REAL is non empty non trivial non finite V100() V101() V102() V106() set
NAT is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal V100() V101() V102() V103() V104() V105() V106() Element of K32(REAL)
K32(REAL) is non trivial non finite V79() set
COMPLEX is non empty non trivial non finite V100() V106() set
NAT is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal V100() V101() V102() V103() V104() V105() V106() set
K32(NAT) is non trivial non finite V79() set
K32(NAT) is non trivial non finite V79() set
K232() is set
K32(K232()) is set
K32(K32(K232())) is set
K240() is Element of K32(K32(K232()))
Real>=0 is set
RAT is non empty non trivial non finite V100() V101() V102() V103() V106() set
INT is non empty non trivial non finite V100() V101() V102() V103() V104() V106() set
{} is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real integer finite finite-yielding V36() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V100() V101() V102() V103() V104() V105() V106() FinSequence-yielding finite-support Function-yielding V199() set
2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
K33(NAT,REAL) is non trivial Relation-like non finite complex-valued ext-real-valued real-valued set
K32(K33(NAT,REAL)) is non trivial non finite set
1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
K224(1,NAT) is M11( NAT )
{{},1} is non empty finite V36() V100() V101() V102() V103() V104() V105() set
3 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
_GraphSelectors is non empty V100() V101() V102() V103() V104() V105() Element of K32(NAT)
VertexSelector is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
EdgeSelector is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
SourceSelector is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
TargetSelector is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
4 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
{VertexSelector,EdgeSelector,SourceSelector,TargetSelector} is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
card {} is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real integer finite finite-yielding V36() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V100() V101() V102() V103() V104() V105() V106() FinSequence-yielding finite-support Function-yielding V199() set
0 is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real integer finite finite-yielding V36() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative V77() complex-valued ext-real-valued real-valued natural-valued V100() V101() V102() V103() V104() V105() V106() FinSequence-yielding finite-support Function-yielding V199() Element of NAT
Real>=0 is V100() V101() V102() Element of K32(REAL)
{ b1 where b1 is V28() real ext-real Element of REAL : 0 <= b1 } is set
G is Relation-like Function-like set
dom G is set
source is set
sink is set
source .--> sink is Relation-like {source} -defined Function-like one-to-one finite finite-support set
{source} is non empty trivial finite 1 -element set
{source} --> sink is non empty Relation-like {source} -defined {sink} -valued Function-like constant total V18({source},{sink}) finite finite-support Element of K32(K33({source},{sink}))
{sink} is non empty trivial finite 1 -element set
K33({source},{sink}) is Relation-like finite set
K32(K33({source},{sink})) is finite V36() set
G +* (source .--> sink) is Relation-like Function-like set
dom (G +* (source .--> sink)) is set
(dom G) \/ {source} is non empty set
dom (source .--> sink) is finite Element of K32({source})
K32({source}) is finite V36() V79() set
(dom G) \/ (dom (source .--> sink)) is set
G is Relation-like Function-like set
source is set
sink is set
source .--> sink is Relation-like {source} -defined Function-like one-to-one finite finite-support set
{source} is non empty trivial finite 1 -element set
{source} --> sink is non empty Relation-like {source} -defined {sink} -valued Function-like constant total V18({source},{sink}) finite finite-support Element of K32(K33({source},{sink}))
{sink} is non empty trivial finite 1 -element set
K33({source},{sink}) is Relation-like finite set
K32(K33({source},{sink})) is finite V36() set
G +* (source .--> sink) is Relation-like Function-like set
dom (G +* (source .--> sink)) is set
dom (source .--> sink) is finite Element of K32({source})
K32({source}) is finite V36() V79() set
G is Relation-like Function-like set
source is set
sink is set
source .--> sink is Relation-like {source} -defined Function-like one-to-one finite finite-support set
{source} is non empty trivial finite 1 -element set
{source} --> sink is non empty Relation-like {source} -defined {sink} -valued Function-like constant total V18({source},{sink}) finite finite-support Element of K32(K33({source},{sink}))
{sink} is non empty trivial finite 1 -element set
K33({source},{sink}) is Relation-like finite set
K32(K33({source},{sink})) is finite V36() set
G +* (source .--> sink) is Relation-like Function-like set
(G +* (source .--> sink)) . source is set
dom (source .--> sink) is finite Element of K32({source})
K32({source}) is finite V36() V79() set
(source .--> sink) . source is set
G is Relation-like Function-like set
source is set
CS is set
sink is set
source .--> sink is Relation-like {source} -defined Function-like one-to-one finite finite-support set
{source} is non empty trivial finite 1 -element set
{source} --> sink is non empty Relation-like {source} -defined {sink} -valued Function-like constant total V18({source},{sink}) finite finite-support Element of K32(K33({source},{sink}))
{sink} is non empty trivial finite 1 -element set
K33({source},{sink}) is Relation-like finite set
K32(K33({source},{sink})) is finite V36() set
G +* (source .--> sink) is Relation-like Function-like set
(G +* (source .--> sink)) . CS is set
G . CS is set
dom (source .--> sink) is finite Element of K32({source})
K32({source}) is finite V36() V79() set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] [Weighted] set
the_Weight_of G is Relation-like the_Edges_of G -defined Function-like total set
the_Edges_of G is set
G . EdgeSelector is set
WeightSelector is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
5 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
G . WeightSelector is set
source is set
rng (the_Weight_of G) is set
sink is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
{1} is non empty trivial finite V36() 1 -element V100() V101() V102() V103() V104() V105() Element of K32(NAT)
K33({},{1}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
K32(K33({},{1})) is finite V36() set
sink is empty Relation-like non-empty empty-yielding {} -defined {1} -valued Function-like one-to-one constant functional total V18( {} ,{1}) epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real integer finite finite-yielding V36() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V100() V101() V102() V103() V104() V105() V106() FinSequence-yielding finite-support Function-yielding V199() Element of K32(K33({},{1}))
createGraph ({1},{},sink,sink) is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple V221() V222() Tree-like set
the_Edges_of (createGraph ({1},{},sink,sink)) is finite set
(createGraph ({1},{},sink,sink)) . EdgeSelector is set
K33((the_Edges_of (createGraph ({1},{},sink,sink))),NAT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K32(K33((the_Edges_of (createGraph ({1},{},sink,sink))),NAT)) is set
the Relation-like the_Edges_of (createGraph ({1},{},sink,sink)) -defined NAT -valued Function-like total V18( the_Edges_of (createGraph ({1},{},sink,sink)), NAT ) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33((the_Edges_of (createGraph ({1},{},sink,sink))),NAT)) is Relation-like the_Edges_of (createGraph ({1},{},sink,sink)) -defined NAT -valued Function-like total V18( the_Edges_of (createGraph ({1},{},sink,sink)), NAT ) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33((the_Edges_of (createGraph ({1},{},sink,sink))),NAT))
WeightSelector is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
5 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(createGraph ({1},{},sink,sink)) .set (WeightSelector, the Relation-like the_Edges_of (createGraph ({1},{},sink,sink)) -defined NAT -valued Function-like total V18( the_Edges_of (createGraph ({1},{},sink,sink)), NAT ) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33((the_Edges_of (createGraph ({1},{},sink,sink))),NAT))) is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite loopless trivial non-multi non-Dmulti simple Dsimple V221() V222() Tree-like [Weighted] set
WeightSelector .--> the Relation-like the_Edges_of (createGraph ({1},{},sink,sink)) -defined NAT -valued Function-like total V18( the_Edges_of (createGraph ({1},{},sink,sink)), NAT ) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33((the_Edges_of (createGraph ({1},{},sink,sink))),NAT)) is Relation-like NAT -defined {WeightSelector} -defined Function-like one-to-one finite finite-support Function-yielding V199() set
{WeightSelector} is non empty trivial finite V36() 1 -element V100() V101() V102() V103() V104() V105() set
{WeightSelector} --> the Relation-like the_Edges_of (createGraph ({1},{},sink,sink)) -defined NAT -valued Function-like total V18( the_Edges_of (createGraph ({1},{},sink,sink)), NAT ) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33((the_Edges_of (createGraph ({1},{},sink,sink))),NAT)) is non empty Relation-like {WeightSelector} -defined { the Relation-like the_Edges_of (createGraph ({1},{},sink,sink)) -defined NAT -valued Function-like total V18( the_Edges_of (createGraph ({1},{},sink,sink)), NAT ) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33((the_Edges_of (createGraph ({1},{},sink,sink))),NAT))} -valued Function-like constant total V18({WeightSelector},{ the Relation-like the_Edges_of (createGraph ({1},{},sink,sink)) -defined NAT -valued Function-like total V18( the_Edges_of (createGraph ({1},{},sink,sink)), NAT ) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33((the_Edges_of (createGraph ({1},{},sink,sink))),NAT))}) finite finite-support Function-yielding V199() Element of K32(K33({WeightSelector},{ the Relation-like the_Edges_of (createGraph ({1},{},sink,sink)) -defined NAT -valued Function-like total V18( the_Edges_of (createGraph ({1},{},sink,sink)), NAT ) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33((the_Edges_of (createGraph ({1},{},sink,sink))),NAT))}))
{ the Relation-like the_Edges_of (createGraph ({1},{},sink,sink)) -defined NAT -valued Function-like total V18( the_Edges_of (createGraph ({1},{},sink,sink)), NAT ) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33((the_Edges_of (createGraph ({1},{},sink,sink))),NAT))} is non empty trivial functional finite V36() 1 -element set
K33({WeightSelector},{ the Relation-like the_Edges_of (createGraph ({1},{},sink,sink)) -defined NAT -valued Function-like total V18( the_Edges_of (createGraph ({1},{},sink,sink)), NAT ) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33((the_Edges_of (createGraph ({1},{},sink,sink))),NAT))}) is Relation-like finite set
K32(K33({WeightSelector},{ the Relation-like the_Edges_of (createGraph ({1},{},sink,sink)) -defined NAT -valued Function-like total V18( the_Edges_of (createGraph ({1},{},sink,sink)), NAT ) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33((the_Edges_of (createGraph ({1},{},sink,sink))),NAT))})) is finite V36() set
(createGraph ({1},{},sink,sink)) +* (WeightSelector .--> the Relation-like the_Edges_of (createGraph ({1},{},sink,sink)) -defined NAT -valued Function-like total V18( the_Edges_of (createGraph ({1},{},sink,sink)), NAT ) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33((the_Edges_of (createGraph ({1},{},sink,sink))),NAT))) is Relation-like Function-like finite finite-support set
the_Weight_of ((createGraph ({1},{},sink,sink)) .set (WeightSelector, the Relation-like the_Edges_of (createGraph ({1},{},sink,sink)) -defined NAT -valued Function-like total V18( the_Edges_of (createGraph ({1},{},sink,sink)), NAT ) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33((the_Edges_of (createGraph ({1},{},sink,sink))),NAT)))) is Relation-like the_Edges_of ((createGraph ({1},{},sink,sink)) .set (WeightSelector, the Relation-like the_Edges_of (createGraph ({1},{},sink,sink)) -defined NAT -valued Function-like total V18( the_Edges_of (createGraph ({1},{},sink,sink)), NAT ) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33((the_Edges_of (createGraph ({1},{},sink,sink))),NAT)))) -defined Function-like total finite finite-support set
the_Edges_of ((createGraph ({1},{},sink,sink)) .set (WeightSelector, the Relation-like the_Edges_of (createGraph ({1},{},sink,sink)) -defined NAT -valued Function-like total V18( the_Edges_of (createGraph ({1},{},sink,sink)), NAT ) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33((the_Edges_of (createGraph ({1},{},sink,sink))),NAT)))) is finite set
((createGraph ({1},{},sink,sink)) .set (WeightSelector, the Relation-like the_Edges_of (createGraph ({1},{},sink,sink)) -defined NAT -valued Function-like total V18( the_Edges_of (createGraph ({1},{},sink,sink)), NAT ) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33((the_Edges_of (createGraph ({1},{},sink,sink))),NAT)))) . EdgeSelector is set
((createGraph ({1},{},sink,sink)) .set (WeightSelector, the Relation-like the_Edges_of (createGraph ({1},{},sink,sink)) -defined NAT -valued Function-like total V18( the_Edges_of (createGraph ({1},{},sink,sink)), NAT ) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33((the_Edges_of (createGraph ({1},{},sink,sink))),NAT)))) . WeightSelector is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] [Weighted] real-weighted nonnegative-weighted () set
the_Weight_of G is Relation-like the_Edges_of G -defined Function-like total complex-valued ext-real-valued real-valued set
the_Edges_of G is set
G . EdgeSelector is set
WeightSelector is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
5 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
G . WeightSelector is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite [Weighted] real-weighted set
the_Edges_of G is finite set
G . EdgeSelector is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite [Weighted] real-weighted set
the_Edges_of G is finite set
G . EdgeSelector is set
CS is set
{CS} is non empty trivial finite 1 -element set
G .edgesInto {CS} is finite Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is finite V36() set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
source | (G .edgesInto {CS}) is Relation-like the_Edges_of G -defined G .edgesInto {CS} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (G .edgesInto {CS})) is V28() real ext-real set
G .edgesOutOf {CS} is finite Element of K32((the_Edges_of G))
source | (G .edgesOutOf {CS}) is Relation-like the_Edges_of G -defined G .edgesOutOf {CS} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (G .edgesOutOf {CS})) is V28() real ext-real set
(Sum (source | (G .edgesInto {CS}))) - (Sum (source | (G .edgesOutOf {CS}))) is V28() real ext-real set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite [Weighted] real-weighted set
the_Edges_of G is finite set
G . EdgeSelector is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] set
the_Edges_of G is set
G . EdgeSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
{1} is non empty trivial finite V36() 1 -element V100() V101() V102() V103() V104() V105() Element of K32(NAT)
{1} \/ (the_Edges_of G) is non empty set
K33((the_Vertices_of G),({1} \/ (the_Edges_of G))) is Relation-like set
K32(K33((the_Vertices_of G),({1} \/ (the_Edges_of G)))) is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] [Weighted] real-weighted set
the_Edges_of G is set
G . EdgeSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
{1} \/ (the_Edges_of G) is non empty set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] [Weighted] real-weighted set
the_Edges_of G is set
G . EdgeSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
{1} \/ (the_Edges_of G) is non empty set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] [Weighted] real-weighted set
the_Edges_of G is set
G . EdgeSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] [Weighted] real-weighted set
the_Edges_of G is set
G . EdgeSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued set
sink is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
len sink is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
CS is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative non even set
sink . CS is set
CS + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . (CS + 2) is set
CS + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
sink . (CS + 1) is set
the_Weight_of G is Relation-like the_Edges_of G -defined Function-like total complex-valued ext-real-valued real-valued set
G . WeightSelector is set
(the_Weight_of G) . (sink . (CS + 1)) is V28() real ext-real set
source . (sink . (CS + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] [Weighted] real-weighted set
the_Edges_of G is set
G . EdgeSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued set
sink is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
CS is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
n is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
sink .cut (CS,n) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
len sink is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
P is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative non even set
(sink .cut (CS,n)) . P is set
P + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
(sink .cut (CS,n)) . (P + 1) is set
P + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
(sink .cut (CS,n)) . (P + 2) is set
len (sink .cut (CS,n)) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
E1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
dom (sink .cut (CS,n)) is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
Gn1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
P is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
E1 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(sink .cut (CS,n)) . (E1 + 2) is set
Gn1 + (E1 + 2) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(Gn1 + (E1 + 2)) - 1 is V28() real integer ext-real set
sink . ((Gn1 + (E1 + 2)) - 1) is set
E1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(sink .cut (CS,n)) . (E1 + 1) is set
Gn1 + (E1 + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(Gn1 + (E1 + 1)) - 1 is V28() real integer ext-real set
sink . ((Gn1 + (E1 + 1)) - 1) is set
Gn1 + E1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(Gn1 + E1) - 1 is V28() real integer ext-real set
dom sink is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
Gn1 + P is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
(Gn1 + P) - 1 is non empty V28() real integer ext-real non even set
CS + (P + 2) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(CS + (P + 2)) - 1 is V28() real integer ext-real set
E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
B2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . B2 is set
B2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
sink . (B2 + 1) is set
B2 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . (B2 + 2) is set
A2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(len sink) - 0 is non empty V28() real integer ext-real positive non negative set
((CS + (P + 2)) - 1) - 2 is V28() real integer ext-real set
the_Weight_of G is Relation-like the_Edges_of G -defined Function-like total complex-valued ext-real-valued real-valued set
G . WeightSelector is set
(the_Weight_of G) . ((sink .cut (CS,n)) . (P + 1)) is V28() real ext-real set
source . ((sink .cut (CS,n)) . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
len sink is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
len sink is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] [Weighted] real-weighted set
the_Edges_of G is set
G . EdgeSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
the_Weight_of G is Relation-like the_Edges_of G -defined Function-like total complex-valued ext-real-valued real-valued set
G . WeightSelector is set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued set
sink is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
sink .vertices() is finite Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is V79() set
sink .last() is Element of the_Vertices_of G
n is set
CS is set
(the_Weight_of G) . CS is V28() real ext-real set
source . CS is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
sink .addEdge CS is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
len (sink .addEdge CS) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
Gn1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative non even set
(sink .addEdge CS) . Gn1 is set
Gn1 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
(sink .addEdge CS) . (Gn1 + 2) is set
Gn1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
(sink .addEdge CS) . (Gn1 + 1) is set
(the_Weight_of G) . ((sink .addEdge CS) . (Gn1 + 1)) is V28() real ext-real set
source . ((sink .addEdge CS) . (Gn1 + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
len sink is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
P is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
P + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
dom sink is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
sink . (Gn1 + 1) is set
P + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
sink . (Gn1 + 2) is set
sink . Gn1 is set
len sink is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
2 * 1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
(len sink) + (2 * 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
(len sink) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
((len sink) + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
dom sink is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
sink . Gn1 is set
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is set
G . SourceSelector is set
(the_Source_of G) . CS is set
len sink is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] [Weighted] real-weighted set
the_Edges_of G is set
G . EdgeSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
{1} \/ (the_Edges_of G) is non empty set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued set
K32((the_Edges_of G)) is set
sink is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
CS is Element of K32((the_Edges_of G))
n is set
CS is Element of K32((the_Edges_of G))
n is Element of K32((the_Edges_of G))
Gn is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] [Weighted] real-weighted set
the_Edges_of G is set
G . EdgeSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
{1} \/ (the_Edges_of G) is non empty set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued set
sink is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
(G,source,sink) is Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is set
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is set
G . SourceSelector is set
choose (G,source,sink) is Element of (G,source,sink)
(the_Source_of G) . (choose (G,source,sink)) is set
dom sink is Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is V79() set
((the_Source_of G) . (choose (G,source,sink))) .--> (choose (G,source,sink)) is Relation-like {((the_Source_of G) . (choose (G,source,sink)))} -defined Function-like one-to-one finite finite-support set
{((the_Source_of G) . (choose (G,source,sink)))} is non empty trivial finite 1 -element set
{((the_Source_of G) . (choose (G,source,sink)))} --> (choose (G,source,sink)) is non empty Relation-like {((the_Source_of G) . (choose (G,source,sink)))} -defined {(choose (G,source,sink))} -valued Function-like constant total V18({((the_Source_of G) . (choose (G,source,sink)))},{(choose (G,source,sink))}) finite finite-support Element of K32(K33({((the_Source_of G) . (choose (G,source,sink)))},{(choose (G,source,sink))}))
{(choose (G,source,sink))} is non empty trivial finite 1 -element set
K33({((the_Source_of G) . (choose (G,source,sink)))},{(choose (G,source,sink))}) is Relation-like finite set
K32(K33({((the_Source_of G) . (choose (G,source,sink)))},{(choose (G,source,sink))})) is finite V36() set
sink +* (((the_Source_of G) . (choose (G,source,sink))) .--> (choose (G,source,sink))) is Relation-like Function-like set
the_Target_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
G . TargetSelector is set
(the_Target_of G) . (choose (G,source,sink)) is set
((the_Target_of G) . (choose (G,source,sink))) .--> (choose (G,source,sink)) is Relation-like {((the_Target_of G) . (choose (G,source,sink)))} -defined Function-like one-to-one finite finite-support set
{((the_Target_of G) . (choose (G,source,sink)))} is non empty trivial finite 1 -element set
{((the_Target_of G) . (choose (G,source,sink)))} --> (choose (G,source,sink)) is non empty Relation-like {((the_Target_of G) . (choose (G,source,sink)))} -defined {(choose (G,source,sink))} -valued Function-like constant total V18({((the_Target_of G) . (choose (G,source,sink)))},{(choose (G,source,sink))}) finite finite-support Element of K32(K33({((the_Target_of G) . (choose (G,source,sink)))},{(choose (G,source,sink))}))
K33({((the_Target_of G) . (choose (G,source,sink)))},{(choose (G,source,sink))}) is Relation-like finite set
K32(K33({((the_Target_of G) . (choose (G,source,sink)))},{(choose (G,source,sink))})) is finite V36() set
sink +* (((the_Target_of G) . (choose (G,source,sink))) .--> (choose (G,source,sink))) is Relation-like Function-like set
E1 is set
E1 is set
rng (((the_Target_of G) . (choose (G,source,sink))) .--> (choose (G,source,sink))) is finite set
rng sink is Element of K32(({1} \/ (the_Edges_of G)))
K32(({1} \/ (the_Edges_of G))) is V79() set
(rng sink) \/ (rng (((the_Target_of G) . (choose (G,source,sink))) .--> (choose (G,source,sink)))) is set
rng (sink +* (((the_Target_of G) . (choose (G,source,sink))) .--> (choose (G,source,sink)))) is set
E1 is set
rng (((the_Source_of G) . (choose (G,source,sink))) .--> (choose (G,source,sink))) is finite set
(rng sink) \/ (rng (((the_Source_of G) . (choose (G,source,sink))) .--> (choose (G,source,sink)))) is set
rng (sink +* (((the_Source_of G) . (choose (G,source,sink))) .--> (choose (G,source,sink)))) is set
E1 is set
dom (sink +* (((the_Target_of G) . (choose (G,source,sink))) .--> (choose (G,source,sink)))) is set
dom (((the_Target_of G) . (choose (G,source,sink))) .--> (choose (G,source,sink))) is finite Element of K32({((the_Target_of G) . (choose (G,source,sink)))})
K32({((the_Target_of G) . (choose (G,source,sink)))}) is finite V36() V79() set
(dom sink) \/ (dom (((the_Target_of G) . (choose (G,source,sink))) .--> (choose (G,source,sink)))) is set
(dom sink) \/ {((the_Target_of G) . (choose (G,source,sink)))} is non empty set
K33((the_Vertices_of G),({1} \/ (the_Edges_of G))) is Relation-like set
K32(K33((the_Vertices_of G),({1} \/ (the_Edges_of G)))) is set
dom (sink +* (((the_Source_of G) . (choose (G,source,sink))) .--> (choose (G,source,sink)))) is set
dom (((the_Source_of G) . (choose (G,source,sink))) .--> (choose (G,source,sink))) is finite Element of K32({((the_Source_of G) . (choose (G,source,sink)))})
K32({((the_Source_of G) . (choose (G,source,sink)))}) is finite V36() V79() set
(dom sink) \/ (dom (((the_Source_of G) . (choose (G,source,sink))) .--> (choose (G,source,sink)))) is set
(dom sink) \/ {((the_Source_of G) . (choose (G,source,sink)))} is non empty set
CS is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] set
the_Edges_of G is set
G . EdgeSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
{1} \/ (the_Edges_of G) is non empty set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued set
NAT --> {} is non empty Relation-like NAT -defined RAT -valued INT -valued {{}} -valued Function-like constant total V18( NAT ,{{}}) T-Sequence-like complex-valued ext-real-valued real-valued natural-valued Function-yielding V199() Element of K32(K33(NAT,{{}}))
{{}} is non empty trivial functional finite V36() 1 -element V100() V101() V102() V103() V104() V105() set
K33(NAT,{{}}) is non trivial Relation-like RAT -valued INT -valued non finite complex-valued ext-real-valued real-valued natural-valued set
K32(K33(NAT,{{}})) is non trivial non finite set
CS is Relation-like NAT -defined Function-like total set
n is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
CS . n is set
K33((the_Vertices_of G),({1} \/ (the_Edges_of G))) is Relation-like set
K32(K33((the_Vertices_of G),({1} \/ (the_Edges_of G)))) is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] set
the_Edges_of G is set
G . EdgeSelector is set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued set
sink is Relation-like NAT -defined Function-like total (G,source)
CS is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
sink . CS is set
the_Vertices_of G is non empty set
G . VertexSelector is set
{1} \/ (the_Edges_of G) is non empty set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] [Weighted] real-weighted set
the_Edges_of G is set
G . EdgeSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued set
sink is Element of the_Vertices_of G
sink .--> 1 is Relation-like the_Vertices_of G -defined {sink} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{sink} is non empty trivial finite 1 -element set
{sink} --> 1 is non empty Relation-like non-empty {sink} -defined NAT -valued RAT -valued INT -valued {1} -valued Function-like constant total V18({sink},{1}) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33({sink},{1}))
{1} is non empty trivial finite V36() 1 -element V100() V101() V102() V103() V104() V105() set
K33({sink},{1}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
K32(K33({sink},{1})) is finite V36() set
{1} \/ (the_Edges_of G) is non empty set
rng (sink .--> 1) is finite V100() V101() V102() V103() V104() V105() Element of K32(RAT)
K32(RAT) is non trivial non finite V79() set
n is set
CS is set
Gn is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
(G,source,Gn) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
Gn1 is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
P is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
(G,source,Gn1) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
n is set
CS is set
n is set
CS is set
CS is set
n is set
Gn1 is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
Gn is set
P is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
(G,source,Gn1) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
P is set
n is set
CS is Relation-like Function-like set
dom CS is set
CS . 0 is set
n is Relation-like NAT -defined Function-like total set
Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
n . Gn is set
Gn + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
n . (Gn + 1) is set
Gn1 is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
P is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
(G,source,Gn1) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
dom (sink .--> 1) is finite Element of K32({sink})
K32({sink}) is finite V36() V79() set
{sink} is non empty trivial finite 1 -element Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is V79() set
K33((the_Vertices_of G),({1} \/ (the_Edges_of G))) is Relation-like set
K32(K33((the_Vertices_of G),({1} \/ (the_Edges_of G)))) is set
n . 0 is set
Gn is Relation-like NAT -defined Function-like total (G,source)
(G,source,Gn,0) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
Gn1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,Gn,(Gn1 + 1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
(G,source,Gn,Gn1) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
(G,source,(G,source,Gn,Gn1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
P is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
P is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
(G,source,P) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
CS is Relation-like NAT -defined Function-like total (G,source)
(G,source,CS,0) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
n is Relation-like NAT -defined Function-like total (G,source)
(G,source,n,0) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(G,source,CS,Gn) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
(G,source,n,Gn) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
Gn + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,CS,(Gn + 1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
(G,source,(G,source,n,Gn)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
(G,source,n,(Gn + 1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(G,source,CS,Gn) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
(G,source,n,Gn) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
Gn + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,CS,(Gn + 1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
(G,source,n,(Gn + 1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
Gn is set
CS . Gn is set
n . Gn is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] [Weighted] real-weighted set
the_Edges_of G is set
G . EdgeSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued set
sink is Element of the_Vertices_of G
(G,source,sink) is Relation-like NAT -defined Function-like total (G,source)
(G,source,(G,source,sink),0) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
{1} \/ (the_Edges_of G) is non empty set
dom (G,source,(G,source,sink),0) is Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is V79() set
{sink} is non empty trivial finite 1 -element Element of K32((the_Vertices_of G))
sink .--> 1 is Relation-like the_Vertices_of G -defined {sink} -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{sink} is non empty trivial finite 1 -element set
{sink} --> 1 is non empty Relation-like non-empty {sink} -defined NAT -valued RAT -valued INT -valued {1} -valued Function-like constant total V18({sink},{1}) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33({sink},{1}))
K33({sink},{1}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
K32(K33({sink},{1})) is finite V36() set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] [Weighted] real-weighted set
the_Edges_of G is set
G . EdgeSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued set
sink is Element of the_Vertices_of G
(G,source,sink) is Relation-like NAT -defined Function-like total (G,source)
CS is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
n is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(G,source,(G,source,sink),CS) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
{1} \/ (the_Edges_of G) is non empty set
dom (G,source,(G,source,sink),CS) is Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is V79() set
(G,source,(G,source,sink),n) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
dom (G,source,(G,source,sink),n) is Element of K32((the_Vertices_of G))
Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
CS + Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
P is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
CS + P is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(CS + P)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
P + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
CS + (P + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(CS + (P + 1))) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
(G,source,(G,source,(G,source,sink),(CS + P))) is Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is set
choose (G,source,(G,source,(G,source,sink),(CS + P))) is Element of (G,source,(G,source,(G,source,sink),(CS + P)))
(CS + P) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),((CS + P) + 1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
(G,source,(G,source,(G,source,sink),(CS + P))) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
dom (G,source,(G,source,sink),(CS + P)) is Element of K32((the_Vertices_of G))
dom (G,source,(G,source,sink),(CS + (P + 1))) is Element of K32((the_Vertices_of G))
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is set
G . SourceSelector is set
(the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P)))) is set
((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P))))) .--> (choose (G,source,(G,source,(G,source,sink),(CS + P)))) is Relation-like {((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P)))))} -defined Function-like one-to-one finite finite-support set
{((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P)))))} is non empty trivial finite 1 -element set
{((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P)))))} --> (choose (G,source,(G,source,(G,source,sink),(CS + P)))) is non empty Relation-like {((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P)))))} -defined {(choose (G,source,(G,source,(G,source,sink),(CS + P))))} -valued Function-like constant total V18({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P)))))},{(choose (G,source,(G,source,(G,source,sink),(CS + P))))}) finite finite-support Element of K32(K33({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P)))))},{(choose (G,source,(G,source,(G,source,sink),(CS + P))))}))
{(choose (G,source,(G,source,(G,source,sink),(CS + P))))} is non empty trivial finite 1 -element set
K33({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P)))))},{(choose (G,source,(G,source,(G,source,sink),(CS + P))))}) is Relation-like finite set
K32(K33({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P)))))},{(choose (G,source,(G,source,(G,source,sink),(CS + P))))})) is finite V36() set
(G,source,(G,source,sink),(CS + P)) +* (((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P))))) .--> (choose (G,source,(G,source,(G,source,sink),(CS + P))))) is Relation-like Function-like set
dom (G,source,(G,source,sink),(CS + (P + 1))) is Element of K32((the_Vertices_of G))
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is set
G . SourceSelector is set
(the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P)))) is set
the_Target_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
G . TargetSelector is set
(the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P)))) is set
((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P))))) .--> (choose (G,source,(G,source,(G,source,sink),(CS + P)))) is Relation-like {((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P)))))} -defined Function-like one-to-one finite finite-support set
{((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P)))))} is non empty trivial finite 1 -element set
{((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P)))))} --> (choose (G,source,(G,source,(G,source,sink),(CS + P)))) is non empty Relation-like {((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P)))))} -defined {(choose (G,source,(G,source,(G,source,sink),(CS + P))))} -valued Function-like constant total V18({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P)))))},{(choose (G,source,(G,source,(G,source,sink),(CS + P))))}) finite finite-support Element of K32(K33({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P)))))},{(choose (G,source,(G,source,(G,source,sink),(CS + P))))}))
{(choose (G,source,(G,source,(G,source,sink),(CS + P))))} is non empty trivial finite 1 -element set
K33({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P)))))},{(choose (G,source,(G,source,(G,source,sink),(CS + P))))}) is Relation-like finite set
K32(K33({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P)))))},{(choose (G,source,(G,source,(G,source,sink),(CS + P))))})) is finite V36() set
(G,source,(G,source,sink),(CS + P)) +* (((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P))))) .--> (choose (G,source,(G,source,(G,source,sink),(CS + P))))) is Relation-like Function-like set
dom (G,source,(G,source,sink),(CS + (P + 1))) is Element of K32((the_Vertices_of G))
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is set
G . SourceSelector is set
(the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + P)))) is set
dom (G,source,(G,source,sink),(CS + (P + 1))) is Element of K32((the_Vertices_of G))
dom (G,source,(G,source,sink),(CS + (P + 1))) is Element of K32((the_Vertices_of G))
CS + 0 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(CS + 0)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
dom (G,source,(G,source,sink),(CS + 0)) is Element of K32((the_Vertices_of G))
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] [Weighted] real-weighted set
the_Edges_of G is set
G . EdgeSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued set
sink is Element of the_Vertices_of G
(G,source,sink) is Relation-like NAT -defined Function-like total (G,source)
(G,source,sink) .Result() is set
(G,source,sink) .Lifespan() is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,sink) . ((G,source,sink) .Lifespan()) is set
{1} \/ (the_Edges_of G) is non empty set
(G,source,(G,source,sink),((G,source,sink) .Lifespan())) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite [Weighted] real-weighted set
the_Edges_of G is finite set
G . EdgeSelector is set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
sink is Element of the_Vertices_of G
(G,source,sink) is Relation-like NAT -defined Function-like total (G,source)
card (the_Vertices_of G) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),Gn) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
{1} \/ (the_Edges_of G) is non empty finite set
Gn + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(Gn + 1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
(G,source,(G,source,(G,source,sink),Gn)) is finite Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is finite V36() set
choose (G,source,(G,source,(G,source,sink),Gn)) is Element of (G,source,(G,source,(G,source,sink),Gn))
(G,source,(G,source,(G,source,sink),Gn)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
dom (G,source,(G,source,sink),Gn) is finite Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is finite V36() V79() set
card (dom (G,source,(G,source,sink),Gn)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
dom (G,source,(G,source,sink),(Gn + 1)) is finite Element of K32((the_Vertices_of G))
card (dom (G,source,(G,source,sink),(Gn + 1))) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(Gn + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . SourceSelector is set
(the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))) is set
((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn)))) .--> (choose (G,source,(G,source,(G,source,sink),Gn))) is Relation-like {((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} -defined Function-like one-to-one finite finite-support set
{((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} is non empty trivial finite 1 -element set
{((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} --> (choose (G,source,(G,source,(G,source,sink),Gn))) is non empty Relation-like {((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} -defined {(choose (G,source,(G,source,(G,source,sink),Gn)))} -valued Function-like constant total V18({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))},{(choose (G,source,(G,source,(G,source,sink),Gn)))}) finite finite-support Element of K32(K33({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))},{(choose (G,source,(G,source,(G,source,sink),Gn)))}))
{(choose (G,source,(G,source,(G,source,sink),Gn)))} is non empty trivial finite 1 -element set
K33({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))},{(choose (G,source,(G,source,(G,source,sink),Gn)))}) is Relation-like finite set
K32(K33({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))},{(choose (G,source,(G,source,(G,source,sink),Gn)))})) is finite V36() set
(G,source,(G,source,sink),Gn) +* (((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn)))) .--> (choose (G,source,(G,source,(G,source,sink),Gn)))) is Relation-like Function-like finite finite-support set
dom (G,source,(G,source,sink),(Gn + 1)) is finite Element of K32((the_Vertices_of G))
(dom (G,source,(G,source,sink),Gn)) \/ {((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} is non empty finite set
card (dom (G,source,(G,source,sink),(Gn + 1))) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(Gn + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . SourceSelector is set
(the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))) is set
the_Target_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
G . TargetSelector is set
(the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))) is set
((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn)))) .--> (choose (G,source,(G,source,(G,source,sink),Gn))) is Relation-like {((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} -defined Function-like one-to-one finite finite-support set
{((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} is non empty trivial finite 1 -element set
{((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} --> (choose (G,source,(G,source,(G,source,sink),Gn))) is non empty Relation-like {((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} -defined {(choose (G,source,(G,source,(G,source,sink),Gn)))} -valued Function-like constant total V18({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))},{(choose (G,source,(G,source,(G,source,sink),Gn)))}) finite finite-support Element of K32(K33({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))},{(choose (G,source,(G,source,(G,source,sink),Gn)))}))
{(choose (G,source,(G,source,(G,source,sink),Gn)))} is non empty trivial finite 1 -element set
K33({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))},{(choose (G,source,(G,source,(G,source,sink),Gn)))}) is Relation-like finite set
K32(K33({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))},{(choose (G,source,(G,source,(G,source,sink),Gn)))})) is finite V36() set
(G,source,(G,source,sink),Gn) +* (((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn)))) .--> (choose (G,source,(G,source,(G,source,sink),Gn)))) is Relation-like Function-like finite finite-support set
dom (G,source,(G,source,sink),(Gn + 1)) is finite Element of K32((the_Vertices_of G))
(dom (G,source,(G,source,sink),Gn)) \/ {((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} is non empty finite set
card (dom (G,source,(G,source,sink),(Gn + 1))) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(Gn + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . SourceSelector is set
(the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))) is set
dom (G,source,(G,source,sink),(Gn + 1)) is finite Element of K32((the_Vertices_of G))
card (dom (G,source,(G,source,sink),(Gn + 1))) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(Gn + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
dom (G,source,(G,source,sink),(Gn + 1)) is finite Element of K32((the_Vertices_of G))
card (dom (G,source,(G,source,sink),(Gn + 1))) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(Gn + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),0) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
dom (G,source,(G,source,sink),0) is finite Element of K32((the_Vertices_of G))
{sink} is non empty trivial finite 1 -element Element of K32((the_Vertices_of G))
card (dom (G,source,(G,source,sink),0)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(card (the_Vertices_of G))) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
dom (G,source,(G,source,sink),(card (the_Vertices_of G))) is finite Element of K32((the_Vertices_of G))
card (dom (G,source,(G,source,sink),(card (the_Vertices_of G)))) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(card (the_Vertices_of G)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
1 + (card (the_Vertices_of G)) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(card (the_Vertices_of G)) + 0 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),n) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(n + 1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite [Weighted] real-weighted set
the_Edges_of G is finite set
G . EdgeSelector is set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
sink is Element of the_Vertices_of G
(G,source,sink) is Relation-like NAT -defined Function-like total (G,source)
(G,source,sink) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
{1} \/ (the_Edges_of G) is non empty finite set
(G,source,sink) .Result() is set
(G,source,sink) .Lifespan() is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,sink) . ((G,source,sink) .Lifespan()) is set
CS is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(G,source,(G,source,sink),CS) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
dom (G,source,(G,source,sink),CS) is finite Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is finite V36() V79() set
n is set
(G,source,(G,source,sink),CS) . n is set
(G,source,sink) . n is set
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . SourceSelector is set
the_Target_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
G . TargetSelector is set
(G,source,(G,source,sink),((G,source,sink) .Lifespan())) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
((G,source,sink) .Lifespan()) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(((G,source,sink) .Lifespan()) + 1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
B1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
((G,source,sink) .Lifespan()) + B1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(((G,source,sink) .Lifespan()) + B1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),((((G,source,sink) .Lifespan()) + B1) + 1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
(G,source,(G,source,sink),(((G,source,sink) .Lifespan()) + B1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
(G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan()))) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
B1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
((G,source,sink) .Lifespan()) + (B1 + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(((G,source,sink) .Lifespan()) + (B1 + 1))) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
((G,source,sink) .Lifespan()) + 0 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(((G,source,sink) .Lifespan()) + 0)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
B1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
CS + B1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(CS + B1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
(CS + B1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),((CS + B1) + 1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
(G,source,(G,source,(G,source,sink),(CS + B1))) is finite Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is finite V36() set
choose (G,source,(G,source,(G,source,sink),(CS + B1))) is Element of (G,source,(G,source,(G,source,sink),(CS + B1)))
(G,source,(G,source,(G,source,sink),(CS + B1))) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
B1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
CS + (B1 + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(CS + (B1 + 1))) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
x is set
(G,source,(G,source,sink),CS) . x is set
(G,source,(G,source,sink),(CS + (B1 + 1))) . x is set
(the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1)))) is set
dom (G,source,(G,source,sink),(CS + B1)) is finite Element of K32((the_Vertices_of G))
((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1))))) .--> (choose (G,source,(G,source,(G,source,sink),(CS + B1)))) is Relation-like {((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1)))))} -defined Function-like one-to-one finite finite-support set
{((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1)))))} is non empty trivial finite 1 -element set
{((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1)))))} --> (choose (G,source,(G,source,(G,source,sink),(CS + B1)))) is non empty Relation-like {((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1)))))} -defined {(choose (G,source,(G,source,(G,source,sink),(CS + B1))))} -valued Function-like constant total V18({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1)))))},{(choose (G,source,(G,source,(G,source,sink),(CS + B1))))}) finite finite-support Element of K32(K33({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1)))))},{(choose (G,source,(G,source,(G,source,sink),(CS + B1))))}))
{(choose (G,source,(G,source,(G,source,sink),(CS + B1))))} is non empty trivial finite 1 -element set
K33({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1)))))},{(choose (G,source,(G,source,(G,source,sink),(CS + B1))))}) is Relation-like finite set
K32(K33({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1)))))},{(choose (G,source,(G,source,(G,source,sink),(CS + B1))))})) is finite V36() set
(G,source,(G,source,sink),(CS + B1)) +* (((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1))))) .--> (choose (G,source,(G,source,(G,source,sink),(CS + B1))))) is Relation-like Function-like finite finite-support set
x is set
(G,source,(G,source,sink),CS) . x is set
(G,source,(G,source,sink),(CS + B1)) . x is set
(G,source,(G,source,sink),((CS + B1) + 1)) . x is set
B1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
CS + (B1 + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(CS + (B1 + 1))) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
x is set
(G,source,(G,source,sink),CS) . x is set
(G,source,(G,source,sink),(CS + (B1 + 1))) . x is set
(the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1)))) is set
dom (G,source,(G,source,sink),(CS + B1)) is finite Element of K32((the_Vertices_of G))
(the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1)))) is set
((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1))))) .--> (choose (G,source,(G,source,(G,source,sink),(CS + B1)))) is Relation-like {((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1)))))} -defined Function-like one-to-one finite finite-support set
{((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1)))))} is non empty trivial finite 1 -element set
{((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1)))))} --> (choose (G,source,(G,source,(G,source,sink),(CS + B1)))) is non empty Relation-like {((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1)))))} -defined {(choose (G,source,(G,source,(G,source,sink),(CS + B1))))} -valued Function-like constant total V18({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1)))))},{(choose (G,source,(G,source,(G,source,sink),(CS + B1))))}) finite finite-support Element of K32(K33({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1)))))},{(choose (G,source,(G,source,(G,source,sink),(CS + B1))))}))
{(choose (G,source,(G,source,(G,source,sink),(CS + B1))))} is non empty trivial finite 1 -element set
K33({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1)))))},{(choose (G,source,(G,source,(G,source,sink),(CS + B1))))}) is Relation-like finite set
K32(K33({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1)))))},{(choose (G,source,(G,source,(G,source,sink),(CS + B1))))})) is finite V36() set
(G,source,(G,source,sink),(CS + B1)) +* (((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1))))) .--> (choose (G,source,(G,source,(G,source,sink),(CS + B1))))) is Relation-like Function-like finite finite-support set
x is set
(G,source,(G,source,sink),CS) . x is set
(G,source,(G,source,sink),(CS + B1)) . x is set
(G,source,(G,source,sink),((CS + B1) + 1)) . x is set
B1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
CS + (B1 + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(CS + (B1 + 1))) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
x is set
(G,source,(G,source,sink),CS) . x is set
(G,source,(G,source,sink),(CS + (B1 + 1))) . x is set
(the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),(CS + B1)))) is set
dom (G,source,(G,source,sink),(CS + B1)) is finite Element of K32((the_Vertices_of G))
B1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
CS + (B1 + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(CS + (B1 + 1))) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
B1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
CS + (B1 + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(CS + (B1 + 1))) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
x is set
(G,source,(G,source,sink),CS) . x is set
(G,source,(G,source,sink),(CS + (B1 + 1))) . x is set
B1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
CS + B1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(CS + B1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
e is set
(G,source,(G,source,sink),CS) . e is set
B1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
CS + (B1 + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(CS + (B1 + 1))) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
(G,source,(G,source,sink),(CS + (B1 + 1))) . e is set
CS + 0 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(CS + 0)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
B1 is set
(G,source,(G,source,sink),CS) . B1 is set
(G,source,(G,source,sink),(CS + 0)) . B1 is set
B1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
CS + B1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
CS + e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
B1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
((G,source,sink) .Lifespan()) + B1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
((G,source,sink) .Lifespan()) + e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite [Weighted] real-weighted set
the_Edges_of G is finite set
G . EdgeSelector is set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
CS is Element of the_Vertices_of G
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
sink is Element of the_Vertices_of G
(G,source,sink) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
{1} \/ (the_Edges_of G) is non empty finite set
(G,source,sink) is Relation-like NAT -defined Function-like total (G,source)
(G,source,sink) .Result() is set
(G,source,sink) .Lifespan() is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,sink) . ((G,source,sink) .Lifespan()) is set
dom (G,source,sink) is finite Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is finite V36() V79() set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty finite set
G .walkOf sink is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support closed V234(G) trivial Trail-like Path-like vertex-distinct Walk of G
Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(G,source,(G,source,sink),Gn1) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
dom (G,source,(G,source,sink),Gn1) is finite Element of K32((the_Vertices_of G))
Gn1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(Gn1 + 1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
(G,source,(G,source,(G,source,sink),Gn1)) is finite Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is finite V36() set
choose (G,source,(G,source,(G,source,sink),Gn1)) is Element of (G,source,(G,source,(G,source,sink),Gn1))
(G,source,(G,source,(G,source,sink),Gn1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
dom (G,source,(G,source,sink),(Gn1 + 1)) is finite Element of K32((the_Vertices_of G))
B1 is set
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . SourceSelector is set
(the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))) is set
source . (choose (G,source,(G,source,(G,source,sink),Gn1))) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1)))) .--> (choose (G,source,(G,source,(G,source,sink),Gn1))) is Relation-like {((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))))} -defined Function-like one-to-one finite finite-support set
{((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))))} is non empty trivial finite 1 -element set
{((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))))} --> (choose (G,source,(G,source,(G,source,sink),Gn1))) is non empty Relation-like {((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))))} -defined {(choose (G,source,(G,source,(G,source,sink),Gn1)))} -valued Function-like constant total V18({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))))},{(choose (G,source,(G,source,(G,source,sink),Gn1)))}) finite finite-support Element of K32(K33({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))))},{(choose (G,source,(G,source,(G,source,sink),Gn1)))}))
{(choose (G,source,(G,source,(G,source,sink),Gn1)))} is non empty trivial finite 1 -element set
K33({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))))},{(choose (G,source,(G,source,(G,source,sink),Gn1)))}) is Relation-like finite set
K32(K33({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))))},{(choose (G,source,(G,source,(G,source,sink),Gn1)))})) is finite V36() set
(G,source,(G,source,sink),Gn1) +* (((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1)))) .--> (choose (G,source,(G,source,(G,source,sink),Gn1)))) is Relation-like Function-like finite finite-support set
dom (G,source,(G,source,sink),(Gn1 + 1)) is finite Element of K32((the_Vertices_of G))
(dom (G,source,(G,source,sink),Gn1)) \/ {((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))))} is non empty finite set
the_Target_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
G . TargetSelector is set
(the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))) is set
B1 is set
e is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
e .vertices() is finite Element of K32((the_Vertices_of G))
dom e is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
E2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
E2 .vertices() is finite Element of K32((the_Vertices_of G))
dom E2 is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
A2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative even set
E2 . A2 is set
A2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
E2 . (A2 + 1) is set
(G,source,sink) . (E2 . (A2 + 1)) is set
e is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
e .vertices() is finite Element of K32((the_Vertices_of G))
dom e is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
e .addEdge (choose (G,source,(G,source,(G,source,sink),Gn1))) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
e .last() is Element of the_Vertices_of G
A2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
e .first() is Element of the_Vertices_of G
B2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
B2 .vertices() is finite Element of K32((the_Vertices_of G))
{B1} is non empty trivial finite 1 -element set
(e .vertices()) \/ {B1} is non empty finite set
x is set
x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative even set
dom B2 is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
len B2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
len e is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
x + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
1 + x is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
B2 . (x + 1) is set
e . (x + 1) is set
B2 . x is set
e . x is set
(G,source,sink) . (B2 . (x + 1)) is set
len e is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
2 * 1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
(len e) + (2 * 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
(len e) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
((len e) + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
B2 . x is set
x + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(len e) + (1 + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
B2 . (x + 1) is set
(G,source,(G,source,sink),(Gn1 + 1)) . B1 is set
(G,source,sink) . (B2 . (x + 1)) is set
len e is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
B2 . x is set
x + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
B2 . (x + 1) is set
(G,source,sink) . (B2 . (x + 1)) is set
B2 . x is set
x + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
B2 . (x + 1) is set
(G,source,sink) . (B2 . (x + 1)) is set
e is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
e .vertices() is finite Element of K32((the_Vertices_of G))
dom e is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
e is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
e .vertices() is finite Element of K32((the_Vertices_of G))
dom e is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
B1 is set
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . SourceSelector is set
(the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))) is set
the_Target_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
G . TargetSelector is set
(the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))) is set
((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1)))) .--> (choose (G,source,(G,source,(G,source,sink),Gn1))) is Relation-like {((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))))} -defined Function-like one-to-one finite finite-support set
{((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))))} is non empty trivial finite 1 -element set
{((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))))} --> (choose (G,source,(G,source,(G,source,sink),Gn1))) is non empty Relation-like {((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))))} -defined {(choose (G,source,(G,source,(G,source,sink),Gn1)))} -valued Function-like constant total V18({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))))},{(choose (G,source,(G,source,(G,source,sink),Gn1)))}) finite finite-support Element of K32(K33({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))))},{(choose (G,source,(G,source,(G,source,sink),Gn1)))}))
{(choose (G,source,(G,source,(G,source,sink),Gn1)))} is non empty trivial finite 1 -element set
K33({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))))},{(choose (G,source,(G,source,(G,source,sink),Gn1)))}) is Relation-like finite set
K32(K33({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))))},{(choose (G,source,(G,source,(G,source,sink),Gn1)))})) is finite V36() set
(G,source,(G,source,sink),Gn1) +* (((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1)))) .--> (choose (G,source,(G,source,(G,source,sink),Gn1)))) is Relation-like Function-like finite finite-support set
dom (G,source,(G,source,sink),(Gn1 + 1)) is finite Element of K32((the_Vertices_of G))
(dom (G,source,(G,source,sink),Gn1)) \/ {((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))))} is non empty finite set
the_Weight_of G is Relation-like the_Edges_of G -defined Function-like total finite complex-valued ext-real-valued real-valued finite-support set
G . WeightSelector is set
(the_Weight_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))) is V28() real ext-real set
source . (choose (G,source,(G,source,(G,source,sink),Gn1))) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
B1 is set
e is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
e .vertices() is finite Element of K32((the_Vertices_of G))
dom e is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
E2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
E2 .vertices() is finite Element of K32((the_Vertices_of G))
dom E2 is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
A2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative even set
E2 . A2 is set
A2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
E2 . (A2 + 1) is set
(G,source,sink) . (E2 . (A2 + 1)) is set
e is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
e .vertices() is finite Element of K32((the_Vertices_of G))
dom e is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
e .addEdge (choose (G,source,(G,source,(G,source,sink),Gn1))) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
e .last() is Element of the_Vertices_of G
A2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
e .first() is Element of the_Vertices_of G
B2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
B2 .vertices() is finite Element of K32((the_Vertices_of G))
{B1} is non empty trivial finite 1 -element set
(e .vertices()) \/ {B1} is non empty finite set
x is set
x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative even set
dom B2 is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
len B2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
len e is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
x + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
1 + x is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
B2 . (x + 1) is set
e . (x + 1) is set
B2 . x is set
e . x is set
(G,source,sink) . (B2 . (x + 1)) is set
len e is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
2 * 1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
(len e) + (2 * 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
(len e) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
((len e) + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
B2 . x is set
x + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(len e) + (1 + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
B2 . (x + 1) is set
(G,source,(G,source,sink),(Gn1 + 1)) . B1 is set
(G,source,sink) . (B2 . (x + 1)) is set
len e is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
B2 . x is set
x + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
B2 . (x + 1) is set
(G,source,sink) . (B2 . (x + 1)) is set
B2 . x is set
x + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
B2 . (x + 1) is set
(G,source,sink) . (B2 . (x + 1)) is set
e is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
e .vertices() is finite Element of K32((the_Vertices_of G))
dom e is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
e is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
e .vertices() is finite Element of K32((the_Vertices_of G))
dom e is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
B1 is set
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . SourceSelector is set
(the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn1))) is set
dom (G,source,(G,source,sink),(Gn1 + 1)) is finite Element of K32((the_Vertices_of G))
dom (G,source,(G,source,sink),(Gn1 + 1)) is finite Element of K32((the_Vertices_of G))
B1 is set
Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(G,source,(G,source,sink),Gn1) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
dom (G,source,(G,source,sink),Gn1) is finite Element of K32((the_Vertices_of G))
P is set
Gn1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(Gn1 + 1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
dom (G,source,(G,source,sink),(Gn1 + 1)) is finite Element of K32((the_Vertices_of G))
P is set
(G,source,(G,source,sink),0) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
dom (G,source,(G,source,sink),0) is finite Element of K32((the_Vertices_of G))
{sink} is non empty trivial finite 1 -element Element of K32((the_Vertices_of G))
P is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support closed V234(G) trivial Trail-like Path-like vertex-distinct Walk of G
P .vertices() is finite Element of K32((the_Vertices_of G))
E1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative even set
dom P is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
len P is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
P . E1 is set
E1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
P . (E1 + 1) is set
(G,source,sink) . (P . (E1 + 1)) is set
Gn1 is set
Gn1 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
Gn1 .vertices() is finite Element of K32((the_Vertices_of G))
dom Gn1 is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
P is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
dom P is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
P is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative even set
P . P is set
P + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
P . (P + 1) is set
(G,source,sink) . (P . (P + 1)) is set
Gn1 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
dom Gn1 is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
P is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
dom P is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
(G,source,(G,source,sink),0) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
E1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(G,source,(G,source,sink),E1) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
dom (G,source,(G,source,sink),E1) is finite Element of K32((the_Vertices_of G))
E1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(E1 + 1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
(G,source,(G,source,(G,source,sink),E1)) is finite Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is finite V36() set
choose (G,source,(G,source,(G,source,sink),E1)) is Element of (G,source,(G,source,(G,source,sink),E1))
(G,source,(G,source,(G,source,sink),E1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
dom (G,source,(G,source,sink),(E1 + 1)) is finite Element of K32((the_Vertices_of G))
A2 is set
B2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
x is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
dom B2 is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
dom x is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . SourceSelector is set
(the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),E1))) is set
{sink} is non empty trivial finite 1 -element Element of K32((the_Vertices_of G))
dom (G,source,(G,source,sink),0) is finite Element of K32((the_Vertices_of G))
the_Target_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
G . TargetSelector is set
(the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),E1))) is set
((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),E1)))) .--> (choose (G,source,(G,source,(G,source,sink),E1))) is Relation-like {((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),E1))))} -defined Function-like one-to-one finite finite-support set
{((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),E1))))} is non empty trivial finite 1 -element set
{((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),E1))))} --> (choose (G,source,(G,source,(G,source,sink),E1))) is non empty Relation-like {((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),E1))))} -defined {(choose (G,source,(G,source,(G,source,sink),E1)))} -valued Function-like constant total V18({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),E1))))},{(choose (G,source,(G,source,(G,source,sink),E1)))}) finite finite-support Element of K32(K33({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),E1))))},{(choose (G,source,(G,source,(G,source,sink),E1)))}))
{(choose (G,source,(G,source,(G,source,sink),E1)))} is non empty trivial finite 1 -element set
K33({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),E1))))},{(choose (G,source,(G,source,(G,source,sink),E1)))}) is Relation-like finite set
K32(K33({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),E1))))},{(choose (G,source,(G,source,(G,source,sink),E1)))})) is finite V36() set
(G,source,(G,source,sink),E1) +* (((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),E1)))) .--> (choose (G,source,(G,source,(G,source,sink),E1)))) is Relation-like Function-like finite finite-support set
dom (G,source,(G,source,sink),(E1 + 1)) is finite Element of K32((the_Vertices_of G))
(dom (G,source,(G,source,sink),E1)) \/ {((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),E1))))} is non empty finite set
A2 is set
B2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
x is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
dom B2 is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
dom x is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
len B2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
B2 . (len B2) is set
x . 1 is set
len x is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
x . (len x) is set
B2 . 1 is set
(G,source,(G,source,sink),(E1 + 1)) . A2 is set
(G,source,sink) . A2 is set
B2 .last() is Element of the_Vertices_of G
B2 .first() is Element of the_Vertices_of G
x .last() is Element of the_Vertices_of G
x .first() is Element of the_Vertices_of G
(len x) - 0 is non empty V28() real integer ext-real positive non negative set
3 - 2 is V28() real integer ext-real set
(len B2) - 0 is non empty V28() real integer ext-real positive non negative set
(len B2) - 1 is V28() real integer ext-real even set
(len x) - 1 is V28() real integer ext-real even set
v1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
v1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
B2 . v1 is set
v1 - 1 is non empty V28() real integer ext-real non even set
m is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
B2 . m is set
2 * 0 is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real integer finite finite-yielding V36() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative V77() complex-valued ext-real-valued real-valued natural-valued V100() V101() V102() V103() V104() V105() V106() FinSequence-yielding finite-support Function-yielding V199() even Element of NAT
(2 * 0) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
B2 .cut (((2 * 0) + 1),m) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
EA is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative even set
dom (B2 .cut (((2 * 0) + 1),m)) is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
len (B2 .cut (((2 * 0) + 1),m)) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
EA + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
(B2 .cut (((2 * 0) + 1),m)) . (EA + 1) is set
B2 . (EA + 1) is set
(B2 .cut (((2 * 0) + 1),m)) . EA is set
B2 . EA is set
(G,source,sink) . ((B2 .cut (((2 * 0) + 1),m)) . (EA + 1)) is set
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
m + (1 + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
B2 .cut (m,(len B2)) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
G .walkOf (((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),E1)))),(choose (G,source,(G,source,(G,source,sink),E1))),A2) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
(B2 .cut (((2 * 0) + 1),m)) .append (B2 .cut (m,(len B2))) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
B2 .cut (((2 * 0) + 1),(len B2)) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
v2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
v2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
x . v2 is set
v2 - 1 is non empty V28() real integer ext-real non even set
EA is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
x . EA is set
EA + (1 + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
x .cut (((2 * 0) + 1),EA) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
EB is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative even set
dom (x .cut (((2 * 0) + 1),EA)) is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
len (x .cut (((2 * 0) + 1),EA)) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
EB + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
(x .cut (((2 * 0) + 1),EA)) . (EB + 1) is set
x . (EB + 1) is set
(x .cut (((2 * 0) + 1),EA)) . EB is set
x . EB is set
(G,source,sink) . ((x .cut (((2 * 0) + 1),EA)) . (EB + 1)) is set
x .cut (EA,(len x)) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
(x .cut (((2 * 0) + 1),EA)) .append (x .cut (EA,(len x))) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
x .cut (((2 * 0) + 1),(len x)) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
EA + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
A2 is set
B2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
x is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
dom B2 is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
dom x is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . SourceSelector is set
(the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),E1))) is set
{sink} is non empty trivial finite 1 -element Element of K32((the_Vertices_of G))
dom (G,source,(G,source,sink),0) is finite Element of K32((the_Vertices_of G))
the_Target_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
G . TargetSelector is set
(the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),E1))) is set
((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),E1)))) .--> (choose (G,source,(G,source,(G,source,sink),E1))) is Relation-like {((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),E1))))} -defined Function-like one-to-one finite finite-support set
{((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),E1))))} is non empty trivial finite 1 -element set
{((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),E1))))} --> (choose (G,source,(G,source,(G,source,sink),E1))) is non empty Relation-like {((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),E1))))} -defined {(choose (G,source,(G,source,(G,source,sink),E1)))} -valued Function-like constant total V18({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),E1))))},{(choose (G,source,(G,source,(G,source,sink),E1)))}) finite finite-support Element of K32(K33({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),E1))))},{(choose (G,source,(G,source,(G,source,sink),E1)))}))
{(choose (G,source,(G,source,(G,source,sink),E1)))} is non empty trivial finite 1 -element set
K33({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),E1))))},{(choose (G,source,(G,source,(G,source,sink),E1)))}) is Relation-like finite set
K32(K33({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),E1))))},{(choose (G,source,(G,source,(G,source,sink),E1)))})) is finite V36() set
(G,source,(G,source,sink),E1) +* (((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),E1)))) .--> (choose (G,source,(G,source,(G,source,sink),E1)))) is Relation-like Function-like finite finite-support set
dom (G,source,(G,source,sink),(E1 + 1)) is finite Element of K32((the_Vertices_of G))
(dom (G,source,(G,source,sink),E1)) \/ {((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),E1))))} is non empty finite set
A2 is set
B2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
x is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
dom B2 is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
dom x is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
len B2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
B2 . (len B2) is set
x . 1 is set
len x is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
x . (len x) is set
B2 . 1 is set
(G,source,(G,source,sink),(E1 + 1)) . A2 is set
(G,source,sink) . A2 is set
B2 .last() is Element of the_Vertices_of G
B2 .first() is Element of the_Vertices_of G
x .last() is Element of the_Vertices_of G
x .first() is Element of the_Vertices_of G
(len x) - 0 is non empty V28() real integer ext-real positive non negative set
3 - 2 is V28() real integer ext-real set
(len B2) - 0 is non empty V28() real integer ext-real positive non negative set
(len B2) - 1 is V28() real integer ext-real even set
(len x) - 1 is V28() real integer ext-real even set
v1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
v1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
B2 . v1 is set
v1 - 1 is non empty V28() real integer ext-real non even set
m is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
B2 . m is set
2 * 0 is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real integer finite finite-yielding V36() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative V77() complex-valued ext-real-valued real-valued natural-valued V100() V101() V102() V103() V104() V105() V106() FinSequence-yielding finite-support Function-yielding V199() even Element of NAT
(2 * 0) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
B2 .cut (((2 * 0) + 1),m) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
EA is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative even set
dom (B2 .cut (((2 * 0) + 1),m)) is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
len (B2 .cut (((2 * 0) + 1),m)) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
EA + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
(B2 .cut (((2 * 0) + 1),m)) . (EA + 1) is set
B2 . (EA + 1) is set
(B2 .cut (((2 * 0) + 1),m)) . EA is set
B2 . EA is set
(G,source,sink) . ((B2 .cut (((2 * 0) + 1),m)) . (EA + 1)) is set
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
m + (1 + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
B2 .cut (m,(len B2)) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
G .walkOf (((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),E1)))),(choose (G,source,(G,source,(G,source,sink),E1))),A2) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
(B2 .cut (((2 * 0) + 1),m)) .append (B2 .cut (m,(len B2))) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
B2 .cut (((2 * 0) + 1),(len B2)) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
v2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
v2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
x . v2 is set
v2 - 1 is non empty V28() real integer ext-real non even set
EA is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
x . EA is set
EA + (1 + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
x .cut (((2 * 0) + 1),EA) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
EB is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative even set
dom (x .cut (((2 * 0) + 1),EA)) is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
len (x .cut (((2 * 0) + 1),EA)) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
EB + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
(x .cut (((2 * 0) + 1),EA)) . (EB + 1) is set
x . (EB + 1) is set
(x .cut (((2 * 0) + 1),EA)) . EB is set
x . EB is set
(G,source,sink) . ((x .cut (((2 * 0) + 1),EA)) . (EB + 1)) is set
x .cut (EA,(len x)) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
(x .cut (((2 * 0) + 1),EA)) .append (x .cut (EA,(len x))) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
x .cut (((2 * 0) + 1),(len x)) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
EA + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
A2 is set
B2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
x is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
dom B2 is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
dom x is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . SourceSelector is set
(the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),E1))) is set
dom (G,source,(G,source,sink),(E1 + 1)) is finite Element of K32((the_Vertices_of G))
dom (G,source,(G,source,sink),(E1 + 1)) is finite Element of K32((the_Vertices_of G))
A2 is set
B2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
x is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
dom B2 is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
dom x is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
E1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(G,source,(G,source,sink),E1) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
dom (G,source,(G,source,sink),E1) is finite Element of K32((the_Vertices_of G))
A1 is set
E1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(E1 + 1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
dom (G,source,(G,source,sink),(E1 + 1)) is finite Element of K32((the_Vertices_of G))
B1 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
e is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
dom B1 is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
dom e is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
E1 is set
dom (G,source,(G,source,sink),0) is finite Element of K32((the_Vertices_of G))
A1 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
B1 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
dom A1 is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
dom B1 is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
{sink} is non empty trivial finite 1 -element Element of K32((the_Vertices_of G))
2 * 0 is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real integer finite finite-yielding V36() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative V77() complex-valued ext-real-valued real-valued natural-valued V100() V101() V102() V103() V104() V105() V106() FinSequence-yielding finite-support Function-yielding V199() even Element of NAT
(2 * 0) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
A1 . ((2 * 0) + 1) is set
B1 . ((2 * 0) + 1) is set
len A1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
A1 . (len A1) is set
<*E1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support set
len B1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
B1 . (len B1) is set
E1 is set
A1 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
B1 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
dom A1 is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
dom B1 is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] [Weighted] real-weighted set
the_Edges_of G is set
G . EdgeSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued set
sink is Element of the_Vertices_of G
(G,source,sink) is Relation-like NAT -defined Function-like total (G,source)
(G,source,(G,source,sink),0) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
{1} \/ (the_Edges_of G) is non empty set
Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(G,source,(G,source,sink),Gn) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
Gn + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(Gn + 1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
(G,source,(G,source,(G,source,sink),Gn)) is Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is set
choose (G,source,(G,source,(G,source,sink),Gn)) is Element of (G,source,(G,source,(G,source,sink),Gn))
dom (G,source,(G,source,sink),Gn) is Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is V79() set
(G,source,(G,source,(G,source,sink),Gn)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
dom (G,source,(G,source,sink),(Gn + 1)) is Element of K32((the_Vertices_of G))
A1 is set
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is set
G . SourceSelector is set
(the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))) is set
the_Target_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
G . TargetSelector is set
(the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))) is set
the_Weight_of G is Relation-like the_Edges_of G -defined Function-like total complex-valued ext-real-valued real-valued set
G . WeightSelector is set
(the_Weight_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))) is V28() real ext-real set
source . (choose (G,source,(G,source,(G,source,sink),Gn))) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
e is set
dom (G,source,(G,source,sink),(Gn + 1)) is Element of K32((the_Vertices_of G))
((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn)))) .--> (choose (G,source,(G,source,(G,source,sink),Gn))) is Relation-like {((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} -defined Function-like one-to-one finite finite-support set
{((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} is non empty trivial finite 1 -element set
{((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} --> (choose (G,source,(G,source,(G,source,sink),Gn))) is non empty Relation-like {((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} -defined {(choose (G,source,(G,source,(G,source,sink),Gn)))} -valued Function-like constant total V18({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))},{(choose (G,source,(G,source,(G,source,sink),Gn)))}) finite finite-support Element of K32(K33({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))},{(choose (G,source,(G,source,(G,source,sink),Gn)))}))
{(choose (G,source,(G,source,(G,source,sink),Gn)))} is non empty trivial finite 1 -element set
K33({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))},{(choose (G,source,(G,source,(G,source,sink),Gn)))}) is Relation-like finite set
K32(K33({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))},{(choose (G,source,(G,source,(G,source,sink),Gn)))})) is finite V36() set
(G,source,(G,source,sink),Gn) +* (((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn)))) .--> (choose (G,source,(G,source,(G,source,sink),Gn)))) is Relation-like Function-like set
(dom (G,source,(G,source,sink),Gn)) \/ {((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} is non empty set
E2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
E2 .vertices() is finite Element of K32((the_Vertices_of G))
A2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
A2 .vertices() is finite Element of K32((the_Vertices_of G))
G .walkOf (((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn)))),(choose (G,source,(G,source,(G,source,sink),Gn))),((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
A2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
len A2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
B2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative non even set
2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
2 * 1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
<*((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn)))),(choose (G,source,(G,source,(G,source,sink),Gn))),((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))*> is non empty Relation-like NAT -defined Function-like finite 3 -element FinSequence-like FinSubsequence-like finite-support set
A2 . B2 is set
B2 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
A2 . (B2 + 2) is set
B2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
A2 . (B2 + 1) is set
(the_Weight_of G) . (A2 . (B2 + 1)) is V28() real ext-real set
source . (A2 . (B2 + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
B2 is set
A2 .vertices() is finite Element of K32((the_Vertices_of G))
{((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn)))),((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} is non empty finite set
E2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
E2 .vertices() is finite Element of K32((the_Vertices_of G))
E2 .addEdge (choose (G,source,(G,source,(G,source,sink),Gn))) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
E2 .last() is Element of the_Vertices_of G
E2 .first() is Element of the_Vertices_of G
B2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
x is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
v1 is set
x .vertices() is finite Element of K32((the_Vertices_of G))
(E2 .vertices()) \/ {((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} is non empty finite set
E2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
E2 .vertices() is finite Element of K32((the_Vertices_of G))
E2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
E2 .vertices() is finite Element of K32((the_Vertices_of G))
source . (choose (G,source,(G,source,(G,source,sink),Gn))) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
e is set
dom (G,source,(G,source,sink),(Gn + 1)) is Element of K32((the_Vertices_of G))
((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn)))) .--> (choose (G,source,(G,source,(G,source,sink),Gn))) is Relation-like {((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} -defined Function-like one-to-one finite finite-support set
{((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} is non empty trivial finite 1 -element set
{((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} --> (choose (G,source,(G,source,(G,source,sink),Gn))) is non empty Relation-like {((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} -defined {(choose (G,source,(G,source,(G,source,sink),Gn)))} -valued Function-like constant total V18({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))},{(choose (G,source,(G,source,(G,source,sink),Gn)))}) finite finite-support Element of K32(K33({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))},{(choose (G,source,(G,source,(G,source,sink),Gn)))}))
{(choose (G,source,(G,source,(G,source,sink),Gn)))} is non empty trivial finite 1 -element set
K33({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))},{(choose (G,source,(G,source,(G,source,sink),Gn)))}) is Relation-like finite set
K32(K33({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))},{(choose (G,source,(G,source,(G,source,sink),Gn)))})) is finite V36() set
(G,source,(G,source,sink),Gn) +* (((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn)))) .--> (choose (G,source,(G,source,(G,source,sink),Gn)))) is Relation-like Function-like set
(dom (G,source,(G,source,sink),Gn)) \/ {((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} is non empty set
E2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
E2 .vertices() is finite Element of K32((the_Vertices_of G))
A2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
A2 .vertices() is finite Element of K32((the_Vertices_of G))
G .walkOf (((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn)))),(choose (G,source,(G,source,(G,source,sink),Gn))),((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
A2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
len A2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
B2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative non even set
2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
2 * 1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
<*((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn)))),(choose (G,source,(G,source,(G,source,sink),Gn))),((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))*> is non empty Relation-like NAT -defined Function-like finite 3 -element FinSequence-like FinSubsequence-like finite-support set
B2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
A2 . (B2 + 1) is set
A2 . B2 is set
B2 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
A2 . (B2 + 2) is set
the_Weight_of G is Relation-like the_Edges_of G -defined Function-like total complex-valued ext-real-valued real-valued set
G . WeightSelector is set
(the_Weight_of G) . (A2 . (B2 + 1)) is V28() real ext-real set
source . (A2 . (B2 + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
B2 is set
A2 .vertices() is finite Element of K32((the_Vertices_of G))
{((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn)))),((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} is non empty finite set
E2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
E2 .vertices() is finite Element of K32((the_Vertices_of G))
E2 .addEdge (choose (G,source,(G,source,(G,source,sink),Gn))) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
E2 .last() is Element of the_Vertices_of G
E2 .first() is Element of the_Vertices_of G
B2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
x is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
v1 is set
x .vertices() is finite Element of K32((the_Vertices_of G))
(E2 .vertices()) \/ {((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),Gn))))} is non empty finite set
E2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
E2 .vertices() is finite Element of K32((the_Vertices_of G))
E2 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
E2 .vertices() is finite Element of K32((the_Vertices_of G))
dom (G,source,(G,source,sink),(Gn + 1)) is Element of K32((the_Vertices_of G))
dom (G,source,(G,source,sink),(Gn + 1)) is Element of K32((the_Vertices_of G))
e is set
dom (G,source,(G,source,sink),(Gn + 1)) is Element of K32((the_Vertices_of G))
dom (G,source,(G,source,sink),(Gn + 1)) is Element of K32((the_Vertices_of G))
A1 is set
Gn is set
dom (G,source,(G,source,sink),0) is Element of K32((the_Vertices_of G))
Gn1 is Element of the_Vertices_of G
G .walkOf Gn1 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support closed V234(G) trivial Trail-like Path-like vertex-distinct Walk of G
P is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support closed V234(G) trivial Trail-like Path-like vertex-distinct Walk of G
{sink} is non empty trivial finite 1 -element Element of K32((the_Vertices_of G))
P .vertices() is finite Element of K32((the_Vertices_of G))
{Gn1} is non empty trivial finite 1 -element Element of K32((the_Vertices_of G))
Gn is set
Gn1 is set
Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(G,source,(G,source,sink),Gn) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like (G,source)
dom (G,source,(G,source,sink),Gn) is Element of K32((the_Vertices_of G))
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite [Weighted] real-weighted set
the_Edges_of G is finite set
G . EdgeSelector is set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty finite set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
sink is Element of the_Vertices_of G
(G,source,sink) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
{1} \/ (the_Edges_of G) is non empty finite set
(G,source,sink) is Relation-like NAT -defined Function-like total (G,source)
(G,source,sink) .Result() is set
(G,source,sink) .Lifespan() is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,sink) . ((G,source,sink) .Lifespan()) is set
dom (G,source,sink) is finite Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is finite V36() V79() set
CS is set
Gn1 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
Gn1 .vertices() is finite Element of K32((the_Vertices_of G))
Gn1 is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
2 * 0 is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real integer finite finite-yielding V36() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative V77() complex-valued ext-real-valued real-valued natural-valued V100() V101() V102() V103() V104() V105() V106() FinSequence-yielding finite-support Function-yielding V199() even Element of NAT
(2 * 0) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
Gn1 . ((2 * 0) + 1) is set
{sink} is non empty trivial finite 1 -element Element of K32((the_Vertices_of G))
(G,source,(G,source,sink),0) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
dom (G,source,(G,source,sink),0) is finite Element of K32((the_Vertices_of G))
(G,source,(G,source,sink),((G,source,sink) .Lifespan())) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
((G,source,sink) .Lifespan()) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,sink),(((G,source,sink) .Lifespan()) + 1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
len Gn1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
Gn1 . (len Gn1) is set
E1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
Gn1 . E1 is set
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
A1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
2 * 1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
A1 - (2 * 1) is non empty V28() real integer ext-real non even set
E1 - 0 is V28() real integer ext-real non negative set
B1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
Gn1 . B1 is set
(G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan()))) is finite Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is finite V36() set
choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan()))) is Element of (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))
B1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
Gn1 . (B1 + 1) is set
B1 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
Gn1 . (B1 + 2) is set
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . SourceSelector is set
(the_Source_of G) . (Gn1 . (B1 + 1)) is set
dom (G,source,(G,source,sink),((G,source,sink) .Lifespan())) is finite Element of K32((the_Vertices_of G))
the_Target_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
G . TargetSelector is set
(the_Target_of G) . (Gn1 . (B1 + 1)) is set
the_Weight_of G is Relation-like the_Edges_of G -defined Function-like total finite complex-valued ext-real-valued real-valued finite-support set
G . WeightSelector is set
(the_Weight_of G) . (Gn1 . (B1 + 1)) is V28() real ext-real set
source . (Gn1 . (B1 + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
the_Target_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . TargetSelector is set
(the_Target_of G) . (Gn1 . (B1 + 1)) is set
dom (G,source,(G,source,sink),((G,source,sink) .Lifespan())) is finite Element of K32((the_Vertices_of G))
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
G . SourceSelector is set
(the_Source_of G) . (Gn1 . (B1 + 1)) is set
source . (Gn1 . (B1 + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan()))) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . SourceSelector is set
(the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))) is set
dom (G,source,(G,source,sink),((G,source,sink) .Lifespan())) is finite Element of K32((the_Vertices_of G))
((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan()))))) .--> (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))) is Relation-like {((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))))} -defined Function-like one-to-one finite finite-support set
{((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))))} is non empty trivial finite 1 -element set
{((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))))} --> (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))) is non empty Relation-like {((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))))} -defined {(choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan()))))} -valued Function-like constant total V18({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))))},{(choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan()))))}) finite finite-support Element of K32(K33({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))))},{(choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan()))))}))
{(choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan()))))} is non empty trivial finite 1 -element set
K33({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))))},{(choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan()))))}) is Relation-like finite set
K32(K33({((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))))},{(choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan()))))})) is finite V36() set
(G,source,(G,source,sink),((G,source,sink) .Lifespan())) +* (((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan()))))) .--> (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan()))))) is Relation-like Function-like finite finite-support set
(dom (G,source,(G,source,sink),((G,source,sink) .Lifespan()))) \/ {((the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))))} is non empty finite set
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . SourceSelector is set
(the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))) is set
dom (G,source,(G,source,sink),((G,source,sink) .Lifespan())) is finite Element of K32((the_Vertices_of G))
the_Target_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
G . TargetSelector is set
(the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))) is set
((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan()))))) .--> (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))) is Relation-like {((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))))} -defined Function-like one-to-one finite finite-support set
{((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))))} is non empty trivial finite 1 -element set
{((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))))} --> (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))) is non empty Relation-like {((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))))} -defined {(choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan()))))} -valued Function-like constant total V18({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))))},{(choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan()))))}) finite finite-support Element of K32(K33({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))))},{(choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan()))))}))
{(choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan()))))} is non empty trivial finite 1 -element set
K33({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))))},{(choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan()))))}) is Relation-like finite set
K32(K33({((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))))},{(choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan()))))})) is finite V36() set
(G,source,(G,source,sink),((G,source,sink) .Lifespan())) +* (((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan()))))) .--> (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan()))))) is Relation-like Function-like finite finite-support set
(dom (G,source,(G,source,sink),((G,source,sink) .Lifespan()))) \/ {((the_Target_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))))} is non empty finite set
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . SourceSelector is set
(the_Source_of G) . (choose (G,source,(G,source,(G,source,sink),((G,source,sink) .Lifespan())))) is set
dom (G,source,(G,source,sink),((G,source,sink) .Lifespan())) is finite Element of K32((the_Vertices_of G))
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite [Weighted] real-weighted set
the_Edges_of G is finite set
G . EdgeSelector is set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
sink is Element of the_Vertices_of G
(G,source,sink) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
{1} \/ (the_Edges_of G) is non empty finite set
(G,source,sink) is Relation-like NAT -defined Function-like total (G,source)
(G,source,sink) .Result() is set
(G,source,sink) .Lifespan() is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,sink) . ((G,source,sink) .Lifespan()) is set
dom (G,source,sink) is finite Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is finite V36() V79() set
(G,source,(G,source,sink),0) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
dom (G,source,(G,source,sink),0) is finite Element of K32((the_Vertices_of G))
{sink} is non empty trivial finite 1 -element Element of K32((the_Vertices_of G))
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] [Weighted] real-weighted nonnegative-weighted () set
the_Edges_of G is set
G . EdgeSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued set
sink is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
the_Weight_of G is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued set
G . WeightSelector is set
sink .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support EdgeSeq of G
dom (sink .edgeSeq()) is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
CS is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
len (sink .edgeSeq()) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
Seg (len (sink .edgeSeq())) is finite len (sink .edgeSeq()) -element V100() V101() V102() V103() V104() V105() Element of K32(NAT)
2 * CS is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
(2 * CS) - 1 is non empty V28() real integer ext-real non even set
sink . ((2 * CS) - 1) is set
(2 * CS) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . ((2 * CS) + 1) is set
sink . (2 * CS) is set
(the_Weight_of G) . (sink . (2 * CS)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . (sink . (2 * CS)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((the_Weight_of G) . (sink . (2 * CS))) - (source . (sink . (2 * CS))) is V28() real integer ext-real set
2 * CS is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
(2 * CS) - 1 is non empty V28() real integer ext-real non even set
sink . ((2 * CS) - 1) is set
(2 * CS) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . ((2 * CS) + 1) is set
sink . (2 * CS) is set
(the_Weight_of G) . (sink . (2 * CS)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . (sink . (2 * CS)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((the_Weight_of G) . (sink . (2 * CS))) - (source . (sink . (2 * CS))) is V28() real integer ext-real set
2 * CS is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
(2 * CS) - 1 is non empty V28() real integer ext-real non even set
sink . ((2 * CS) - 1) is set
(2 * CS) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . ((2 * CS) + 1) is set
sink . (2 * CS) is set
(the_Weight_of G) . (sink . (2 * CS)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . (sink . (2 * CS)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((the_Weight_of G) . (sink . (2 * CS))) - (source . (sink . (2 * CS))) is V28() real integer ext-real set
2 * CS is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
(2 * CS) - 1 is non empty V28() real integer ext-real non even set
sink . ((2 * CS) - 1) is set
(2 * CS) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . ((2 * CS) + 1) is set
sink . (2 * CS) is set
(the_Weight_of G) . (sink . (2 * CS)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . (sink . (2 * CS)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((the_Weight_of G) . (sink . (2 * CS))) - (source . (sink . (2 * CS))) is V28() real integer ext-real set
n is set
CS is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
2 * CS is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
(2 * CS) - 1 is non empty V28() real integer ext-real non even set
sink . ((2 * CS) - 1) is set
(2 * CS) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . ((2 * CS) + 1) is set
sink . (2 * CS) is set
(the_Weight_of G) . (sink . (2 * CS)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . (sink . (2 * CS)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((the_Weight_of G) . (sink . (2 * CS))) - (source . (sink . (2 * CS))) is V28() real integer ext-real set
CS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom CS is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
n is set
rng CS is finite set
Gn is set
CS . Gn is set
Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
2 * Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
(2 * Gn1) - 1 is non empty V28() real integer ext-real non even set
sink . ((2 * Gn1) - 1) is set
(2 * Gn1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . ((2 * Gn1) + 1) is set
sink . (2 * Gn1) is set
dom sink is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
len sink is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
(len sink) - 0 is non empty V28() real integer ext-real positive non negative set
P is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
P + (1 + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
CS . Gn1 is set
(the_Weight_of G) . (sink . (2 * Gn1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . (sink . (2 * Gn1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((the_Weight_of G) . (sink . (2 * Gn1))) - (source . (sink . (2 * Gn1))) is V28() real integer ext-real set
P + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
2 * Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
(2 * Gn1) - 1 is non empty V28() real integer ext-real non even set
sink . ((2 * Gn1) - 1) is set
(2 * Gn1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . ((2 * Gn1) + 1) is set
sink . (2 * Gn1) is set
CS . Gn1 is set
source . (sink . (2 * Gn1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
2 * Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
(2 * Gn1) - 1 is non empty V28() real integer ext-real non even set
sink . ((2 * Gn1) - 1) is set
(2 * Gn1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . ((2 * Gn1) + 1) is set
sink . (2 * Gn1) is set
n is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued V180() finite-support FinSequence of NAT
dom n is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
2 * Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
(2 * Gn) - 1 is non empty V28() real integer ext-real non even set
sink . ((2 * Gn) - 1) is set
(2 * Gn) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . ((2 * Gn) + 1) is set
sink . (2 * Gn) is set
n . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(the_Weight_of G) . (sink . (2 * Gn)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . (sink . (2 * Gn)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((the_Weight_of G) . (sink . (2 * Gn))) - (source . (sink . (2 * Gn))) is V28() real integer ext-real set
CS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued V180() finite-support FinSequence of NAT
dom CS is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
n is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued V180() finite-support FinSequence of NAT
dom n is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
2 * Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
(2 * Gn) - 1 is non empty V28() real integer ext-real non even set
sink . ((2 * Gn) - 1) is set
(2 * Gn) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . ((2 * Gn) + 1) is set
sink . (2 * Gn) is set
CS . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(the_Weight_of G) . (sink . (2 * Gn)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . (sink . (2 * Gn)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((the_Weight_of G) . (sink . (2 * Gn))) - (source . (sink . (2 * Gn))) is V28() real integer ext-real set
n . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
2 * Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
(2 * Gn) - 1 is non empty V28() real integer ext-real non even set
sink . ((2 * Gn) - 1) is set
(2 * Gn) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . ((2 * Gn) + 1) is set
sink . (2 * Gn) is set
CS . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
source . (sink . (2 * Gn)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
n . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
2 * Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
(2 * Gn) - 1 is non empty V28() real integer ext-real non even set
sink . ((2 * Gn) - 1) is set
(2 * Gn) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . ((2 * Gn) + 1) is set
sink . (2 * Gn) is set
CS . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
n . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
CS . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
n . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] [Weighted] real-weighted nonnegative-weighted () set
the_Edges_of G is set
G . EdgeSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued set
sink is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
(G,source,sink) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued V180() finite-support FinSequence of NAT
rng (G,source,sink) is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
sink .edges() is finite Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is set
sink .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support EdgeSeq of G
rng (sink .edgeSeq()) is finite Element of K32((the_Edges_of G))
n is set
dom (sink .edgeSeq()) is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
Gn is set
(sink .edgeSeq()) . Gn is set
dom (G,source,sink) is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
(G,source,sink) . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
Gn1 is non empty finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
P is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() Element of Gn1
P is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
E1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
A1 is V28() real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
CS is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
n is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] [Weighted] real-weighted nonnegative-weighted () set
the_Edges_of G is set
G . EdgeSelector is set
the_Vertices_of G is non empty set
G . VertexSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued set
sink is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
sink .edges() is finite Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is set
len sink is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
(G,source,sink) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
CS is set
source . CS is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
Gn is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
Gn + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
sink . (Gn + 1) is set
sink . Gn is set
Gn + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . (Gn + 2) is set
source . (sink . (Gn + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source . (sink . (Gn + 1))) + (G,source,sink) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(source . (sink . (Gn + 1))) - (G,source,sink) is V28() real integer ext-real set
n is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
sink . (n + 1) is set
sink . n is set
n + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . (n + 2) is set
source . (sink . (n + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source . (sink . (n + 1))) + (G,source,sink) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
source . CS is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
Gn1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
Gn1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
sink . (Gn1 + 1) is set
sink . Gn1 is set
Gn1 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . (Gn1 + 2) is set
source . (sink . (Gn1 + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source . (sink . (Gn1 + 1))) - (G,source,sink) is V28() real integer ext-real set
Gn1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
Gn1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
sink . (Gn1 + 1) is set
sink . Gn1 is set
Gn1 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . (Gn1 + 2) is set
source . (sink . (Gn1 + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source . (sink . (Gn1 + 1))) + (G,source,sink) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(source . (sink . (Gn1 + 1))) - (G,source,sink) is V28() real integer ext-real set
sink . n is set
n + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . (n + 2) is set
source . (sink . (n + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source . (sink . (n + 1))) - (G,source,sink) is V28() real integer ext-real set
source . CS is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
Gn1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
Gn1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
sink . (Gn1 + 1) is set
sink . Gn1 is set
Gn1 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . (Gn1 + 2) is set
(source . (sink . (n + 1))) + (G,source,sink) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
Gn1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
Gn1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
sink . (Gn1 + 1) is set
sink . Gn1 is set
Gn1 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . (Gn1 + 2) is set
source . (sink . (Gn1 + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source . (sink . (Gn1 + 1))) + (G,source,sink) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(source . (sink . (Gn1 + 1))) - (G,source,sink) is V28() real integer ext-real set
sink . n is set
n + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . (n + 2) is set
source . CS is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . CS is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
Gn is set
source . CS is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . CS is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
n is set
CS is set
source . CS is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
CS is Relation-like Function-like set
dom CS is set
rng CS is set
n is set
Gn is set
CS . Gn is set
source . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
Gn1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
Gn1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
sink . (Gn1 + 1) is set
sink . Gn1 is set
Gn1 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . (Gn1 + 2) is set
source . (sink . (Gn1 + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source . (sink . (Gn1 + 1))) + (G,source,sink) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
sink . Gn1 is set
Gn1 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . (Gn1 + 2) is set
(Gn1 + 1) div 2 is V28() real integer ext-real set
sink .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support EdgeSeq of G
dom (sink .edgeSeq()) is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
(G,source,sink) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued V180() finite-support FinSequence of NAT
dom (G,source,sink) is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
2 * ((Gn1 + 1) div 2) is V28() real integer ext-real even set
(2 * ((Gn1 + 1) div 2)) + 1 is non empty V28() real integer ext-real non even set
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
Gn1 + (1 + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(2 * ((Gn1 + 1) div 2)) - 1 is non empty V28() real integer ext-real non even set
(G,source,sink) . ((Gn1 + 1) div 2) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
source . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
rng (G,source,sink) is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
(source . Gn) - (G,source,sink) is V28() real integer ext-real set
sink . Gn1 is set
Gn1 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . (Gn1 + 2) is set
n is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued set
Gn is set
n . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
Gn is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative non even set
sink . Gn is set
Gn + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . (Gn + 2) is set
Gn + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
sink . (Gn + 1) is set
n . (sink . (Gn + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . (sink . (Gn + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source . (sink . (Gn + 1))) + (G,source,sink) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(source . (sink . (Gn + 1))) - (G,source,sink) is V28() real integer ext-real set
Gn1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
Gn1 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . (Gn1 + 2) is set
CS is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued set
n is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued set
Gn is set
CS . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
n . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
Gn1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
Gn1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
sink . (Gn1 + 1) is set
sink . Gn1 is set
Gn1 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . (Gn1 + 2) is set
CS . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . (sink . (Gn1 + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source . (sink . (Gn1 + 1))) + (G,source,sink) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
n . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
sink . Gn1 is set
Gn1 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . (Gn1 + 2) is set
CS . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . (sink . (Gn1 + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source . (sink . (Gn1 + 1))) - (G,source,sink) is V28() real integer ext-real set
n . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
sink . Gn1 is set
Gn1 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . (Gn1 + 2) is set
CS . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
n . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
CS . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
n . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
CS . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
n . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
CS . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
n . Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite [Weighted] real-weighted nonnegative-weighted () set
the_Edges_of G is finite set
G . EdgeSelector is set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
sink is Element of the_Vertices_of G
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CS is Element of the_Vertices_of G
(G,source,CS) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
{1} \/ (the_Edges_of G) is non empty finite set
(G,source,CS) is Relation-like NAT -defined Function-like total (G,source)
(G,source,CS) .Result() is set
(G,source,CS) .Lifespan() is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,CS) . ((G,source,CS) .Lifespan()) is set
dom (G,source,CS) is finite Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is finite V36() V79() set
(G,source,CS,sink) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
(the_Vertices_of G) \/ (the_Edges_of G) is non empty finite set
(G,source,(G,source,CS,sink)) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] set
the_Edges_of G is set
G . EdgeSelector is set
(the_Edges_of G) --> 0 is Relation-like the_Edges_of G -defined NAT -valued RAT -valued INT -valued Function-like constant total V18( the_Edges_of G, NAT ) complex-valued ext-real-valued real-valued natural-valued Function-yielding V199() Element of K32(K33((the_Edges_of G),NAT))
K33((the_Edges_of G),NAT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K32(K33((the_Edges_of G),NAT)) is set
{0} is non empty trivial functional finite V36() 1 -element V100() V101() V102() V103() V104() V105() set
K33((the_Edges_of G),{0}) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
NAT --> ((the_Edges_of G) --> 0) is non empty Relation-like NAT -defined {((the_Edges_of G) --> 0)} -valued Function-like constant total V18( NAT ,{((the_Edges_of G) --> 0)}) T-Sequence-like Function-yielding V199() Element of K32(K33(NAT,{((the_Edges_of G) --> 0)}))
{((the_Edges_of G) --> 0)} is non empty trivial functional finite 1 -element set
K33(NAT,{((the_Edges_of G) --> 0)}) is non trivial Relation-like non finite set
K32(K33(NAT,{((the_Edges_of G) --> 0)})) is non trivial non finite set
source is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(NAT --> ((the_Edges_of G) --> 0)) . source is Relation-like Function-like set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] set
source is Relation-like NAT -defined Function-like total (G)
sink is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
source . sink is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] set
the_Edges_of G is set
G . EdgeSelector is set
source is Relation-like NAT -defined Function-like total (G)
sink is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
source . sink is Relation-like Function-like set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] set
source is Relation-like NAT -defined Function-like total (G)
sink is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
source . sink is Relation-like the_Edges_of G -defined Function-like set
the_Edges_of G is set
G . EdgeSelector is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite [Weighted] real-weighted nonnegative-weighted () set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
the_Edges_of G is finite set
G . EdgeSelector is set
(the_Edges_of G) --> 0 is Relation-like the_Edges_of G -defined NAT -valued RAT -valued INT -valued Function-like constant total V18( the_Edges_of G, NAT ) finite complex-valued ext-real-valued real-valued natural-valued finite-support Function-yielding V199() Element of K32(K33((the_Edges_of G),NAT))
K33((the_Edges_of G),NAT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K32(K33((the_Edges_of G),NAT)) is set
{0} is non empty trivial functional finite V36() 1 -element V100() V101() V102() V103() V104() V105() set
K33((the_Edges_of G),{0}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
sink is Element of the_Vertices_of G
source is Element of the_Vertices_of G
n is set
Gn is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Gn is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(G,Gn,sink,source) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CS is set
P is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
P is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(G,P,sink,source) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
n is set
CS is set
n is set
Gn is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CS is set
CS is set
n is set
Gn1 is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Gn is set
(G,Gn1,sink,source) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
P is set
n is set
CS is Relation-like Function-like set
dom CS is set
CS . 0 is set
n is Relation-like NAT -defined Function-like total set
Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
n . Gn is set
Gn1 is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Gn1 is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Gn + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
n . (Gn + 1) is set
P is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
P is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(G,P,sink,source) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
n . 0 is set
Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
n . Gn is set
Gn1 is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Gn is Relation-like NAT -defined Function-like total (G)
Gn . 0 is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
Gn1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
Gn . (Gn1 + 1) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Gn . Gn1 is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(G,(Gn . Gn1),sink,source) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
P is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
P + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
Gn . (P + 1) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
P is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(G,P,sink,source) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CS is Relation-like NAT -defined Function-like total (G)
CS . 0 is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
n is Relation-like NAT -defined Function-like total (G)
n . 0 is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
CS . Gn is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
n . Gn is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Gn + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
n . (Gn + 1) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(G,(n . Gn),sink,source) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
CS . (Gn + 1) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Gn is set
CS . Gn is set
n . Gn is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite [Weighted] real-weighted nonnegative-weighted () set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
sink is Element of the_Vertices_of G
source is Element of the_Vertices_of G
(G,sink,source) is Relation-like NAT -defined Function-like total (G)
(G,sink,source) .Result() is set
(G,sink,source) .Lifespan() is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,sink,source) . ((G,sink,source) .Lifespan()) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
the_Edges_of G is finite set
G . EdgeSelector is set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite [Weighted] real-weighted set
the_Edges_of G is finite set
G . EdgeSelector is set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
K32((the_Vertices_of G)) is finite V36() V79() set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
sink is set
CS is set
(G,source,sink,CS) is V28() real ext-real set
{CS} is non empty trivial finite 1 -element set
G .edgesInto {CS} is finite Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is finite V36() set
source | (G .edgesInto {CS}) is Relation-like the_Edges_of G -defined G .edgesInto {CS} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (G .edgesInto {CS})) is V28() real ext-real set
G .edgesOutOf {CS} is finite Element of K32((the_Edges_of G))
source | (G .edgesOutOf {CS}) is Relation-like the_Edges_of G -defined G .edgesOutOf {CS} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (G .edgesOutOf {CS})) is V28() real ext-real set
(Sum (source | (G .edgesInto {CS}))) - (Sum (source | (G .edgesOutOf {CS}))) is V28() real ext-real set
n is finite Element of K32((the_Vertices_of G))
(the_Vertices_of G) \ n is finite Element of K32((the_Vertices_of G))
G .edgesDBetween (n,((the_Vertices_of G) \ n)) is finite Element of K32((the_Edges_of G))
source | (G .edgesDBetween (n,((the_Vertices_of G) \ n))) is Relation-like the_Edges_of G -defined G .edgesDBetween (n,((the_Vertices_of G) \ n)) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (G .edgesDBetween (n,((the_Vertices_of G) \ n)))) is V28() real ext-real set
G .edgesDBetween (((the_Vertices_of G) \ n),n) is finite Element of K32((the_Edges_of G))
source | (G .edgesDBetween (((the_Vertices_of G) \ n),n)) is Relation-like the_Edges_of G -defined G .edgesDBetween (((the_Vertices_of G) \ n),n) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (G .edgesDBetween (((the_Vertices_of G) \ n),n))) is V28() real ext-real set
(Sum (source | (G .edgesDBetween (n,((the_Vertices_of G) \ n))))) - (Sum (source | (G .edgesDBetween (((the_Vertices_of G) \ n),n)))) is V28() real ext-real set
card ((the_Vertices_of G) \ n) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
the_Target_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . TargetSelector is set
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
G . SourceSelector is set
E1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative set
A1 is finite Element of K32((the_Vertices_of G))
(the_Vertices_of G) \ A1 is finite Element of K32((the_Vertices_of G))
card ((the_Vertices_of G) \ A1) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
E1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
((the_Vertices_of G) \ A1) \ {CS} is finite Element of K32((the_Vertices_of G))
choose (((the_Vertices_of G) \ A1) \ {CS}) is Element of ((the_Vertices_of G) \ A1) \ {CS}
{(choose (((the_Vertices_of G) \ A1) \ {CS}))} is non empty trivial finite 1 -element set
A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))} is non empty finite set
(the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}) is finite Element of K32((the_Vertices_of G))
G .edgesDBetween ((A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) is finite Element of K32((the_Edges_of G))
G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),(A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})) is finite Element of K32((the_Edges_of G))
G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) is finite Element of K32((the_Edges_of G))
G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}) is finite Element of K32((the_Edges_of G))
card (((the_Vertices_of G) \ A1) \ {CS}) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
card {CS} is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(E1 + 1) - (card {CS}) is V28() real integer ext-real set
(E1 + 1) - 1 is V28() real integer ext-real set
v1 is finite Element of K32((the_Vertices_of G))
(the_Vertices_of G) \ v1 is finite Element of K32((the_Vertices_of G))
((the_Vertices_of G) \ A1) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))} is finite Element of K32((the_Vertices_of G))
card ((the_Vertices_of G) \ v1) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
card {(choose (((the_Vertices_of G) \ A1) \ {CS}))} is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(card ((the_Vertices_of G) \ A1)) - (card {(choose (((the_Vertices_of G) \ A1) \ {CS}))}) is V28() real integer ext-real set
source | (G .edgesDBetween ((A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) is Relation-like the_Edges_of G -defined G .edgesDBetween ((A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (G .edgesDBetween ((A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))))) is V28() real ext-real set
source | (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),(A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) is Relation-like the_Edges_of G -defined G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),(A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),(A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) is V28() real ext-real set
(Sum (source | (G .edgesDBetween ((A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))))) - (Sum (source | (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),(A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))))) is V28() real ext-real set
(the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))} is finite Element of K32((the_Vertices_of G))
G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})) is finite Element of K32((the_Edges_of G))
G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1) is finite Element of K32((the_Edges_of G))
G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}) is finite Element of K32((the_Edges_of G))
(G .edgesDBetween ((A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) \/ (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) is finite Element of K32((the_Edges_of G))
EA is finite Element of K32((the_Edges_of G))
EA \ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) is finite Element of K32((the_Edges_of G))
EA \ (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) is finite Element of K32((the_Edges_of G))
(G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),(A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) \/ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1)) is finite Element of K32((the_Edges_of G))
EC is finite Element of K32((the_Edges_of G))
EC \ (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) is finite Element of K32((the_Edges_of G))
EC \ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1)) is finite Element of K32((the_Edges_of G))
source | EA is Relation-like the_Edges_of G -defined EA -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom (source | EA) is finite Element of K32(EA)
K32(EA) is finite V36() set
(G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),(A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) /\ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1)) is finite Element of K32((the_Edges_of G))
choose ((G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),(A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) /\ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) is Element of (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),(A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) /\ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))
(the_Source_of G) . (choose ((G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),(A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) /\ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1)))) is set
(G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),(A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) \ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1)) is finite Element of K32((the_Edges_of G))
ED is finite Element of K32((the_Edges_of G))
EXV1cb is set
(the_Source_of G) . EXV1cb is set
(the_Target_of G) . EXV1cb is set
(G .edgesDBetween ((A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) /\ (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) is finite Element of K32((the_Edges_of G))
choose ((G .edgesDBetween ((A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) /\ (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) is Element of (G .edgesDBetween ((A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) /\ (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))
(the_Target_of G) . (choose ((G .edgesDBetween ((A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) /\ (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) is set
(G .edgesDBetween ((A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) \ (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) is finite Element of K32((the_Edges_of G))
EB is finite Element of K32((the_Edges_of G))
source | EB is Relation-like the_Edges_of G -defined EB -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom (source | EB) is finite Element of K32(EB)
K32(EB) is finite V36() set
EXV1cb is set
source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) is Relation-like the_Edges_of G -defined G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | EB) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | EB)) . EXV1cb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | EB) . EXV1cb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . EXV1cb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) is Relation-like the_Edges_of G -defined G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | EB) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | EB)) . EXV1cb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) . EXV1cb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . EXV1cb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) is Relation-like the_Edges_of G -defined G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | EB) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | EB)) . EXV1cb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . EXV1cb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) is Relation-like the_Edges_of G -defined G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | EB) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | EB)) . EXV1cb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . EXV1cb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | EA) . EXV1cb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
EXV1cb is set
(G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) \ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1)) is finite Element of K32((the_Edges_of G))
(the_Source_of G) . EXV1cb is set
(the_Target_of G) . EXV1cb is set
source | ED is Relation-like the_Edges_of G -defined ED -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom (source | ED) is finite Element of K32(ED)
K32(ED) is finite V36() set
EXV1cb is set
source | EC is Relation-like the_Edges_of G -defined EC -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom (source | EC) is finite Element of K32(EC)
K32(EC) is finite V36() set
source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1)) is Relation-like the_Edges_of G -defined G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) +* (source | ED) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) +* (source | ED)) . EXV1cb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | ED) . EXV1cb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . EXV1cb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1)) is Relation-like the_Edges_of G -defined G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) +* (source | ED) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) +* (source | ED)) . EXV1cb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) . EXV1cb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . EXV1cb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1)) is Relation-like the_Edges_of G -defined G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) +* (source | ED) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) +* (source | ED)) . EXV1cb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . EXV1cb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1)) is Relation-like the_Edges_of G -defined G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) +* (source | ED) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) +* (source | ED)) . EXV1cb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . EXV1cb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | EC) . EXV1cb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
G .edgesDBetween (((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}) is finite Element of K32((the_Edges_of G))
EV1Xdb is set
(G .edgesDBetween (((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) \ (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) is finite Element of K32((the_Edges_of G))
(the_Target_of G) . EV1Xdb is set
(the_Source_of G) . EV1Xdb is set
EV1Xdb is set
(the_Target_of G) . EV1Xdb is set
(the_Source_of G) . EV1Xdb is set
EV1Xdb is set
(the_Source_of G) . EV1Xdb is set
(the_Target_of G) . EV1Xdb is set
A1 \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))} is finite Element of K32(A1)
K32(A1) is finite V36() set
((G .edgesDBetween ((A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) \/ (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) \ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) is finite Element of K32(((G .edgesDBetween ((A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) \/ (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))))
K32(((G .edgesDBetween ((A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) \/ (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) is finite V36() set
EV1Xdb is set
G .edgesDBetween (A1,((the_Vertices_of G) \ A1)) is finite Element of K32((the_Edges_of G))
(the_Source_of G) . EV1Xdb is set
(the_Target_of G) . EV1Xdb is set
((G .edgesDBetween ((A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) \/ (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) \ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) is finite Element of K32((the_Edges_of G))
((G .edgesDBetween ((A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) \/ (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) \ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) is finite Element of K32((the_Edges_of G))
((G .edgesDBetween ((A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) \/ (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) \ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) is finite Element of K32((the_Edges_of G))
((G .edgesDBetween ((A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) \/ (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) \ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) is finite Element of K32((the_Edges_of G))
v1 \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))} is finite Element of K32((the_Vertices_of G))
A1 \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))} is finite Element of K32((the_Vertices_of G))
((G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),(A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) \/ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) \ (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) is finite Element of K32(((G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),(A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) \/ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))))
K32(((G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),(A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) \/ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1)))) is finite V36() set
EV1Xdb is set
G .edgesDBetween (((the_Vertices_of G) \ A1),A1) is finite Element of K32((the_Edges_of G))
(the_Target_of G) . EV1Xdb is set
(the_Source_of G) . EV1Xdb is set
((G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),(A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) \/ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) \ (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) is finite Element of K32((the_Edges_of G))
((G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),(A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) \/ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) \ (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) is finite Element of K32((the_Edges_of G))
((G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),(A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) \/ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) \ (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) is finite Element of K32((the_Edges_of G))
((G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),(A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) \/ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) \ (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) is finite Element of K32((the_Edges_of G))
v1 \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))} is finite Element of K32((the_Vertices_of G))
A1 \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))} is finite Element of K32((the_Vertices_of G))
E2 is finite Element of K32((the_Edges_of G))
source | E2 is Relation-like the_Edges_of G -defined E2 -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom (source | E2) is finite Element of K32(E2)
K32(E2) is finite V36() set
EV1Xdb is set
source | (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) is Relation-like the_Edges_of G -defined G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(source | (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | E2) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | E2)) . EV1Xdb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | E2) . EV1Xdb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . EV1Xdb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source | (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) is Relation-like the_Edges_of G -defined G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(source | (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | E2) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | E2)) . EV1Xdb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) . EV1Xdb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . EV1Xdb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source | (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) is Relation-like the_Edges_of G -defined G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(source | (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | E2) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | E2)) . EV1Xdb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . EV1Xdb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source | (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) is Relation-like the_Edges_of G -defined G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(source | (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | E2) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | E2)) . EV1Xdb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . EV1Xdb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | EC) . EV1Xdb is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
dom (source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) is finite Element of K32((G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1)))
K32((G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) is finite V36() set
dom ((source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) +* (source | ED)) is finite set
(G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1)) \/ ED is finite Element of K32((the_Edges_of G))
(G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1)) \/ ((G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),(A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) \/ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) is finite Element of K32((the_Edges_of G))
Sum (source | EC) is V28() real ext-real set
Sum (source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) is V28() real ext-real set
(Sum (source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1)))) + (Sum (source | (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),(A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))))) is V28() real ext-real set
dom (source | (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) is finite Element of K32((G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})))
K32((G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) is finite V36() set
dom ((source | (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | E2)) is finite set
(G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) \/ (EC \ (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) is finite Element of K32((the_Edges_of G))
(G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) \/ ((G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),(A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) \/ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) is finite Element of K32((the_Edges_of G))
Sum (source | E2) is V28() real ext-real set
Sum (source | (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) is V28() real ext-real set
(Sum (source | E2)) + (Sum (source | (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) is V28() real ext-real set
dom (source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) is finite Element of K32((G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))})))
K32((G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) is finite V36() set
dom ((source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | EB)) is finite set
(G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) \/ EB is finite Element of K32((the_Edges_of G))
(G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) \/ ((G .edgesDBetween ((A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) \/ (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) is finite Element of K32((the_Edges_of G))
Sum (source | EA) is V28() real ext-real set
Sum (source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) is V28() real ext-real set
(Sum (source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) + (Sum (source | (G .edgesDBetween ((A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))))) is V28() real ext-real set
EV1Xdb is finite Element of K32((the_Edges_of G))
source | EV1Xdb is Relation-like the_Edges_of G -defined EV1Xdb -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom (source | EV1Xdb) is finite Element of K32(EV1Xdb)
K32(EV1Xdb) is finite V36() set
x is set
(the_Target_of G) . x is set
(the_Source_of G) . x is set
E1 is finite Element of K32((the_Edges_of G))
source | E1 is Relation-like the_Edges_of G -defined E1 -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom (source | E1) is finite Element of K32(E1)
K32(E1) is finite V36() set
x is set
source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) is Relation-like the_Edges_of G -defined G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))))) +* (source | E1) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))))) +* (source | E1)) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | E1) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) is Relation-like the_Edges_of G -defined G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))))) +* (source | E1) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))))) +* (source | E1)) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))))) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) is Relation-like the_Edges_of G -defined G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))))) +* (source | E1) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))))) +* (source | E1)) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) is Relation-like the_Edges_of G -defined G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))))) +* (source | E1) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))))) +* (source | E1)) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | EA) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source | (G .edgesDBetween (((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) is Relation-like the_Edges_of G -defined G .edgesDBetween (((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom (source | (G .edgesDBetween (((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) is finite Element of K32((G .edgesDBetween (((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})))
K32((G .edgesDBetween (((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) is finite V36() set
x is set
(source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | EV1Xdb) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | EV1Xdb)) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | EV1Xdb) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | EV1Xdb)) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | EV1Xdb) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | EV1Xdb) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | EV1Xdb)) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | EV1Xdb) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | EV1Xdb)) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween (((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source | ((G .edgesDBetween (((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) \ (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) is Relation-like the_Edges_of G -defined (G .edgesDBetween (((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) \ (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | ((G .edgesDBetween (((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) \ (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom ((source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) +* (source | ((G .edgesDBetween (((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) \ (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))))) is finite set
(G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) \/ ((G .edgesDBetween (((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) \ (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) is finite Element of K32((the_Edges_of G))
(G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) \/ (G .edgesDBetween (((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})) is finite Element of K32((the_Edges_of G))
(Sum (source | (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) + (Sum (source | (G .edgesDBetween (((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) is V28() real ext-real set
Sum (source | (G .edgesDBetween (((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) is V28() real ext-real set
dom (source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))))) is finite Element of K32((G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))))
K32((G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))))) is finite V36() set
dom ((source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))))) +* (source | E1)) is finite set
(G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) \/ (EA \ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))))) is finite Element of K32((the_Edges_of G))
(G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) \/ ((G .edgesDBetween ((A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) \/ (G .edgesDBetween (A1,{(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) is finite Element of K32((the_Edges_of G))
Sum (source | E1) is V28() real ext-real set
Sum (source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))))) is V28() real ext-real set
(Sum (source | E1)) + (Sum (source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))))) is V28() real ext-real set
EXV1cb is finite Element of K32((the_Edges_of G))
source | EXV1cb is Relation-like the_Edges_of G -defined EXV1cb -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom (source | EXV1cb) is finite Element of K32(EXV1cb)
K32(EXV1cb) is finite V36() set
source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) is Relation-like the_Edges_of G -defined G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom (source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) is finite Element of K32((G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))))
K32((G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) is finite V36() set
x is set
(source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) +* (source | EXV1cb) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) +* (source | EXV1cb)) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) +* (source | EXV1cb) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) +* (source | EXV1cb)) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | EXV1cb) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) +* (source | EXV1cb) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) +* (source | EXV1cb)) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) +* (source | EXV1cb) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) +* (source | EXV1cb)) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source | ((G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) \ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) is Relation-like the_Edges_of G -defined (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) \ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1)) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) +* (source | ((G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) \ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1)))) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom ((source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) +* (source | ((G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) \ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))))) is finite set
(G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1)) \/ ((G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) \ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1))) is finite Element of K32((the_Edges_of G))
(G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1)) \/ (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))) is finite Element of K32((the_Edges_of G))
(Sum (source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},A1)))) + (Sum (source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ (A1 \/ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))))) is V28() real ext-real set
Sum (source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) is V28() real ext-real set
x is Element of the_Vertices_of G
x .edgesOut() is finite Element of K32((the_Edges_of G))
{x} is non empty trivial finite 1 -element Element of K32((the_Vertices_of G))
G .edgesOutOf {x} is finite Element of K32((the_Edges_of G))
G .edgesDBetween ({x},(the_Vertices_of G)) is finite Element of K32((the_Edges_of G))
G .edgesDBetween ({x},{x}) is finite Element of K32((the_Edges_of G))
(G .edgesDBetween ({x},(the_Vertices_of G))) \ (G .edgesDBetween ({x},{x})) is finite Element of K32((the_Edges_of G))
G .edgesDBetween ((the_Vertices_of G),{x}) is finite Element of K32((the_Edges_of G))
(G .edgesDBetween ((the_Vertices_of G),{x})) \ (G .edgesDBetween ({x},{x})) is finite Element of K32((the_Edges_of G))
source | (G .edgesDBetween ((the_Vertices_of G),{x})) is Relation-like the_Edges_of G -defined G .edgesDBetween ((the_Vertices_of G),{x}) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom (source | (G .edgesDBetween ((the_Vertices_of G),{x}))) is finite Element of K32((G .edgesDBetween ((the_Vertices_of G),{x})))
K32((G .edgesDBetween ((the_Vertices_of G),{x}))) is finite V36() set
e is set
(the_Source_of G) . e is set
(the_Target_of G) . e is set
(the_Vertices_of G) \ {x} is finite Element of K32((the_Vertices_of G))
EXXfb is finite Element of K32((the_Edges_of G))
source | EXXfb is Relation-like the_Edges_of G -defined EXXfb -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom (source | EXXfb) is finite Element of K32(EXXfb)
K32(EXXfb) is finite V36() set
e is set
source | (G .edgesDBetween ({x},{x})) is Relation-like the_Edges_of G -defined G .edgesDBetween ({x},{x}) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(source | (G .edgesDBetween ({x},{x}))) +* (source | EXXfb) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({x},{x}))) +* (source | EXXfb)) . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween ({x},{x}))) . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source | (G .edgesDBetween ({x},{x})) is Relation-like the_Edges_of G -defined G .edgesDBetween ({x},{x}) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(source | (G .edgesDBetween ({x},{x}))) +* (source | EXXfb) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({x},{x}))) +* (source | EXXfb)) . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | EXXfb) . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source | (G .edgesDBetween ({x},{x})) is Relation-like the_Edges_of G -defined G .edgesDBetween ({x},{x}) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(source | (G .edgesDBetween ({x},{x}))) +* (source | EXXfb) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({x},{x}))) +* (source | EXXfb)) . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source | (G .edgesDBetween ({x},{x})) is Relation-like the_Edges_of G -defined G .edgesDBetween ({x},{x}) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(source | (G .edgesDBetween ({x},{x}))) +* (source | EXXfb) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({x},{x}))) +* (source | EXXfb)) . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween ((the_Vertices_of G),{x}))) . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
e is set
(the_Target_of G) . e is set
(the_Source_of G) . e is set
source | (G .edgesDBetween ({x},(the_Vertices_of G))) is Relation-like the_Edges_of G -defined G .edgesDBetween ({x},(the_Vertices_of G)) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom (source | (G .edgesDBetween ({x},(the_Vertices_of G)))) is finite Element of K32((G .edgesDBetween ({x},(the_Vertices_of G))))
K32((G .edgesDBetween ({x},(the_Vertices_of G)))) is finite V36() set
EXXeb is finite Element of K32((the_Edges_of G))
source | EXXeb is Relation-like the_Edges_of G -defined EXXeb -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom (source | EXXeb) is finite Element of K32(EXXeb)
K32(EXXeb) is finite V36() set
e is set
(source | (G .edgesDBetween ({x},{x}))) +* (source | EXXeb) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({x},{x}))) +* (source | EXXeb)) . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween ({x},{x}))) . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween ({x},{x}))) +* (source | EXXeb) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({x},{x}))) +* (source | EXXeb)) . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | EXXeb) . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween ({x},{x}))) +* (source | EXXeb) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({x},{x}))) +* (source | EXXeb)) . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween ({x},{x}))) +* (source | EXXeb) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({x},{x}))) +* (source | EXXeb)) . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween ({x},(the_Vertices_of G)))) . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
dom (source | (G .edgesDBetween ({x},{x}))) is finite Element of K32((G .edgesDBetween ({x},{x})))
K32((G .edgesDBetween ({x},{x}))) is finite V36() set
dom ((source | (G .edgesDBetween ({x},{x}))) +* (source | EXXfb)) is finite set
(G .edgesDBetween ({x},{x})) \/ EXXfb is finite Element of K32((the_Edges_of G))
(G .edgesDBetween ({x},{x})) \/ (G .edgesDBetween ((the_Vertices_of G),{x})) is finite Element of K32((the_Edges_of G))
Sum (source | (G .edgesDBetween ((the_Vertices_of G),{x}))) is V28() real ext-real set
Sum (source | (G .edgesDBetween ({x},{x}))) is V28() real ext-real set
(Sum (source | (G .edgesDBetween (((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}),{(choose (((the_Vertices_of G) \ A1) \ {CS}))})))) + (Sum (source | (G .edgesDBetween ({x},{x})))) is V28() real ext-real set
dom ((source | (G .edgesDBetween ({x},{x}))) +* (source | EXXeb)) is finite set
(G .edgesDBetween ({x},{x})) \/ EXXeb is finite Element of K32((the_Edges_of G))
(G .edgesDBetween ({x},{x})) \/ (G .edgesDBetween ({x},(the_Vertices_of G))) is finite Element of K32((the_Edges_of G))
Sum (source | (G .edgesDBetween ({x},(the_Vertices_of G)))) is V28() real ext-real set
(Sum (source | (G .edgesDBetween ({(choose (((the_Vertices_of G) \ A1) \ {CS}))},((the_Vertices_of G) \ {(choose (((the_Vertices_of G) \ A1) \ {CS}))}))))) + (Sum (source | (G .edgesDBetween ({x},{x})))) is V28() real ext-real set
x .edgesIn() is finite Element of K32((the_Edges_of G))
G .edgesInto {x} is finite Element of K32((the_Edges_of G))
source | (G .edgesDBetween (A1,((the_Vertices_of G) \ A1))) is Relation-like the_Edges_of G -defined G .edgesDBetween (A1,((the_Vertices_of G) \ A1)) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (G .edgesDBetween (A1,((the_Vertices_of G) \ A1)))) is V28() real ext-real set
source | (G .edgesDBetween (((the_Vertices_of G) \ A1),A1)) is Relation-like the_Edges_of G -defined G .edgesDBetween (((the_Vertices_of G) \ A1),A1) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (G .edgesDBetween (((the_Vertices_of G) \ A1),A1))) is V28() real ext-real set
(Sum (source | (G .edgesDBetween (A1,((the_Vertices_of G) \ A1))))) - (Sum (source | (G .edgesDBetween (((the_Vertices_of G) \ A1),A1)))) is V28() real ext-real set
A1 is finite Element of K32((the_Vertices_of G))
(the_Vertices_of G) \ A1 is finite Element of K32((the_Vertices_of G))
card ((the_Vertices_of G) \ A1) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
G .edgesDBetween (A1,((the_Vertices_of G) \ A1)) is finite Element of K32((the_Edges_of G))
source | (G .edgesDBetween (A1,((the_Vertices_of G) \ A1))) is Relation-like the_Edges_of G -defined G .edgesDBetween (A1,((the_Vertices_of G) \ A1)) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (G .edgesDBetween (A1,((the_Vertices_of G) \ A1)))) is V28() real ext-real set
G .edgesDBetween (((the_Vertices_of G) \ A1),A1) is finite Element of K32((the_Edges_of G))
source | (G .edgesDBetween (((the_Vertices_of G) \ A1),A1)) is Relation-like the_Edges_of G -defined G .edgesDBetween (((the_Vertices_of G) \ A1),A1) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (G .edgesDBetween (((the_Vertices_of G) \ A1),A1))) is V28() real ext-real set
(Sum (source | (G .edgesDBetween (A1,((the_Vertices_of G) \ A1))))) - (Sum (source | (G .edgesDBetween (((the_Vertices_of G) \ A1),A1)))) is V28() real ext-real set
G .edgesDBetween ({CS},{CS}) is finite Element of K32((the_Edges_of G))
A1 is finite Element of K32((the_Vertices_of G))
(the_Vertices_of G) \ A1 is finite Element of K32((the_Vertices_of G))
card ((the_Vertices_of G) \ A1) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G .edgesOutOf {CS}) \ (G .edgesDBetween ({CS},{CS})) is finite Element of K32((the_Edges_of G))
e is set
{e} is non empty trivial finite 1 -element set
E2 is set
(the_Vertices_of G) \ {CS} is finite Element of K32((the_Vertices_of G))
E2 is set
G .edgesDBetween (((the_Vertices_of G) \ A1),A1) is finite Element of K32((the_Edges_of G))
(the_Target_of G) . E2 is set
(the_Source_of G) . E2 is set
B1 is finite Element of K32((the_Edges_of G))
(G .edgesOutOf {CS}) \ (G .edgesDBetween ({CS},{CS})) is finite Element of K32((G .edgesOutOf {CS}))
K32((G .edgesOutOf {CS})) is finite V36() set
source | (G .edgesDBetween ({CS},{CS})) is Relation-like the_Edges_of G -defined G .edgesDBetween ({CS},{CS}) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(G .edgesInto {CS}) \ (G .edgesDBetween ({CS},{CS})) is finite Element of K32((the_Edges_of G))
dom (source | (G .edgesInto {CS})) is finite Element of K32((G .edgesInto {CS}))
K32((G .edgesInto {CS})) is finite V36() set
B2 is set
G .edgesDBetween (A1,((the_Vertices_of G) \ A1)) is finite Element of K32((the_Edges_of G))
(the_Source_of G) . B2 is set
(the_Target_of G) . B2 is set
A2 is finite Element of K32((the_Edges_of G))
(G .edgesInto {CS}) \ (G .edgesDBetween ({CS},{CS})) is finite Element of K32((G .edgesInto {CS}))
B2 is set
(the_Source_of G) . B2 is set
B2 is set
(the_Target_of G) . B2 is set
dom (source | (G .edgesDBetween ({CS},{CS}))) is finite Element of K32((G .edgesDBetween ({CS},{CS})))
K32((G .edgesDBetween ({CS},{CS}))) is finite V36() set
source | B1 is Relation-like the_Edges_of G -defined B1 -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom (source | B1) is finite Element of K32(B1)
K32(B1) is finite V36() set
B2 is set
dom (source | (G .edgesOutOf {CS})) is finite Element of K32((G .edgesOutOf {CS}))
(source | (G .edgesDBetween ({CS},{CS}))) +* (source | B1) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({CS},{CS}))) +* (source | B1)) . B2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween ({CS},{CS}))) . B2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . B2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween ({CS},{CS}))) +* (source | B1) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({CS},{CS}))) +* (source | B1)) . B2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | B1) . B2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . B2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween ({CS},{CS}))) +* (source | B1) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({CS},{CS}))) +* (source | B1)) . B2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . B2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween ({CS},{CS}))) +* (source | B1) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({CS},{CS}))) +* (source | B1)) . B2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . B2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesOutOf {CS})) . B2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source | A2 is Relation-like the_Edges_of G -defined A2 -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom (source | A2) is finite Element of K32(A2)
K32(A2) is finite V36() set
B2 is set
(source | (G .edgesDBetween ({CS},{CS}))) +* (source | A2) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({CS},{CS}))) +* (source | A2)) . B2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween ({CS},{CS}))) . B2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . B2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween ({CS},{CS}))) +* (source | A2) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({CS},{CS}))) +* (source | A2)) . B2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | A2) . B2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . B2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween ({CS},{CS}))) +* (source | A2) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({CS},{CS}))) +* (source | A2)) . B2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . B2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween ({CS},{CS}))) +* (source | A2) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((source | (G .edgesDBetween ({CS},{CS}))) +* (source | A2)) . B2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . B2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesInto {CS})) . B2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(G .edgesDBetween ({CS},{CS})) \/ A2 is finite Element of K32((the_Edges_of G))
(G .edgesInto {CS}) \/ (G .edgesDBetween ({CS},{CS})) is finite Element of K32((the_Edges_of G))
dom ((source | (G .edgesDBetween ({CS},{CS}))) +* (source | A2)) is finite set
Sum (source | A2) is V28() real ext-real set
Sum (source | (G .edgesDBetween ({CS},{CS}))) is V28() real ext-real set
(Sum (source | A2)) + (Sum (source | (G .edgesDBetween ({CS},{CS})))) is V28() real ext-real set
(G .edgesDBetween ({CS},{CS})) \/ B1 is finite Element of K32((the_Edges_of G))
(G .edgesOutOf {CS}) \/ (G .edgesDBetween ({CS},{CS})) is finite Element of K32((the_Edges_of G))
dom ((source | (G .edgesDBetween ({CS},{CS}))) +* (source | B1)) is finite set
Sum (source | B1) is V28() real ext-real set
(Sum (source | (G .edgesDBetween ({CS},{CS})))) + (Sum (source | B1)) is V28() real ext-real set
((Sum (source | A2)) + (Sum (source | (G .edgesDBetween ({CS},{CS}))))) - ((Sum (source | (G .edgesDBetween ({CS},{CS})))) + (Sum (source | B1))) is V28() real ext-real set
(Sum (source | A2)) - (Sum (source | B1)) is V28() real ext-real set
source | (G .edgesDBetween (A1,((the_Vertices_of G) \ A1))) is Relation-like the_Edges_of G -defined G .edgesDBetween (A1,((the_Vertices_of G) \ A1)) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (G .edgesDBetween (A1,((the_Vertices_of G) \ A1)))) is V28() real ext-real set
source | (G .edgesDBetween (((the_Vertices_of G) \ A1),A1)) is Relation-like the_Edges_of G -defined G .edgesDBetween (((the_Vertices_of G) \ A1),A1) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (G .edgesDBetween (((the_Vertices_of G) \ A1),A1))) is V28() real ext-real set
(Sum (source | (G .edgesDBetween (A1,((the_Vertices_of G) \ A1))))) - (Sum (source | (G .edgesDBetween (((the_Vertices_of G) \ A1),A1)))) is V28() real ext-real set
E1 is finite Element of K32((the_Vertices_of G))
(the_Vertices_of G) \ E1 is finite Element of K32((the_Vertices_of G))
card ((the_Vertices_of G) \ E1) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
G .edgesDBetween (E1,((the_Vertices_of G) \ E1)) is finite Element of K32((the_Edges_of G))
source | (G .edgesDBetween (E1,((the_Vertices_of G) \ E1))) is Relation-like the_Edges_of G -defined G .edgesDBetween (E1,((the_Vertices_of G) \ E1)) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (G .edgesDBetween (E1,((the_Vertices_of G) \ E1)))) is V28() real ext-real set
G .edgesDBetween (((the_Vertices_of G) \ E1),E1) is finite Element of K32((the_Edges_of G))
source | (G .edgesDBetween (((the_Vertices_of G) \ E1),E1)) is Relation-like the_Edges_of G -defined G .edgesDBetween (((the_Vertices_of G) \ E1),E1) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (G .edgesDBetween (((the_Vertices_of G) \ E1),E1))) is V28() real ext-real set
(Sum (source | (G .edgesDBetween (E1,((the_Vertices_of G) \ E1))))) - (Sum (source | (G .edgesDBetween (((the_Vertices_of G) \ E1),E1)))) is V28() real ext-real set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite [Weighted] real-weighted set
the_Edges_of G is finite set
G . EdgeSelector is set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
K32((the_Vertices_of G)) is finite V36() V79() set
the_Weight_of G is Relation-like the_Edges_of G -defined Function-like total finite complex-valued ext-real-valued real-valued finite-support set
G . WeightSelector is set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
sink is set
CS is set
(G,source,sink,CS) is V28() real ext-real set
{CS} is non empty trivial finite 1 -element set
G .edgesInto {CS} is finite Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is finite V36() set
source | (G .edgesInto {CS}) is Relation-like the_Edges_of G -defined G .edgesInto {CS} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (G .edgesInto {CS})) is V28() real ext-real set
G .edgesOutOf {CS} is finite Element of K32((the_Edges_of G))
source | (G .edgesOutOf {CS}) is Relation-like the_Edges_of G -defined G .edgesOutOf {CS} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (G .edgesOutOf {CS})) is V28() real ext-real set
(Sum (source | (G .edgesInto {CS}))) - (Sum (source | (G .edgesOutOf {CS}))) is V28() real ext-real set
n is finite Element of K32((the_Vertices_of G))
(the_Vertices_of G) \ n is finite Element of K32((the_Vertices_of G))
G .edgesDBetween (n,((the_Vertices_of G) \ n)) is finite Element of K32((the_Edges_of G))
(the_Weight_of G) | (G .edgesDBetween (n,((the_Vertices_of G) \ n))) is Relation-like the_Edges_of G -defined G .edgesDBetween (n,((the_Vertices_of G) \ n)) -defined the_Edges_of G -defined Function-like total finite complex-valued ext-real-valued real-valued finite-support set
Sum ((the_Weight_of G) | (G .edgesDBetween (n,((the_Vertices_of G) \ n)))) is V28() real ext-real set
G .edgesDBetween (((the_Vertices_of G) \ n),n) is finite Element of K32((the_Edges_of G))
source | (G .edgesDBetween (((the_Vertices_of G) \ n),n)) is Relation-like the_Edges_of G -defined G .edgesDBetween (((the_Vertices_of G) \ n),n) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
source | (G .edgesDBetween (n,((the_Vertices_of G) \ n))) is Relation-like the_Edges_of G -defined G .edgesDBetween (n,((the_Vertices_of G) \ n)) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
P is set
((the_Weight_of G) | (G .edgesDBetween (n,((the_Vertices_of G) \ n)))) . P is V28() real ext-real set
(the_Weight_of G) . P is V28() real ext-real set
(source | (G .edgesDBetween (n,((the_Vertices_of G) \ n)))) . P is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . P is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
Sum (source | (G .edgesDBetween (n,((the_Vertices_of G) \ n)))) is V28() real ext-real set
Sum (source | (G .edgesDBetween (((the_Vertices_of G) \ n),n))) is V28() real ext-real set
(Sum (source | (G .edgesDBetween (n,((the_Vertices_of G) \ n))))) - (Sum (source | (G .edgesDBetween (((the_Vertices_of G) \ n),n)))) is V28() real ext-real set
(Sum ((the_Weight_of G) | (G .edgesDBetween (n,((the_Vertices_of G) \ n))))) - (Sum (source | (G .edgesDBetween (((the_Vertices_of G) \ n),n)))) is V28() real ext-real set
EmptyBag (G .edgesDBetween (((the_Vertices_of G) \ n),n)) is Relation-like G .edgesDBetween (((the_Vertices_of G) \ n),n) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags (G .edgesDBetween (((the_Vertices_of G) \ n),n))
Bags (G .edgesDBetween (((the_Vertices_of G) \ n),n)) is non empty set
Bags (G .edgesDBetween (((the_Vertices_of G) \ n),n)) is non empty functional Element of K32((Bags (G .edgesDBetween (((the_Vertices_of G) \ n),n))))
K32((Bags (G .edgesDBetween (((the_Vertices_of G) \ n),n)))) is V79() set
(G .edgesDBetween (((the_Vertices_of G) \ n),n)) --> 0 is Relation-like G .edgesDBetween (((the_Vertices_of G) \ n),n) -defined NAT -valued RAT -valued INT -valued Function-like constant total V18(G .edgesDBetween (((the_Vertices_of G) \ n),n), NAT ) finite complex-valued ext-real-valued real-valued natural-valued finite-support Function-yielding V199() Element of K32(K33((G .edgesDBetween (((the_Vertices_of G) \ n),n)),NAT))
K33((G .edgesDBetween (((the_Vertices_of G) \ n),n)),NAT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K32(K33((G .edgesDBetween (((the_Vertices_of G) \ n),n)),NAT)) is set
K33((G .edgesDBetween (((the_Vertices_of G) \ n),n)),{0}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
E1 is set
(EmptyBag (G .edgesDBetween (((the_Vertices_of G) \ n),n))) . E1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesDBetween (((the_Vertices_of G) \ n),n))) . E1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
Sum (EmptyBag (G .edgesDBetween (((the_Vertices_of G) \ n),n))) is V28() real ext-real set
(Sum ((the_Weight_of G) | (G .edgesDBetween (n,((the_Vertices_of G) \ n))))) - 0 is V28() real ext-real set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite [Weighted] real-weighted nonnegative-weighted () set
the_Edges_of G is finite set
G . EdgeSelector is set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty finite set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
sink is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Walk of G
(G,source,sink) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(G,source,sink) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued V180() finite-support FinSequence of NAT
rng (G,source,sink) is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
dom (G,source,sink) is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
n is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(G,source,sink) . n is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
sink .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support EdgeSeq of G
dom (sink .edgeSeq()) is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
2 * Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
dom sink is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
(2 * Gn) - 1 is non empty V28() real integer ext-real non even set
len sink is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
(len sink) - 0 is non empty V28() real integer ext-real positive non negative set
Gn1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . Gn1 is set
sink . (2 * Gn) is set
(2 * Gn) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
sink . ((2 * Gn) + 1) is set
((2 * Gn) - 1) + 2 is non empty V28() real integer ext-real non even set
((2 * Gn) - 1) + 1 is V28() real integer ext-real even set
the_Weight_of G is Relation-like the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
G . WeightSelector is set
(the_Weight_of G) . (sink . (2 * Gn)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . (sink . (2 * Gn)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((the_Weight_of G) . (sink . (2 * Gn))) - (source . (sink . (2 * Gn))) is V28() real integer ext-real set
(source . (sink . (2 * Gn))) - (source . (sink . (2 * Gn))) is V28() real integer ext-real set
source . (sink . (2 * Gn)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite [Weighted] real-weighted nonnegative-weighted () set
the_Edges_of G is finite set
G . EdgeSelector is set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty finite set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
sink is set
CS is set
n is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
(G,source,n) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Gn1 is set
source . Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
the_Weight_of G is Relation-like the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
G . WeightSelector is set
(the_Weight_of G) . Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
n .edges() is finite Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is finite V36() set
(G,source,n) . Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
n .edges() is finite Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is finite V36() set
len n is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
P is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
P + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
n . (P + 1) is set
(G,source,n) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued V180() finite-support FinSequence of NAT
(P + 1) div 2 is V28() real integer ext-real set
n .edgeSeq() is Relation-like NAT -defined the_Edges_of G -valued Function-like finite FinSequence-like FinSubsequence-like finite-support EdgeSeq of G
dom (n .edgeSeq()) is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
dom (G,source,n) is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
P + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
P + 0 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
n . P is set
n . (P + 2) is set
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . SourceSelector is set
(the_Source_of G) . Gn1 is set
n .last() is Element of the_Vertices_of G
n .first() is Element of the_Vertices_of G
2 * ((P + 1) div 2) is V28() real integer ext-real even set
(2 * ((P + 1) div 2)) - 1 is non empty V28() real integer ext-real non even set
(2 * ((P + 1) div 2)) + 1 is non empty V28() real integer ext-real non even set
(G,source,n) . ((P + 1) div 2) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
((the_Weight_of G) . Gn1) - (source . Gn1) is V28() real integer ext-real set
rng (G,source,n) is finite V100() V101() V102() V103() V104() V105() Element of K32(NAT)
(G,source,n) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(G,source,n) . Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source . Gn1) + (G,source,n) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(((the_Weight_of G) . Gn1) - (source . Gn1)) + (source . Gn1) is V28() real integer ext-real set
(G,source,n) . Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(G,source,n) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(source . Gn1) - (G,source,n) is V28() real integer ext-real set
(source . Gn1) - 0 is V28() real integer ext-real non negative set
(G,source,n) . Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(G,source,n) . Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
n .edges() is finite Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is finite V36() set
(G,source,n) . Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(G,source,n) . Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
Gn1 is set
(G,source,n) . Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(the_Weight_of G) . Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
Gn1 is Element of the_Vertices_of G
Gn1 .edgesIn() is finite Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is finite V36() set
{Gn1} is non empty trivial finite 1 -element Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is finite V36() V79() set
G .edgesInto {Gn1} is finite Element of K32((the_Edges_of G))
source | (Gn1 .edgesIn()) is Relation-like the_Edges_of G -defined Gn1 .edgesIn() -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (Gn1 .edgesIn())) is V28() real ext-real set
Gn1 .edgesOut() is finite Element of K32((the_Edges_of G))
G .edgesOutOf {Gn1} is finite Element of K32((the_Edges_of G))
source | (Gn1 .edgesOut()) is Relation-like the_Edges_of G -defined Gn1 .edgesOut() -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (Gn1 .edgesOut())) is V28() real ext-real set
n .vertices() is finite Element of K32((the_Vertices_of G))
len n is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
P is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
n . P is set
n .last() is Element of the_Vertices_of G
n .first() is Element of the_Vertices_of G
P + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
P + 0 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
n . (P + 2) is set
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
2 * 1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
P - (2 * 1) is non empty V28() real integer ext-real non even set
P is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
P + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
n . (P + 1) is set
P + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
n . (P + 1) is set
(G,source,n) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
P + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
n . (P + 2) is set
e is set
n .edges() is finite Element of K32((the_Edges_of G))
B2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
B2 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
E2 is Element of the_Vertices_of G
n . B2 is set
B2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
n . (B2 + 1) is set
A2 is Element of the_Vertices_of G
n . (B2 + 2) is set
the_Target_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . TargetSelector is set
(the_Target_of G) . e is set
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . SourceSelector is set
(the_Source_of G) . e is set
(len n) - 0 is non empty V28() real integer ext-real positive non negative set
(B2 + 2) - 2 is V28() real integer ext-real set
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . SourceSelector is set
(the_Source_of G) . (n . (P + 1)) is set
P - 0 is non empty V28() real integer ext-real positive non negative set
n . P is set
(the_Source_of G) . (n . (P + 1)) is set
source . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source . (n . (P + 1))) + (G,source,n) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n)) is Relation-like {(n . (P + 1))} -defined RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(n . (P + 1))} is non empty trivial finite 1 -element set
{(n . (P + 1))} --> ((source . (n . (P + 1))) + (G,source,n)) is non empty Relation-like {(n . (P + 1))} -defined RAT -valued INT -valued {((source . (n . (P + 1))) + (G,source,n))} -valued Function-like constant total V18({(n . (P + 1))},{((source . (n . (P + 1))) + (G,source,n))}) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33({(n . (P + 1))},{((source . (n . (P + 1))) + (G,source,n))}))
{((source . (n . (P + 1))) + (G,source,n))} is non empty trivial finite V36() 1 -element V100() V101() V102() V103() V104() V105() set
K33({(n . (P + 1))},{((source . (n . (P + 1))) + (G,source,n))}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
K32(K33({(n . (P + 1))},{((source . (n . (P + 1))) + (G,source,n))})) is finite V36() set
(source | (Gn1 .edgesIn())) +* ((n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n))) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom ((n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n))) is finite Element of K32({(n . (P + 1))})
K32({(n . (P + 1))}) is finite V36() V79() set
dom ((source | (Gn1 .edgesIn())) +* ((n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n)))) is finite set
dom (source | (Gn1 .edgesIn())) is finite Element of K32((Gn1 .edgesIn()))
K32((Gn1 .edgesIn())) is finite V36() set
(dom (source | (Gn1 .edgesIn()))) \/ {(n . (P + 1))} is non empty finite set
(Gn1 .edgesIn()) \/ {(n . (P + 1))} is non empty finite set
A2 is set
(G,source,n) | (Gn1 .edgesIn()) is Relation-like the_Edges_of G -defined Gn1 .edgesIn() -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom ((G,source,n) | (Gn1 .edgesIn())) is finite Element of K32((Gn1 .edgesIn()))
the_Target_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
G . TargetSelector is set
(the_Target_of G) . A2 is set
E2 is Relation-like Gn1 .edgesIn() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
E2 . A2 is V28() real ext-real set
((n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n))) . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(G,source,n) . A2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
v1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
v1 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
B2 is Element of the_Vertices_of G
n . v1 is set
v1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
n . (v1 + 1) is set
x is Element of the_Vertices_of G
n . (v1 + 2) is set
(v1 + 2) - 2 is V28() real integer ext-real set
(P + 2) - 0 is non empty V28() real integer ext-real positive non negative set
(P + 2) - 2 is V28() real integer ext-real set
E2 is Relation-like Gn1 .edgesIn() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
E2 . A2 is V28() real ext-real set
(source | (Gn1 .edgesIn())) . A2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . A2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(G,source,n) . A2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
E2 is Relation-like Gn1 .edgesIn() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
E2 . A2 is V28() real ext-real set
(G,source,n) . A2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
E2 is Relation-like Gn1 .edgesIn() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
E2 . A2 is V28() real ext-real set
(G,source,n) . A2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((G,source,n) | (Gn1 .edgesIn())) . A2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
Sum ((G,source,n) | (Gn1 .edgesIn())) is V28() real ext-real set
Sum E2 is V28() real ext-real set
(G,source,n) | (Gn1 .edgesOut()) is Relation-like the_Edges_of G -defined Gn1 .edgesOut() -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom ((G,source,n) | (Gn1 .edgesOut())) is finite Element of K32((Gn1 .edgesOut()))
K32((Gn1 .edgesOut())) is finite V36() set
source . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source . (n . (P + 1))) + (G,source,n) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n)) is Relation-like {(n . (P + 1))} -defined RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(n . (P + 1))} is non empty trivial finite 1 -element set
{(n . (P + 1))} --> ((source . (n . (P + 1))) + (G,source,n)) is non empty Relation-like {(n . (P + 1))} -defined RAT -valued INT -valued {((source . (n . (P + 1))) + (G,source,n))} -valued Function-like constant total V18({(n . (P + 1))},{((source . (n . (P + 1))) + (G,source,n))}) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33({(n . (P + 1))},{((source . (n . (P + 1))) + (G,source,n))}))
{((source . (n . (P + 1))) + (G,source,n))} is non empty trivial finite V36() 1 -element V100() V101() V102() V103() V104() V105() set
K33({(n . (P + 1))},{((source . (n . (P + 1))) + (G,source,n))}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
K32(K33({(n . (P + 1))},{((source . (n . (P + 1))) + (G,source,n))})) is finite V36() set
(source | (Gn1 .edgesOut())) +* ((n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n))) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom ((n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n))) is finite Element of K32({(n . (P + 1))})
K32({(n . (P + 1))}) is finite V36() V79() set
dom ((source | (Gn1 .edgesOut())) +* ((n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n)))) is finite set
dom (source | (Gn1 .edgesOut())) is finite Element of K32((Gn1 .edgesOut()))
(dom (source | (Gn1 .edgesOut()))) \/ {(n . (P + 1))} is non empty finite set
(Gn1 .edgesOut()) \/ {(n . (P + 1))} is non empty finite set
x is set
(the_Source_of G) . x is set
B2 is Relation-like Gn1 .edgesOut() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
B2 . x is V28() real ext-real set
((n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n))) . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(G,source,n) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
m is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
m + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
v1 is Element of the_Vertices_of G
n . m is set
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
n . (m + 1) is set
v2 is Element of the_Vertices_of G
n . (m + 2) is set
(m + 2) - 2 is V28() real integer ext-real set
B2 is Relation-like Gn1 .edgesOut() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
B2 . x is V28() real ext-real set
(source | (Gn1 .edgesOut())) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(G,source,n) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
B2 is Relation-like Gn1 .edgesOut() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
B2 . x is V28() real ext-real set
(G,source,n) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
B2 is Relation-like Gn1 .edgesOut() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
B2 . x is V28() real ext-real set
(G,source,n) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((G,source,n) | (Gn1 .edgesOut())) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(G,source,n) + (source . (n . (P + 1))) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(Sum (source | (Gn1 .edgesIn()))) + ((G,source,n) + (source . (n . (P + 1)))) is V28() real ext-real set
(source | (Gn1 .edgesIn())) . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((Sum (source | (Gn1 .edgesIn()))) + ((G,source,n) + (source . (n . (P + 1))))) - ((source | (Gn1 .edgesIn())) . (n . (P + 1))) is V28() real ext-real set
(Sum (source | (Gn1 .edgesOut()))) + (G,source,n) is V28() real ext-real set
((Sum (source | (Gn1 .edgesOut()))) + (G,source,n)) + (source . (n . (P + 1))) is V28() real ext-real set
(((Sum (source | (Gn1 .edgesOut()))) + (G,source,n)) + (source . (n . (P + 1)))) - (source . (n . (P + 1))) is V28() real ext-real set
((Sum (source | (Gn1 .edgesOut()))) + (G,source,n)) + (source . (n . (P + 1))) is V28() real ext-real set
(((Sum (source | (Gn1 .edgesOut()))) + (G,source,n)) + (source . (n . (P + 1)))) - (source . (n . (P + 1))) is V28() real ext-real set
(G,source,n) + (source . (n . (P + 1))) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(Sum (source | (Gn1 .edgesOut()))) + ((G,source,n) + (source . (n . (P + 1)))) is V28() real ext-real set
(source | (Gn1 .edgesOut())) . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((Sum (source | (Gn1 .edgesOut()))) + ((G,source,n) + (source . (n . (P + 1))))) - ((source | (Gn1 .edgesOut())) . (n . (P + 1))) is V28() real ext-real set
Sum B2 is V28() real ext-real set
Sum ((G,source,n) | (Gn1 .edgesOut())) is V28() real ext-real set
(G,source,n) | (Gn1 .edgesOut()) is Relation-like the_Edges_of G -defined Gn1 .edgesOut() -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom ((G,source,n) | (Gn1 .edgesOut())) is finite Element of K32((Gn1 .edgesOut()))
K32((Gn1 .edgesOut())) is finite V36() set
e is set
(source | (Gn1 .edgesOut())) . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(the_Source_of G) . e is set
((G,source,n) | (Gn1 .edgesOut())) . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(G,source,n) . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
dom (source | (Gn1 .edgesOut())) is finite Element of K32((Gn1 .edgesOut()))
source . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source . (n . (P + 1))) + (G,source,n) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n)) is Relation-like {(n . (P + 1))} -defined RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(n . (P + 1))} is non empty trivial finite 1 -element set
{(n . (P + 1))} --> ((source . (n . (P + 1))) + (G,source,n)) is non empty Relation-like {(n . (P + 1))} -defined RAT -valued INT -valued {((source . (n . (P + 1))) + (G,source,n))} -valued Function-like constant total V18({(n . (P + 1))},{((source . (n . (P + 1))) + (G,source,n))}) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33({(n . (P + 1))},{((source . (n . (P + 1))) + (G,source,n))}))
{((source . (n . (P + 1))) + (G,source,n))} is non empty trivial finite V36() 1 -element V100() V101() V102() V103() V104() V105() set
K33({(n . (P + 1))},{((source . (n . (P + 1))) + (G,source,n))}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
K32(K33({(n . (P + 1))},{((source . (n . (P + 1))) + (G,source,n))})) is finite V36() set
(source | (Gn1 .edgesIn())) +* ((n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n))) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
source . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source . (n . (P + 1))) - (G,source,n) is V28() real integer ext-real set
(n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n)) is Relation-like {(n . (P + 1))} -defined INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued finite-support set
{(n . (P + 1))} is non empty trivial finite 1 -element set
{(n . (P + 1))} --> ((source . (n . (P + 1))) - (G,source,n)) is non empty Relation-like {(n . (P + 1))} -defined INT -valued {((source . (n . (P + 1))) - (G,source,n))} -valued Function-like constant total V18({(n . (P + 1))},{((source . (n . (P + 1))) - (G,source,n))}) finite complex-valued ext-real-valued real-valued finite-support Element of K32(K33({(n . (P + 1))},{((source . (n . (P + 1))) - (G,source,n))}))
{((source . (n . (P + 1))) - (G,source,n))} is non empty trivial finite 1 -element V100() V101() V102() V103() V104() set
K33({(n . (P + 1))},{((source . (n . (P + 1))) - (G,source,n))}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued set
K32(K33({(n . (P + 1))},{((source . (n . (P + 1))) - (G,source,n))})) is finite V36() set
((source | (Gn1 .edgesIn())) +* ((n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n)))) +* ((n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n))) is Relation-like Function-like finite complex-valued ext-real-valued real-valued finite-support set
(G,source,n) | (Gn1 .edgesIn()) is Relation-like the_Edges_of G -defined Gn1 .edgesIn() -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom ((G,source,n) | (Gn1 .edgesIn())) is finite Element of K32((Gn1 .edgesIn()))
K32((Gn1 .edgesIn())) is finite V36() set
(G,source,n) . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
dom ((n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n))) is finite Element of K32({(n . (P + 1))})
K32({(n . (P + 1))}) is finite V36() V79() set
dom ((source | (Gn1 .edgesIn())) +* ((n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n)))) is finite set
dom (source | (Gn1 .edgesIn())) is finite Element of K32((Gn1 .edgesIn()))
dom ((n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n))) is finite Element of K32({(n . (P + 1))})
K32({(n . (P + 1))}) is finite V36() V79() set
(dom (source | (Gn1 .edgesIn()))) \/ (dom ((n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n)))) is finite set
(dom (source | (Gn1 .edgesIn()))) \/ {(n . (P + 1))} is non empty finite set
(Gn1 .edgesIn()) \/ {(n . (P + 1))} is non empty finite set
dom (((source | (Gn1 .edgesIn())) +* ((n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n)))) +* ((n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n)))) is finite set
A2 is Relation-like Gn1 .edgesIn() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
dom A2 is finite Element of K32((Gn1 .edgesIn()))
(dom A2) \/ (dom ((n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n)))) is finite set
(Gn1 .edgesIn()) \/ {(n . (P + 1))} is non empty finite set
(G,source,n) . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
x is set
((G,source,n) | (Gn1 .edgesIn())) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(G,source,n) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
B2 is Relation-like Gn1 .edgesIn() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
B2 . x is V28() real ext-real set
A2 . x is V28() real ext-real set
((n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n))) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
B2 is Relation-like Gn1 .edgesIn() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
B2 . x is V28() real ext-real set
((n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n))) . (n . (P + 1)) is V28() real integer ext-real set
B2 is Relation-like Gn1 .edgesIn() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
B2 . x is V28() real ext-real set
A2 . x is V28() real ext-real set
(source | (Gn1 .edgesIn())) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
B2 is Relation-like Gn1 .edgesIn() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
B2 . x is V28() real ext-real set
B2 is Relation-like Gn1 .edgesIn() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
B2 . x is V28() real ext-real set
A2 . (n . (P + 1)) is V28() real ext-real set
(source | (Gn1 .edgesIn())) . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
Sum ((G,source,n) | (Gn1 .edgesIn())) is V28() real ext-real set
Sum A2 is V28() real ext-real set
(Sum A2) + ((source . (n . (P + 1))) - (G,source,n)) is V28() real ext-real set
((Sum A2) + ((source . (n . (P + 1))) - (G,source,n))) - (source . (n . (P + 1))) is V28() real ext-real set
(source . (n . (P + 1))) - ((source . (n . (P + 1))) - (G,source,n)) is V28() real integer ext-real set
(Sum A2) - ((source . (n . (P + 1))) - ((source . (n . (P + 1))) - (G,source,n))) is V28() real ext-real set
(Sum (source | (Gn1 .edgesIn()))) + ((source . (n . (P + 1))) + (G,source,n)) is V28() real ext-real set
(source | (Gn1 .edgesIn())) . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((Sum (source | (Gn1 .edgesIn()))) + ((source . (n . (P + 1))) + (G,source,n))) - ((source | (Gn1 .edgesIn())) . (n . (P + 1))) is V28() real ext-real set
(((Sum (source | (Gn1 .edgesIn()))) + ((source . (n . (P + 1))) + (G,source,n))) - ((source | (Gn1 .edgesIn())) . (n . (P + 1)))) - (G,source,n) is V28() real ext-real set
(Sum (source | (Gn1 .edgesIn()))) + (G,source,n) is V28() real ext-real set
((Sum (source | (Gn1 .edgesIn()))) + (G,source,n)) + (source . (n . (P + 1))) is V28() real ext-real set
(((Sum (source | (Gn1 .edgesIn()))) + (G,source,n)) + (source . (n . (P + 1)))) - (source . (n . (P + 1))) is V28() real ext-real set
((((Sum (source | (Gn1 .edgesIn()))) + (G,source,n)) + (source . (n . (P + 1)))) - (source . (n . (P + 1)))) - (G,source,n) is V28() real ext-real set
Sum ((G,source,n) | (Gn1 .edgesOut())) is V28() real ext-real set
(G,source,n) | (Gn1 .edgesIn()) is Relation-like the_Edges_of G -defined Gn1 .edgesIn() -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom ((G,source,n) | (Gn1 .edgesIn())) is finite Element of K32((Gn1 .edgesIn()))
K32((Gn1 .edgesIn())) is finite V36() set
e is set
(source | (Gn1 .edgesIn())) . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
the_Target_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
G . TargetSelector is set
(the_Target_of G) . e is set
((G,source,n) | (Gn1 .edgesIn())) . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(G,source,n) . e is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source . (n . (P + 1))) - (G,source,n) is V28() real integer ext-real set
(n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n)) is Relation-like {(n . (P + 1))} -defined INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued finite-support set
{(n . (P + 1))} is non empty trivial finite 1 -element set
{(n . (P + 1))} --> ((source . (n . (P + 1))) - (G,source,n)) is non empty Relation-like {(n . (P + 1))} -defined INT -valued {((source . (n . (P + 1))) - (G,source,n))} -valued Function-like constant total V18({(n . (P + 1))},{((source . (n . (P + 1))) - (G,source,n))}) finite complex-valued ext-real-valued real-valued finite-support Element of K32(K33({(n . (P + 1))},{((source . (n . (P + 1))) - (G,source,n))}))
{((source . (n . (P + 1))) - (G,source,n))} is non empty trivial finite 1 -element V100() V101() V102() V103() V104() set
K33({(n . (P + 1))},{((source . (n . (P + 1))) - (G,source,n))}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued set
K32(K33({(n . (P + 1))},{((source . (n . (P + 1))) - (G,source,n))})) is finite V36() set
(source | (Gn1 .edgesOut())) +* ((n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n))) is Relation-like Function-like finite complex-valued ext-real-valued real-valued finite-support set
source . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source . (n . (P + 1))) + (G,source,n) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n)) is Relation-like {(n . (P + 1))} -defined RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(n . (P + 1))} is non empty trivial finite 1 -element set
{(n . (P + 1))} --> ((source . (n . (P + 1))) + (G,source,n)) is non empty Relation-like {(n . (P + 1))} -defined RAT -valued INT -valued {((source . (n . (P + 1))) + (G,source,n))} -valued Function-like constant total V18({(n . (P + 1))},{((source . (n . (P + 1))) + (G,source,n))}) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33({(n . (P + 1))},{((source . (n . (P + 1))) + (G,source,n))}))
{((source . (n . (P + 1))) + (G,source,n))} is non empty trivial finite V36() 1 -element V100() V101() V102() V103() V104() V105() set
K33({(n . (P + 1))},{((source . (n . (P + 1))) + (G,source,n))}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
K32(K33({(n . (P + 1))},{((source . (n . (P + 1))) + (G,source,n))})) is finite V36() set
((source | (Gn1 .edgesOut())) +* ((n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n)))) +* ((n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n))) is Relation-like Function-like finite complex-valued ext-real-valued real-valued finite-support set
(G,source,n) | (Gn1 .edgesOut()) is Relation-like the_Edges_of G -defined Gn1 .edgesOut() -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom ((G,source,n) | (Gn1 .edgesOut())) is finite Element of K32((Gn1 .edgesOut()))
K32((Gn1 .edgesOut())) is finite V36() set
dom (source | (Gn1 .edgesIn())) is finite Element of K32((Gn1 .edgesIn()))
(G,source,n) . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
dom ((n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n))) is finite Element of K32({(n . (P + 1))})
K32({(n . (P + 1))}) is finite V36() V79() set
dom ((source | (Gn1 .edgesOut())) +* ((n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n)))) is finite set
dom (source | (Gn1 .edgesOut())) is finite Element of K32((Gn1 .edgesOut()))
dom ((n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n))) is finite Element of K32({(n . (P + 1))})
K32({(n . (P + 1))}) is finite V36() V79() set
(dom (source | (Gn1 .edgesOut()))) \/ (dom ((n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n)))) is finite set
(dom (source | (Gn1 .edgesOut()))) \/ {(n . (P + 1))} is non empty finite set
(Gn1 .edgesOut()) \/ {(n . (P + 1))} is non empty finite set
dom (((source | (Gn1 .edgesOut())) +* ((n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n)))) +* ((n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n)))) is finite set
A2 is Relation-like Gn1 .edgesOut() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
dom A2 is finite Element of K32((Gn1 .edgesOut()))
(dom A2) \/ (dom ((n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n)))) is finite set
(Gn1 .edgesOut()) \/ {(n . (P + 1))} is non empty finite set
(G,source,n) . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
x is set
((G,source,n) | (Gn1 .edgesOut())) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(G,source,n) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
B2 is Relation-like Gn1 .edgesOut() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
B2 . x is V28() real ext-real set
A2 . x is V28() real ext-real set
((n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n))) . x is V28() real integer ext-real set
B2 is Relation-like Gn1 .edgesOut() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
B2 . x is V28() real ext-real set
((n . (P + 1)) .--> ((source . (n . (P + 1))) + (G,source,n))) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
B2 is Relation-like Gn1 .edgesOut() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
B2 . x is V28() real ext-real set
A2 . x is V28() real ext-real set
(source | (Gn1 .edgesOut())) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
B2 is Relation-like Gn1 .edgesOut() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
B2 . x is V28() real ext-real set
B2 is Relation-like Gn1 .edgesOut() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
B2 . x is V28() real ext-real set
A2 . (n . (P + 1)) is V28() real ext-real set
(source | (Gn1 .edgesOut())) . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
Sum ((G,source,n) | (Gn1 .edgesOut())) is V28() real ext-real set
Sum A2 is V28() real ext-real set
(Sum A2) + ((source . (n . (P + 1))) + (G,source,n)) is V28() real ext-real set
((Sum A2) + ((source . (n . (P + 1))) + (G,source,n))) - (source . (n . (P + 1))) is V28() real ext-real set
(Sum A2) - (source . (n . (P + 1))) is V28() real ext-real set
((Sum A2) - (source . (n . (P + 1)))) + (source . (n . (P + 1))) is V28() real ext-real set
(((Sum A2) - (source . (n . (P + 1)))) + (source . (n . (P + 1)))) + (G,source,n) is V28() real ext-real set
(Sum (source | (Gn1 .edgesOut()))) + ((source . (n . (P + 1))) - (G,source,n)) is V28() real ext-real set
(source | (Gn1 .edgesOut())) . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((Sum (source | (Gn1 .edgesOut()))) + ((source . (n . (P + 1))) - (G,source,n))) - ((source | (Gn1 .edgesOut())) . (n . (P + 1))) is V28() real ext-real set
(((Sum (source | (Gn1 .edgesOut()))) + ((source . (n . (P + 1))) - (G,source,n))) - ((source | (Gn1 .edgesOut())) . (n . (P + 1)))) + (G,source,n) is V28() real ext-real set
(Sum (source | (Gn1 .edgesOut()))) + (source . (n . (P + 1))) is V28() real ext-real set
((Sum (source | (Gn1 .edgesOut()))) + (source . (n . (P + 1)))) - (G,source,n) is V28() real ext-real set
(((Sum (source | (Gn1 .edgesOut()))) + (source . (n . (P + 1)))) - (G,source,n)) - (source . (n . (P + 1))) is V28() real ext-real set
((((Sum (source | (Gn1 .edgesOut()))) + (source . (n . (P + 1)))) - (G,source,n)) - (source . (n . (P + 1)))) + (G,source,n) is V28() real ext-real set
Sum ((G,source,n) | (Gn1 .edgesIn())) is V28() real ext-real set
source . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source . (n . (P + 1))) - (G,source,n) is V28() real integer ext-real set
(n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n)) is Relation-like {(n . (P + 1))} -defined INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued finite-support set
{(n . (P + 1))} is non empty trivial finite 1 -element set
{(n . (P + 1))} --> ((source . (n . (P + 1))) - (G,source,n)) is non empty Relation-like {(n . (P + 1))} -defined INT -valued {((source . (n . (P + 1))) - (G,source,n))} -valued Function-like constant total V18({(n . (P + 1))},{((source . (n . (P + 1))) - (G,source,n))}) finite complex-valued ext-real-valued real-valued finite-support Element of K32(K33({(n . (P + 1))},{((source . (n . (P + 1))) - (G,source,n))}))
{((source . (n . (P + 1))) - (G,source,n))} is non empty trivial finite 1 -element V100() V101() V102() V103() V104() set
K33({(n . (P + 1))},{((source . (n . (P + 1))) - (G,source,n))}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued set
K32(K33({(n . (P + 1))},{((source . (n . (P + 1))) - (G,source,n))})) is finite V36() set
(source | (Gn1 .edgesIn())) +* ((n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n))) is Relation-like Function-like finite complex-valued ext-real-valued real-valued finite-support set
dom ((n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n))) is finite Element of K32({(n . (P + 1))})
K32({(n . (P + 1))}) is finite V36() V79() set
dom ((source | (Gn1 .edgesIn())) +* ((n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n)))) is finite set
dom (source | (Gn1 .edgesIn())) is finite Element of K32((Gn1 .edgesIn()))
K32((Gn1 .edgesIn())) is finite V36() set
(dom (source | (Gn1 .edgesIn()))) \/ {(n . (P + 1))} is non empty finite set
(Gn1 .edgesIn()) \/ {(n . (P + 1))} is non empty finite set
(G,source,n) . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
A2 is set
(G,source,n) | (Gn1 .edgesIn()) is Relation-like the_Edges_of G -defined Gn1 .edgesIn() -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom ((G,source,n) | (Gn1 .edgesIn())) is finite Element of K32((Gn1 .edgesIn()))
the_Target_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
G . TargetSelector is set
(the_Target_of G) . A2 is set
E2 is Relation-like Gn1 .edgesIn() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
E2 . A2 is V28() real ext-real set
((n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n))) . (n . (P + 1)) is V28() real integer ext-real set
(G,source,n) . A2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
E2 is Relation-like Gn1 .edgesIn() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
E2 . A2 is V28() real ext-real set
(source | (Gn1 .edgesIn())) . A2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . A2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(G,source,n) . A2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
E2 is Relation-like Gn1 .edgesIn() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
E2 . A2 is V28() real ext-real set
(G,source,n) . A2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
E2 is Relation-like Gn1 .edgesIn() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
E2 . A2 is V28() real ext-real set
(G,source,n) . A2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((G,source,n) | (Gn1 .edgesIn())) . A2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
Sum ((G,source,n) | (Gn1 .edgesIn())) is V28() real ext-real set
(Sum (source | (Gn1 .edgesIn()))) + ((source . (n . (P + 1))) - (G,source,n)) is V28() real ext-real set
(source | (Gn1 .edgesIn())) . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((Sum (source | (Gn1 .edgesIn()))) + ((source . (n . (P + 1))) - (G,source,n))) - ((source | (Gn1 .edgesIn())) . (n . (P + 1))) is V28() real ext-real set
(Sum (source | (Gn1 .edgesIn()))) + (source . (n . (P + 1))) is V28() real ext-real set
((Sum (source | (Gn1 .edgesIn()))) + (source . (n . (P + 1)))) - (G,source,n) is V28() real ext-real set
(((Sum (source | (Gn1 .edgesIn()))) + (source . (n . (P + 1)))) - (G,source,n)) - (source . (n . (P + 1))) is V28() real ext-real set
(Sum (source | (Gn1 .edgesIn()))) - (G,source,n) is V28() real ext-real set
source . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source . (n . (P + 1))) - (G,source,n) is V28() real integer ext-real set
(n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n)) is Relation-like {(n . (P + 1))} -defined INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued finite-support set
{(n . (P + 1))} is non empty trivial finite 1 -element set
{(n . (P + 1))} --> ((source . (n . (P + 1))) - (G,source,n)) is non empty Relation-like {(n . (P + 1))} -defined INT -valued {((source . (n . (P + 1))) - (G,source,n))} -valued Function-like constant total V18({(n . (P + 1))},{((source . (n . (P + 1))) - (G,source,n))}) finite complex-valued ext-real-valued real-valued finite-support Element of K32(K33({(n . (P + 1))},{((source . (n . (P + 1))) - (G,source,n))}))
{((source . (n . (P + 1))) - (G,source,n))} is non empty trivial finite 1 -element V100() V101() V102() V103() V104() set
K33({(n . (P + 1))},{((source . (n . (P + 1))) - (G,source,n))}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued set
K32(K33({(n . (P + 1))},{((source . (n . (P + 1))) - (G,source,n))})) is finite V36() set
(source | (Gn1 .edgesOut())) +* ((n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n))) is Relation-like Function-like finite complex-valued ext-real-valued real-valued finite-support set
dom ((n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n))) is finite Element of K32({(n . (P + 1))})
K32({(n . (P + 1))}) is finite V36() V79() set
dom ((source | (Gn1 .edgesOut())) +* ((n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n)))) is finite set
dom (source | (Gn1 .edgesOut())) is finite Element of K32((Gn1 .edgesOut()))
K32((Gn1 .edgesOut())) is finite V36() set
(dom (source | (Gn1 .edgesOut()))) \/ {(n . (P + 1))} is non empty finite set
(Gn1 .edgesOut()) \/ {(n . (P + 1))} is non empty finite set
(G,source,n) . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
x is set
(G,source,n) | (Gn1 .edgesOut()) is Relation-like the_Edges_of G -defined Gn1 .edgesOut() -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom ((G,source,n) | (Gn1 .edgesOut())) is finite Element of K32((Gn1 .edgesOut()))
(the_Source_of G) . x is set
B2 is Relation-like Gn1 .edgesOut() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
B2 . x is V28() real ext-real set
((n . (P + 1)) .--> ((source . (n . (P + 1))) - (G,source,n))) . (n . (P + 1)) is V28() real integer ext-real set
(G,source,n) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
B2 is Relation-like Gn1 .edgesOut() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
B2 . x is V28() real ext-real set
(source | (Gn1 .edgesOut())) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(G,source,n) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
B2 is Relation-like Gn1 .edgesOut() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
B2 . x is V28() real ext-real set
(G,source,n) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
B2 is Relation-like Gn1 .edgesOut() -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
B2 . x is V28() real ext-real set
(G,source,n) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((G,source,n) | (Gn1 .edgesOut())) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
Sum ((G,source,n) | (Gn1 .edgesOut())) is V28() real ext-real set
(Sum (source | (Gn1 .edgesOut()))) + ((source . (n . (P + 1))) - (G,source,n)) is V28() real ext-real set
(source | (Gn1 .edgesOut())) . (n . (P + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((Sum (source | (Gn1 .edgesOut()))) + ((source . (n . (P + 1))) - (G,source,n))) - ((source | (Gn1 .edgesOut())) . (n . (P + 1))) is V28() real ext-real set
(Sum (source | (Gn1 .edgesOut()))) + (source . (n . (P + 1))) is V28() real ext-real set
((Sum (source | (Gn1 .edgesOut()))) + (source . (n . (P + 1)))) - (G,source,n) is V28() real ext-real set
(((Sum (source | (Gn1 .edgesOut()))) + (source . (n . (P + 1)))) - (G,source,n)) - (source . (n . (P + 1))) is V28() real ext-real set
(G,source,n) | (Gn1 .edgesIn()) is Relation-like the_Edges_of G -defined Gn1 .edgesIn() -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum ((G,source,n) | (Gn1 .edgesIn())) is V28() real ext-real set
(G,source,n) | (Gn1 .edgesOut()) is Relation-like the_Edges_of G -defined Gn1 .edgesOut() -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum ((G,source,n) | (Gn1 .edgesOut())) is V28() real ext-real set
(G,source,n) | (Gn1 .edgesIn()) is Relation-like the_Edges_of G -defined Gn1 .edgesIn() -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum ((G,source,n) | (Gn1 .edgesIn())) is V28() real ext-real set
(G,source,n) | (Gn1 .edgesOut()) is Relation-like the_Edges_of G -defined Gn1 .edgesOut() -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum ((G,source,n) | (Gn1 .edgesOut())) is V28() real ext-real set
n .vertices() is finite Element of K32((the_Vertices_of G))
dom (source | (Gn1 .edgesOut())) is finite Element of K32((Gn1 .edgesOut()))
K32((Gn1 .edgesOut())) is finite V36() set
P is set
(G,source,n) | (Gn1 .edgesOut()) is Relation-like the_Edges_of G -defined Gn1 .edgesOut() -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((G,source,n) | (Gn1 .edgesOut())) . P is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(G,source,n) . P is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
P is set
n .edges() is finite Element of K32((the_Edges_of G))
(source | (Gn1 .edgesOut())) . P is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . P is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
dom (source | (Gn1 .edgesIn())) is finite Element of K32((Gn1 .edgesIn()))
K32((Gn1 .edgesIn())) is finite V36() set
P is set
(G,source,n) | (Gn1 .edgesIn()) is Relation-like the_Edges_of G -defined Gn1 .edgesIn() -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((G,source,n) | (Gn1 .edgesIn())) . P is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(G,source,n) . P is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
P is set
(source | (Gn1 .edgesIn())) . P is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . P is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
dom ((G,source,n) | (Gn1 .edgesOut())) is finite Element of K32((Gn1 .edgesOut()))
dom ((G,source,n) | (Gn1 .edgesIn())) is finite Element of K32((Gn1 .edgesIn()))
Sum ((G,source,n) | (Gn1 .edgesIn())) is V28() real ext-real set
Sum ((G,source,n) | (Gn1 .edgesOut())) is V28() real ext-real set
n .vertices() is finite Element of K32((the_Vertices_of G))
(G,source,n) | (Gn1 .edgesIn()) is Relation-like the_Edges_of G -defined Gn1 .edgesIn() -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum ((G,source,n) | (Gn1 .edgesIn())) is V28() real ext-real set
(G,source,n) | (Gn1 .edgesOut()) is Relation-like the_Edges_of G -defined Gn1 .edgesOut() -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum ((G,source,n) | (Gn1 .edgesOut())) is V28() real ext-real set
(G,source,n) | (Gn1 .edgesIn()) is Relation-like the_Edges_of G -defined Gn1 .edgesIn() -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum ((G,source,n) | (Gn1 .edgesIn())) is V28() real ext-real set
(G,source,n) | (Gn1 .edgesOut()) is Relation-like the_Edges_of G -defined Gn1 .edgesOut() -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum ((G,source,n) | (Gn1 .edgesOut())) is V28() real ext-real set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite [Weighted] real-weighted nonnegative-weighted () set
the_Edges_of G is finite set
G . EdgeSelector is set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty finite set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
sink is set
CS is set
(G,source,sink,CS) is V28() real ext-real set
{CS} is non empty trivial finite 1 -element set
G .edgesInto {CS} is finite Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is finite V36() set
source | (G .edgesInto {CS}) is Relation-like the_Edges_of G -defined G .edgesInto {CS} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (G .edgesInto {CS})) is V28() real ext-real set
G .edgesOutOf {CS} is finite Element of K32((the_Edges_of G))
source | (G .edgesOutOf {CS}) is Relation-like the_Edges_of G -defined G .edgesOutOf {CS} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (G .edgesOutOf {CS})) is V28() real ext-real set
(Sum (source | (G .edgesInto {CS}))) - (Sum (source | (G .edgesOutOf {CS}))) is V28() real ext-real set
n is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
(G,source,n) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(G,source,sink,CS) + (G,source,n) is V28() real ext-real set
(G,source,n) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(G,(G,source,n),sink,CS) is V28() real ext-real set
(G,source,n) | (G .edgesInto {CS}) is Relation-like the_Edges_of G -defined G .edgesInto {CS} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum ((G,source,n) | (G .edgesInto {CS})) is V28() real ext-real set
(G,source,n) | (G .edgesOutOf {CS}) is Relation-like the_Edges_of G -defined G .edgesOutOf {CS} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum ((G,source,n) | (G .edgesOutOf {CS})) is V28() real ext-real set
(Sum ((G,source,n) | (G .edgesInto {CS}))) - (Sum ((G,source,n) | (G .edgesOutOf {CS}))) is V28() real ext-real set
n .last() is Element of the_Vertices_of G
n .first() is Element of the_Vertices_of G
len n is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
2 * 1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
(len n) - (2 * 1) is non empty V28() real integer ext-real non even set
Gn is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
Gn + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
n . (Gn + 1) is set
n . (len n) is set
(len n) - 0 is non empty V28() real integer ext-real positive non negative set
n . Gn is set
Gn + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
n . (Gn + 2) is set
the_Target_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . TargetSelector is set
(the_Target_of G) . (n . (Gn + 1)) is set
(source | (G .edgesInto {CS})) . (n . (Gn + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((source | (G .edgesInto {CS})) . (n . (Gn + 1))) + (G,source,n) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(n . (Gn + 1)) .--> (((source | (G .edgesInto {CS})) . (n . (Gn + 1))) + (G,source,n)) is Relation-like {(n . (Gn + 1))} -defined RAT -valued INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued natural-valued finite-support set
{(n . (Gn + 1))} is non empty trivial finite 1 -element set
{(n . (Gn + 1))} --> (((source | (G .edgesInto {CS})) . (n . (Gn + 1))) + (G,source,n)) is non empty Relation-like {(n . (Gn + 1))} -defined RAT -valued INT -valued {(((source | (G .edgesInto {CS})) . (n . (Gn + 1))) + (G,source,n))} -valued Function-like constant total V18({(n . (Gn + 1))},{(((source | (G .edgesInto {CS})) . (n . (Gn + 1))) + (G,source,n))}) finite complex-valued ext-real-valued real-valued natural-valued finite-support Element of K32(K33({(n . (Gn + 1))},{(((source | (G .edgesInto {CS})) . (n . (Gn + 1))) + (G,source,n))}))
{(((source | (G .edgesInto {CS})) . (n . (Gn + 1))) + (G,source,n))} is non empty trivial finite V36() 1 -element V100() V101() V102() V103() V104() V105() set
K33({(n . (Gn + 1))},{(((source | (G .edgesInto {CS})) . (n . (Gn + 1))) + (G,source,n))}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
K32(K33({(n . (Gn + 1))},{(((source | (G .edgesInto {CS})) . (n . (Gn + 1))) + (G,source,n))})) is finite V36() set
(source | (G .edgesInto {CS})) +* ((n . (Gn + 1)) .--> (((source | (G .edgesInto {CS})) . (n . (Gn + 1))) + (G,source,n))) is Relation-like RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued finite-support set
dom ((G,source,n) | (G .edgesInto {CS})) is finite Element of K32((G .edgesInto {CS}))
K32((G .edgesInto {CS})) is finite V36() set
dom ((source | (G .edgesInto {CS})) +* ((n . (Gn + 1)) .--> (((source | (G .edgesInto {CS})) . (n . (Gn + 1))) + (G,source,n)))) is finite set
dom (source | (G .edgesInto {CS})) is finite Element of K32((G .edgesInto {CS}))
dom ((n . (Gn + 1)) .--> (((source | (G .edgesInto {CS})) . (n . (Gn + 1))) + (G,source,n))) is finite Element of K32({(n . (Gn + 1))})
K32({(n . (Gn + 1))}) is finite V36() V79() set
(dom (source | (G .edgesInto {CS}))) \/ (dom ((n . (Gn + 1)) .--> (((source | (G .edgesInto {CS})) . (n . (Gn + 1))) + (G,source,n)))) is finite set
(dom (source | (G .edgesInto {CS}))) \/ {(n . (Gn + 1))} is non empty finite set
(G .edgesInto {CS}) \/ {(n . (Gn + 1))} is non empty finite set
(G,source,n) . (n . (Gn + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . (n . (Gn + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source . (n . (Gn + 1))) + (G,source,n) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
E2 is set
((G,source,n) | (G .edgesInto {CS})) . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(G,source,n) . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(the_Target_of G) . E2 is set
e is Relation-like G .edgesInto {CS} -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
e . E2 is V28() real ext-real set
((n . (Gn + 1)) .--> (((source | (G .edgesInto {CS})) . (n . (Gn + 1))) + (G,source,n))) . (n . (Gn + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
n .edges() is finite Element of K32((the_Edges_of G))
x is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
x + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
A2 is Element of the_Vertices_of G
n . x is set
x + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
n . (x + 1) is set
B2 is Element of the_Vertices_of G
n . (x + 2) is set
(x + 2) - 2 is V28() real integer ext-real set
1 - 2 is V28() real integer ext-real set
e is Relation-like G .edgesInto {CS} -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
e . E2 is V28() real ext-real set
(source | (G .edgesInto {CS})) . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
e is Relation-like G .edgesInto {CS} -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
e . E2 is V28() real ext-real set
e is Relation-like G .edgesInto {CS} -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
e . E2 is V28() real ext-real set
(G,source,n) + ((source | (G .edgesInto {CS})) . (n . (Gn + 1))) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(Sum (source | (G .edgesInto {CS}))) + ((G,source,n) + ((source | (G .edgesInto {CS})) . (n . (Gn + 1)))) is V28() real ext-real set
((Sum (source | (G .edgesInto {CS}))) + ((G,source,n) + ((source | (G .edgesInto {CS})) . (n . (Gn + 1))))) - ((source | (G .edgesInto {CS})) . (n . (Gn + 1))) is V28() real ext-real set
(Sum (source | (G .edgesInto {CS}))) + (G,source,n) is V28() real ext-real set
dom ((G,source,n) | (G .edgesOutOf {CS})) is finite Element of K32((G .edgesOutOf {CS}))
K32((G .edgesOutOf {CS})) is finite V36() set
E2 is set
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
G . SourceSelector is set
(the_Source_of G) . E2 is set
n .edges() is finite Element of K32((the_Edges_of G))
x is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
x + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
A2 is Element of the_Vertices_of G
n . x is set
x + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
n . (x + 1) is set
B2 is Element of the_Vertices_of G
n . (x + 2) is set
(x + 2) - 2 is V28() real integer ext-real set
1 - 2 is V28() real integer ext-real set
(G,source,n) . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesOutOf {CS})) . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((G,source,n) | (G .edgesOutOf {CS})) . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
dom (source | (G .edgesOutOf {CS})) is finite Element of K32((G .edgesOutOf {CS}))
((Sum (source | (G .edgesInto {CS}))) + (G,source,n)) - (Sum (source | (G .edgesOutOf {CS}))) is V28() real ext-real set
((Sum (source | (G .edgesInto {CS}))) - (Sum (source | (G .edgesOutOf {CS})))) + (G,source,n) is V28() real ext-real set
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . SourceSelector is set
(the_Source_of G) . (n . (Gn + 1)) is set
(source | (G .edgesOutOf {CS})) . (n . (Gn + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((source | (G .edgesOutOf {CS})) . (n . (Gn + 1))) - (G,source,n) is V28() real integer ext-real set
(n . (Gn + 1)) .--> (((source | (G .edgesOutOf {CS})) . (n . (Gn + 1))) - (G,source,n)) is Relation-like {(n . (Gn + 1))} -defined INT -valued Function-like one-to-one finite complex-valued ext-real-valued real-valued finite-support set
{(n . (Gn + 1))} is non empty trivial finite 1 -element set
{(n . (Gn + 1))} --> (((source | (G .edgesOutOf {CS})) . (n . (Gn + 1))) - (G,source,n)) is non empty Relation-like {(n . (Gn + 1))} -defined INT -valued {(((source | (G .edgesOutOf {CS})) . (n . (Gn + 1))) - (G,source,n))} -valued Function-like constant total V18({(n . (Gn + 1))},{(((source | (G .edgesOutOf {CS})) . (n . (Gn + 1))) - (G,source,n))}) finite complex-valued ext-real-valued real-valued finite-support Element of K32(K33({(n . (Gn + 1))},{(((source | (G .edgesOutOf {CS})) . (n . (Gn + 1))) - (G,source,n))}))
{(((source | (G .edgesOutOf {CS})) . (n . (Gn + 1))) - (G,source,n))} is non empty trivial finite 1 -element V100() V101() V102() V103() V104() set
K33({(n . (Gn + 1))},{(((source | (G .edgesOutOf {CS})) . (n . (Gn + 1))) - (G,source,n))}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued set
K32(K33({(n . (Gn + 1))},{(((source | (G .edgesOutOf {CS})) . (n . (Gn + 1))) - (G,source,n))})) is finite V36() set
(source | (G .edgesOutOf {CS})) +* ((n . (Gn + 1)) .--> (((source | (G .edgesOutOf {CS})) . (n . (Gn + 1))) - (G,source,n))) is Relation-like Function-like finite complex-valued ext-real-valued real-valued finite-support set
dom ((G,source,n) | (G .edgesOutOf {CS})) is finite Element of K32((G .edgesOutOf {CS}))
K32((G .edgesOutOf {CS})) is finite V36() set
dom ((source | (G .edgesOutOf {CS})) +* ((n . (Gn + 1)) .--> (((source | (G .edgesOutOf {CS})) . (n . (Gn + 1))) - (G,source,n)))) is finite set
dom (source | (G .edgesOutOf {CS})) is finite Element of K32((G .edgesOutOf {CS}))
dom ((n . (Gn + 1)) .--> (((source | (G .edgesOutOf {CS})) . (n . (Gn + 1))) - (G,source,n))) is finite Element of K32({(n . (Gn + 1))})
K32({(n . (Gn + 1))}) is finite V36() V79() set
(dom (source | (G .edgesOutOf {CS}))) \/ (dom ((n . (Gn + 1)) .--> (((source | (G .edgesOutOf {CS})) . (n . (Gn + 1))) - (G,source,n)))) is finite set
(dom (source | (G .edgesOutOf {CS}))) \/ {(n . (Gn + 1))} is non empty finite set
(G .edgesOutOf {CS}) \/ {(n . (Gn + 1))} is non empty finite set
(G,source,n) . (n . (Gn + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . (n . (Gn + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source . (n . (Gn + 1))) - (G,source,n) is V28() real integer ext-real set
E2 is set
((G,source,n) | (G .edgesOutOf {CS})) . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(G,source,n) . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(the_Source_of G) . E2 is set
e is Relation-like G .edgesOutOf {CS} -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
e . E2 is V28() real ext-real set
((n . (Gn + 1)) .--> (((source | (G .edgesOutOf {CS})) . (n . (Gn + 1))) - (G,source,n))) . (n . (Gn + 1)) is V28() real integer ext-real set
n .edges() is finite Element of K32((the_Edges_of G))
x is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
x + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
A2 is Element of the_Vertices_of G
n . x is set
x + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
n . (x + 1) is set
B2 is Element of the_Vertices_of G
n . (x + 2) is set
(x + 2) - 2 is V28() real integer ext-real set
1 - 2 is V28() real integer ext-real set
e is Relation-like G .edgesOutOf {CS} -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
e . E2 is V28() real ext-real set
(source | (G .edgesOutOf {CS})) . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
e is Relation-like G .edgesOutOf {CS} -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
e . E2 is V28() real ext-real set
e is Relation-like G .edgesOutOf {CS} -defined Function-like total complex-valued ext-real-valued real-valued finite-support set
e . E2 is V28() real ext-real set
(Sum (source | (G .edgesOutOf {CS}))) + (((source | (G .edgesOutOf {CS})) . (n . (Gn + 1))) - (G,source,n)) is V28() real ext-real set
((Sum (source | (G .edgesOutOf {CS}))) + (((source | (G .edgesOutOf {CS})) . (n . (Gn + 1))) - (G,source,n))) - ((source | (G .edgesOutOf {CS})) . (n . (Gn + 1))) is V28() real ext-real set
(Sum (source | (G .edgesOutOf {CS}))) - (G,source,n) is V28() real ext-real set
dom ((G,source,n) | (G .edgesInto {CS})) is finite Element of K32((G .edgesInto {CS}))
K32((G .edgesInto {CS})) is finite V36() set
E2 is set
the_Target_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
G . TargetSelector is set
(the_Target_of G) . E2 is set
n .edges() is finite Element of K32((the_Edges_of G))
x is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
x + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() non even Element of NAT
A2 is Element of the_Vertices_of G
n . x is set
x + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() even Element of NAT
n . (x + 1) is set
B2 is Element of the_Vertices_of G
n . (x + 2) is set
(x + 2) - 2 is V28() real integer ext-real set
1 - 2 is V28() real integer ext-real set
(G,source,n) . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(source | (G .edgesInto {CS})) . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((G,source,n) | (G .edgesInto {CS})) . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
dom (source | (G .edgesInto {CS})) is finite Element of K32((G .edgesInto {CS}))
(Sum (source | (G .edgesInto {CS}))) - ((Sum (source | (G .edgesOutOf {CS}))) - (G,source,n)) is V28() real ext-real set
((Sum (source | (G .edgesInto {CS}))) - (Sum (source | (G .edgesOutOf {CS})))) + (G,source,n) is V28() real ext-real set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite [Weighted] real-weighted nonnegative-weighted () set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
source is Element of the_Vertices_of G
sink is Element of the_Vertices_of G
(G,source,sink) is Relation-like NAT -defined Function-like total (G)
CS is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(G,source,sink) . CS is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
the_Edges_of G is finite set
G . EdgeSelector is set
(G,source,sink) . 0 is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(the_Edges_of G) --> 0 is Relation-like the_Edges_of G -defined NAT -valued RAT -valued INT -valued Function-like constant total V18( the_Edges_of G, NAT ) finite complex-valued ext-real-valued real-valued natural-valued finite-support Function-yielding V199() Element of K32(K33((the_Edges_of G),NAT))
K33((the_Edges_of G),NAT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K32(K33((the_Edges_of G),NAT)) is set
K33((the_Edges_of G),{0}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
the_Weight_of G is Relation-like the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
G . WeightSelector is set
Gn1 is set
((G,source,sink) . 0) . Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(the_Weight_of G) . Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
Gn1 is Element of the_Vertices_of G
Gn1 .edgesIn() is finite Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is finite V36() set
{Gn1} is non empty trivial finite 1 -element Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is finite V36() V79() set
G .edgesInto {Gn1} is finite Element of K32((the_Edges_of G))
EmptyBag (Gn1 .edgesIn()) is Relation-like Gn1 .edgesIn() -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags (Gn1 .edgesIn())
Bags (Gn1 .edgesIn()) is non empty set
Bags (Gn1 .edgesIn()) is non empty functional Element of K32((Bags (Gn1 .edgesIn())))
K32((Bags (Gn1 .edgesIn()))) is V79() set
Gn1 .edgesOut() is finite Element of K32((the_Edges_of G))
G .edgesOutOf {Gn1} is finite Element of K32((the_Edges_of G))
EmptyBag (Gn1 .edgesOut()) is Relation-like Gn1 .edgesOut() -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags (Gn1 .edgesOut())
Bags (Gn1 .edgesOut()) is non empty set
Bags (Gn1 .edgesOut()) is non empty functional Element of K32((Bags (Gn1 .edgesOut())))
K32((Bags (Gn1 .edgesOut()))) is V79() set
((G,source,sink) . 0) | (Gn1 .edgesIn()) is Relation-like the_Edges_of G -defined Gn1 .edgesIn() -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((G,source,sink) . 0) | (Gn1 .edgesOut()) is Relation-like the_Edges_of G -defined Gn1 .edgesOut() -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
B1 is set
(((G,source,sink) . 0) | (Gn1 .edgesOut())) . B1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((G,source,sink) . 0) . B1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(EmptyBag (Gn1 .edgesOut())) . B1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
Sum (((G,source,sink) . 0) | (Gn1 .edgesOut())) is V28() real ext-real set
Sum (EmptyBag (Gn1 .edgesOut())) is V28() real ext-real set
B1 is set
(((G,source,sink) . 0) | (Gn1 .edgesIn())) . B1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((G,source,sink) . 0) . B1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(EmptyBag (Gn1 .edgesIn())) . B1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
Sum (((G,source,sink) . 0) | (Gn1 .edgesIn())) is V28() real ext-real set
Sum (EmptyBag (Gn1 .edgesIn())) is V28() real ext-real set
Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(G,source,sink) . Gn is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Gn + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,sink) . (Gn + 1) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(G,((G,source,sink) . Gn),sink,source) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(G,((G,source,sink) . Gn),source) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,(G,source,sink) . Gn)
{1} \/ (the_Edges_of G) is non empty finite set
(G,((G,source,sink) . Gn),source) is Relation-like NAT -defined Function-like total (G,(G,source,sink) . Gn)
(G,((G,source,sink) . Gn),source) .Result() is set
(G,((G,source,sink) . Gn),source) .Lifespan() is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,((G,source,sink) . Gn),source) . ((G,((G,source,sink) . Gn),source) .Lifespan()) is set
dom (G,((G,source,sink) . Gn),source) is finite Element of K32((the_Vertices_of G))
(G,((G,source,sink) . Gn),source,sink) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
(the_Vertices_of G) \/ (the_Edges_of G) is non empty finite set
(G,((G,source,sink) . Gn),(G,((G,source,sink) . Gn),source,sink)) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(G,((G,source,sink) . Gn),source) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,(G,source,sink) . Gn)
{1} \/ (the_Edges_of G) is non empty finite set
(G,((G,source,sink) . Gn),source) is Relation-like NAT -defined Function-like total (G,(G,source,sink) . Gn)
(G,((G,source,sink) . Gn),source) .Result() is set
(G,((G,source,sink) . Gn),source) .Lifespan() is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,((G,source,sink) . Gn),source) . ((G,((G,source,sink) . Gn),source) .Lifespan()) is set
dom (G,((G,source,sink) . Gn),source) is finite Element of K32((the_Vertices_of G))
(G,((G,source,sink) . Gn),source) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,(G,source,sink) . Gn)
{1} \/ (the_Edges_of G) is non empty finite set
(G,((G,source,sink) . Gn),source) is Relation-like NAT -defined Function-like total (G,(G,source,sink) . Gn)
(G,((G,source,sink) . Gn),source) .Result() is set
(G,((G,source,sink) . Gn),source) .Lifespan() is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,((G,source,sink) . Gn),source) . ((G,((G,source,sink) . Gn),source) .Lifespan()) is set
dom (G,((G,source,sink) . Gn),source) is finite Element of K32((the_Vertices_of G))
Gn is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(G,source,sink) . Gn is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
Gn + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,sink) . (Gn + 1) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite [Weighted] real-weighted nonnegative-weighted () set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
source is Element of the_Vertices_of G
sink is Element of the_Vertices_of G
(G,source,sink) is Relation-like NAT -defined Function-like total (G)
{source} is non empty trivial finite 1 -element Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is finite V36() V79() set
the_Weight_of G is Relation-like the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
the_Edges_of G is finite set
G . EdgeSelector is set
G . WeightSelector is set
(the_Vertices_of G) \ {source} is finite Element of K32((the_Vertices_of G))
G .edgesDBetween ({source},((the_Vertices_of G) \ {source})) is finite Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is finite V36() set
(the_Weight_of G) | (G .edgesDBetween ({source},((the_Vertices_of G) \ {source}))) is Relation-like the_Edges_of G -defined G .edgesDBetween ({source},((the_Vertices_of G) \ {source})) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
degree ((the_Weight_of G) | (G .edgesDBetween ({source},((the_Vertices_of G) \ {source})))) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
Sum ((the_Weight_of G) | (G .edgesDBetween ({source},((the_Vertices_of G) \ {source})))) is V28() real ext-real set
Gn1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
Gn1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,sink) . (Gn1 + 1) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
P is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,sink) . P is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
P + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,sink) . (P + 1) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(G,((G,source,sink) . P),source,sink) is V28() real ext-real set
{sink} is non empty trivial finite 1 -element set
G .edgesInto {sink} is finite Element of K32((the_Edges_of G))
((G,source,sink) . P) | (G .edgesInto {sink}) is Relation-like the_Edges_of G -defined G .edgesInto {sink} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (((G,source,sink) . P) | (G .edgesInto {sink})) is V28() real ext-real set
G .edgesOutOf {sink} is finite Element of K32((the_Edges_of G))
((G,source,sink) . P) | (G .edgesOutOf {sink}) is Relation-like the_Edges_of G -defined G .edgesOutOf {sink} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (((G,source,sink) . P) | (G .edgesOutOf {sink})) is V28() real ext-real set
(Sum (((G,source,sink) . P) | (G .edgesInto {sink}))) - (Sum (((G,source,sink) . P) | (G .edgesOutOf {sink}))) is V28() real ext-real set
(G,((G,source,sink) . P),source,sink) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
(the_Vertices_of G) \/ (the_Edges_of G) is non empty finite set
(G,((G,source,sink) . P),sink,source) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(G,((G,source,sink) . P),source) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,(G,source,sink) . P)
{1} \/ (the_Edges_of G) is non empty finite set
(G,((G,source,sink) . P),source) is Relation-like NAT -defined Function-like total (G,(G,source,sink) . P)
(G,((G,source,sink) . P),source) .Result() is set
(G,((G,source,sink) . P),source) .Lifespan() is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,((G,source,sink) . P),source) . ((G,((G,source,sink) . P),source) .Lifespan()) is set
dom (G,((G,source,sink) . P),source) is finite Element of K32((the_Vertices_of G))
(G,((G,source,sink) . P),source,sink) .last() is Element of the_Vertices_of G
(G,((G,source,sink) . P),(G,((G,source,sink) . P),source,sink)) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
B1 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,((G,source,sink) . P),(G,((G,source,sink) . P),source,sink)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
B1 + (G,((G,source,sink) . P),(G,((G,source,sink) . P),source,sink)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,((G,source,sink) . (P + 1)),source,sink) is V28() real ext-real set
((G,source,sink) . (P + 1)) | (G .edgesInto {sink}) is Relation-like the_Edges_of G -defined G .edgesInto {sink} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (((G,source,sink) . (P + 1)) | (G .edgesInto {sink})) is V28() real ext-real set
((G,source,sink) . (P + 1)) | (G .edgesOutOf {sink}) is Relation-like the_Edges_of G -defined G .edgesOutOf {sink} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (((G,source,sink) . (P + 1)) | (G .edgesOutOf {sink})) is V28() real ext-real set
(Sum (((G,source,sink) . (P + 1)) | (G .edgesInto {sink}))) - (Sum (((G,source,sink) . (P + 1)) | (G .edgesOutOf {sink}))) is V28() real ext-real set
(G,((G,source,sink) . P),source,sink) .first() is Element of the_Vertices_of G
E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
E2 - 0 is V28() real integer ext-real non negative set
(B1 + (G,((G,source,sink) . P),(G,((G,source,sink) . P),source,sink))) - (G,((G,source,sink) . P),(G,((G,source,sink) . P),source,sink)) is V28() real integer ext-real set
P is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,sink) . P is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(G,((G,source,sink) . P),source,sink) is V28() real ext-real set
((G,source,sink) . P) | (G .edgesInto {sink}) is Relation-like the_Edges_of G -defined G .edgesInto {sink} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (((G,source,sink) . P) | (G .edgesInto {sink})) is V28() real ext-real set
((G,source,sink) . P) | (G .edgesOutOf {sink}) is Relation-like the_Edges_of G -defined G .edgesOutOf {sink} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (((G,source,sink) . P) | (G .edgesOutOf {sink})) is V28() real ext-real set
(Sum (((G,source,sink) . P) | (G .edgesInto {sink}))) - (Sum (((G,source,sink) . P) | (G .edgesOutOf {sink}))) is V28() real ext-real set
P + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,sink) . (P + 1) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(G,((G,source,sink) . (P + 1)),source,sink) is V28() real ext-real set
((G,source,sink) . (P + 1)) | (G .edgesInto {sink}) is Relation-like the_Edges_of G -defined G .edgesInto {sink} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (((G,source,sink) . (P + 1)) | (G .edgesInto {sink})) is V28() real ext-real set
((G,source,sink) . (P + 1)) | (G .edgesOutOf {sink}) is Relation-like the_Edges_of G -defined G .edgesOutOf {sink} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (((G,source,sink) . (P + 1)) | (G .edgesOutOf {sink})) is V28() real ext-real set
(Sum (((G,source,sink) . (P + 1)) | (G .edgesInto {sink}))) - (Sum (((G,source,sink) . (P + 1)) | (G .edgesOutOf {sink}))) is V28() real ext-real set
{sink} is non empty trivial finite 1 -element Element of K32((the_Vertices_of G))
G .edgesInto {sink} is finite Element of K32((the_Edges_of G))
EmptyBag (G .edgesInto {sink}) is Relation-like G .edgesInto {sink} -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags (G .edgesInto {sink})
Bags (G .edgesInto {sink}) is non empty set
Bags (G .edgesInto {sink}) is non empty functional Element of K32((Bags (G .edgesInto {sink})))
K32((Bags (G .edgesInto {sink}))) is V79() set
G .edgesOutOf {sink} is finite Element of K32((the_Edges_of G))
EmptyBag (G .edgesOutOf {sink}) is Relation-like G .edgesOutOf {sink} -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags (G .edgesOutOf {sink})
Bags (G .edgesOutOf {sink}) is non empty set
Bags (G .edgesOutOf {sink}) is non empty functional Element of K32((Bags (G .edgesOutOf {sink})))
K32((Bags (G .edgesOutOf {sink}))) is V79() set
(G,source,sink) . 0 is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
((G,source,sink) . 0) | (G .edgesInto {sink}) is Relation-like the_Edges_of G -defined G .edgesInto {sink} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
((G,source,sink) . 0) | (G .edgesOutOf {sink}) is Relation-like the_Edges_of G -defined G .edgesOutOf {sink} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(the_Edges_of G) --> 0 is Relation-like the_Edges_of G -defined NAT -valued RAT -valued INT -valued Function-like constant total V18( the_Edges_of G, NAT ) finite complex-valued ext-real-valued real-valued natural-valued finite-support Function-yielding V199() Element of K32(K33((the_Edges_of G),NAT))
K33((the_Edges_of G),NAT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K32(K33((the_Edges_of G),NAT)) is set
K33((the_Edges_of G),{0}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
E2 is set
(((G,source,sink) . 0) | (G .edgesInto {sink})) . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((G,source,sink) . 0) . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(EmptyBag (G .edgesInto {sink})) . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
Sum (((G,source,sink) . 0) | (G .edgesInto {sink})) is V28() real ext-real set
Sum (EmptyBag (G .edgesInto {sink})) is V28() real ext-real set
E2 is set
(((G,source,sink) . 0) | (G .edgesOutOf {sink})) . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
((G,source,sink) . 0) . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(EmptyBag (G .edgesOutOf {sink})) . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
Sum (((G,source,sink) . 0) | (G .edgesOutOf {sink})) is V28() real ext-real set
Sum (EmptyBag (G .edgesOutOf {sink})) is V28() real ext-real set
(G,((G,source,sink) . 0),source,sink) is V28() real ext-real set
((G,source,sink) . 0) | (G .edgesInto {sink}) is Relation-like the_Edges_of G -defined G .edgesInto {sink} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (((G,source,sink) . 0) | (G .edgesInto {sink})) is V28() real ext-real set
((G,source,sink) . 0) | (G .edgesOutOf {sink}) is Relation-like the_Edges_of G -defined G .edgesOutOf {sink} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (((G,source,sink) . 0) | (G .edgesOutOf {sink})) is V28() real ext-real set
(Sum (((G,source,sink) . 0) | (G .edgesInto {sink}))) - (Sum (((G,source,sink) . 0) | (G .edgesOutOf {sink}))) is V28() real ext-real set
0 - 0 is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real integer finite finite-yielding V36() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V100() V101() V102() V103() V104() V105() V106() FinSequence-yielding finite-support Function-yielding V199() set
(G,((G,source,sink) . (Gn1 + 1)),source,sink) is V28() real ext-real set
((G,source,sink) . (Gn1 + 1)) | (G .edgesInto {sink}) is Relation-like the_Edges_of G -defined G .edgesInto {sink} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (((G,source,sink) . (Gn1 + 1)) | (G .edgesInto {sink})) is V28() real ext-real set
((G,source,sink) . (Gn1 + 1)) | (G .edgesOutOf {sink}) is Relation-like the_Edges_of G -defined G .edgesOutOf {sink} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (((G,source,sink) . (Gn1 + 1)) | (G .edgesOutOf {sink})) is V28() real ext-real set
(Sum (((G,source,sink) . (Gn1 + 1)) | (G .edgesInto {sink}))) - (Sum (((G,source,sink) . (Gn1 + 1)) | (G .edgesOutOf {sink}))) is V28() real ext-real set
(Sum ((the_Weight_of G) | (G .edgesDBetween ({source},((the_Vertices_of G) \ {source}))))) + 1 is V28() real ext-real set
P is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,sink) . n is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,sink) . (n + 1) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite [Weighted] real-weighted nonnegative-weighted () set
the_Edges_of G is finite set
G . EdgeSelector is set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty finite set
source is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
sink is set
CS is set
n is Element of the_Vertices_of G
(G,source,n) is Relation-like NAT -defined Function-like total (G,source)
(G,source,n) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
{1} \/ (the_Edges_of G) is non empty finite set
(G,source,n) .Result() is set
(G,source,n) .Lifespan() is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,n) . ((G,source,n) .Lifespan()) is set
((G,source,n) .Lifespan()) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,(G,source,n),(((G,source,n) .Lifespan()) + 1)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
K32((the_Vertices_of G)) is finite V36() V79() set
dom (G,source,n) is finite Element of K32((the_Vertices_of G))
P is finite Element of K32((the_Vertices_of G))
(the_Vertices_of G) \ P is finite Element of K32((the_Vertices_of G))
G .edgesDBetween (P,((the_Vertices_of G) \ P)) is finite Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is finite V36() set
source | (G .edgesDBetween (P,((the_Vertices_of G) \ P))) is Relation-like the_Edges_of G -defined G .edgesDBetween (P,((the_Vertices_of G) \ P)) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
the_Weight_of G is Relation-like the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
G . WeightSelector is set
(the_Weight_of G) | (G .edgesDBetween (P,((the_Vertices_of G) \ P))) is Relation-like the_Edges_of G -defined G .edgesDBetween (P,((the_Vertices_of G) \ P)) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
(G,source,(G,source,n)) is finite Element of K32((the_Edges_of G))
choose (G,source,(G,source,n)) is Element of (G,source,(G,source,n))
(G,source,(G,source,n)) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,source)
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . SourceSelector is set
(the_Source_of G) . (choose (G,source,(G,source,n))) is set
the_Target_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
G . TargetSelector is set
(the_Target_of G) . (choose (G,source,(G,source,n))) is set
((the_Target_of G) . (choose (G,source,(G,source,n)))) .--> (choose (G,source,(G,source,n))) is Relation-like {((the_Target_of G) . (choose (G,source,(G,source,n))))} -defined Function-like one-to-one finite finite-support set
{((the_Target_of G) . (choose (G,source,(G,source,n))))} is non empty trivial finite 1 -element set
{((the_Target_of G) . (choose (G,source,(G,source,n))))} --> (choose (G,source,(G,source,n))) is non empty Relation-like {((the_Target_of G) . (choose (G,source,(G,source,n))))} -defined {(choose (G,source,(G,source,n)))} -valued Function-like constant total V18({((the_Target_of G) . (choose (G,source,(G,source,n))))},{(choose (G,source,(G,source,n)))}) finite finite-support Element of K32(K33({((the_Target_of G) . (choose (G,source,(G,source,n))))},{(choose (G,source,(G,source,n)))}))
{(choose (G,source,(G,source,n)))} is non empty trivial finite 1 -element set
K33({((the_Target_of G) . (choose (G,source,(G,source,n))))},{(choose (G,source,(G,source,n)))}) is Relation-like finite set
K32(K33({((the_Target_of G) . (choose (G,source,(G,source,n))))},{(choose (G,source,(G,source,n)))})) is finite V36() set
(G,source,n) +* (((the_Target_of G) . (choose (G,source,(G,source,n)))) .--> (choose (G,source,(G,source,n)))) is Relation-like Function-like finite finite-support set
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . SourceSelector is set
(the_Source_of G) . (choose (G,source,(G,source,n))) is set
((the_Source_of G) . (choose (G,source,(G,source,n)))) .--> (choose (G,source,(G,source,n))) is Relation-like {((the_Source_of G) . (choose (G,source,(G,source,n))))} -defined Function-like one-to-one finite finite-support set
{((the_Source_of G) . (choose (G,source,(G,source,n))))} is non empty trivial finite 1 -element set
{((the_Source_of G) . (choose (G,source,(G,source,n))))} --> (choose (G,source,(G,source,n))) is non empty Relation-like {((the_Source_of G) . (choose (G,source,(G,source,n))))} -defined {(choose (G,source,(G,source,n)))} -valued Function-like constant total V18({((the_Source_of G) . (choose (G,source,(G,source,n))))},{(choose (G,source,(G,source,n)))}) finite finite-support Element of K32(K33({((the_Source_of G) . (choose (G,source,(G,source,n))))},{(choose (G,source,(G,source,n)))}))
{(choose (G,source,(G,source,n)))} is non empty trivial finite 1 -element set
K33({((the_Source_of G) . (choose (G,source,(G,source,n))))},{(choose (G,source,(G,source,n)))}) is Relation-like finite set
K32(K33({((the_Source_of G) . (choose (G,source,(G,source,n))))},{(choose (G,source,(G,source,n)))})) is finite V36() set
(G,source,n) +* (((the_Source_of G) . (choose (G,source,(G,source,n)))) .--> (choose (G,source,(G,source,n)))) is Relation-like Function-like finite finite-support set
E2 is set
(source | (G .edgesDBetween (P,((the_Vertices_of G) \ P)))) . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
the_Target_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
K33((the_Edges_of G),(the_Vertices_of G)) is Relation-like finite set
K32(K33((the_Edges_of G),(the_Vertices_of G))) is finite V36() set
G . TargetSelector is set
(the_Target_of G) . E2 is set
((the_Weight_of G) | (G .edgesDBetween (P,((the_Vertices_of G) \ P)))) . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(the_Weight_of G) . E2 is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
the_Source_of G is Relation-like the_Edges_of G -defined the_Vertices_of G -valued Function-like total V18( the_Edges_of G, the_Vertices_of G) finite finite-support Element of K32(K33((the_Edges_of G),(the_Vertices_of G)))
G . SourceSelector is set
(the_Source_of G) . E2 is set
G .edgesDBetween (((the_Vertices_of G) \ P),P) is finite Element of K32((the_Edges_of G))
source | (G .edgesDBetween (((the_Vertices_of G) \ P),P)) is Relation-like the_Edges_of G -defined G .edgesDBetween (((the_Vertices_of G) \ P),P) -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
EmptyBag (G .edgesDBetween (((the_Vertices_of G) \ P),P)) is Relation-like G .edgesDBetween (((the_Vertices_of G) \ P),P) -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support Element of Bags (G .edgesDBetween (((the_Vertices_of G) \ P),P))
Bags (G .edgesDBetween (((the_Vertices_of G) \ P),P)) is non empty set
Bags (G .edgesDBetween (((the_Vertices_of G) \ P),P)) is non empty functional Element of K32((Bags (G .edgesDBetween (((the_Vertices_of G) \ P),P))))
K32((Bags (G .edgesDBetween (((the_Vertices_of G) \ P),P)))) is V79() set
x is set
(the_Target_of G) . x is set
(the_Source_of G) . x is set
(source | (G .edgesDBetween (((the_Vertices_of G) \ P),P))) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
source . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
(G .edgesDBetween (((the_Vertices_of G) \ P),P)) --> 0 is Relation-like G .edgesDBetween (((the_Vertices_of G) \ P),P) -defined NAT -valued RAT -valued INT -valued Function-like constant total V18(G .edgesDBetween (((the_Vertices_of G) \ P),P), NAT ) finite complex-valued ext-real-valued real-valued natural-valued finite-support Function-yielding V199() Element of K32(K33((G .edgesDBetween (((the_Vertices_of G) \ P),P)),NAT))
K33((G .edgesDBetween (((the_Vertices_of G) \ P),P)),NAT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K32(K33((G .edgesDBetween (((the_Vertices_of G) \ P),P)),NAT)) is set
K33((G .edgesDBetween (((the_Vertices_of G) \ P),P)),{0}) is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
(EmptyBag (G .edgesDBetween (((the_Vertices_of G) \ P),P))) . x is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() set
Sum (source | (G .edgesDBetween (((the_Vertices_of G) \ P),P))) is V28() real ext-real set
Sum (EmptyBag (G .edgesDBetween (((the_Vertices_of G) \ P),P))) is V28() real ext-real set
(G,source,sink,CS) is V28() real ext-real set
{CS} is non empty trivial finite 1 -element set
G .edgesInto {CS} is finite Element of K32((the_Edges_of G))
source | (G .edgesInto {CS}) is Relation-like the_Edges_of G -defined G .edgesInto {CS} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (G .edgesInto {CS})) is V28() real ext-real set
G .edgesOutOf {CS} is finite Element of K32((the_Edges_of G))
source | (G .edgesOutOf {CS}) is Relation-like the_Edges_of G -defined G .edgesOutOf {CS} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (source | (G .edgesOutOf {CS})) is V28() real ext-real set
(Sum (source | (G .edgesInto {CS}))) - (Sum (source | (G .edgesOutOf {CS}))) is V28() real ext-real set
Sum (source | (G .edgesDBetween (P,((the_Vertices_of G) \ P)))) is V28() real ext-real set
(Sum (source | (G .edgesDBetween (P,((the_Vertices_of G) \ P))))) - (Sum (source | (G .edgesDBetween (((the_Vertices_of G) \ P),P)))) is V28() real ext-real set
Sum ((the_Weight_of G) | (G .edgesDBetween (P,((the_Vertices_of G) \ P)))) is V28() real ext-real set
x is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(G,x,sink,CS) is V28() real ext-real set
x | (G .edgesInto {CS}) is Relation-like the_Edges_of G -defined G .edgesInto {CS} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (x | (G .edgesInto {CS})) is V28() real ext-real set
x | (G .edgesOutOf {CS}) is Relation-like the_Edges_of G -defined G .edgesOutOf {CS} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (x | (G .edgesOutOf {CS})) is V28() real ext-real set
(Sum (x | (G .edgesInto {CS}))) - (Sum (x | (G .edgesOutOf {CS}))) is V28() real ext-real set
G is Relation-like NAT -defined Function-like finite finite-support [Graph-like] finite [Weighted] real-weighted nonnegative-weighted () set
the_Vertices_of G is non empty finite set
G . VertexSelector is set
sink is Element of the_Vertices_of G
source is Element of the_Vertices_of G
(G,sink,source) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
the_Edges_of G is finite set
G . EdgeSelector is set
(G,source,sink) is Relation-like NAT -defined Function-like total (G)
(G,source,sink) .Result() is set
(G,source,sink) .Lifespan() is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,sink) . ((G,source,sink) .Lifespan()) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
((G,source,sink) .Lifespan()) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real positive non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,source,sink) . (((G,source,sink) .Lifespan()) + 1) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(G,((G,source,sink) . ((G,source,sink) .Lifespan())),sink,source) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(the_Vertices_of G) \/ (the_Edges_of G) is non empty finite set
P is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like Walk of G
(G,((G,source,sink) . ((G,source,sink) .Lifespan())),source,sink) is Relation-like NAT -defined (the_Vertices_of G) \/ (the_Edges_of G) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Trail-like Path-like vertex-distinct Walk of G
(G,((G,source,sink) . ((G,source,sink) .Lifespan())),source) is Relation-like the_Vertices_of G -defined {1} \/ (the_Edges_of G) -valued Function-like finite finite-support (G,(G,source,sink) . ((G,source,sink) .Lifespan()))
{1} \/ (the_Edges_of G) is non empty finite set
(G,((G,source,sink) . ((G,source,sink) .Lifespan())),source) is Relation-like NAT -defined Function-like total (G,(G,source,sink) . ((G,source,sink) .Lifespan()))
(G,((G,source,sink) . ((G,source,sink) .Lifespan())),source) .Result() is set
(G,((G,source,sink) . ((G,source,sink) .Lifespan())),source) .Lifespan() is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative V77() V100() V101() V102() V103() V104() V105() Element of NAT
(G,((G,source,sink) . ((G,source,sink) .Lifespan())),source) . ((G,((G,source,sink) . ((G,source,sink) .Lifespan())),source) .Lifespan()) is set
dom (G,((G,source,sink) . ((G,source,sink) .Lifespan())),source) is finite Element of K32((the_Vertices_of G))
K32((the_Vertices_of G)) is finite V36() V79() set
(G,((G,source,sink) . ((G,source,sink) .Lifespan())),source,sink) .first() is Element of the_Vertices_of G
(G,((G,source,sink) . ((G,source,sink) .Lifespan())),source,sink) .last() is Element of the_Vertices_of G
(G,((G,source,sink) . ((G,source,sink) .Lifespan())),(G,((G,source,sink) . ((G,source,sink) .Lifespan())),source,sink)) is Relation-like the_Edges_of G -defined RAT -valued Function-like total complex-valued ext-real-valued real-valued natural-valued finite-support set
(G,((G,source,sink) . ((G,source,sink) .Lifespan())),source,sink) is V28() real ext-real set
{sink} is non empty trivial finite 1 -element set
G .edgesInto {sink} is finite Element of K32((the_Edges_of G))
K32((the_Edges_of G)) is finite V36() set
((G,source,sink) . ((G,source,sink) .Lifespan())) | (G .edgesInto {sink}) is Relation-like the_Edges_of G -defined G .edgesInto {sink} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (((G,source,sink) . ((G,source,sink) .Lifespan())) | (G .edgesInto {sink})) is V28() real ext-real set
G .edgesOutOf {sink} is finite Element of K32((the_Edges_of G))
((G,source,sink) . ((G,source,sink) .Lifespan())) | (G .edgesOutOf {sink}) is Relation-like the_Edges_of G -defined G .edgesOutOf {sink} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (((G,source,sink) . ((G,source,sink) .Lifespan())) | (G .edgesOutOf {sink})) is V28() real ext-real set
(Sum (((G,source,sink) . ((G,source,sink) .Lifespan())) | (G .edgesInto {sink}))) - (Sum (((G,source,sink) . ((G,source,sink) .Lifespan())) | (G .edgesOutOf {sink}))) is V28() real ext-real set
(G,((G,source,sink) . ((G,source,sink) .Lifespan())),(G,((G,source,sink) . ((G,source,sink) .Lifespan())),source,sink)) is epsilon-transitive epsilon-connected ordinal natural V28() real integer finite cardinal ext-real non negative set
(G,((G,source,sink) . ((G,source,sink) .Lifespan())),source,sink) + (G,((G,source,sink) . ((G,source,sink) .Lifespan())),(G,((G,source,sink) . ((G,source,sink) .Lifespan())),source,sink)) is V28() real ext-real set
(G,((G,source,sink) . (((G,source,sink) .Lifespan()) + 1)),source,sink) is V28() real ext-real set
((G,source,sink) . (((G,source,sink) .Lifespan()) + 1)) | (G .edgesInto {sink}) is Relation-like the_Edges_of G -defined G .edgesInto {sink} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (((G,source,sink) . (((G,source,sink) .Lifespan()) + 1)) | (G .edgesInto {sink})) is V28() real ext-real set
((G,source,sink) . (((G,source,sink) .Lifespan()) + 1)) | (G .edgesOutOf {sink}) is Relation-like the_Edges_of G -defined G .edgesOutOf {sink} -defined the_Edges_of G -defined RAT -valued Function-like total finite complex-valued ext-real-valued real-valued natural-valued finite-support set
Sum (((G,source,sink) . (((G,source,sink) .Lifespan()) + 1)) | (G .edgesOutOf {sink})) is V28() real ext-real set
(Sum (((G,source,sink) . (((G,source,sink) .Lifespan()) + 1)) | (G .edgesInto {sink}))) - (Sum (((G,source,sink) . (((G,source,sink) .Lifespan()) + 1)) | (G .edgesOutOf {sink}))) is V28() real ext-real set