier' of G, the Source of G, the Target of G #) is set
the carrier of v2 \/ the carrier of G9 is non empty set
the carrier of v2 /\ the carrier of G9 is set
p is Element of the carrier of G
i is Element of the carrier of G
m is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
ep is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
ep . 1 is set
len ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep . (len ep) is set
dom ep is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
len m is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len m) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
rng m is finite set
t is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
ep . t is set
1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
s is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
s + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
m . s is set
dom m is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
the Target of v2 . (m . s) is set
the Source of v2 . (m . s) is set
ep . s is set
the Target of G . (m . s) is set
ep . (s + 1) is set
the Source of G . (m . s) is set
ep . s is set
the Source of G . (m . s) is set
ep . (s + 1) is set
the Target of G . (m . s) is set
ep . s is set
the Target of G . (m . s) is set
ep . (s + 1) is set
the Source of G . (m . s) is set
the Target of G9 . (m . s) is set
the Source of G9 . (m . s) is set
ep . s is set
the Target of G . (m . s) is set
ep . (s + 1) is set
the Source of G . (m . s) is set
ep . s is set
the Source of G . (m . s) is set
ep . (s + 1) is set
the Target of G . (m . s) is set
ep . s is set
the Target of G . (m . s) is set
ep . (s + 1) is set
the Source of G . (m . s) is set
G is non empty V68() connected MultiGraphStruct
the carrier of G is non empty set
the carrier' of G is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
V is set
(G,V) is Element of bool the carrier of G
bool the carrier of G is set
{ b₁ where b₁ is Element of the carrier of G : ex b₂ being Element of the carrier' of G st
( b₂ in V & ( b₁ = the Source of G . b₂ or b₁ = the Target of G . b₂ ) ) } is set
E is Element of the carrier of G
v1 is set
v1 is set
v2 is Element of the carrier of G
G9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
E9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
E9 . 1 is set
len E9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E9 . (len E9) is set
len G9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len G9) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
1 + 0 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
P9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
P9 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
E9 . (P9 + 1) is set
dom E9 is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
E9 . P9 is set
p9 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
rng p9 is finite set
dom p9 is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
p9 . P9 is set
n is Element of the carrier of G
p is Element of the carrier' of G
the Target of G . p is set
the Source of G . p is set
vs9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
1 + vs9 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
len p9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
vs9 is Element of the carrier of G
G is non empty V68() MultiGraphStruct
the carrier of G is non empty set
the carrier' of G is set
bool the carrier' of G is set
E is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
V is Element of the carrier of G
v1 is set
v2 is set
v2 is set
the Target of G . v2 is set
G9 is set
the Target of G . G9 is set
v1 is Element of bool the carrier' of G
v2 is Element of bool the carrier' of G
G9 is set
the Target of G . G9 is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
v1 is set
v2 is set
v2 is set
the Source of G . v2 is set
G9 is set
the Source of G . G9 is set
v1 is Element of bool the carrier' of G
v2 is Element of bool the carrier' of G
G9 is set
the Source of G . G9 is set
G is non empty V68() MultiGraphStruct
the carrier of G is non empty set
the carrier' of G is set
V is Element of the carrier of G
E is set
(G,V,E) is Element of bool the carrier' of G
bool the carrier' of G is set
(G,V,E) is Element of bool the carrier' of G
(G,V,E) \/ (G,V,E) is Element of bool the carrier' of G
G is non empty V68() finite MultiGraphStruct
the carrier of G is non empty set
V is Element of the carrier of G
E is set
(G,V,E) is Element of bool the carrier' of G
the carrier' of G is set
bool the carrier' of G is set
(G,V,E) is Element of bool the carrier' of G
(G,V,E) is Element of bool the carrier' of G
(G,V,E) \/ (G,V,E) is finite Element of bool the carrier' of G
G is non empty V68() MultiGraphStruct
the carrier of G is non empty set
V is Element of the carrier of G
E is Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() set
(G,V,E) is Element of bool the carrier' of G
the carrier' of G is set
bool the carrier' of G is set
v1 is set
(G,V,E) is Element of bool the carrier' of G
v1 is set
(G,V,E) is Element of bool the carrier' of G
(G,V,E) \/ (G,V,E) is Relation-like finite V32() V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool the carrier' of G
G is non empty V68() MultiGraphStruct
the carrier of G is non empty set
V is Element of the carrier of G
the carrier' of G is set
(G,V, the carrier' of G) is Element of bool the carrier' of G
bool the carrier' of G is set
(G,V, the carrier' of G) is Element of bool the carrier' of G
G is non empty V68() MultiGraphStruct
the carrier of G is non empty set
V is Element of the carrier of G
(G,V) is Element of bool the carrier' of G
the carrier' of G is set
bool the carrier' of G is set
(G,V, the carrier' of G) is Element of bool the carrier' of G
E is set
(G,V,E) is Element of bool the carrier' of G
v1 is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G . v1 is set
G is non empty V68() MultiGraphStruct
the carrier of G is non empty set
V is Element of the carrier of G
(G,V) is Element of bool the carrier' of G
the carrier' of G is set
bool the carrier' of G is set
(G,V, the carrier' of G) is Element of bool the carrier' of G
E is set
(G,V,E) is Element of bool the carrier' of G
v1 is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Source of G . v1 is set
G is non empty V68() finite MultiGraphStruct
the carrier of G is non empty set
V is Element of the carrier of G
(G,V) is Element of bool the carrier' of G
the carrier' of G is set
bool the carrier' of G is set
(G,V, the carrier' of G) is finite Element of bool the carrier' of G
(G,V) is Element of bool the carrier' of G
(G,V, the carrier' of G) is finite Element of bool the carrier' of G
G is non empty V68() finite MultiGraphStruct
the carrier of G is non empty set
V is Element of the carrier of G
(G,V) is finite Element of bool the carrier' of G
the carrier' of G is set
bool the carrier' of G is set
(G,V, the carrier' of G) is finite Element of bool the carrier' of G
card (G,V) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesIn V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
E is finite set
card E is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v1 is set
the Target of G . v1 is set
G is non empty V68() finite MultiGraphStruct
the carrier of G is non empty set
V is Element of the carrier of G
(G,V) is finite Element of bool the carrier' of G
the carrier' of G is set
bool the carrier' of G is set
(G,V, the carrier' of G) is finite Element of bool the carrier' of G
card (G,V) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesOut V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
E is finite set
card E is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v1 is set
the Source of G . v1 is set
G is non empty V68() finite MultiGraphStruct
the carrier of G is non empty set
V is Element of the carrier of G
E is set
(G,V,E) is finite Element of bool the carrier' of G
the carrier' of G is set
bool the carrier' of G is set
card (G,V,E) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,E) is finite Element of bool the carrier' of G
card (G,V,E) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,V,E)) + (card (G,V,E)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G is non empty V68() finite MultiGraphStruct
the carrier of G is non empty set
the carrier' of G is set
V is Element of the carrier of G
Degree V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesIn V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesOut V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(EdgesIn V) + (EdgesOut V) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V, the carrier' of G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V, the carrier' of G) is finite Element of bool the carrier' of G
bool the carrier' of G is set
card (G,V, the carrier' of G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V, the carrier' of G) is finite Element of bool the carrier' of G
card (G,V, the carrier' of G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,V, the carrier' of G)) + (card (G,V, the carrier' of G)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V) is finite Element of bool the carrier' of G
card (G,V) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,V)) + (EdgesOut V) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V) is finite Element of bool the carrier' of G
card (G,V) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,V, the carrier' of G)) + (card (G,V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G is set
V is non empty V68() finite MultiGraphStruct
the carrier of V is non empty set
E is Element of the carrier of V
(V,E,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(V,E,G) is finite Element of bool the carrier' of V
the carrier' of V is set
bool the carrier' of V is set
card (V,E,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(V,E,G) is finite Element of bool the carrier' of V
card (V,E,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (V,E,G)) + (card (V,E,G)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(V,E,G) is finite Element of bool the carrier' of V
(V,E,G) \/ (V,E,G) is finite Element of bool the carrier' of V
G is set
V is set
E is non empty V68() finite MultiGraphStruct
the carrier of E is non empty set
the carrier' of E is set
the Target of E is Relation-like the carrier' of E -defined the carrier of E -valued Function-like V25( the carrier' of E, the carrier of E) Element of bool [: the carrier' of E, the carrier of E:]
[: the carrier' of E, the carrier of E:] is Relation-like set
bool [: the carrier' of E, the carrier of E:] is set
the Target of E . G is set
the Source of E is Relation-like the carrier' of E -defined the carrier of E -valued Function-like V25( the carrier' of E, the carrier of E) Element of bool [: the carrier' of E, the carrier of E:]
the Source of E . G is set
v1 is Element of the carrier of E
Degree v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesIn v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesOut v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(EdgesIn v1) + (EdgesOut v1) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(E,v1,V) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(E,v1,V) is finite Element of bool the carrier' of E
bool the carrier' of E is set
card (E,v1,V) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(E,v1,V) is finite Element of bool the carrier' of E
card (E,v1,V) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (E,v1,V)) + (card (E,v1,V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(E,v1, the carrier' of E) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(E,v1, the carrier' of E) is finite Element of bool the carrier' of E
card (E,v1, the carrier' of E) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(E,v1, the carrier' of E) is finite Element of bool the carrier' of E
card (E,v1, the carrier' of E) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (E,v1, the carrier' of E)) + (card (E,v1, the carrier' of E)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(E,v1) is finite Element of bool the carrier' of E
(E,v1) is finite Element of bool the carrier' of E
G is non empty V68() finite MultiGraphStruct
the carrier of G is non empty set
V is Element of the carrier of G
E is set
(G,V,E) is finite Element of bool the carrier' of G
the carrier' of G is set
bool the carrier' of G is set
card (G,V,E) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v1 is set
v1 \ E is Element of bool v1
bool v1 is set
(G,V,(v1 \ E)) is finite Element of bool the carrier' of G
card (G,V,(v1 \ E)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,v1) is finite Element of bool the carrier' of G
card (G,V,v1) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,V,v1)) - (card (G,V,E)) is V39() integer ext-real V122() set
E \/ (v1 \ E) is set
v2 is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G . v2 is set
(G,V,E) \/ (G,V,(v1 \ E)) is finite Element of bool the carrier' of G
(G,V,E) /\ (G,V,(v1 \ E)) is finite Element of bool the carrier' of G
v2 is set
(card (G,V,E)) + (card (G,V,(v1 \ E))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G is non empty V68() finite MultiGraphStruct
the carrier of G is non empty set
V is Element of the carrier of G
E is set
(G,V,E) is finite Element of bool the carrier' of G
the carrier' of G is set
bool the carrier' of G is set
card (G,V,E) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v1 is set
v1 \ E is Element of bool v1
bool v1 is set
(G,V,(v1 \ E)) is finite Element of bool the carrier' of G
card (G,V,(v1 \ E)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,v1) is finite Element of bool the carrier' of G
card (G,V,v1) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,V,v1)) - (card (G,V,E)) is V39() integer ext-real V122() set
E \/ (v1 \ E) is set
v2 is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Source of G . v2 is set
(G,V,E) \/ (G,V,(v1 \ E)) is finite Element of bool the carrier' of G
(G,V,E) /\ (G,V,(v1 \ E)) is finite Element of bool the carrier' of G
v2 is set
(card (G,V,E)) + (card (G,V,(v1 \ E))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G is non empty V68() finite MultiGraphStruct
the carrier of G is non empty set
V is Element of the carrier of G
E is set
(G,V,E) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,E) is finite Element of bool the carrier' of G
the carrier' of G is set
bool the carrier' of G is set
card (G,V,E) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,E) is finite Element of bool the carrier' of G
card (G,V,E) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,V,E)) + (card (G,V,E)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v1 is set
v1 \ E is Element of bool v1
bool v1 is set
(G,V,(v1 \ E)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,(v1 \ E)) is finite Element of bool the carrier' of G
card (G,V,(v1 \ E)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,(v1 \ E)) is finite Element of bool the carrier' of G
card (G,V,(v1 \ E)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,V,(v1 \ E))) + (card (G,V,(v1 \ E))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,v1) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,v1) is finite Element of bool the carrier' of G
card (G,V,v1) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,v1) is finite Element of bool the carrier' of G
card (G,V,v1) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,V,v1)) + (card (G,V,v1)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,v1) - (G,V,E) is V39() integer ext-real V122() set
(card (G,V,v1)) - (card (G,V,E)) is V39() integer ext-real V122() set
(card (G,V,v1)) - (card (G,V,E)) is V39() integer ext-real V122() set
G is set
V is non empty V68() finite MultiGraphStruct
the carrier of V is non empty set
the carrier' of V is set
G /\ the carrier' of V is set
E is Element of the carrier of V
(V,E,G) is finite Element of bool the carrier' of V
bool the carrier' of V is set
(V,E,(G /\ the carrier' of V)) is finite Element of bool the carrier' of V
(V,E,G) is finite Element of bool the carrier' of V
(V,E,(G /\ the carrier' of V)) is finite Element of bool the carrier' of V
v2 is set
the Target of V is Relation-like the carrier' of V -defined the carrier of V -valued Function-like V25( the carrier' of V, the carrier of V) Element of bool [: the carrier' of V, the carrier of V:]
[: the carrier' of V, the carrier of V:] is Relation-like set
bool [: the carrier' of V, the carrier of V:] is set
the Target of V . v2 is set
v2 is set
the Source of V is Relation-like the carrier' of V -defined the carrier of V -valued Function-like V25( the carrier' of V, the carrier of V) Element of bool [: the carrier' of V, the carrier of V:]
the Source of V . v2 is set
G is set
V is non empty V68() finite MultiGraphStruct
the carrier of V is non empty set
the carrier' of V is set
G /\ the carrier' of V is set
E is Element of the carrier of V
(V,E,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(V,E,G) is finite Element of bool the carrier' of V
bool the carrier' of V is set
card (V,E,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(V,E,G) is finite Element of bool the carrier' of V
card (V,E,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (V,E,G)) + (card (V,E,G)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(V,E,(G /\ the carrier' of V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(V,E,(G /\ the carrier' of V)) is finite Element of bool the carrier' of V
card (V,E,(G /\ the carrier' of V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(V,E,(G /\ the carrier' of V)) is finite Element of bool the carrier' of V
card (V,E,(G /\ the carrier' of V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (V,E,(G /\ the carrier' of V))) + (card (V,E,(G /\ the carrier' of V))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (V,E,(G /\ the carrier' of V))) + (card (V,E,G)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G is non empty V68() finite MultiGraphStruct
the carrier of G is non empty set
V is Element of the carrier of G
E is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
rng E is finite set
(G,V,(rng E)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,(rng E)) is finite Element of bool the carrier' of G
the carrier' of G is set
bool the carrier' of G is set
card (G,V,(rng E)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,(rng E)) is finite Element of bool the carrier' of G
card (G,V,(rng E)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,V,(rng E))) + (card (G,V,(rng E))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v1 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
rng v1 is finite set
0 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
len E is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
len v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len E) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
dom v1 is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
v2 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
v1 . v2 is set
dom E is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
E . (len E) is set
v1 . (len v1) is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G . (E . (len E)) is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
the Source of G . (E . (len E)) is set
dom E is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
E . v2 is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G . (E . v2) is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
the Source of G . (E . v2) is set
v2 is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G . v2 is set
dom E is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
G9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
E . G9 is set
G9 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
v1 . G9 is set
the Target of G . (E . G9) is set
v1 . (G9 + 1) is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
the Source of G . (E . G9) is set
v2 is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Source of G . v2 is set
dom E is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
G9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
E . G9 is set
G9 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
v1 . G9 is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
the Target of G . (E . G9) is set
v1 . (G9 + 1) is set
the Source of G . (E . G9) is set
G is non empty non void V68() connected finite MultiGraphStruct
the carrier of G is non empty set
V is Element of the carrier of G
Degree V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesIn V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesOut V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(EdgesIn V) + (EdgesOut V) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
the carrier' of G is non empty set
(G,V, the carrier' of G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V, the carrier' of G) is finite Element of bool the carrier' of G
bool the carrier' of G is set
card (G,V, the carrier' of G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V, the carrier' of G) is finite Element of bool the carrier' of G
card (G,V, the carrier' of G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,V, the carrier' of G)) + (card (G,V, the carrier' of G)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
G9 is set
the Source of G . G9 is set
E9 is Element of the carrier of G
E9 is Element of the carrier of G
P9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
n is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
n . 1 is set
len n is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
n . (len n) is set
0 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
len P9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
dom P9 is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
P9 . 1 is set
rng P9 is finite set
the Target of G . (P9 . 1) is set
the Source of G . (P9 . 1) is set
E9 is Element of the carrier of G
G is non empty V68() MultiGraphStruct
the carrier of G is non empty set
the carrier' of G is set
{ the carrier' of G} is non empty trivial finite 1 -element set
the carrier' of G \/ { the carrier' of G} is non empty set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
V is Element of the carrier of G
the carrier' of G .--> V is Relation-like { the carrier' of G} -defined the carrier of G -valued Function-like one-to-one finite set
{ the carrier' of G} --> V is Relation-like { the carrier' of G} -defined the carrier of G -valued {V} -valued Function-like constant non empty total V25({ the carrier' of G},{V}) finite Element of bool [:{ the carrier' of G},{V}:]
{V} is non empty trivial finite 1 -element set
[:{ the carrier' of G},{V}:] is Relation-like finite set
bool [:{ the carrier' of G},{V}:] is finite V32() set
the Source of G +* ( the carrier' of G .--> V) is Relation-like Function-like set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
E is Element of the carrier of G
the carrier' of G .--> E is Relation-like { the carrier' of G} -defined the carrier of G -valued Function-like one-to-one finite set
{ the carrier' of G} --> E is Relation-like { the carrier' of G} -defined the carrier of G -valued {E} -valued Function-like constant non empty total V25({ the carrier' of G},{E}) finite Element of bool [:{ the carrier' of G},{E}:]
{E} is non empty trivial finite 1 -element set
[:{ the carrier' of G},{E}:] is Relation-like finite set
bool [:{ the carrier' of G},{E}:] is finite V32() set
the Target of G +* ( the carrier' of G .--> E) is Relation-like Function-like set
dom ( the carrier' of G .--> E) is finite set
rng ( the carrier' of G .--> E) is finite set
rng the Target of G is set
rng ( the Target of G +* ( the carrier' of G .--> E)) is set
(rng the Target of G) \/ (rng ( the carrier' of G .--> E)) is set
dom ( the Target of G +* ( the carrier' of G .--> E)) is set
dom the Target of G is set
(dom the Target of G) \/ (dom ( the carrier' of G .--> E)) is set
[:( the carrier' of G \/ { the carrier' of G}), the carrier of G:] is Relation-like set
bool [:( the carrier' of G \/ { the carrier' of G}), the carrier of G:] is set
dom ( the carrier' of G .--> V) is finite set
dom ( the Source of G +* ( the carrier' of G .--> V)) is set
dom the Source of G is set
(dom the Source of G) \/ (dom ( the carrier' of G .--> V)) is set
rng ( the carrier' of G .--> V) is finite set
rng the Source of G is set
rng ( the Source of G +* ( the carrier' of G .--> V)) is set
(rng the Source of G) \/ (rng ( the carrier' of G .--> V)) is set
vs is Relation-like the carrier' of G \/ { the carrier' of G} -defined the carrier of G -valued Function-like V25( the carrier' of G \/ { the carrier' of G}, the carrier of G) Element of bool [:( the carrier' of G \/ { the carrier' of G}), the carrier of G:]
p9 is Relation-like the carrier' of G \/ { the carrier' of G} -defined the carrier of G -valued Function-like V25( the carrier' of G \/ { the carrier' of G}, the carrier of G) Element of bool [:( the carrier' of G \/ { the carrier' of G}), the carrier of G:]
MultiGraphStruct(# the carrier of G,( the carrier' of G \/ { the carrier' of G}),vs,p9 #) is strict MultiGraphStruct
vs is non empty V68() strict MultiGraphStruct
the carrier of vs is non empty set
the carrier' of vs is set
the Source of vs is Relation-like the carrier' of vs -defined the carrier of vs -valued Function-like V25( the carrier' of vs, the carrier of vs) Element of bool [: the carrier' of vs, the carrier of vs:]
[: the carrier' of vs, the carrier of vs:] is Relation-like set
bool [: the carrier' of vs, the carrier of vs:] is set
the Target of vs is Relation-like the carrier' of vs -defined the carrier of vs -valued Function-like V25( the carrier' of vs, the carrier of vs) Element of bool [: the carrier' of vs, the carrier of vs:]
v1 is non empty V68() strict MultiGraphStruct
the carrier of v1 is non empty set
the carrier' of v1 is set
the Source of v1 is Relation-like the carrier' of v1 -defined the carrier of v1 -valued Function-like V25( the carrier' of v1, the carrier of v1) Element of bool [: the carrier' of v1, the carrier of v1:]
[: the carrier' of v1, the carrier of v1:] is Relation-like set
bool [: the carrier' of v1, the carrier of v1:] is set
the Target of v1 is Relation-like the carrier' of v1 -defined the carrier of v1 -valued Function-like V25( the carrier' of v1, the carrier of v1) Element of bool [: the carrier' of v1, the carrier of v1:]
v2 is non empty V68() strict MultiGraphStruct
the carrier of v2 is non empty set
the carrier' of v2 is set
the Source of v2 is Relation-like the carrier' of v2 -defined the carrier of v2 -valued Function-like V25( the carrier' of v2, the carrier of v2) Element of bool [: the carrier' of v2, the carrier of v2:]
[: the carrier' of v2, the carrier of v2:] is Relation-like set
bool [: the carrier' of v2, the carrier of v2:] is set
the Target of v2 is Relation-like the carrier' of v2 -defined the carrier of v2 -valued Function-like V25( the carrier' of v2, the carrier of v2) Element of bool [: the carrier' of v2, the carrier of v2:]
G is non empty V68() finite MultiGraphStruct
the carrier of G is non empty set
V is Element of the carrier of G
E is Element of the carrier of G
(G,V,E) is non empty V68() strict MultiGraphStruct
the carrier' of G is set
the carrier of (G,V,E) is non empty set
v2 is finite set
the carrier' of (G,V,E) is set
v1 is finite set
{ the carrier' of G} is non empty trivial finite 1 -element set
v1 \/ { the carrier' of G} is non empty finite set
G is non empty V68() MultiGraphStruct
the carrier of G is non empty set
the carrier' of G is set
{ the carrier' of G} is non empty trivial finite 1 -element set
V is Element of the carrier of G
E is Element of the carrier of G
(G,V,E) is non empty V68() strict MultiGraphStruct
the carrier' of (G,V,E) is set
the carrier' of (G,V,E) \ { the carrier' of G} is Element of bool the carrier' of (G,V,E)
bool the carrier' of (G,V,E) is set
the Source of (G,V,E) is Relation-like the carrier' of (G,V,E) -defined the carrier of (G,V,E) -valued Function-like V25( the carrier' of (G,V,E), the carrier of (G,V,E)) Element of bool [: the carrier' of (G,V,E), the carrier of (G,V,E):]
the carrier of (G,V,E) is non empty set
[: the carrier' of (G,V,E), the carrier of (G,V,E):] is Relation-like set
bool [: the carrier' of (G,V,E), the carrier of (G,V,E):] is set
the Source of (G,V,E) . the carrier' of G is set
the Target of (G,V,E) is Relation-like the carrier' of (G,V,E) -defined the carrier of (G,V,E) -valued Function-like V25( the carrier' of (G,V,E), the carrier of (G,V,E)) Element of bool [: the carrier' of (G,V,E), the carrier of (G,V,E):]
the Target of (G,V,E) . the carrier' of G is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
the carrier' of G \/ { the carrier' of G} is non empty set
n is set
the carrier' of G .--> V is Relation-like { the carrier' of G} -defined the carrier of G -valued Function-like one-to-one finite set
{ the carrier' of G} --> V is Relation-like { the carrier' of G} -defined the carrier of G -valued {V} -valued Function-like constant non empty total V25({ the carrier' of G},{V}) finite Element of bool [:{ the carrier' of G},{V}:]
{V} is non empty trivial finite 1 -element set
[:{ the carrier' of G},{V}:] is Relation-like finite set
bool [:{ the carrier' of G},{V}:] is finite V32() set
dom ( the carrier' of G .--> V) is finite set
the Source of G +* ( the carrier' of G .--> V) is Relation-like Function-like set
( the carrier' of G .--> V) . the carrier' of G is set
the carrier' of G .--> E is Relation-like { the carrier' of G} -defined the carrier of G -valued Function-like one-to-one finite set
{ the carrier' of G} --> E is Relation-like { the carrier' of G} -defined the carrier of G -valued {E} -valued Function-like constant non empty total V25({ the carrier' of G},{E}) finite Element of bool [:{ the carrier' of G},{E}:]
{E} is non empty trivial finite 1 -element set
[:{ the carrier' of G},{E}:] is Relation-like finite set
bool [:{ the carrier' of G},{E}:] is finite V32() set
dom ( the carrier' of G .--> E) is finite set
the Target of G +* ( the carrier' of G .--> E) is Relation-like Function-like set
( the carrier' of G .--> E) . the carrier' of G is set
G is set
V is non empty V68() MultiGraphStruct
the carrier of V is non empty set
the carrier' of V is set
the Source of V is Relation-like the carrier' of V -defined the carrier of V -valued Function-like V25( the carrier' of V, the carrier of V) Element of bool [: the carrier' of V, the carrier of V:]
[: the carrier' of V, the carrier of V:] is Relation-like set
bool [: the carrier' of V, the carrier of V:] is set
the Source of V . G is set
the Target of V is Relation-like the carrier' of V -defined the carrier of V -valued Function-like V25( the carrier' of V, the carrier of V) Element of bool [: the carrier' of V, the carrier of V:]
the Target of V . G is set
E is Element of the carrier of V
v1 is Element of the carrier of V
(V,E,v1) is non empty V68() strict MultiGraphStruct
the Source of (V,E,v1) is Relation-like the carrier' of (V,E,v1) -defined the carrier of (V,E,v1) -valued Function-like V25( the carrier' of (V,E,v1), the carrier of (V,E,v1)) Element of bool [: the carrier' of (V,E,v1), the carrier of (V,E,v1):]
the carrier' of (V,E,v1) is set
the carrier of (V,E,v1) is non empty set
[: the carrier' of (V,E,v1), the carrier of (V,E,v1):] is Relation-like set
bool [: the carrier' of (V,E,v1), the carrier of (V,E,v1):] is set
the Source of (V,E,v1) . G is set
the Target of (V,E,v1) is Relation-like the carrier' of (V,E,v1) -defined the carrier of (V,E,v1) -valued Function-like V25( the carrier' of (V,E,v1), the carrier of (V,E,v1)) Element of bool [: the carrier' of (V,E,v1), the carrier of (V,E,v1):]
the Target of (V,E,v1) . G is set
the carrier' of V .--> E is Relation-like { the carrier' of V} -defined the carrier of V -valued Function-like one-to-one finite set
{ the carrier' of V} is non empty trivial finite 1 -element set
{ the carrier' of V} --> E is Relation-like { the carrier' of V} -defined the carrier of V -valued {E} -valued Function-like constant non empty total V25({ the carrier' of V},{E}) finite Element of bool [:{ the carrier' of V},{E}:]
{E} is non empty trivial finite 1 -element set
[:{ the carrier' of V},{E}:] is Relation-like finite set
bool [:{ the carrier' of V},{E}:] is finite V32() set
dom ( the carrier' of V .--> E) is finite set
the Source of V +* ( the carrier' of V .--> E) is Relation-like Function-like set
( the Source of V +* ( the carrier' of V .--> E)) . G is set
the carrier' of V .--> v1 is Relation-like { the carrier' of V} -defined the carrier of V -valued Function-like one-to-one finite set
{ the carrier' of V} --> v1 is Relation-like { the carrier' of V} -defined the carrier of V -valued {v1} -valued Function-like constant non empty total V25({ the carrier' of V},{v1}) finite Element of bool [:{ the carrier' of V},{v1}:]
{v1} is non empty trivial finite 1 -element set
[:{ the carrier' of V},{v1}:] is Relation-like finite set
bool [:{ the carrier' of V},{v1}:] is finite V32() set
dom ( the carrier' of V .--> v1) is finite set
the Target of V +* ( the carrier' of V .--> v1) is Relation-like Function-like set
( the Target of V +* ( the carrier' of V .--> v1)) . G is set
G is non empty V68() MultiGraphStruct
the carrier of G is non empty set
V is Element of the carrier of G
E is Element of the carrier of G
(G,V,E) is non empty V68() strict MultiGraphStruct
the carrier of (G,V,E) is non empty set
v1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
v2 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
G9 is Relation-like NAT -defined the carrier of (G,V,E) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (G,V,E)
len G9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
len v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len v1) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
E9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G9 /. E9 is Element of the carrier of (G,V,E)
E9 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
G9 /. (E9 + 1) is Element of the carrier of (G,V,E)
v1 . E9 is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
the carrier' of G is set
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
v2 /. E9 is Element of the carrier of G
v2 /. (E9 + 1) is Element of the carrier of G
the Source of G . (v1 . E9) is set
the Target of G . (v1 . E9) is set
the Source of (G,V,E) is Relation-like the carrier' of (G,V,E) -defined the carrier of (G,V,E) -valued Function-like V25( the carrier' of (G,V,E), the carrier of (G,V,E)) Element of bool [: the carrier' of (G,V,E), the carrier of (G,V,E):]
the carrier' of (G,V,E) is set
[: the carrier' of (G,V,E), the carrier of (G,V,E):] is Relation-like set
bool [: the carrier' of (G,V,E), the carrier of (G,V,E):] is set
the Target of (G,V,E) is Relation-like the carrier' of (G,V,E) -defined the carrier of (G,V,E) -valued Function-like V25( the carrier' of (G,V,E), the carrier of (G,V,E)) Element of bool [: the carrier' of (G,V,E), the carrier of (G,V,E):]
rng v1 is finite set
dom v1 is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
the Source of (G,V,E) . (v1 . E9) is set
the Target of (G,V,E) . (v1 . E9) is set
G is non empty V68() MultiGraphStruct
the carrier of G is non empty set
V is Element of the carrier of G
E is Element of the carrier of G
(G,V,E) is non empty V68() strict MultiGraphStruct
v1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
G9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
the carrier' of G is set
rng v1 is finite set
the carrier' of (G,V,E) is set
{ the carrier' of G} is non empty trivial finite 1 -element set
the carrier' of G \/ { the carrier' of G} is non empty set
the carrier of (G,V,E) is non empty set
E9 is Relation-like NAT -defined the carrier of (G,V,E) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (G,V,E)
G is non empty V68() MultiGraphStruct
the carrier of G is non empty set
the carrier' of G is set
v1 is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G
V is Element of the carrier of G
E is Element of the carrier of G
(G,V,E) is non empty V68() strict MultiGraphStruct
the carrier' of (G,V,E) is set
G is set
V is non empty V68() MultiGraphStruct
the carrier of V is non empty set
E is Element of the carrier of V
(V,E,G) is Element of bool the carrier' of V
the carrier' of V is set
bool the carrier' of V is set
v1 is Element of the carrier of V
(V,E,v1) is non empty V68() strict MultiGraphStruct
the carrier of (V,E,v1) is non empty set
v2 is Element of the carrier of (V,E,v1)
((V,E,v1),v2,G) is Element of bool the carrier' of (V,E,v1)
the carrier' of (V,E,v1) is set
bool the carrier' of (V,E,v1) is set
the Target of V is Relation-like the carrier' of V -defined the carrier of V -valued Function-like V25( the carrier' of V, the carrier of V) Element of bool [: the carrier' of V, the carrier of V:]
[: the carrier' of V, the carrier of V:] is Relation-like set
bool [: the carrier' of V, the carrier of V:] is set
the Target of (V,E,v1) is Relation-like the carrier' of (V,E,v1) -defined the carrier of (V,E,v1) -valued Function-like V25( the carrier' of (V,E,v1), the carrier of (V,E,v1)) Element of bool [: the carrier' of (V,E,v1), the carrier of (V,E,v1):]
[: the carrier' of (V,E,v1), the carrier of (V,E,v1):] is Relation-like set
bool [: the carrier' of (V,E,v1), the carrier of (V,E,v1):] is set
{ the carrier' of V} is non empty trivial finite 1 -element set
the carrier' of V \/ { the carrier' of V} is non empty set
p is set
the Target of (V,E,v1) . p is set
the Target of (V,E,v1) . the carrier' of V is set
the Target of V . p is set
G is set
V is non empty V68() MultiGraphStruct
the carrier of V is non empty set
E is Element of the carrier of V
(V,E,G) is Element of bool the carrier' of V
the carrier' of V is set
bool the carrier' of V is set
v1 is Element of the carrier of V
(V,v1,E) is non empty V68() strict MultiGraphStruct
the carrier of (V,v1,E) is non empty set
v2 is Element of the carrier of (V,v1,E)
((V,v1,E),v2,G) is Element of bool the carrier' of (V,v1,E)
the carrier' of (V,v1,E) is set
bool the carrier' of (V,v1,E) is set
the Source of V is Relation-like the carrier' of V -defined the carrier of V -valued Function-like V25( the carrier' of V, the carrier of V) Element of bool [: the carrier' of V, the carrier of V:]
[: the carrier' of V, the carrier of V:] is Relation-like set
bool [: the carrier' of V, the carrier of V:] is set
the Source of (V,v1,E) is Relation-like the carrier' of (V,v1,E) -defined the carrier of (V,v1,E) -valued Function-like V25( the carrier' of (V,v1,E), the carrier of (V,v1,E)) Element of bool [: the carrier' of (V,v1,E), the carrier of (V,v1,E):]
[: the carrier' of (V,v1,E), the carrier of (V,v1,E):] is Relation-like set
bool [: the carrier' of (V,v1,E), the carrier of (V,v1,E):] is set
{ the carrier' of V} is non empty trivial finite 1 -element set
the carrier' of V \/ { the carrier' of V} is non empty set
p is set
the Source of (V,v1,E) . p is set
the Source of (V,v1,E) . the carrier' of V is set
the Source of V . p is set
G is set
V is non empty V68() MultiGraphStruct
the carrier of V is non empty set
the carrier' of V is set
{ the carrier' of V} is non empty trivial finite 1 -element set
E is Element of the carrier of V
v1 is Element of the carrier of V
(V,v1,E) is non empty V68() strict MultiGraphStruct
the carrier of (V,v1,E) is non empty set
(V,v1,G) is Element of bool the carrier' of V
bool the carrier' of V is set
(V,v1,G) \/ { the carrier' of V} is non empty set
v2 is Element of the carrier of (V,v1,E)
((V,v1,E),v2,G) is Element of bool the carrier' of (V,v1,E)
the carrier' of (V,v1,E) is set
bool the carrier' of (V,v1,E) is set
the Source of V is Relation-like the carrier' of V -defined the carrier of V -valued Function-like V25( the carrier' of V, the carrier of V) Element of bool [: the carrier' of V, the carrier of V:]
[: the carrier' of V, the carrier of V:] is Relation-like set
bool [: the carrier' of V, the carrier of V:] is set
the Source of (V,v1,E) is Relation-like the carrier' of (V,v1,E) -defined the carrier of (V,v1,E) -valued Function-like V25( the carrier' of (V,v1,E), the carrier of (V,v1,E)) Element of bool [: the carrier' of (V,v1,E), the carrier of (V,v1,E):]
[: the carrier' of (V,v1,E), the carrier of (V,v1,E):] is Relation-like set
bool [: the carrier' of (V,v1,E), the carrier of (V,v1,E):] is set
the carrier' of V \/ { the carrier' of V} is non empty set
p is set
the Source of (V,v1,E) . p is set
the Source of V . p is set
the Source of V . p is set
the Source of (V,v1,E) . the carrier' of V is set
(V,v1,G) /\ { the carrier' of V} is finite Element of bool the carrier' of V
p is set
G is set
V is non empty V68() MultiGraphStruct
the carrier of V is non empty set
the carrier' of V is set
{ the carrier' of V} is non empty trivial finite 1 -element set
E is Element of the carrier of V
v1 is Element of the carrier of V
(V,E,v1) is non empty V68() strict MultiGraphStruct
the carrier of (V,E,v1) is non empty set
(V,v1,G) is Element of bool the carrier' of V
bool the carrier' of V is set
(V,v1,G) \/ { the carrier' of V} is non empty set
v2 is Element of the carrier of (V,E,v1)
((V,E,v1),v2,G) is Element of bool the carrier' of (V,E,v1)
the carrier' of (V,E,v1) is set
bool the carrier' of (V,E,v1) is set
the Target of V is Relation-like the carrier' of V -defined the carrier of V -valued Function-like V25( the carrier' of V, the carrier of V) Element of bool [: the carrier' of V, the carrier of V:]
[: the carrier' of V, the carrier of V:] is Relation-like set
bool [: the carrier' of V, the carrier of V:] is set
the Target of (V,E,v1) is Relation-like the carrier' of (V,E,v1) -defined the carrier of (V,E,v1) -valued Function-like V25( the carrier' of (V,E,v1), the carrier of (V,E,v1)) Element of bool [: the carrier' of (V,E,v1), the carrier of (V,E,v1):]
[: the carrier' of (V,E,v1), the carrier of (V,E,v1):] is Relation-like set
bool [: the carrier' of (V,E,v1), the carrier of (V,E,v1):] is set
the carrier' of V \/ { the carrier' of V} is non empty set
p is set
the Target of (V,E,v1) . p is set
the Target of V . p is set
the Target of V . p is set
the Target of (V,E,v1) . the carrier' of V is set
(V,v1,G) /\ { the carrier' of V} is finite Element of bool the carrier' of V
p is set
G is set
V is non empty V68() MultiGraphStruct
the carrier of V is non empty set
E is Element of the carrier of V
v1 is Element of the carrier of V
(V,v1,G) is Element of bool the carrier' of V
the carrier' of V is set
bool the carrier' of V is set
v2 is Element of the carrier of V
(V,E,v2) is non empty V68() strict MultiGraphStruct
the carrier of (V,E,v2) is non empty set
G9 is Element of the carrier of (V,E,v2)
((V,E,v2),G9,G) is Element of bool the carrier' of (V,E,v2)
the carrier' of (V,E,v2) is set
bool the carrier' of (V,E,v2) is set
the Target of V is Relation-like the carrier' of V -defined the carrier of V -valued Function-like V25( the carrier' of V, the carrier of V) Element of bool [: the carrier' of V, the carrier of V:]
[: the carrier' of V, the carrier of V:] is Relation-like set
bool [: the carrier' of V, the carrier of V:] is set
the Target of (V,E,v2) is Relation-like the carrier' of (V,E,v2) -defined the carrier of (V,E,v2) -valued Function-like V25( the carrier' of (V,E,v2), the carrier of (V,E,v2)) Element of bool [: the carrier' of (V,E,v2), the carrier of (V,E,v2):]
[: the carrier' of (V,E,v2), the carrier of (V,E,v2):] is Relation-like set
bool [: the carrier' of (V,E,v2), the carrier of (V,E,v2):] is set
{ the carrier' of V} is non empty trivial finite 1 -element set
the carrier' of V \/ { the carrier' of V} is non empty set
vs9 is set
the Target of (V,E,v2) . vs9 is set
the Target of (V,E,v2) . the carrier' of V is set
the Target of V . vs9 is set
G is set
V is non empty V68() MultiGraphStruct
the carrier of V is non empty set
E is Element of the carrier of V
v1 is Element of the carrier of V
(V,v1,G) is Element of bool the carrier' of V
the carrier' of V is set
bool the carrier' of V is set
v2 is Element of the carrier of V
(V,v2,E) is non empty V68() strict MultiGraphStruct
the carrier of (V,v2,E) is non empty set
G9 is Element of the carrier of (V,v2,E)
((V,v2,E),G9,G) is Element of bool the carrier' of (V,v2,E)
the carrier' of (V,v2,E) is set
bool the carrier' of (V,v2,E) is set
the Source of V is Relation-like the carrier' of V -defined the carrier of V -valued Function-like V25( the carrier' of V, the carrier of V) Element of bool [: the carrier' of V, the carrier of V:]
[: the carrier' of V, the carrier of V:] is Relation-like set
bool [: the carrier' of V, the carrier of V:] is set
the Source of (V,v2,E) is Relation-like the carrier' of (V,v2,E) -defined the carrier of (V,v2,E) -valued Function-like V25( the carrier' of (V,v2,E), the carrier of (V,v2,E)) Element of bool [: the carrier' of (V,v2,E), the carrier of (V,v2,E):]
[: the carrier' of (V,v2,E), the carrier of (V,v2,E):] is Relation-like set
bool [: the carrier' of (V,v2,E), the carrier of (V,v2,E):] is set
{ the carrier' of V} is non empty trivial finite 1 -element set
the carrier' of V \/ { the carrier' of V} is non empty set
vs9 is set
the Source of (V,v2,E) . vs9 is set
the Source of (V,v2,E) . the carrier' of V is set
the Source of V . vs9 is set
G is non empty V68() MultiGraphStruct
the carrier of G is non empty set
the carrier' of G is set
V is Element of the carrier of G
E is Element of the carrier of G
(G,V,E) is non empty V68() strict MultiGraphStruct
the carrier' of (G,V,E) is set
v1 is Relation-like NAT -defined the carrier' of (G,V,E) -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of (G,V,E)
rng v1 is finite set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
the Source of (G,V,E) is Relation-like the carrier' of (G,V,E) -defined the carrier of (G,V,E) -valued Function-like V25( the carrier' of (G,V,E), the carrier of (G,V,E)) Element of bool [: the carrier' of (G,V,E), the carrier of (G,V,E):]
the carrier of (G,V,E) is non empty set
[: the carrier' of (G,V,E), the carrier of (G,V,E):] is Relation-like set
bool [: the carrier' of (G,V,E), the carrier of (G,V,E):] is set
the Target of (G,V,E) is Relation-like the carrier' of (G,V,E) -defined the carrier of (G,V,E) -valued Function-like V25( the carrier' of (G,V,E), the carrier of (G,V,E)) Element of bool [: the carrier' of (G,V,E), the carrier of (G,V,E):]
{ the carrier' of G} is non empty trivial finite 1 -element set
the carrier' of G \/ { the carrier' of G} is non empty set
p is set
p is Relation-like NAT -defined the carrier of (G,V,E) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (G,V,E)
vs9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
len vs9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
len v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len v1) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
p1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
vs9 /. p1 is Element of the carrier of G
p1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
vs9 /. (p1 + 1) is Element of the carrier of G
v1 . p1 is set
p /. p1 is Element of the carrier of (G,V,E)
p /. (p1 + 1) is Element of the carrier of (G,V,E)
the Source of (G,V,E) . (v1 . p1) is set
vs is Element of the carrier of (G,V,E)
the Target of (G,V,E) . (v1 . p1) is set
p is Element of the carrier of (G,V,E)
dom vs9 is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
m is Element of the carrier of G
vs9 . (p1 + 1) is set
dom v1 is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
the Source of G . (v1 . p1) is set
the Target of G . (v1 . p1) is set
i is Element of the carrier of G
vs9 . p1 is set
p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
G is non empty V68() MultiGraphStruct
the carrier of G is non empty set
the carrier' of G is set
V is Element of the carrier of G
E is Element of the carrier of G
(G,V,E) is non empty V68() strict MultiGraphStruct
the carrier' of (G,V,E) is set
the carrier of (G,V,E) is non empty set
v1 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
v2 is Relation-like NAT -defined the carrier' of (G,V,E) -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of (G,V,E)
rng v2 is finite set
G9 is Relation-like NAT -defined the carrier of (G,V,E) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (G,V,E)
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
the Source of (G,V,E) is Relation-like the carrier' of (G,V,E) -defined the carrier of (G,V,E) -valued Function-like V25( the carrier' of (G,V,E), the carrier of (G,V,E)) Element of bool [: the carrier' of (G,V,E), the carrier of (G,V,E):]
[: the carrier' of (G,V,E), the carrier of (G,V,E):] is Relation-like set
bool [: the carrier' of (G,V,E), the carrier of (G,V,E):] is set
the Target of (G,V,E) is Relation-like the carrier' of (G,V,E) -defined the carrier of (G,V,E) -valued Function-like V25( the carrier' of (G,V,E), the carrier of (G,V,E)) Element of bool [: the carrier' of (G,V,E), the carrier of (G,V,E):]
{ the carrier' of G} is non empty trivial finite 1 -element set
the carrier' of G \/ { the carrier' of G} is non empty set
p1 is set
len v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
len v2 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len v2) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
p1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v1 /. p1 is Element of the carrier of G
p1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
v1 /. (p1 + 1) is Element of the carrier of G
v2 . p1 is set
G9 /. p1 is Element of the carrier of (G,V,E)
G9 /. (p1 + 1) is Element of the carrier of (G,V,E)
the Source of (G,V,E) . (v2 . p1) is set
vs is Element of the carrier of (G,V,E)
the Target of (G,V,E) . (v2 . p1) is set
p is Element of the carrier of (G,V,E)
dom v1 is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
m is Element of the carrier of G
v1 . (p1 + 1) is set
dom v2 is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
the Source of G . (v2 . p1) is set
the Target of G . (v2 . p1) is set
i is Element of the carrier of G
v1 . p1 is set
G is non empty V68() connected MultiGraphStruct
the carrier of G is non empty set
V is Element of the carrier of G
E is Element of the carrier of G
(G,V,E) is non empty V68() strict MultiGraphStruct
the carrier of (G,V,E) is non empty set
v2 is Element of the carrier of (G,V,E)
G9 is Element of the carrier of (G,V,E)
E9 is Element of the carrier of G
P9 is Element of the carrier of G
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
p9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
p9 . 1 is set
len p9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p9 . (len p9) is set
vs9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of (G,V,E)
p is Relation-like NAT -defined the carrier of (G,V,E) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (G,V,E)
p1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of (G,V,E)
vs is Relation-like NAT -defined the carrier of (G,V,E) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (G,V,E)
vs . 1 is set
len vs is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
vs . (len vs) is set
G is set
V is non empty V68() finite MultiGraphStruct
the carrier of V is non empty set
the carrier' of V is set
E is Element of the carrier of V
(V,E,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(V,E,G) is finite Element of bool the carrier' of V
bool the carrier' of V is set
card (V,E,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(V,E,G) is finite Element of bool the carrier' of V
card (V,E,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (V,E,G)) + (card (V,E,G)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(V,E,G) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
v1 is Element of the carrier of V
v2 is Element of the carrier of V
(V,v1,v2) is non empty V68() strict finite MultiGraphStruct
the carrier of (V,v1,v2) is non empty set
G9 is Element of the carrier of (V,v1,v2)
((V,v1,v2),G9,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
((V,v1,v2),G9,G) is finite Element of bool the carrier' of (V,v1,v2)
the carrier' of (V,v1,v2) is set
bool the carrier' of (V,v1,v2) is set
card ((V,v1,v2),G9,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
((V,v1,v2),G9,G) is finite Element of bool the carrier' of (V,v1,v2)
card ((V,v1,v2),G9,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card ((V,v1,v2),G9,G)) + (card ((V,v1,v2),G9,G)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
{ the carrier' of V} is non empty trivial finite 1 -element set
(V,E,G) \/ { the carrier' of V} is non empty finite set
card { the carrier' of V} is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(card (V,E,G)) + (card { the carrier' of V}) is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(card (V,E,G)) + ((card (V,E,G)) + (card { the carrier' of V})) is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
((card (V,E,G)) + (card (V,E,G))) + (card { the carrier' of V}) is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
{ the carrier' of V} is non empty trivial finite 1 -element set
(V,E,G) \/ { the carrier' of V} is non empty finite set
card { the carrier' of V} is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(card (V,E,G)) + (card { the carrier' of V}) is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
((card (V,E,G)) + (card { the carrier' of V})) + (card (V,E,G)) is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
((card (V,E,G)) + (card (V,E,G))) + (card { the carrier' of V}) is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
G is set
V is non empty V68() finite MultiGraphStruct
the carrier of V is non empty set
E is Element of the carrier of V
(V,E,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(V,E,G) is finite Element of bool the carrier' of V
the carrier' of V is set
bool the carrier' of V is set
card (V,E,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(V,E,G) is finite Element of bool the carrier' of V
card (V,E,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (V,E,G)) + (card (V,E,G)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v1 is Element of the carrier of V
v2 is Element of the carrier of V
(V,v1,v2) is non empty V68() strict finite MultiGraphStruct
the carrier of (V,v1,v2) is non empty set
G9 is Element of the carrier of (V,v1,v2)
((V,v1,v2),G9,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
((V,v1,v2),G9,G) is finite Element of bool the carrier' of (V,v1,v2)
the carrier' of (V,v1,v2) is set
bool the carrier' of (V,v1,v2) is set
card ((V,v1,v2),G9,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
((V,v1,v2),G9,G) is finite Element of bool the carrier' of (V,v1,v2)
card ((V,v1,v2),G9,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card ((V,v1,v2),G9,G)) + (card ((V,v1,v2),G9,G)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (V,E,G)) + (card ((V,v1,v2),G9,G)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G is non empty V68() finite MultiGraphStruct
the carrier' of G is set
the carrier of G is non empty set
V is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like cyclic Chain of G
rng V is finite set
E is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
rng E is finite set
v1 is Element of the carrier of G
(G,v1,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,v1,(rng V)) is finite Element of bool the carrier' of G
bool the carrier' of G is set
card (G,v1,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,v1,(rng V)) is finite Element of bool the carrier' of G
card (G,v1,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,v1,(rng V))) + (card (G,v1,(rng V))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
E9 is Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() set
(G,v1,E9) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,v1,E9) is Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() Element of bool the carrier' of G
card (G,v1,E9) is Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() V123() Element of NAT
(G,v1,E9) is Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() Element of bool the carrier' of G
card (G,v1,E9) is Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() V123() Element of NAT
(card (G,v1,E9)) + (card (G,v1,E9)) is Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() V123() Element of NAT
2 * 0 is Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer even ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() V123() Element of NAT
len V is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
{ b₁ where b₁ is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT : ( 1 <= b₁ & b₁ <= len V & E . b₁ = v1 ) } is set
Seg (len V) is finite len V -element V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
P9 is set
n is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E . n is set
len E is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len V) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
{1} is non empty trivial finite V32() 1 -element V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() set
P9 is non empty set
(G,v1,P9) is finite Element of bool the carrier' of G
[:{1},(G,v1,P9):] is Relation-like finite set
{0} is non empty trivial finite V32() 1 -element V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() set
(G,v1,P9) is finite Element of bool the carrier' of G
[:{0},(G,v1,P9):] is Relation-like finite set
card [:{1},(G,v1,P9):] is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
card {1} is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
card (G,v1,P9) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card {1}) * (card (G,v1,P9)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
1 * (card (G,v1,P9)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
card [:{0},(G,v1,P9):] is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
card {0} is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
card (G,v1,P9) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card {0}) * (card (G,v1,P9)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
1 * (card (G,v1,P9)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
[:{0},(G,v1,P9):] \/ [:{1},(G,v1,P9):] is Relation-like finite set
(G,v1,P9) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,v1,P9)) + (card (G,v1,P9)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
0 + 0 is Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() V123() Element of NAT
[:{0},(G,v1,P9):] /\ [:{1},(G,v1,P9):] is Relation-like finite set
vs9 is set
p1 is set
vs is set
[p1,vs] is set
{p1,vs} is non empty finite set
{p1} is non empty trivial finite 1 -element set
{{p1,vs},{p1}} is non empty finite V32() set
vs is set
p is set
[vs,p] is set
{vs,p} is non empty finite set
{vs} is non empty trivial finite 1 -element set
{{vs,p},{vs}} is non empty finite V32() set
bool (Seg (len V)) is finite V32() set
p1 is non empty non void V68() finite MultiGraphStruct
the carrier of p1 is non empty set
vs is Relation-like NAT -defined the carrier of p1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of p1
vs . 1 is set
E . (len E) is set
0 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
dom E is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
vs is set
E . vs is set
p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
vs9 is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool (Seg (len V))
vs is non empty finite set
[:2,vs:] is Relation-like finite set
p is non empty set
E . 1 is set
V . (len V) is set
the Target of G . (V . (len V)) is set
[0,(V . (len V))] is set
{0,(V . (len V))} is non empty finite set
{{0,(V . (len V))},{0}} is non empty finite V32() set
the Source of G . (V . (len V)) is set
[1,(V . (len V))] is set
{1,(V . (len V))} is non empty finite set
{{1,(V . (len V))},{1}} is non empty finite V32() set
{ [b₁,b₂] where b₁ is Element of [:2,vs:], b₂ is Element of p : ex b₃ being V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT st
( 1 <= b₃ & b₃ <= len V & ( S₂[b₁,b₂,b₃] or S₁[b₁,b₂,b₃] ) ) } is set
i is set
m is set
ep is set
t is set
[ep,t] is set
{ep,t} is non empty finite set
{ep} is non empty trivial finite 1 -element set
{{ep,t},{ep}} is non empty finite V32() set
ts is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E . ts is set
p1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
1 + p1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
dom V is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
V . p1 is set
X9 is Element of P9
the Target of G . (V . p1) is set
p1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
E . (p1 + 1) is set
[0,(V . p1)] is set
{0,(V . p1)} is non empty finite set
{{0,(V . p1)},{0}} is non empty finite V32() set
vs1 is set
[m,vs1] is set
{m,vs1} is non empty finite set
{m} is non empty trivial finite 1 -element set
{{m,vs1},{m}} is non empty finite V32() set
s is Element of [:2,vs:]
e9 is Element of p
[0,ts] is set
{0,ts} is non empty finite V32() V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() set
{{0,ts},{0}} is non empty finite V32() set
p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . p is set
the Target of G . (V . p) is set
[0,(V . p)] is set
{0,(V . p)} is non empty finite set
{{0,(V . p)},{0}} is non empty finite V32() set
the Source of G . (V . p) is set
[1,(V . p)] is set
{1,(V . p)} is non empty finite set
{{1,(V . p)},{1}} is non empty finite V32() set
the Source of G . (V . p1) is set
p1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
E . (p1 + 1) is set
the Target of G . (V . p1) is set
[1,(V . p1)] is set
{1,(V . p1)} is non empty finite set
{{1,(V . p1)},{1}} is non empty finite V32() set
vs1 is set
[m,vs1] is set
{m,vs1} is non empty finite set
{m} is non empty trivial finite 1 -element set
{{m,vs1},{m}} is non empty finite V32() set
s is Element of [:2,vs:]
e9 is Element of p
[0,ts] is set
{0,ts} is non empty finite V32() V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() set
{{0,ts},{0}} is non empty finite V32() set
p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . p is set
the Target of G . (V . p) is set
[0,(V . p)] is set
{0,(V . p)} is non empty finite set
{{0,(V . p)},{0}} is non empty finite V32() set
the Source of G . (V . p) is set
[1,(V . p)] is set
{1,(V . p)} is non empty finite set
{{1,(V . p)},{1}} is non empty finite V32() set
the Target of G . (V . p1) is set
p1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
E . (p1 + 1) is set
the Source of G . (V . p1) is set
dom V is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
p1 is Element of P9
E . ((len V) + 1) is set
X9 is set
[m,X9] is set
{m,X9} is non empty finite set
{m} is non empty trivial finite 1 -element set
{{m,X9},{m}} is non empty finite V32() set
s is Element of [:2,vs:]
vs1 is Element of p
[0,1] is set
{0,1} is non empty finite V32() V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() set
{{0,1},{0}} is non empty finite V32() set
e9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
e9 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . e9 is set
the Target of G . (V . e9) is set
[0,(V . e9)] is set
{0,(V . e9)} is non empty finite set
{{0,(V . e9)},{0}} is non empty finite V32() set
the Source of G . (V . e9) is set
[1,(V . e9)] is set
{1,(V . e9)} is non empty finite set
{{1,(V . e9)},{1}} is non empty finite V32() set
X9 is set
[m,X9] is set
{m,X9} is non empty finite set
{m} is non empty trivial finite 1 -element set
{{m,X9},{m}} is non empty finite V32() set
s is Element of [:2,vs:]
vs1 is Element of p
[0,1] is set
{0,1} is non empty finite V32() V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() set
{{0,1},{0}} is non empty finite V32() set
e9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
e9 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . e9 is set
the Target of G . (V . e9) is set
[0,(V . e9)] is set
{0,(V . e9)} is non empty finite set
{{0,(V . e9)},{0}} is non empty finite V32() set
the Source of G . (V . e9) is set
[1,(V . e9)] is set
{1,(V . e9)} is non empty finite set
{{1,(V . e9)},{1}} is non empty finite V32() set
dom V is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
V . ts is set
p1 is Element of P9
the Source of G . (V . ts) is set
[1,(V . ts)] is set
{1,(V . ts)} is non empty finite set
{{1,(V . ts)},{1}} is non empty finite V32() set
X9 is set
[m,X9] is set
{m,X9} is non empty finite set
{m} is non empty trivial finite 1 -element set
{{m,X9},{m}} is non empty finite V32() set
s is Element of [:2,vs:]
vs1 is Element of p
[1,ts] is set
{1,ts} is non empty finite V32() V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() set
{{1,ts},{1}} is non empty finite V32() set
the Target of G . (V . ts) is set
[0,(V . ts)] is set
{0,(V . ts)} is non empty finite set
{{0,(V . ts)},{0}} is non empty finite V32() set
the Target of G . (V . ts) is set
the Source of G . (V . ts) is set
[0,(V . ts)] is set
{0,(V . ts)} is non empty finite set
{{0,(V . ts)},{0}} is non empty finite V32() set
X9 is set
[m,X9] is set
{m,X9} is non empty finite set
{m} is non empty trivial finite 1 -element set
{{m,X9},{m}} is non empty finite V32() set
s is Element of [:2,vs:]
vs1 is Element of p
[1,ts] is set
{1,ts} is non empty finite V32() V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() set
{{1,ts},{1}} is non empty finite V32() set
[1,(V . ts)] is set
{1,(V . ts)} is non empty finite set
{{1,(V . ts)},{1}} is non empty finite V32() set
the Source of G . (V . ts) is set
the Target of G . (V . ts) is set
m is set
t is set
s is set
[t,s] is set
{t,s} is non empty finite set
{t} is non empty trivial finite 1 -element set
{{t,s},{t}} is non empty finite V32() set
the Target of G . s is set
dom V is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
ts is set
V . ts is set
p1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
E . (p1 + 1) is set
V . p1 is set
the Target of G . (V . p1) is set
[0,1] is set
{0,1} is non empty finite V32() V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() set
{{0,1},{0}} is non empty finite V32() set
X9 is set
[X9,m] is set
{X9,m} is non empty finite set
{X9} is non empty trivial finite 1 -element set
{{X9,m},{X9}} is non empty finite V32() set
vs1 is Element of [:2,vs:]
ep is Element of p
e9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
e9 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . e9 is set
the Target of G . (V . e9) is set
[0,(V . e9)] is set
{0,(V . e9)} is non empty finite set
{{0,(V . e9)},{0}} is non empty finite V32() set
the Source of G . (V . e9) is set
[1,(V . e9)] is set
{1,(V . e9)} is non empty finite set
{{1,(V . e9)},{1}} is non empty finite V32() set
[0,(p1 + 1)] is set
{0,(p1 + 1)} is non empty finite V32() V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() set
{{0,(p1 + 1)},{0}} is non empty finite V32() set
X9 is set
[X9,m] is set
{X9,m} is non empty finite set
{X9} is non empty trivial finite 1 -element set
{{X9,m},{X9}} is non empty finite V32() set
vs1 is Element of [:2,vs:]
ep is Element of p
e9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
e9 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . e9 is set
the Target of G . (V . e9) is set
[0,(V . e9)] is set
{0,(V . e9)} is non empty finite set
{{0,(V . e9)},{0}} is non empty finite V32() set
the Source of G . (V . e9) is set
[1,(V . e9)] is set
{1,(V . e9)} is non empty finite set
{{1,(V . e9)},{1}} is non empty finite V32() set
E . p1 is set
V . p1 is set
the Target of G . (V . p1) is set
the Source of G . (V . p1) is set
[1,p1] is set
{1,p1} is non empty finite V32() V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() set
{{1,p1},{1}} is non empty finite V32() set
X9 is set
[X9,m] is set
{X9,m} is non empty finite set
{X9} is non empty trivial finite 1 -element set
{{X9,m},{X9}} is non empty finite V32() set
vs1 is Element of [:2,vs:]
ep is Element of p
[1,(V . p1)] is set
{1,(V . p1)} is non empty finite set
{{1,(V . p1)},{1}} is non empty finite V32() set
[0,(V . p1)] is set
{0,(V . p1)} is non empty finite set
{{0,(V . p1)},{0}} is non empty finite V32() set
p1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
E . (p1 + 1) is set
V . p1 is set
the Target of G . (V . p1) is set
E . p1 is set
the Source of G . (V . p1) is set
t is set
s is set
[t,s] is set
{t,s} is non empty finite set
{t} is non empty trivial finite 1 -element set
{{t,s},{t}} is non empty finite V32() set
the Source of G . s is set
dom V is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
ts is set
V . ts is set
p1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
E . (p1 + 1) is set
V . p1 is set
the Source of G . (V . p1) is set
the Target of G . (V . p1) is set
[0,1] is set
{0,1} is non empty finite V32() V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() set
{{0,1},{0}} is non empty finite V32() set
X9 is set
[X9,m] is set
{X9,m} is non empty finite set
{X9} is non empty trivial finite 1 -element set
{{X9,m},{X9}} is non empty finite V32() set
vs1 is Element of [:2,vs:]
ep is Element of p
e9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
e9 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . e9 is set
the Target of G . (V . e9) is set
[0,(V . e9)] is set
{0,(V . e9)} is non empty finite set
{{0,(V . e9)},{0}} is non empty finite V32() set
the Source of G . (V . e9) is set
[1,(V . e9)] is set
{1,(V . e9)} is non empty finite set
{{1,(V . e9)},{1}} is non empty finite V32() set
[0,(p1 + 1)] is set
{0,(p1 + 1)} is non empty finite V32() V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() set
{{0,(p1 + 1)},{0}} is non empty finite V32() set
X9 is set
[X9,m] is set
{X9,m} is non empty finite set
{X9} is non empty trivial finite 1 -element set
{{X9,m},{X9}} is non empty finite V32() set
vs1 is Element of [:2,vs:]
ep is Element of p
e9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
e9 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . e9 is set
the Target of G . (V . e9) is set
[0,(V . e9)] is set
{0,(V . e9)} is non empty finite set
{{0,(V . e9)},{0}} is non empty finite V32() set
the Source of G . (V . e9) is set
[1,(V . e9)] is set
{1,(V . e9)} is non empty finite set
{{1,(V . e9)},{1}} is non empty finite V32() set
E . p1 is set
V . p1 is set
the Source of G . (V . p1) is set
[1,p1] is set
{1,p1} is non empty finite V32() V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() set
{{1,p1},{1}} is non empty finite V32() set
X9 is set
[X9,m] is set
{X9,m} is non empty finite set
{X9} is non empty trivial finite 1 -element set
{{X9,m},{X9}} is non empty finite V32() set
vs1 is Element of [:2,vs:]
ep is Element of p
[1,(V . p1)] is set
{1,(V . p1)} is non empty finite set
{{1,(V . p1)},{1}} is non empty finite V32() set
the Target of G . (V . p1) is set
[0,(V . p1)] is set
{0,(V . p1)} is non empty finite set
{{0,(V . p1)},{0}} is non empty finite V32() set
p1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
E . (p1 + 1) is set
V . p1 is set
the Source of G . (V . p1) is set
the Target of G . (V . p1) is set
E . p1 is set
m is set
ep is set
[m,ep] is set
{m,ep} is non empty finite set
{m} is non empty trivial finite 1 -element set
{{m,ep},{m}} is non empty finite V32() set
t is set
s is set
[t,s] is set
{t,s} is non empty finite set
{t} is non empty trivial finite 1 -element set
{{t,s},{t}} is non empty finite V32() set
ts is Element of [:2,vs:]
p1 is Element of p
[ts,p1] is set
{ts,p1} is non empty finite set
{ts} is non empty trivial finite 1 -element set
{{ts,p1},{ts}} is non empty finite V32() set
X9 is Element of [:2,vs:]
vs1 is Element of p
[X9,vs1] is set
{X9,vs1} is non empty finite set
{X9} is non empty trivial finite 1 -element set
{{X9,vs1},{X9}} is non empty finite V32() set
e9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
[0,e9] is set
{0,e9} is non empty finite V32() V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() set
{{0,e9},{0}} is non empty finite V32() set
p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
E . e9 is set
V . p is set
the Target of G . (V . p) is set
[0,(V . p)] is set
{0,(V . p)} is non empty finite set
{{0,(V . p)},{0}} is non empty finite V32() set
the Source of G . (V . p) is set
[1,(V . p)] is set
{1,(V . p)} is non empty finite set
{{1,(V . p)},{1}} is non empty finite V32() set
[1,e9] is set
{1,e9} is non empty finite V32() V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() set
{{1,e9},{1}} is non empty finite V32() set
V . e9 is set
the Source of G . (V . e9) is set
[1,(V . e9)] is set
{1,(V . e9)} is non empty finite set
{{1,(V . e9)},{1}} is non empty finite V32() set
the Target of G . (V . e9) is set
[0,(V . e9)] is set
{0,(V . e9)} is non empty finite set
{{0,(V . e9)},{0}} is non empty finite V32() set
e9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
[0,e9] is set
{0,e9} is non empty finite V32() V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() set
{{0,e9},{0}} is non empty finite V32() set
E . e9 is set
[1,e9] is set
{1,e9} is non empty finite V32() V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() set
{{1,e9},{1}} is non empty finite V32() set
V . e9 is set
the Source of G . (V . e9) is set
[1,(V . e9)] is set
{1,(V . e9)} is non empty finite set
{{1,(V . e9)},{1}} is non empty finite V32() set
the Target of G . (V . e9) is set
[0,(V . e9)] is set
{0,(V . e9)} is non empty finite set
{{0,(V . e9)},{0}} is non empty finite V32() set
p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
[0,p] is set
{0,p} is non empty finite V32() V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() set
{{0,p},{0}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
E . p is set
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
[1,p] is set
{1,p} is non empty finite V32() V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() set
{{1,p},{1}} is non empty finite V32() set
V . p is set
the Source of G . (V . p) is set
[1,(V . p)] is set
{1,(V . p)} is non empty finite set
{{1,(V . p)},{1}} is non empty finite V32() set
the Target of G . (V . p) is set
[0,(V . p)] is set
{0,(V . p)} is non empty finite set
{{0,(V . p)},{0}} is non empty finite V32() set
p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
[0,p] is set
{0,p} is non empty finite V32() V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() set
{{0,p},{0}} is non empty finite V32() set
E . p is set
[1,p] is set
{1,p} is non empty finite V32() V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() set
{{1,p},{1}} is non empty finite V32() set
V . p is set
the Source of G . (V . p) is set
[1,(V . p)] is set
{1,(V . p)} is non empty finite set
{{1,(V . p)},{1}} is non empty finite V32() set
the Target of G . (V . p) is set
[0,(V . p)] is set
{0,(V . p)} is non empty finite set
{{0,(V . p)},{0}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
xp1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
xp1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . xp1 is set
the Target of G . (V . xp1) is set
[0,(V . xp1)] is set
{0,(V . xp1)} is non empty finite set
{{0,(V . xp1)},{0}} is non empty finite V32() set
the Source of G . (V . xp1) is set
[1,(V . xp1)] is set
{1,(V . xp1)} is non empty finite set
{{1,(V . xp1)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
xp1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
xp1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . xp1 is set
the Target of G . (V . xp1) is set
[0,(V . xp1)] is set
{0,(V . xp1)} is non empty finite set
{{0,(V . xp1)},{0}} is non empty finite V32() set
the Source of G . (V . xp1) is set
[1,(V . xp1)] is set
{1,(V . xp1)} is non empty finite set
{{1,(V . xp1)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
xp1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
xp1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . xp1 is set
the Target of G . (V . xp1) is set
[0,(V . xp1)] is set
{0,(V . xp1)} is non empty finite set
{{0,(V . xp1)},{0}} is non empty finite V32() set
the Source of G . (V . xp1) is set
[1,(V . xp1)] is set
{1,(V . xp1)} is non empty finite set
{{1,(V . xp1)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
xp1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
xp1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . xp1 is set
the Target of G . (V . xp1) is set
[0,(V . xp1)] is set
{0,(V . xp1)} is non empty finite set
{{0,(V . xp1)},{0}} is non empty finite V32() set
the Source of G . (V . xp1) is set
[1,(V . xp1)] is set
{1,(V . xp1)} is non empty finite set
{{1,(V . xp1)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
xp1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
xp1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . xp1 is set
the Target of G . (V . xp1) is set
[0,(V . xp1)] is set
{0,(V . xp1)} is non empty finite set
{{0,(V . xp1)},{0}} is non empty finite V32() set
the Source of G . (V . xp1) is set
[1,(V . xp1)] is set
{1,(V . xp1)} is non empty finite set
{{1,(V . xp1)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
xp1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
xp1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . xp1 is set
the Target of G . (V . xp1) is set
[0,(V . xp1)] is set
{0,(V . xp1)} is non empty finite set
{{0,(V . xp1)},{0}} is non empty finite V32() set
the Source of G . (V . xp1) is set
[1,(V . xp1)] is set
{1,(V . xp1)} is non empty finite set
{{1,(V . xp1)},{1}} is non empty finite V32() set
xp1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
xp1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . xp1 is set
the Target of G . (V . xp1) is set
[0,(V . xp1)] is set
{0,(V . xp1)} is non empty finite set
{{0,(V . xp1)},{0}} is non empty finite V32() set
the Source of G . (V . xp1) is set
[1,(V . xp1)] is set
{1,(V . xp1)} is non empty finite set
{{1,(V . xp1)},{1}} is non empty finite V32() set
xp1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
xp1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . xp1 is set
the Target of G . (V . xp1) is set
[0,(V . xp1)] is set
{0,(V . xp1)} is non empty finite set
{{0,(V . xp1)},{0}} is non empty finite V32() set
the Source of G . (V . xp1) is set
[1,(V . xp1)] is set
{1,(V . xp1)} is non empty finite set
{{1,(V . xp1)},{1}} is non empty finite V32() set
xp1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
xp1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . xp1 is set
the Target of G . (V . xp1) is set
[0,(V . xp1)] is set
{0,(V . xp1)} is non empty finite set
{{0,(V . xp1)},{0}} is non empty finite V32() set
the Source of G . (V . xp1) is set
[1,(V . xp1)] is set
{1,(V . xp1)} is non empty finite set
{{1,(V . xp1)},{1}} is non empty finite V32() set
c₃₁ is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
c₃₁ + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . c₃₁ is set
the Target of G . (V . c₃₁) is set
[0,(V . c₃₁)] is set
{0,(V . c₃₁)} is non empty finite set
{{0,(V . c₃₁)},{0}} is non empty finite V32() set
the Source of G . (V . c₃₁) is set
[1,(V . c₃₁)] is set
{1,(V . c₃₁)} is non empty finite set
{{1,(V . c₃₁)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
xp1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
xp1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . xp1 is set
the Target of G . (V . xp1) is set
[0,(V . xp1)] is set
{0,(V . xp1)} is non empty finite set
{{0,(V . xp1)},{0}} is non empty finite V32() set
the Source of G . (V . xp1) is set
[1,(V . xp1)] is set
{1,(V . xp1)} is non empty finite set
{{1,(V . xp1)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
xp1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
xp1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . xp1 is set
the Target of G . (V . xp1) is set
[0,(V . xp1)] is set
{0,(V . xp1)} is non empty finite set
{{0,(V . xp1)},{0}} is non empty finite V32() set
the Source of G . (V . xp1) is set
[1,(V . xp1)] is set
{1,(V . xp1)} is non empty finite set
{{1,(V . xp1)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
xp1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
xp1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . xp1 is set
the Target of G . (V . xp1) is set
[0,(V . xp1)] is set
{0,(V . xp1)} is non empty finite set
{{0,(V . xp1)},{0}} is non empty finite V32() set
the Source of G . (V . xp1) is set
[1,(V . xp1)] is set
{1,(V . xp1)} is non empty finite set
{{1,(V . xp1)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
xp1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
xp1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . xp1 is set
the Target of G . (V . xp1) is set
[0,(V . xp1)] is set
{0,(V . xp1)} is non empty finite set
{{0,(V . xp1)},{0}} is non empty finite V32() set
the Source of G . (V . xp1) is set
[1,(V . xp1)] is set
{1,(V . xp1)} is non empty finite set
{{1,(V . xp1)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
xp1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
xp1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . xp1 is set
the Target of G . (V . xp1) is set
[0,(V . xp1)] is set
{0,(V . xp1)} is non empty finite set
{{0,(V . xp1)},{0}} is non empty finite V32() set
the Source of G . (V . xp1) is set
[1,(V . xp1)] is set
{1,(V . xp1)} is non empty finite set
{{1,(V . xp1)},{1}} is non empty finite V32() set
xp1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
xp1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . xp1 is set
the Target of G . (V . xp1) is set
[0,(V . xp1)] is set
{0,(V . xp1)} is non empty finite set
{{0,(V . xp1)},{0}} is non empty finite V32() set
the Source of G . (V . xp1) is set
[1,(V . xp1)] is set
{1,(V . xp1)} is non empty finite set
{{1,(V . xp1)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
e9 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
E . (e9 + 1) is set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
xp1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
xp1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . xp1 is set
the Target of G . (V . xp1) is set
[0,(V . xp1)] is set
{0,(V . xp1)} is non empty finite set
{{0,(V . xp1)},{0}} is non empty finite V32() set
the Source of G . (V . xp1) is set
[1,(V . xp1)] is set
{1,(V . xp1)} is non empty finite set
{{1,(V . xp1)},{1}} is non empty finite V32() set
xp1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
xp1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . xp1 is set
the Target of G . (V . xp1) is set
[0,(V . xp1)] is set
{0,(V . xp1)} is non empty finite set
{{0,(V . xp1)},{0}} is non empty finite V32() set
the Source of G . (V . xp1) is set
[1,(V . xp1)] is set
{1,(V . xp1)} is non empty finite set
{{1,(V . xp1)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
p + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
E . (p + 1) is set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . ep is set
the Target of G . (V . ep) is set
[0,(V . ep)] is set
{0,(V . ep)} is non empty finite set
{{0,(V . ep)},{0}} is non empty finite V32() set
the Source of G . (V . ep) is set
[1,(V . ep)] is set
{1,(V . ep)} is non empty finite set
{{1,(V . ep)},{1}} is non empty finite V32() set
xp1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
xp1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
V . xp1 is set
the Target of G . (V . xp1) is set
[0,(V . xp1)] is set
{0,(V . xp1)} is non empty finite set
{{0,(V . xp1)},{0}} is non empty finite V32() set
the Source of G . (V . xp1) is set
[1,(V . xp1)] is set
{1,(V . xp1)} is non empty finite set
{{1,(V . xp1)},{1}} is non empty finite V32() set
i is set
card [:2,vs:] is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
card ([:{0},(G,v1,P9):] \/ [:{1},(G,v1,P9):]) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card [:{0},(G,v1,P9):]) + (card [:{1},(G,v1,P9):]) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
card 2 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
card vs is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(card 2) * (card vs) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
2 * (card vs) is V6() V7() V8() V12() finite cardinal V39() integer even ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G is non empty V68() finite MultiGraphStruct
the carrier of G is non empty set
the carrier' of G is set
V is Element of the carrier of G
E is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like cyclic Chain of G
rng E is finite set
(G,V,(rng E)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,(rng E)) is finite Element of bool the carrier' of G
bool the carrier' of G is set
card (G,V,(rng E)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,(rng E)) is finite Element of bool the carrier' of G
card (G,V,(rng E)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,V,(rng E))) + (card (G,V,(rng E))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v1 is Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() set
(G,V,v1) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,v1) is Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() Element of bool the carrier' of G
card (G,V,v1) is Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() V123() Element of NAT
(G,V,v1) is Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() Element of bool the carrier' of G
card (G,V,v1) is Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() V123() Element of NAT
(card (G,V,v1)) + (card (G,V,v1)) is Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() V123() Element of NAT
2 * 0 is Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer even ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() V123() Element of NAT
v1 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
rng v1 is finite set
rng v1 is finite set
2 * 0 is Relation-like non-empty empty-yielding V6() V7() V8() V10() V11() V12() functional empty finite finite-yielding V32() cardinal {} -element FinSequence-like FinSequence-membered V39() integer even ext-real non positive non negative V100() V101() V102() V103() V104() V105() V106() V109() V110() V111() V112() V122() V123() Element of NAT
rng v1 is finite set
G is non empty V68() finite MultiGraphStruct
the carrier of G is non empty set
the carrier' of G is set
V is Element of the carrier of G
E is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
E . 1 is set
len E is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E . (len E) is set
v1 is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G
rng v1 is finite set
(G,V,(rng v1)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,(rng v1)) is finite Element of bool the carrier' of G
bool the carrier' of G is set
card (G,V,(rng v1)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,(rng v1)) is finite Element of bool the carrier' of G
card (G,V,(rng v1)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,V,(rng v1))) + (card (G,V,(rng v1))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
len v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len v1) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
dom E is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
v2 is Element of the carrier of G
G9 is Element of the carrier of G
(G,v2,G9) is non empty V68() strict finite MultiGraphStruct
the carrier of (G,v2,G9) is non empty set
the carrier' of (G,v2,G9) is set
P9 is Relation-like NAT -defined the carrier of (G,v2,G9) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (G,v2,G9)
n is Relation-like NAT -defined the carrier' of (G,v2,G9) -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of (G,v2,G9)
vs9 is Element of the carrier of (G,v2,G9)
p is Element of the carrier of (G,v2,G9)
<*vs9,p*> is Relation-like NAT -defined the carrier of (G,v2,G9) -valued Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of (G,v2,G9)
P9 ^' <*vs9,p*> is Relation-like NAT -defined the carrier of (G,v2,G9) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (G,v2,G9)
len <*vs9,p*> is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(2,(len <*vs9,p*>)) -cut <*vs9,p*> is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
P9 ^ ((2,(len <*vs9,p*>)) -cut <*vs9,p*>) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (P9 ^' <*vs9,p*>) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(P9 ^' <*vs9,p*>) . (len (P9 ^' <*vs9,p*>)) is set
<*vs9,p*> . 2 is set
{ the carrier' of G} is non empty trivial finite 1 -element set
the carrier' of G \/ { the carrier' of G} is non empty set
<* the carrier' of G*> is Relation-like NAT -defined Function-like non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
i is Relation-like NAT -defined the carrier' of (G,v2,G9) -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of (G,v2,G9)
rng i is finite set
(rng i) /\ the carrier' of G is finite set
the Source of (G,v2,G9) is Relation-like the carrier' of (G,v2,G9) -defined the carrier of (G,v2,G9) -valued Function-like V25( the carrier' of (G,v2,G9), the carrier of (G,v2,G9)) Element of bool [: the carrier' of (G,v2,G9), the carrier of (G,v2,G9):]
[: the carrier' of (G,v2,G9), the carrier of (G,v2,G9):] is Relation-like set
bool [: the carrier' of (G,v2,G9), the carrier of (G,v2,G9):] is set
the Source of (G,v2,G9) . the carrier' of G is set
the Target of (G,v2,G9) is Relation-like the carrier' of (G,v2,G9) -defined the carrier of (G,v2,G9) -valued Function-like V25( the carrier' of (G,v2,G9), the carrier of (G,v2,G9)) Element of bool [: the carrier' of (G,v2,G9), the carrier of (G,v2,G9):]
the Target of (G,v2,G9) . the carrier' of G is set
len P9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
P9 . (len P9) is set
<*vs9,p*> . 1 is set
rng n is finite set
m is set
n ^ i is Relation-like NAT -defined the carrier' of (G,v2,G9) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of (G,v2,G9)
m is Relation-like NAT -defined the carrier' of (G,v2,G9) -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of (G,v2,G9)
(P9 ^' <*vs9,p*>) . 1 is set
ep is Relation-like NAT -defined the carrier' of (G,v2,G9) -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like cyclic Chain of (G,v2,G9)
rng ep is finite set
(rng v1) \/ (rng i) is finite set
(rng ep) /\ the carrier' of G is finite set
((rng v1) \/ (rng i)) /\ the carrier' of G is finite set
(rng v1) /\ the carrier' of G is finite set
((rng v1) /\ the carrier' of G) \/ {} is finite set
(G,V,(rng ep)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,(rng ep)) is finite Element of bool the carrier' of G
card (G,V,(rng ep)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,(rng ep)) is finite Element of bool the carrier' of G
card (G,V,(rng ep)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,V,(rng ep))) + (card (G,V,(rng ep))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p9 is Element of the carrier of (G,v2,G9)
((G,v2,G9),p9,(rng ep)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
((G,v2,G9),p9,(rng ep)) is finite Element of bool the carrier' of (G,v2,G9)
bool the carrier' of (G,v2,G9) is set
card ((G,v2,G9),p9,(rng ep)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
((G,v2,G9),p9,(rng ep)) is finite Element of bool the carrier' of (G,v2,G9)
card ((G,v2,G9),p9,(rng ep)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card ((G,v2,G9),p9,(rng ep))) + (card ((G,v2,G9),p9,(rng ep))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,(rng ep)) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
t is V6() V7() V8() V12() finite cardinal V39() integer even ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
t - 1 is non empty V39() integer non even ext-real V122() set
G is non empty V68() MultiGraphStruct
the carrier' of G is set
the carrier' of G * is functional non empty FinSequence-membered FinSequenceSet of the carrier' of G
{ b₁ where b₁ is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier' of G * : S₁[b₁] } is set
bool ( the carrier' of G *) is set
E is set
the carrier of G is non empty set
the Element of the carrier of G is Element of the carrier of G
E is functional FinSequence-membered FinSequenceSet of the carrier' of G
G9 is functional FinSequence-membered FinSequenceSet of the carrier' of G
E9 is set
P9 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier' of G *
V is functional FinSequence-membered FinSequenceSet of the carrier' of G
E is functional FinSequence-membered FinSequenceSet of the carrier' of G
v1 is set
G is non empty V68() MultiGraphStruct
(G) is functional FinSequence-membered FinSequenceSet of the carrier' of G
the carrier' of G is set
the carrier of G is non empty set
the Element of the carrier of G is Element of the carrier of G
<* the Element of the carrier of G*> is Relation-like NAT -defined the carrier of G -valued Function-like non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of G
V is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G
<* the Element of the carrier of G*> . 1 is set
len <* the Element of the carrier of G*> is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
<* the Element of the carrier of G*> . (len <* the Element of the carrier of G*>) is set
G is non empty V68() MultiGraphStruct
(G) is functional FinSequence-membered FinSequenceSet of the carrier' of G
the carrier' of G is set
G is non empty V68() MultiGraphStruct
the carrier of G is non empty set
the carrier' of G is set
(G) is functional non empty FinSequence-membered FinSequenceSet of the carrier' of G
bool (G) is set
V is Element of the carrier of G
E is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
rng E is finite set
(G,(rng E)) is Element of bool the carrier of G
bool the carrier of G is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
{ b₁ where b₁ is Element of the carrier of G : ex b₂ being Element of the carrier' of G st
( b₂ in rng E & ( b₁ = the Source of G . b₂ or b₁ = the Target of G . b₂ ) ) } is set
{ b₁ where b₁ is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G) : ( rng b₁ = rng E & ex b₂ being Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G st
( b₂ is_vertex_seq_of b₁ & b₂ . 1 = V ) ) } is set
v2 is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like cyclic Chain of G
G9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
len G9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
len E is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len E) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
rng v2 is finite set
(G,(rng v2)) is Element of bool the carrier of G
{ b₁ where b₁ is Element of the carrier of G : ex b₂ being Element of the carrier' of G st
( b₂ in rng v2 & ( b₁ = the Source of G . b₂ or b₁ = the Target of G . b₂ ) ) } is set
rng G9 is finite set
E9 is Element of the carrier of G
P9 is Element of the carrier' of G
the Source of G . P9 is set
the Target of G . P9 is set
dom G9 is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
E9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
G9 . E9 is set
Seg (len G9) is finite len G9 -element V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
P9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
0 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
n is Element of the carrier of G
p9 is Element of the carrier' of G
the Source of G . p9 is set
the Target of G . p9 is set
G9 . 1 is set
(P9,(len G9)) -cut G9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
p9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
1 + p9 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
p9 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(1,(p9 + 1)) -cut G9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
(p9 + 1) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
len ((1,(p9 + 1)) -cut G9) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len ((1,(p9 + 1)) -cut G9)) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
((1,(p9 + 1)) -cut G9) . 1 is set
1 + 0 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
G9 . (1 + 0) is set
(1,p9) -cut v2 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
(P9,(len E)) -cut v2 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
p1 is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G
len ((P9,(len G9)) -cut G9) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len ((P9,(len G9)) -cut G9)) + P9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len G9) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(len G9) + 0 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
vs is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
vs + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
((P9,(len G9)) -cut G9) ^' ((1,(p9 + 1)) -cut G9) is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
(2,(len ((1,(p9 + 1)) -cut G9))) -cut ((1,(p9 + 1)) -cut G9) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((P9,(len G9)) -cut G9) ^ ((2,(len ((1,(p9 + 1)) -cut G9))) -cut ((1,(p9 + 1)) -cut G9)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
vs is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
vs . 1 is set
0 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
((P9,(len G9)) -cut G9) . (0 + 1) is set
P9 + 0 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G9 . (P9 + 0) is set
vs9 is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G
((P9,(len G9)) -cut G9) . (len ((P9,(len G9)) -cut G9)) is set
P9 + vs is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G9 . (P9 + vs) is set
rng vs9 is finite set
rng p1 is finite set
p is set
dom p1 is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
i is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
p1 . i is set
dom v2 is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
P9 + i is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
dom vs9 is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
m is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
vs9 . m is set
1 + m is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E . ep is set
ep + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
t is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E . t is set
t + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
p1 ^ vs9 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
p is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G
vs9 ^ p1 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
len vs is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
vs . (len vs) is set
((1,(p9 + 1)) -cut G9) . (len ((1,(p9 + 1)) -cut G9)) is set
G9 . P9 is set
i is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like cyclic Chain of G
m is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
rng m is finite set
(rng p1) \/ (rng vs9) is finite set
n is set
p9 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
rng p9 is finite set
p is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
p . 1 is set
G is non empty V68() MultiGraphStruct
the carrier of G is non empty set
the carrier' of G is set
(G) is functional non empty FinSequence-membered FinSequenceSet of the carrier' of G
V is Element of the carrier of G
E is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
rng E is finite set
(G,(rng E)) is Element of bool the carrier of G
bool the carrier of G is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
{ b₁ where b₁ is Element of the carrier of G : ex b₂ being Element of the carrier' of G st
( b₂ in rng E & ( b₁ = the Source of G . b₂ or b₁ = the Target of G . b₂ ) ) } is set
{ b₁ where b₁ is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G) : ( rng b₁ = rng E & ex b₂ being Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G st
( b₂ is_vertex_seq_of b₁ & b₂ . 1 = V ) ) } is set
choose { b₁ where b₁ is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G) : ( rng b₁ = rng E & ex b₂ being Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G st
( b₂ is_vertex_seq_of b₁ & b₂ . 1 = V ) ) } is Element of { b₁ where b₁ is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G) : ( rng b₁ = rng E & ex b₂ being Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G st
( b₂ is_vertex_seq_of b₁ & b₂ . 1 = V ) ) }
G9 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
rng G9 is finite set
E9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
E9 . 1 is set
G is non empty V68() MultiGraphStruct
the carrier' of G is set
(G) is functional non empty FinSequence-membered FinSequenceSet of the carrier' of G
the carrier of G is non empty set
V is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
rng V is finite set
(G,(rng V)) is Element of bool the carrier of G
bool the carrier of G is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
{ b₁ where b₁ is Element of the carrier of G : ex b₂ being Element of the carrier' of G st
( b₂ in rng V & ( b₁ = the Source of G . b₂ or b₁ = the Target of G . b₂ ) ) } is set
E is Element of the carrier of G
(G,E,V) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
rng (G,E,V) is finite set
bool (G) is set
{ b₁ where b₁ is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G) : ( rng b₁ = rng V & ex b₂ being Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G st
( b₂ is_vertex_seq_of b₁ & b₂ . 1 = E ) ) } is set
v1 is functional non empty FinSequence-membered Element of bool (G)
choose v1 is FinSequence-like Element of v1
v2 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
rng v2 is finite set
G9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
G9 . 1 is set
G is non empty V68() MultiGraphStruct
the carrier' of G is set
(G) is functional non empty FinSequence-membered FinSequenceSet of the carrier' of G
V is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
rng V is finite set
(G,(rng V)) is Element of bool the carrier of G
the carrier of G is non empty set
bool the carrier of G is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
{ b₁ where b₁ is Element of the carrier of G : ex b₂ being Element of the carrier' of G st
( b₂ in rng V & ( b₁ = the Source of G . b₂ or b₁ = the Target of G . b₂ ) ) } is set
E is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
rng E is finite set
(G,(rng E)) is Element of bool the carrier of G
{ b₁ where b₁ is Element of the carrier of G : ex b₂ being Element of the carrier' of G st
( b₂ in rng E & ( b₁ = the Source of G . b₂ or b₁ = the Target of G . b₂ ) ) } is set
(G,(rng V)) /\ (G,(rng E)) is Element of bool the carrier of G
choose ((G,(rng V)) /\ (G,(rng E))) is Element of (G,(rng V)) /\ (G,(rng E))
bool (G) is set
v2 is Element of the carrier of G
{ b₁ where b₁ is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G) : ( rng b₁ = rng E & ex b₂ being Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G st
( b₂ is_vertex_seq_of b₁ & b₂ . 1 = v2 ) ) } is set
(G,v2,E) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
G9 is functional non empty FinSequence-membered Element of bool (G)
choose G9 is FinSequence-like Element of G9
P9 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
rng P9 is finite set
n is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
n . 1 is set
n is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
n . 1 is set
p9 is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like cyclic Chain of G
len P9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len P9) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
0 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
len n is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
{ b₁ where b₁ is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G) : ( rng b₁ = rng V & ex b₂ being Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G st
( b₂ is_vertex_seq_of b₁ & b₂ . 1 = v2 ) ) } is set
(G,v2,V) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
p is functional non empty FinSequence-membered Element of bool (G)
choose p is FinSequence-like Element of p
p1 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
rng p1 is finite set
vs is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
vs . 1 is set
vs is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
vs . 1 is set
vs is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like cyclic Chain of G
len vs is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
vs . (len vs) is set
vs ^' n is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
(2,(len n)) -cut n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
vs ^ ((2,(len n)) -cut n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len p1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len p1) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(vs ^' n) . 1 is set
n . (len n) is set
len (vs ^' n) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(vs ^' n) . (len (vs ^' n)) is set
(G,v2,V) ^ (G,v2,E) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
i is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G
m is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
G9 is Element of the carrier of G
v1 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
(G,G9,V) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
(G,G9,E) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
(G,G9,V) ^ (G,G9,E) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
E9 is Element of the carrier of G
v2 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
(G,E9,V) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
(G,E9,E) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
(G,E9,V) ^ (G,E9,E) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
G is non empty V68() MultiGraphStruct
the carrier' of G is set
(G) is functional non empty FinSequence-membered FinSequenceSet of the carrier' of G
V is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
rng V is finite set
(G,(rng V)) is Element of bool the carrier of G
the carrier of G is non empty set
bool the carrier of G is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
{ b₁ where b₁ is Element of the carrier of G : ex b₂ being Element of the carrier' of G st
( b₂ in rng V & ( b₁ = the Source of G . b₂ or b₁ = the Target of G . b₂ ) ) } is set
E is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
rng E is finite set
(G,(rng E)) is Element of bool the carrier of G
{ b₁ where b₁ is Element of the carrier of G : ex b₂ being Element of the carrier' of G st
( b₂ in rng E & ( b₁ = the Source of G . b₂ or b₁ = the Target of G . b₂ ) ) } is set
(G,V,E) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
(G,(rng V)) /\ (G,(rng E)) is Element of bool the carrier of G
choose ((G,(rng V)) /\ (G,(rng E))) is Element of (G,(rng V)) /\ (G,(rng E))
v1 is Element of the carrier of G
(G,v1,V) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
(G,v1,E) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
(G,v1,V) ^ (G,v1,E) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
rng (G,v1,V) is finite set
rng (G,v1,E) is finite set
G is non empty V68() finite MultiGraphStruct
the carrier of G is non empty set
V is Element of the carrier of G
E is set
(G,V,E) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,E) is finite Element of bool the carrier' of G
the carrier' of G is set
bool the carrier' of G is set
card (G,V,E) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,E) is finite Element of bool the carrier' of G
card (G,V,E) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,V,E)) + (card (G,V,E)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E * is functional non empty FinSequence-membered FinSequenceSet of E
{ b₁ where b₁ is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like Element of E * : ( b₁ is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G & not b₁ is empty & ex b₂ being Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G st
( b₂ is_vertex_seq_of b₁ & b₂ . 1 = V ) ) } is set
(G,V,E) is finite Element of bool the carrier' of G
(G,V,E) \/ (G,V,E) is finite Element of bool the carrier' of G
choose (G,V,E) is Element of (G,V,E)
G9 is set
E9 is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like Element of E *
P9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
P9 . 1 is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G . (choose (G,V,E)) is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Source of G . (choose (G,V,E)) is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
G9 is Element of E
the Target of G . G9 is set
the Source of G . G9 is set
G9 is Element of E
the Target of G . G9 is set
the Source of G . G9 is set
E9 is non empty set
P9 is Element of E9
<*P9*> is Relation-like NAT -defined E9 -valued Function-like non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of E9
n is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like Element of E *
the Source of G . P9 is set
the Target of G . P9 is set
p1 is Element of the carrier of G
p is Element of the carrier of G
<*p1,p*> is Relation-like NAT -defined the carrier of G -valued Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of G
<*p1,p*> . 1 is set
p is Element of the carrier of G
p1 is Element of the carrier of G
<*p,p1*> is Relation-like NAT -defined the carrier of G -valued Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of G
<*p,p1*> . 1 is set
p9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
p9 . 1 is set
G is set
V is non empty V68() finite MultiGraphStruct
the carrier of V is non empty set
the carrier' of V is set
E is Element of the carrier of V
(V,E,G) is functional non empty FinSequence-membered FinSequenceSet of the carrier' of V
(V,E,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(V,E,G) is finite Element of bool the carrier' of V
bool the carrier' of V is set
card (V,E,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(V,E,G) is finite Element of bool the carrier' of V
card (V,E,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (V,E,G)) + (card (V,E,G)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v1 is Relation-like NAT -defined the carrier' of V -valued Function-like finite FinSequence-like FinSubsequence-like Element of (V,E,G)
len v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v2 is finite set
card v2 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G * is functional non empty FinSequence-membered FinSequenceSet of G
{ b₁ where b₁ is Relation-like NAT -defined G -valued Function-like finite FinSequence-like FinSubsequence-like Element of G * : ( b₁ is Relation-like NAT -defined the carrier' of V -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of V & not b₁ is empty & ex b₂ being Relation-like NAT -defined the carrier of V -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V st
( b₂ is_vertex_seq_of b₁ & b₂ . 1 = E ) ) } is set
rng v1 is finite set
card (rng v1) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G9 is Relation-like NAT -defined G -valued Function-like finite FinSequence-like FinSubsequence-like Element of G *
E9 is Relation-like NAT -defined the carrier of V -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V
E9 . 1 is set
G is non empty V68() finite MultiGraphStruct
the carrier of G is non empty set
E is set
V is Element of the carrier of G
(G,V,E) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,E) is finite Element of bool the carrier' of G
the carrier' of G is set
bool the carrier' of G is set
card (G,V,E) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,V,E) is finite Element of bool the carrier' of G
card (G,V,E) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,V,E)) + (card (G,V,E)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G) is functional non empty FinSequence-membered FinSequenceSet of the carrier' of G
{ b₁ where b₁ is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G) : ( rng b₁ c= E & not b₁ is empty & ex b₂ being Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G st
( b₂ is_vertex_seq_of b₁ & b₂ . 1 = V ) ) } is set
bool (G) is set
(G,V,E) is functional non empty FinSequence-membered FinSequenceSet of the carrier' of G
{ (len b₁) where b₁ is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G,V,E) : verum } is set
the Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G,V,E) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G,V,E)
len the Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G,V,E) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
P9 is set
n is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G,V,E)
len n is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E * is functional non empty FinSequence-membered FinSequenceSet of E
{ b₁ where b₁ is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like Element of E * : ( b₁ is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G & not b₁ is empty & ex b₂ being Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G st
( b₂ is_vertex_seq_of b₁ & b₂ . 1 = V ) ) } is set
v1 is finite set
card v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
Seg (card v1) is finite card v1 -element V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
P9 is set
n is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G,V,E)
len n is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
0 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
p9 is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like Element of E *
p is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
p . 1 is set
P9 is non empty finite V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() Element of bool NAT
max P9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() V123() set
p9 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G,V,E)
len p9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like Element of E *
rng p is finite set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
vs9 is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G
rng vs9 is finite set
vs is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
vs . 1 is set
vs is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
vs . 1 is set
len vs is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
len vs9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len vs9) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
dom vs is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
vs . (len vs) is set
p is Element of the carrier of G
(G,p,(rng vs9)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p,(rng vs9)) is finite Element of bool the carrier' of G
card (G,p,(rng vs9)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p,(rng vs9)) is finite Element of bool the carrier' of G
card (G,p,(rng vs9)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,p,(rng vs9))) + (card (G,p,(rng vs9))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E \ (rng vs9) is Element of bool E
bool E is set
m is set
i is non empty set
(G,p,i) is finite Element of bool the carrier' of G
(G,p,i) is finite Element of bool the carrier' of G
(G,p,i) is finite Element of bool the carrier' of G
(G,p,i) \/ (G,p,i) is finite Element of bool the carrier' of G
choose (G,p,i) is Element of (G,p,i)
(G,p,i) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
card (G,p,i) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
card (G,p,i) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,p,i)) + (card (G,p,i)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p,E) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p,E) is finite Element of bool the carrier' of G
card (G,p,E) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p,E) is finite Element of bool the carrier' of G
card (G,p,E) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,p,E)) + (card (G,p,E)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p,E) - (G,p,(rng vs9)) is V39() integer ext-real V122() set
the Target of G . (choose (G,p,i)) is set
the Source of G . (choose (G,p,i)) is set
<*(choose (G,p,i))*> is Relation-like NAT -defined Function-like non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
t is Element of i
the Target of G . t is set
the Source of G . t is set
the Target of G . (choose (G,p,i)) is set
the Source of G . (choose (G,p,i)) is set
ts is Element of i
the Target of G . ts is set
the Source of G . ts is set
ep is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G
rng ep is finite set
ts is set
{(choose (G,p,i))} is non empty trivial finite 1 -element set
p1 is Element of i
the Target of G . p1 is set
the Source of G . p1 is set
t is Element of the carrier of G
s is Element of the carrier of G
<*t,s*> is Relation-like NAT -defined the carrier of G -valued Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of G
ts is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
ts . 1 is set
X9 is Element of i
the Target of G . X9 is set
the Source of G . X9 is set
vs ^' ts is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
len ts is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(2,(len ts)) -cut ts is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
vs ^ ((2,(len ts)) -cut ts) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
p1 is non empty set
e9 is Element of i
the Target of G . e9 is set
the Source of G . e9 is set
X9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
X9 . 1 is set
vs9 ^ ep is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
e9 is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G
len e9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
len ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len vs9) + (len ep) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
vs1 is Element of p1
<*vs1*> is Relation-like NAT -defined p1 -valued Function-like non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of p1
p is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of E
ep is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of E
p ^ ep is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of E
xp1 is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like Element of E *
xp1 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G,V,E)
len xp1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
len p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len p) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(len p) + 0 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
s is Element of the carrier of G
t is Element of the carrier of G
<*s,t*> is Relation-like NAT -defined the carrier of G -valued Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of G
ts is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
ts . 1 is set
vs9 ^ ep is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
p1 is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G
len p1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
len ep is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len vs9) + (len ep) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
vs1 is Element of i
the Target of G . vs1 is set
the Source of G . vs1 is set
vs ^' ts is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
len ts is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(2,(len ts)) -cut ts is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
vs ^ ((2,(len ts)) -cut ts) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
X9 is non empty set
p is Element of i
the Target of G . p is set
the Source of G . p is set
vs1 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
vs1 . 1 is set
e9 is Element of X9
<*e9*> is Relation-like NAT -defined X9 -valued Function-like non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of X9
p is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of E
ep is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of E
p ^ ep is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of E
xp1 is Relation-like NAT -defined E -valued Function-like finite FinSequence-like FinSubsequence-like Element of E *
xp1 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G,V,E)
len xp1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
len p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len p) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(len p) + 0 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
ts is Element of i
the Target of G . ts is set
the Source of G . ts is set
vs is set
vs is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
rng vs is finite set
p is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
p . 1 is set
p1 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
vs is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
vs . 1 is set
G is set
V is non empty V68() finite MultiGraphStruct
the carrier of V is non empty set
the carrier' of V is set
(V) is functional non empty FinSequence-membered FinSequenceSet of the carrier' of V
E is Element of the carrier of V
(V,E,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(V,E,G) is finite Element of bool the carrier' of V
bool the carrier' of V is set
card (V,E,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(V,E,G) is finite Element of bool the carrier' of V
card (V,E,G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (V,E,G)) + (card (V,E,G)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(V,E,G) is functional non empty FinSequence-membered Element of bool (V)
bool (V) is set
{ b₁ where b₁ is Relation-like NAT -defined the carrier' of V -valued Function-like finite FinSequence-like FinSubsequence-like Element of (V) : ( rng b₁ c= G & not b₁ is empty & ex b₂ being Relation-like NAT -defined the carrier of V -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V st
( b₂ is_vertex_seq_of b₁ & b₂ . 1 = E ) ) } is set
v1 is Relation-like NAT -defined the carrier' of V -valued Function-like finite FinSequence-like FinSubsequence-like ( the carrier' of V,(V),(V,E,G))
rng v1 is finite set
(V,(rng v1)) is Element of bool the carrier of V
bool the carrier of V is set
the Source of V is Relation-like the carrier' of V -defined the carrier of V -valued Function-like V25( the carrier' of V, the carrier of V) Element of bool [: the carrier' of V, the carrier of V:]
[: the carrier' of V, the carrier of V:] is Relation-like set
bool [: the carrier' of V, the carrier of V:] is set
the Target of V is Relation-like the carrier' of V -defined the carrier of V -valued Function-like V25( the carrier' of V, the carrier of V) Element of bool [: the carrier' of V, the carrier of V:]
{ b₁ where b₁ is Element of the carrier of V : ex b₂ being Element of the carrier' of V st
( b₂ in rng v1 & ( b₁ = the Source of V . b₂ or b₁ = the Target of V . b₂ ) ) } is set
v2 is Relation-like NAT -defined the carrier' of V -valued Function-like finite FinSequence-like FinSubsequence-like Element of (V)
rng v2 is finite set
G9 is Relation-like NAT -defined the carrier' of V -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of V
E9 is Relation-like NAT -defined the carrier of V -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V
E9 . 1 is set
E9 is Relation-like NAT -defined the carrier of V -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V
E9 . 1 is set
len E9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
len G9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len G9) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
dom E9 is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
rng G9 is finite set
(V,(rng G9)) is Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : ex b₂ being Element of the carrier' of V st
( b₂ in rng G9 & ( b₁ = the Source of V . b₂ or b₁ = the Target of V . b₂ ) ) } is set
rng E9 is finite set
G is non empty V68() connected finite MultiGraphStruct
the carrier' of G is set
(G) is functional non empty FinSequence-membered FinSequenceSet of the carrier' of G
the carrier of G is non empty set
bool the carrier of G is set
V is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
rng V is finite set
(G,(rng V)) is Element of bool the carrier of G
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
{ b₁ where b₁ is Element of the carrier of G : ex b₂ being Element of the carrier' of G st
( b₂ in rng V & ( b₁ = the Source of G . b₂ or b₁ = the Target of G . b₂ ) ) } is set
{ b₁ where b₁ is Element of the carrier of G : ( b₁ in (G,(rng V)) & not Degree b₁ = (G,b₁,(rng V)) ) } is set
{ b₁ where b₁ is Element of the carrier of G : S₁[b₁] } is set
E9 is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like cyclic Chain of G
P9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
rng E9 is finite set
(G,(rng E9)) is Element of bool the carrier of G
{ b₁ where b₁ is Element of the carrier of G : ex b₂ being Element of the carrier' of G st
( b₂ in rng E9 & ( b₁ = the Source of G . b₂ or b₁ = the Target of G . b₂ ) ) } is set
rng P9 is finite set
n is set
p9 is Element of the carrier' of G
the Target of G . p9 is set
p is Element of the carrier of G
Degree p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesIn p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesOut p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(EdgesIn p) + (EdgesOut p) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p,(rng V)) is finite Element of bool the carrier' of G
bool the carrier' of G is set
card (G,p,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p,(rng V)) is finite Element of bool the carrier' of G
card (G,p,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,p,(rng V))) + (card (G,p,(rng V))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p is Element of the carrier of G
vs9 is set
vs9 is Element of the carrier of G
p1 is Element of the carrier' of G
the Target of G . p1 is set
the Source of G . p1 is set
Degree vs9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesIn vs9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesOut vs9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(EdgesIn vs9) + (EdgesOut vs9) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,vs9,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,vs9,(rng V)) is finite Element of bool the carrier' of G
bool the carrier' of G is set
card (G,vs9,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,vs9,(rng V)) is finite Element of bool the carrier' of G
card (G,vs9,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,vs9,(rng V))) + (card (G,vs9,(rng V))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
vs is set
p is Element of the carrier of G
n is Element of the carrier of G
Degree n is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesIn n is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesOut n is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(EdgesIn n) + (EdgesOut n) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,n,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,n,(rng V)) is finite Element of bool the carrier' of G
bool the carrier' of G is set
card (G,n,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,n,(rng V)) is finite Element of bool the carrier' of G
card (G,n,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,n,(rng V))) + (card (G,n,(rng V))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
n is Element of the carrier of G
Degree n is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesIn n is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesOut n is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(EdgesIn n) + (EdgesOut n) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,n,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,n,(rng V)) is finite Element of bool the carrier' of G
bool the carrier' of G is set
card (G,n,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,n,(rng V)) is finite Element of bool the carrier' of G
card (G,n,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,n,(rng V))) + (card (G,n,(rng V))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G is non empty V68() connected finite MultiGraphStruct
the carrier' of G is set
(G) is functional non empty FinSequence-membered FinSequenceSet of the carrier' of G
V is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
rng V is finite set
the carrier of G is non empty set
(G,(rng V)) is Element of bool the carrier of G
bool the carrier of G is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
{ b₁ where b₁ is Element of the carrier of G : ex b₂ being Element of the carrier' of G st
( b₂ in rng V & ( b₁ = the Source of G . b₂ or b₁ = the Target of G . b₂ ) ) } is set
{ b₁ where b₁ is Element of the carrier of G : ( b₁ in (G,(rng V)) & not Degree b₁ = (G,b₁,(rng V)) ) } is set
choose { b₁ where b₁ is Element of the carrier of G : ( b₁ in (G,(rng V)) & not Degree b₁ = (G,b₁,(rng V)) ) } is Element of { b₁ where b₁ is Element of the carrier of G : ( b₁ in (G,(rng V)) & not Degree b₁ = (G,b₁,(rng V)) ) }
the carrier' of G \ (rng V) is Element of bool the carrier' of G
bool the carrier' of G is set
G9 is Element of the carrier of G
Degree G9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesIn G9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesOut G9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(EdgesIn G9) + (EdgesOut G9) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,G9,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,G9,(rng V)) is finite Element of bool the carrier' of G
card (G,G9,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,G9,(rng V)) is finite Element of bool the carrier' of G
card (G,G9,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,G9,(rng V))) + (card (G,G9,(rng V))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E9 is finite set
E9 \ (rng V) is finite Element of bool E9
bool E9 is finite V32() set
n is set
v2 is Element of the carrier of G
P9 is non empty finite set
(G,v2,P9) is functional non empty FinSequence-membered Element of bool (G)
bool (G) is set
choose (G,v2,P9) is FinSequence-like Element of (G,v2,P9)
p9 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
(G,V,p9) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
p is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
(G,v2,( the carrier' of G \ (rng V))) is functional non empty FinSequence-membered Element of bool (G)
choose (G,v2,( the carrier' of G \ (rng V))) is FinSequence-like Element of (G,v2,( the carrier' of G \ (rng V)))
G9 is Element of the carrier of G
v2 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
(G,G9,( the carrier' of G \ (rng V))) is functional non empty FinSequence-membered Element of bool (G)
bool (G) is set
choose (G,G9,( the carrier' of G \ (rng V))) is FinSequence-like Element of (G,G9,( the carrier' of G \ (rng V)))
E is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
(G,V,v2) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
P9 is Element of the carrier of G
E9 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
(G,P9,( the carrier' of G \ (rng V))) is functional non empty FinSequence-membered Element of bool (G)
choose (G,P9,( the carrier' of G \ (rng V))) is FinSequence-like Element of (G,P9,( the carrier' of G \ (rng V)))
v1 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
(G,V,E9) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
G is non empty V68() connected finite MultiGraphStruct
the carrier' of G is set
(G) is functional non empty FinSequence-membered FinSequenceSet of the carrier' of G
the carrier of G is non empty set
V is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
rng V is finite set
(G,V) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
rng (G,V) is finite set
card (rng (G,V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
card (rng V) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v1 is finite set
v1 \ (rng V) is finite Element of bool v1
bool v1 is finite V32() set
E9 is set
(G,(rng V)) is Element of bool the carrier of G
bool the carrier of G is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
{ b₁ where b₁ is Element of the carrier of G : ex b₂ being Element of the carrier' of G st
( b₂ in rng V & ( b₁ = the Source of G . b₂ or b₁ = the Target of G . b₂ ) ) } is set
{ b₁ where b₁ is Element of the carrier of G : ( b₁ in (G,(rng V)) & not Degree b₁ = (G,b₁,(rng V)) ) } is set
E9 is non empty set
choose E9 is Element of E9
G9 is non empty finite set
n is Element of the carrier of G
P9 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
(G,n,G9) is functional non empty FinSequence-membered Element of bool (G)
bool (G) is set
choose (G,n,G9) is FinSequence-like Element of (G,n,G9)
(G,V,P9) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
p9 is Element of the carrier of G
Degree p9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesIn p9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesOut p9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(EdgesIn p9) + (EdgesOut p9) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9, the carrier' of G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9, the carrier' of G) is finite Element of bool the carrier' of G
bool the carrier' of G is set
card (G,p9, the carrier' of G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9, the carrier' of G) is finite Element of bool the carrier' of G
card (G,p9, the carrier' of G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,p9, the carrier' of G)) + (card (G,p9, the carrier' of G)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9,G9) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9,G9) is finite Element of bool the carrier' of G
card (G,p9,G9) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9,G9) is finite Element of bool the carrier' of G
card (G,p9,G9) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,p9,G9)) + (card (G,p9,G9)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9,v1) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9,v1) is finite Element of bool the carrier' of G
card (G,p9,v1) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9,v1) is finite Element of bool the carrier' of G
card (G,p9,v1) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,p9,v1)) + (card (G,p9,v1)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9,(rng V)) is finite Element of bool the carrier' of G
card (G,p9,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9,(rng V)) is finite Element of bool the carrier' of G
card (G,p9,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,p9,(rng V))) + (card (G,p9,(rng V))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9,v1) - (G,p9,(rng V)) is V39() integer ext-real V122() set
v2 is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like cyclic Chain of G
rng v2 is finite set
(G,p9,(rng v2)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9,(rng v2)) is finite Element of bool the carrier' of G
card (G,p9,(rng v2)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9,(rng v2)) is finite Element of bool the carrier' of G
card (G,p9,(rng v2)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,p9,(rng v2))) + (card (G,p9,(rng v2))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
the carrier' of G \ (rng V) is Element of bool the carrier' of G
(rng V) /\ ( the carrier' of G \ (rng V)) is finite Element of bool the carrier' of G
(G,n,G9) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,n,G9) is finite Element of bool the carrier' of G
card (G,n,G9) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,n,G9) is finite Element of bool the carrier' of G
card (G,n,G9) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,n,G9)) + (card (G,n,G9)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,n,v1) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,n,v1) is finite Element of bool the carrier' of G
card (G,n,v1) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,n,v1) is finite Element of bool the carrier' of G
card (G,n,v1) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,n,v1)) + (card (G,n,v1)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,n,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,n,(rng V)) is finite Element of bool the carrier' of G
card (G,n,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,n,(rng V)) is finite Element of bool the carrier' of G
card (G,n,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,n,(rng V))) + (card (G,n,(rng V))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,n,v1) - (G,n,(rng V)) is V39() integer ext-real V122() set
p9 is Element of the carrier of G
Degree p9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesIn p9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesOut p9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(EdgesIn p9) + (EdgesOut p9) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9,(rng V)) is finite Element of bool the carrier' of G
card (G,p9,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9,(rng V)) is finite Element of bool the carrier' of G
card (G,p9,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,p9,(rng V))) + (card (G,p9,(rng V))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
rng P9 is finite set
(rng V) /\ (rng P9) is finite set
( the carrier' of G \ (rng V)) /\ (rng P9) is finite Element of bool the carrier' of G
(rng V) /\ (( the carrier' of G \ (rng V)) /\ (rng P9)) is finite Element of bool the carrier' of G
{} /\ (rng P9) is Relation-like finite V100() V101() V102() V103() V104() V105() V109() V110() V111() set
(G,(rng P9)) is Element of bool the carrier of G
{ b₁ where b₁ is Element of the carrier of G : ex b₂ being Element of the carrier' of G st
( b₂ in rng P9 & ( b₁ = the Source of G . b₂ or b₁ = the Target of G . b₂ ) ) } is set
p9 is Element of the carrier of G
Degree p9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesIn p9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesOut p9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(EdgesIn p9) + (EdgesOut p9) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9,(rng V)) is finite Element of bool the carrier' of G
card (G,p9,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9,(rng V)) is finite Element of bool the carrier' of G
card (G,p9,(rng V)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,p9,(rng V))) + (card (G,p9,(rng V))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,(rng V)) /\ (G,(rng P9)) is Element of bool the carrier of G
choose ((G,(rng V)) /\ (G,(rng P9))) is Element of (G,(rng V)) /\ (G,(rng P9))
p9 is Element of the carrier of G
(G,p9,V) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
(G,p9,P9) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
(G,p9,V) ^ (G,p9,P9) is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
rng (G,p9,P9) is finite set
rng (G,p9,V) is finite set
(rng V) \/ (rng P9) is finite set
card (rng P9) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (rng V)) + (card (rng P9)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G is non empty V68() MultiGraphStruct
the carrier' of G is set
G is non empty V68() connected MultiGraphStruct
the carrier' of G is set
the carrier of G is non empty set
V is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G
E is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
rng E is finite set
v1 is set
v2 is set
G9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
E9 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
E9 . 1 is set
len E9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E9 . (len E9) is set
len G9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
rng V is finite set
P9 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
dom P9 is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
P9 . 1 is set
the Target of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
[: the carrier' of G, the carrier of G:] is Relation-like set
bool [: the carrier' of G, the carrier of G:] is set
the Target of G . (P9 . 1) is set
the Source of G is Relation-like the carrier' of G -defined the carrier of G -valued Function-like V25( the carrier' of G, the carrier of G) Element of bool [: the carrier' of G, the carrier of G:]
the Source of G . (P9 . 1) is set
G is non empty V68() connected finite MultiGraphStruct
the carrier' of G is set
the carrier of G is non empty set
E is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like cyclic Chain of G
v2 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
v2 . 1 is set
len v2 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v2 . (len v2) is set
rng v2 is finite set
v1 is Element of the carrier of G
rng E is finite set
(G,v1,(rng E)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,v1,(rng E)) is finite Element of bool the carrier' of G
bool the carrier' of G is set
card (G,v1,(rng E)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,v1,(rng E)) is finite Element of bool the carrier' of G
card (G,v1,(rng E)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,v1,(rng E))) + (card (G,v1,(rng E))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
Degree v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesIn v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesOut v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(EdgesIn v1) + (EdgesOut v1) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G) is functional non empty FinSequence-membered FinSequenceSet of the carrier' of G
E is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like cyclic Chain of G
rng E is finite set
E is non empty non void V68() connected finite MultiGraphStruct
the carrier of E is non empty set
choose the carrier of G is Element of the carrier of G
the carrier' of E is non empty set
(E) is functional non empty FinSequence-membered FinSequenceSet of the carrier' of E
v1 is Element of the carrier of E
(E,v1, the carrier' of G) is functional non empty FinSequence-membered Element of bool (E)
bool (E) is set
choose (E,v1, the carrier' of G) is FinSequence-like Element of (E,v1, the carrier' of G)
[:NAT,(E):] is Relation-like non trivial non finite set
bool [:NAT,(E):] is non trivial non finite set
v2 is Relation-like NAT -defined the carrier' of E -valued Function-like finite FinSequence-like FinSubsequence-like Element of (E)
G9 is Relation-like NAT -defined (E) -valued Function-like V25( NAT ,(E)) Function-yielding V50() Element of bool [:NAT,(E):]
G9 . 0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of (E)
E9 is Element of the carrier of G
Degree E9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesIn E9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesOut E9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(EdgesIn E9) + (EdgesOut E9) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,E9, the carrier' of G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,E9, the carrier' of G) is finite Element of bool the carrier' of G
card (G,E9, the carrier' of G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,E9, the carrier' of G) is finite Element of bool the carrier' of G
card (G,E9, the carrier' of G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,E9, the carrier' of G)) + (card (G,E9, the carrier' of G)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
Degree v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesIn v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesOut v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(EdgesIn v1) + (EdgesOut v1) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(E,v1, the carrier' of G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(E,v1, the carrier' of G) is finite Element of bool the carrier' of E
bool the carrier' of E is set
card (E,v1, the carrier' of G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(E,v1, the carrier' of G) is finite Element of bool the carrier' of E
card (E,v1, the carrier' of G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (E,v1, the carrier' of G)) + (card (E,v1, the carrier' of G)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
P9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G9 . P9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of (E)
P9 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
G9 . (P9 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of (E)
n is Relation-like NAT -defined the carrier' of E -valued Function-like finite FinSequence-like FinSubsequence-like Element of (E)
rng n is finite set
card (rng n) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(E,n) is Relation-like NAT -defined the carrier' of E -valued Function-like finite FinSequence-like FinSubsequence-like Element of (E)
p9 is Relation-like NAT -defined the carrier' of E -valued Function-like finite FinSequence-like FinSubsequence-like Element of (E)
rng p9 is finite set
card (rng p9) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
E9 is finite set
rng v2 is finite set
card (rng v2) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G) is functional non empty FinSequence-membered FinSequenceSet of the carrier' of G
E9 is finite set
card E9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card E9) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
G9 . ((card E9) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of (E)
P9 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
rng P9 is finite set
card (rng P9) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card E9) + 0 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
P9 is Relation-like NAT -defined the carrier' of E -valued Function-like finite FinSequence-like FinSubsequence-like Element of (E)
E9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G9 . E9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of (E)
rng P9 is finite set
P9 is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like Element of (G)
E9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
G9 . E9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of (E)
rng P9 is finite set
n is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like cyclic Chain of G
rng n is finite set
G is non empty V68() connected finite MultiGraphStruct
the carrier' of G is set
the carrier of G is non empty set
{ the carrier' of G} is non empty trivial finite 1 -element set
v1 is set
v1 is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G
v2 is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
len v2 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
len v1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len v1) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
dom v2 is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
v2 . 1 is set
v2 . (len v2) is set
G9 is Element of the carrier of G
E9 is Element of the carrier of G
P9 is Element of the carrier of G
n is Element of the carrier of G
p9 is Element of the carrier of G
Degree p9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesIn p9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesOut p9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(EdgesIn p9) + (EdgesOut p9) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9, the carrier' of G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9, the carrier' of G) is finite Element of bool the carrier' of G
bool the carrier' of G is set
card (G,p9, the carrier' of G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9, the carrier' of G) is finite Element of bool the carrier' of G
card (G,p9, the carrier' of G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,p9, the carrier' of G)) + (card (G,p9, the carrier' of G)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
rng v1 is finite set
(G,p9,(rng v1)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9,(rng v1)) is finite Element of bool the carrier' of G
card (G,p9,(rng v1)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,p9,(rng v1)) is finite Element of bool the carrier' of G
card (G,p9,(rng v1)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,p9,(rng v1))) + (card (G,p9,(rng v1))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
v1 is Element of the carrier of G
v2 is Element of the carrier of G
(G,v1,v2) is non empty V68() strict connected finite MultiGraphStruct
the carrier' of (G,v1,v2) is set
the carrier' of G \/ { the carrier' of G} is non empty set
the carrier' of (G,v1,v2) /\ the carrier' of G is set
the carrier of (G,v1,v2) is non empty set
P9 is Element of the carrier of (G,v1,v2)
Degree P9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesIn P9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesOut P9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(EdgesIn P9) + (EdgesOut P9) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
((G,v1,v2),P9, the carrier' of (G,v1,v2)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
((G,v1,v2),P9, the carrier' of (G,v1,v2)) is finite Element of bool the carrier' of (G,v1,v2)
bool the carrier' of (G,v1,v2) is set
card ((G,v1,v2),P9, the carrier' of (G,v1,v2)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
((G,v1,v2),P9, the carrier' of (G,v1,v2)) is finite Element of bool the carrier' of (G,v1,v2)
card ((G,v1,v2),P9, the carrier' of (G,v1,v2)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card ((G,v1,v2),P9, the carrier' of (G,v1,v2))) + (card ((G,v1,v2),P9, the carrier' of (G,v1,v2))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
n is Element of the carrier of G
(G,n, the carrier' of (G,v1,v2)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,n, the carrier' of (G,v1,v2)) is finite Element of bool the carrier' of G
card (G,n, the carrier' of (G,v1,v2)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,n, the carrier' of (G,v1,v2)) is finite Element of bool the carrier' of G
card (G,n, the carrier' of (G,v1,v2)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,n, the carrier' of (G,v1,v2))) + (card (G,n, the carrier' of (G,v1,v2))) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,n, the carrier' of G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,n, the carrier' of G) is finite Element of bool the carrier' of G
card (G,n, the carrier' of G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(G,n, the carrier' of G) is finite Element of bool the carrier' of G
card (G,n, the carrier' of G) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(card (G,n, the carrier' of G)) + (card (G,n, the carrier' of G)) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
Degree n is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesIn n is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesOut n is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(EdgesIn n) + (EdgesOut n) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
Degree n is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesIn n is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
EdgesOut n is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(EdgesIn n) + (EdgesOut n) is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p9 is V6() V7() V8() V12() non empty finite cardinal V39() integer non even ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
p9 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer even ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(G,n, the carrier' of (G,v1,v2)) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(Degree n) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
P9 is Relation-like NAT -defined the carrier' of (G,v1,v2) -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like cyclic Chain of (G,v1,v2)
rng P9 is finite set
dom P9 is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
n is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
P9 . n is set
len P9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p9 is Relation-like NAT -defined the carrier' of (G,v1,v2) -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like cyclic Chain of (G,v1,v2)
p9 . 1 is set
len p9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
rng p9 is finite set
1 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
((1 + 1),(len p9)) -cut p9 is Relation-like NAT -defined the carrier' of (G,v1,v2) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of (G,v1,v2)
vs9 is Relation-like NAT -defined the carrier of (G,v1,v2) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (G,v1,v2)
p is Relation-like NAT -defined the carrier' of (G,v1,v2) -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of (G,v1,v2)
rng p is finite set
dom p is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
p1 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
p . p1 is set
dom p9 is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
(1 + 1) + p1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
vs is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p9 . vs is set
vs + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(1,1) -cut p9 is Relation-like NAT -defined the carrier' of (G,v1,v2) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of (G,v1,v2)
p1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of (G,v1,v2)
p1 ^ (((1 + 1),(len p9)) -cut p9) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len vs9 is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
((1 + 1),(len vs9)) -cut vs9 is Relation-like NAT -defined the carrier of (G,v1,v2) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (G,v1,v2)
(len p9) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
vs is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Chain of G
p is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
p . 1 is set
len p is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
p . (len p) is set
i is Relation-like NAT -defined the carrier' of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of G
dom i is finite V100() V101() V102() V103() V104() V105() V109() V110() V111() Element of bool NAT
rng i is finite set
i . 1 is set
m is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V122() set
P9 . m is set
vs is Relation-like NAT -defined the carrier of (G,v1,v2) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (G,v1,v2)
p is Relation-like NAT -defined the carrier' of G -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of G
the Source of (G,v1,v2) is Relation-like the carrier' of (G,v1,v2) -defined the carrier of (G,v1,v2) -valued Function-like V25( the carrier' of (G,v1,v2), the carrier of (G,v1,v2)) Element of bool [: the carrier' of (G,v1,v2), the carrier of (G,v1,v2):]
[: the carrier' of (G,v1,v2), the carrier of (G,v1,v2):] is Relation-like set
bool [: the carrier' of (G,v1,v2), the carrier of (G,v1,v2):] is set
the Source of (G,v1,v2) . the carrier' of G is set
the Target of (G,v1,v2) is Relation-like the carrier' of (G,v1,v2) -defined the carrier of (G,v1,v2) -valued Function-like V25( the carrier' of (G,v1,v2), the carrier of (G,v1,v2)) Element of bool [: the carrier' of (G,v1,v2), the carrier of (G,v1,v2):]
the Target of (G,v1,v2) . the carrier' of G is set
(len vs9) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
vs is Relation-like NAT -defined the carrier of G -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of G
len vs is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
(len vs) + (1 + 1) is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(len p9) + (1 + 1) is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
0 + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
i is V6() V7() V8() V12() finite cardinal V39() integer ext-real non negative V100() V101() V102() V103() V104() V105() V109() V110() V111() V122() V123() Element of NAT
i + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
(len vs) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
((len vs) + 1) + 1 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
i + (1 + 1) is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
vs9 . 1 is set
vs9 . (len vs9) is set
vs9 . (1 + 1) is set
vs . 1 is set
vs . (len vs) is set
vs . (0 + 1) is set
(1 + 1) + 0 is V6() V7() V8() V12() non empty finite cardinal V39() integer ext-real positive non negative V100() V101() V102() V103() V104() V105() V107() V108() V109() V110() V111() V122() V123() Element of NAT
vs9 . ((1 + 1) + 0) is set
<* the carrier' of G*> is Relation-like NAT -defined Function-like non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
rng <* the carrier' of G*> is non empty trivial finite 1 -element set
rng p is finite set
{ the carrier' of G} \/ (rng p) is non empty finite set