:: GLIB_001 semantic presentation

REAL is set
NAT is non empty non trivial V21() V22() V23() non finite cardinal limit_cardinal Element of K32(REAL)
K32(REAL) is non empty set
COMPLEX is set
NAT is non empty non trivial V21() V22() V23() non finite cardinal limit_cardinal set
K32(NAT) is non empty non trivial non finite set
K32(NAT) is non empty non trivial non finite set
{} is empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V21() V22() V23() V25() V26() V27() V28() V29() V30() ext-real non positive non negative finite finite-yielding V49() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V86() set
1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
3 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
_GraphSelectors is non empty Element of K32(NAT)
card {} is empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V21() V22() V23() V25() V26() V27() V28() V29() V30() ext-real non positive non negative finite finite-yielding V49() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V86() set
Seg 1 is non empty trivial finite 1 -element Element of K32(NAT)
{1} is non empty trivial finite V49() 1 -element set
Seg 2 is non empty finite 2 -element Element of K32(NAT)
{1,2} is non empty finite V49() set
Seg 3 is non empty finite 3 -element Element of K32(NAT)
K5(1,2,3) is non empty finite set
0 is empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V21() V22() V23() V25() V26() V27() V28() V29() V30() ext-real non positive non negative finite finite-yielding V49() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V86() Element of NAT
G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1 + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 - 0 is non empty V28() V29() V30() ext-real positive non negative set
(G1 + 2) - 2 is V28() V29() V30() ext-real set
G1 is set
G2 is Relation-like NAT -defined G1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of G1
K32(G2) is non empty finite V49() set
len G2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W1 is Relation-like NAT -defined G1 -valued Function-like finite FinSubsequence-like Element of K32(G2)
Seq W1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (Seq W1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
dom W1 is finite Element of K32(NAT)
Sgm (dom W1) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom W1)) * W1 is Relation-like NAT -defined G1 -valued Function-like finite set
dom G2 is finite Element of K32(NAT)
Seg (len G2) is finite len G2 -element Element of K32(NAT)
rng (Sgm (dom W1)) is finite Element of K32(NAT)
len (Sgm (dom W1)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
card (dom W1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
card W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G1 is set
G2 is Relation-like NAT -defined G1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of G1
K32(G2) is non empty finite V49() set
dom G2 is finite Element of K32(NAT)
W1 is Relation-like NAT -defined G1 -valued Function-like finite FinSubsequence-like Element of K32(G2)
Seq W1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom (Seq W1) is finite Element of K32(NAT)
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(Seq W1) . W2 is set
dom W1 is finite Element of K32(NAT)
Sgm (dom W1) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom W1)) . W2 is set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
Seg vs is finite vs -element Element of K32(NAT)
(Sgm (dom W1)) * W1 is Relation-like NAT -defined G1 -valued Function-like finite set
dom ((Sgm (dom W1)) * W1) is finite Element of K32(NAT)
W1 . ((Sgm (dom W1)) . W2) is set
[((Sgm (dom W1)) . W2),((Seq W1) . W2)] is V1() set
dom (Sgm (dom W1)) is finite Element of K32(NAT)
G2 . ((Sgm (dom W1)) . W2) is set
G1 is set
G2 is Relation-like NAT -defined G1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of G1
K32(G2) is non empty finite V49() set
W1 is Relation-like NAT -defined G1 -valued Function-like finite FinSubsequence-like Element of K32(G2)
Seq W1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (Seq W1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
card W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
dom W1 is finite Element of K32(NAT)
Sgm (dom W1) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom W1)) * W1 is Relation-like NAT -defined G1 -valued Function-like finite set
rng (Sgm (dom W1)) is finite Element of K32(NAT)
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
Seg W2 is finite W2 -element Element of K32(NAT)
dom (Seq W1) is finite Element of K32(NAT)
dom (Sgm (dom W1)) is finite Element of K32(NAT)
card (dom W1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
Seg (card (dom W1)) is finite card (dom W1) -element Element of K32(NAT)
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
Seg W2 is finite W2 -element Element of K32(NAT)
G1 is set
G2 is Relation-like NAT -defined G1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of G1
K32(G2) is non empty finite V49() set
W1 is Relation-like NAT -defined G1 -valued Function-like finite FinSubsequence-like Element of K32(G2)
Seq W1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom (Seq W1) is finite Element of K32(NAT)
dom W1 is finite Element of K32(NAT)
Sgm (dom W1) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
dom (Sgm (dom W1)) is finite Element of K32(NAT)
rng (Sgm (dom W1)) is finite Element of K32(NAT)
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
Seg W2 is finite W2 -element Element of K32(NAT)
(Sgm (dom W1)) * W1 is Relation-like NAT -defined G1 -valued Function-like finite set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
choose (the_Vertices_of G1) is Element of the_Vertices_of G1
<*(choose (the_Vertices_of G1))*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
W2 is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
len W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 . y is set
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W2 . (y + 1) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Edges_of G1 is set
the_Vertices_of G1 is non empty set
<*> (the_Edges_of G1) is empty Relation-like non-empty empty-yielding NAT -defined the_Edges_of G1 -valued Function-like one-to-one constant functional V21() V22() V23() V25() V26() V27() V28() V29() V30() ext-real non positive non negative finite finite-yielding V49() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V86() FinSequence of the_Edges_of G1
choose (the_Vertices_of G1) is Element of the_Vertices_of G1
<*(choose (the_Vertices_of G1))*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
len (<*> (the_Edges_of G1)) is empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V21() V22() V23() V25() V26() V27() V28() V29() V30() ext-real non positive non negative finite finite-yielding V49() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V86() Element of NAT
(len (<*> (the_Edges_of G1))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W2 is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
len W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 . y is set
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W2 . (y + 1) is set
(<*> (the_Edges_of G1)) . y is empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V21() V22() V23() V25() V26() V27() V28() V29() V30() ext-real non positive non negative finite finite-yielding V49() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V86() set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is set
W2 is Element of (the_Vertices_of G1) \/ (the_Edges_of G1)
<*W2*> is non empty trivial Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
len <*W2*> is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
<*W2*> . 1 is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
<*W2*> . y is set
y + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
<*W2*> . (y + 2) is set
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
<*W2*> . (y + 1) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
G2 is Element of the_Vertices_of G1
<*G2*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
vs is Element of (the_Vertices_of G1) \/ (the_Edges_of G1)
<*vs*> is non empty trivial Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
vs is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
len vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
vs . 1 is set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len <*G2*> is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
vs . vs is set
vs + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs . (vs + 2) is set
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
vs . (vs + 1) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
G2 is set
W1 is set
W2 is set
<*G2,W2,W1*> is non empty Relation-like NAT -defined Function-like finite 3 -element FinSequence-like FinSubsequence-like set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
choose (the_Vertices_of G1) is Element of the_Vertices_of G1
(G1,(choose (the_Vertices_of G1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
<*(choose (the_Vertices_of G1))*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
vs is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
vs . 1 is set
vs . 2 is set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
2 * 0 is empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V21() V22() V23() V25() V26() V27() V28() V29() V30() ext-real non positive non negative finite finite-yielding V49() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V86() even Element of NAT
vs . n is set
n + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs . (n + 2) is set
n + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
vs . (n + 1) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G2 . 1 is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(len G2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(len G2) - (2 * 1) is non empty V28() V29() V30() ext-real non even set
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
W1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (W1 + 1) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,G2) is Element of the_Vertices_of G1
G2 . (len G2) is set
W1 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G2 . (W1 + 2) is set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G2 . (W2 + 1) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
len W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 . 1 is set
(G1,G2) is Element of the_Vertices_of G1
G2 . (len G2) is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) - y is V28() V29() V30() ext-real even set
((len G2) - y) + 1 is non empty V28() V29() V30() ext-real non even set
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len G2) - (y + 1) is non empty V28() V29() V30() ext-real non even set
((len G2) - (y + 1)) + 1 is V28() V29() V30() ext-real even set
y + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) - (y + 2) is V28() V29() V30() ext-real even set
((len G2) - (y + 2)) + 1 is non empty V28() V29() V30() ext-real non even set
(y + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
dom G2 is finite Element of K32(NAT)
W2 . (y + 1) is set
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
G2 . n is set
n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
n + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (n + 1) is set
W2 . y is set
x is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . x is set
n + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (n + 2) is set
1 + 0 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len G2) - 1 is V28() V29() V30() ext-real even set
((len G2) - 1) + 1 is non empty V28() V29() V30() ext-real non even set
G2 . n is set
W2 . (y + 2) is set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
Rev W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
G2 ^' W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
len (G2 ^' W1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G2 ^' W1) . vs is set
vs + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G2 ^' W1) . (vs + 2) is set
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G2 ^' W1) . (vs + 1) is set
(vs + 2) - 2 is V28() V29() V30() ext-real set
(len G2) - 0 is non empty V28() V29() V30() ext-real positive non negative set
G2 . vs is set
(vs + 2) - 1 is V28() V29() V30() ext-real even set
G2 . (vs + 1) is set
G2 . (vs + 2) is set
(len G2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(vs + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
(len G2) + n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
x is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
x + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
0 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len (G2 ^' W1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + (len W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((len G2) + (len W1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len W1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len G2) + ((len W1) + 1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
x + (len G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (x + 1) is set
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(1 + 1) + 0 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W1 . (1 + 1) is set
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
xaa1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
x - xaa1 is V28() V29() V30() ext-real even set
(x + (len G2)) - (len G2) is V28() V29() V30() ext-real even set
2 + (len G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(2 + (len G2)) - (len G2) is V28() V29() V30() ext-real even set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(W2 + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((W2 + 1) + 1) - 1 is non empty V28() V29() V30() ext-real non even set
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(1 + 1) - 1 is V28() V29() V30() ext-real set
(len W1) - 0 is non empty V28() V29() V30() ext-real positive non negative set
es is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
es + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(es + 1) - 1 is non empty V28() V29() V30() ext-real non even set
W1 . (es + 1) is set
(len G2) + es is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G2 ^' W1) . ((len G2) + es) is set
es + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (es + 2) is set
W2 + (1 + 1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len G2) + W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
((len G2) + W2) + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (W2 + 1) is set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + (len W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G2 ^' W1) . 1 is set
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(W1,W2) -cut G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
len ((W1,W2) -cut G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even set
(len ((W1,W2) -cut G2)) + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
((len ((W1,W2) -cut G2)) + vs) - vs is V28() V29() V30() ext-real set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even set
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(vs + 1) - vs is non empty V28() V29() V30() ext-real non even set
n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
n - 1 is V28() V29() V30() ext-real even set
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
n + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
0 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
((W1,W2) -cut G2) . (0 + 1) is set
W1 + 0 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G2 . (W1 + 0) is set
G2 . W1 is set
(G1,G2,W1) is Element of the_Vertices_of G1
((W1,W2) -cut G2) . 1 is set
x is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs + x is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(vs + x) - 1 is non empty V28() V29() V30() ext-real non even set
x - 1 is V28() V29() V30() ext-real even set
x + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(x + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
((W1,W2) -cut G2) . ((x + 1) + 1) is set
W1 + (x + 1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G2 . (W1 + (x + 1)) is set
(len ((W1,W2) -cut G2)) + W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
x + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
x + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W1 + x is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len G2) - 0 is non empty V28() V29() V30() ext-real positive non negative set
(W1 + x) - 1 is V28() V29() V30() ext-real set
xaa1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . xaa1 is set
xaa1 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (xaa1 + 2) is set
xaa1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (xaa1 + 1) is set
(len ((W1,W2) -cut G2)) - 0 is V28() V29() V30() ext-real non negative set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
((W1,W2) -cut G2) . (W2 + 1) is set
W1 + W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G2 . (W1 + W2) is set
((W1,W2) -cut G2) . x is set
x + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
((W1,W2) -cut G2) . (x + 2) is set
((W1,W2) -cut G2) . (x + 1) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
(G1,G2,1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,W2,(len G2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,1,W1),(G1,G2,W2,(len G2))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W1 is set
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W1 div 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
y is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
dom y is finite Element of K32(NAT)
2 * (W1 div 2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs is set
rng y is finite set
vs is set
y . vs is set
Seg (W1 div 2) is finite W1 div 2 -element Element of K32(NAT)
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
vs * 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
n - 1 is non empty V28() V29() V30() ext-real non even set
1 * 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(W1 div 2) * 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
xaa1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 - 1 is non empty V28() V29() V30() ext-real non even set
G2 . xaa1 is set
(G1,G2,xaa1) is Element of the_Vertices_of G1
vs is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
vs . (vs + 1) is set
len vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
n - 1 is non empty V28() V29() V30() ext-real non even set
vs * 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
((len G2) + 1) - 1 is non empty V28() V29() V30() ext-real non even set
xaa1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . xaa1 is set
xaa1 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (xaa1 + 2) is set
xaa1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (xaa1 + 1) is set
dom vs is finite Element of K32(NAT)
2 * (vs + 1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (vs + 1)) - 1 is non empty V28() V29() V30() ext-real non even set
G2 . ((2 * (vs + 1)) - 1) is set
n + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (n + 1) is set
vs . vs is set
vs is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len vs) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
vs . vs is set
2 * vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * vs) - 1 is non empty V28() V29() V30() ext-real non even set
G2 . ((2 * vs) - 1) is set
dom vs is finite Element of K32(NAT)
W1 is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len W1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W2 is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len W2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
dom W1 is finite Element of K32(NAT)
W1 . y is set
2 * y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * y) - 1 is non empty V28() V29() V30() ext-real non even set
G2 . ((2 * y) - 1) is set
W2 . y is set
Seg (len W2) is finite len W2 -element Element of K32(NAT)
dom W2 is finite Element of K32(NAT)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) - 1 is V28() V29() V30() ext-real even set
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W1 div 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
vs is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
dom vs is finite Element of K32(NAT)
vs is set
rng vs is finite set
vs is set
vs . vs is set
Seg y is finite y -element Element of K32(NAT)
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
n * 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
y * 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
n + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
1 * 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
n - 1 is non empty V28() V29() V30() ext-real non even set
x is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . x is set
x + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (x + 2) is set
x + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (x + 1) is set
G2 . (2 * n) is set
2 * y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * y) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
vs is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the_Edges_of G1
len vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len vs) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len vs)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
((2 * (len vs)) + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
n is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len n) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(len vs) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
2 * ((len vs) + 1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
n . n is set
n + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
n . (n + 1) is set
2 * n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
g is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
g - 1 is non empty V28() V29() V30() ext-real non even set
n + n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
n * 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(len vs) * 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(len G2) - 0 is non empty V28() V29() V30() ext-real positive non negative set
es is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
2 * (n + 1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (n + 1)) - 1 is non empty V28() V29() V30() ext-real non even set
G2 . ((2 * (n + 1)) - 1) is set
es + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (es + 2) is set
dom vs is finite Element of K32(NAT)
vs . n is set
es + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (es + 1) is set
(2 * n) - 1 is non empty V28() V29() V30() ext-real non even set
G2 . ((2 * n) - 1) is set
n is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
vs is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len vs) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len vs)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
vs . n is set
2 * n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
G2 . (2 * n) is set
dom vs is finite Element of K32(NAT)
W1 is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len W1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len W1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len W2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len W2)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
dom W1 is finite Element of K32(NAT)
W1 . y is set
2 * y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
G2 . (2 * y) is set
W2 . y is set
Seg (len W2) is finite len W2 -element Element of K32(NAT)
dom W2 is finite Element of K32(NAT)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
dom (G1,G2) is finite Element of K32(NAT)
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
(G1,G2) . y is set
2 * y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even set
vs - 1 is non empty V28() V29() V30() ext-real non even set
y + y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
y * 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(len (G1,G2)) * 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(len G2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((len G2) + 1) - 1 is non empty V28() V29() V30() ext-real non even set
n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . n is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . y is set
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
G2 . y is set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . vs is set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even set
G2 . vs is set
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W2 is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . y is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
G2 . W2 is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . vs is set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even set
G2 . vs is set
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W2 is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . y is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (G1,G2,W1) is set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
G2 . W2 is set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
G2 . W2 is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . vs is set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . vs is set
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W2 is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . y is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
G2 . W2 is set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
G2 . W2 is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . vs is set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . vs is set
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W2 is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . y is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
(G1,G2,W1) is Element of the_Vertices_of G1
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
dom G2 is finite Element of K32(NAT)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W1 - 1 is non empty V28() V29() V30() ext-real non even set
W1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (W1 + 1) is set
G2 . W1 is set
1 + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W2 is set
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(1 + 1) - 1 is V28() V29() V30() ext-real set
(len G2) - 0 is non empty V28() V29() V30() ext-real positive non negative set
W2 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (W2 + 2) is set
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (W2 + 1) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
dom G2 is finite Element of K32(NAT)
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W1 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
G2 is Element of the_Vertices_of G1
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
<*G2*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
(G1,(G1,G2)) is Element of the_Vertices_of G1
(G1,G2) . 1 is set
(G1,(G1,G2)) is Element of the_Vertices_of G1
len (G1,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) . (len (G1,G2)) is set
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) . W2 is set
the_Source_of G1 is Relation-like Function-like V18( the_Edges_of G1, the_Vertices_of G1) Element of K32(K33((the_Edges_of G1),(the_Vertices_of G1)))
K33((the_Edges_of G1),(the_Vertices_of G1)) is Relation-like set
K32(K33((the_Edges_of G1),(the_Vertices_of G1))) is non empty set
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1,G2) . (W2 + 1) is set
(the_Source_of G1) . ((G1,G2) . (W2 + 1)) is set
0 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(G1,(G1,G2)) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,(G1,G2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len (G1,(G1,G2))) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len (G1,(G1,G2)))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,(G1,G2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) . W2 is set
(G1,G2) . y is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
G2 is set
W2 is set
W1 is set
(G1,G2,W2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
len (G1,G2,W2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
<*G2,W1,W2*> is non empty Relation-like NAT -defined Function-like finite 3 -element FinSequence-like FinSubsequence-like set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
G2 is set
W2 is set
W1 is set
(G1,G2,W2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
(G1,(G1,G2,W2,W1)) is Element of the_Vertices_of G1
(G1,G2,W2,W1) . 1 is set
(G1,(G1,G2,W2,W1)) is Element of the_Vertices_of G1
len (G1,G2,W2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W2,W1) . (len (G1,G2,W2,W1)) is set
<*G2,W1,W2*> is non empty Relation-like NAT -defined Function-like finite 3 -element FinSequence-like FinSubsequence-like set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
(G1,(G1,G2)) is Element of the_Vertices_of G1
len (G1,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) . (len (G1,G2)) is set
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,(G1,G2)) is Element of the_Vertices_of G1
(G1,G2) . 1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
dom (G1,G2) is finite Element of K32(NAT)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
dom G2 is finite Element of K32(NAT)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2) . W1 is set
(len G2) - W1 is V28() V29() V30() ext-real set
((len G2) - W1) + 1 is V28() V29() V30() ext-real set
G2 . (((len G2) - W1) + 1) is set
len (G1,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
Seg (len (G1,G2)) is non empty finite len (G1,G2) -element Element of K32(NAT)
Seg (len G2) is non empty finite len G2 -element Element of K32(NAT)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + (len W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 ^' W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len G2) + (len W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((len G2) + (len W1)) - (len W1) is non empty V28() V29() V30() ext-real non even set
((len (G1,G2,W1)) + 1) - 1 is non empty V28() V29() V30() ext-real non even set
(len W1) + (len G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((len W1) + (len G2)) - (len G2) is non empty V28() V29() V30() ext-real non even set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1)) is Element of the_Vertices_of G1
(G1,G2,W1) . 1 is set
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,(G1,G2,W1)) is Element of the_Vertices_of G1
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) . (len (G1,G2,W1)) is set
(G1,W1) is Element of the_Vertices_of G1
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (len W1) is set
G2 ^' W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
(2,1) -cut W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
G2 ^ ((2,1) -cut W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
dom G2 is finite Element of K32(NAT)
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
dom (G1,G2,W1) is finite Element of K32(NAT)
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1) . W2 is set
G2 . W2 is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) is Element of the_Vertices_of G1
G2 . (len G2) is set
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
G2 ^' W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len W1) - 1 is V28() V29() V30() ext-real even set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(len G2) + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len G2) + (len W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
- 1 is V28() V29() V30() ext-real non positive set
((len G2) + (len W1)) + (- 1) is V28() V29() V30() ext-real set
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((len (G1,G2,W1)) + 1) + (- 1) is V28() V29() V30() ext-real set
(G1,G2) is Element of the_Vertices_of G1
G2 . (len G2) is set
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(G1,G2) is Element of the_Vertices_of G1
G2 . (len G2) is set
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
dom (G1,G2,W1) is finite Element of K32(NAT)
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(len G2) + y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(G1,G2,W1) . ((len G2) + y) is set
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W1 . (y + 1) is set
(y + 1) + (len G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len W1) + (len G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((len G2) + y) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 ^' W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
dom G2 is finite Element of K32(NAT)
0 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
dom (G1,G2,W1) is finite Element of K32(NAT)
dom G2 is finite Element of K32(NAT)
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) is Element of the_Vertices_of G1
G2 . (len G2) is set
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(len (G1,G2,W1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len G2) + (len W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W2 - (len G2) is V28() V29() V30() ext-real set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(len G2) + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(len G2) + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(G1,G2) is Element of the_Vertices_of G1
G2 . (len G2) is set
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(G1,G2) is Element of the_Vertices_of G1
G2 . (len G2) is set
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(len G2) + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
dom G2 is finite Element of K32(NAT)
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W1,W2)) + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(W1,W2) -cut G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(G1,G2,W1,W2) . (vs + 1) is set
W1 + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G2 . (W1 + vs) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1,W2)) is Element of the_Vertices_of G1
(G1,G2,W1,W2) . 1 is set
G2 . W1 is set
(G1,(G1,G2,W1,W2)) is Element of the_Vertices_of G1
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) . (len (G1,G2,W1,W2)) is set
G2 . W2 is set
(len (G1,G2,W1,W2)) - 0 is non empty V28() V29() V30() ext-real positive non negative set
1 - 1 is V28() V29() V30() ext-real set
0 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(G1,G2,W1,W2) . (0 + 1) is set
W1 + 0 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G2 . (W1 + 0) is set
W2 - W1 is V28() V29() V30() ext-real even set
(len (G1,G2,W1,W2)) + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((len (G1,G2,W1,W2)) + W1) - W1 is non empty V28() V29() V30() ext-real non even set
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(W2 + 1) - W1 is non empty V28() V29() V30() ext-real non even set
(W2 - W1) + 1 is non empty V28() V29() V30() ext-real non even set
((W2 - W1) + 1) - 1 is V28() V29() V30() ext-real even set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) . ((W2 - W1) + 1) is set
W1 + (W2 - W1) is non empty V28() V29() V30() ext-real non even set
G2 . (W1 + (W2 - W1)) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,W2,y) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1,W2),(G1,G2,W2,y)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,W1,y) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,W1,y) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W1,y)) + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1,(G1,G2,W1,W2)) is Element of the_Vertices_of G1
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) . (len (G1,G2,W1,W2)) is set
G2 . W2 is set
(G1,(G1,G2,W2,y)) is Element of the_Vertices_of G1
(G1,G2,W2,y) . 1 is set
(len (G1,G2,W1,W2)) + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
len (G1,G2,W2,y) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W2,y)) + W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len (G1,G2,W1,W2)) + (len (G1,G2,W2,y)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((len (G1,G2,W1,W2)) + (len (G1,G2,W2,y))) + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
1 + (len (G1,G2,W1,y)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(1 + (len (G1,G2,W1,y))) + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len (G1,(G1,G2,W1,W2),(G1,G2,W2,y)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,(G1,G2,W1,W2),(G1,G2,W2,y))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len (G1,G2,W1,y)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
dom (G1,(G1,G2,W1,W2),(G1,G2,W2,y)) is finite Element of K32(NAT)
n - 1 is V28() V29() V30() ext-real set
(len (G1,(G1,G2,W1,W2),(G1,G2,W2,y))) - 0 is non empty V28() V29() V30() ext-real positive non negative set
x is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
x + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(G1,G2,W1,y) . (x + 1) is set
W1 + x is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G2 . (W1 + x) is set
(len (G1,G2,W1,W2)) - 0 is non empty V28() V29() V30() ext-real positive non negative set
dom (G1,G2,W1,W2) is finite Element of K32(NAT)
(G1,(G1,G2,W1,W2),(G1,G2,W2,y)) . n is set
(G1,G2,W1,W2) . (x + 1) is set
(G1,G2,W1,y) . n is set
xaa1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
(len (G1,G2,W1,W2)) + xaa1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(len (G1,G2,W1,W2)) + W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
((len (G1,G2,W1,W2)) + W2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(W2 + 1) + (len (G1,G2,W1,W2)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
((W2 + 1) + (len (G1,G2,W1,W2))) - (len (G1,G2,W1,W2)) is V28() V29() V30() ext-real set
(len (G1,G2,W2,y)) + (len (G1,G2,W1,W2)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((len (G1,G2,W2,y)) + (len (G1,G2,W1,W2))) - (len (G1,G2,W1,W2)) is non empty V28() V29() V30() ext-real non even set
(len (G1,G2,W2,y)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((len (G1,G2,W2,y)) + 1) - 1 is non empty V28() V29() V30() ext-real non even set
(W2 + 1) - 1 is V28() V29() V30() ext-real set
(G1,(G1,G2,W1,W2),(G1,G2,W2,y)) . n is set
(G1,G2,W2,y) . (W2 + 1) is set
W2 + W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G2 . (W2 + W2) is set
(G1,G2,W1,y) . n is set
(G1,(G1,G2,W1,W2),(G1,G2,W2,y)) . n is set
(G1,G2,W1,y) . n is set
(G1,(G1,G2,W1,W2),(G1,G2,W2,y)) . n is set
(G1,G2,W1,y) . n is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,1,(len G2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(1,(len G2)) -cut G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,W1) is Element of the_Vertices_of G1
<*(G1,G2,W1)*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
G2 . W1 is set
(W1,W1) -cut G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,1,W2),1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len (G1,G2,1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,1,W2)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
len (G1,(G1,G2,1,W2),1,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,(G1,G2,1,W2),1,W1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(1,W1) -cut G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
len (G1,G2,1,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,1,W1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(1,W2) -cut G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
(1,W1) -cut (G1,G2,1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
dom (G1,(G1,G2,1,W2),1,W1) is finite Element of K32(NAT)
vs - 1 is V28() V29() V30() ext-real set
(len (G1,G2,1,W1)) - 0 is non empty V28() V29() V30() ext-real positive non negative set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(len (G1,G2,1,W2)) - 0 is non empty V28() V29() V30() ext-real positive non negative set
(len (G1,(G1,G2,1,W2),1,W1)) - 0 is non empty V28() V29() V30() ext-real positive non negative set
(G1,(G1,G2,1,W2),1,W1) . vs is set
1 + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(G1,G2,1,W2) . (1 + vs) is set
G2 . (1 + vs) is set
(G1,G2,1,W1) . vs is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) is Element of the_Vertices_of G1
G2 . (len G2) is set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,(G1,G2,W1),W2,y) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,W2,y) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(W2,y) -cut G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len (G1,(G1,G2,W1),W2,y) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,(G1,G2,W1),W2,y)) + W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
len (G1,G2,W2,y) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W2,y)) + W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(W2,y) -cut (G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
dom (G1,G2,W2,y) is finite Element of K32(NAT)
vs - 1 is V28() V29() V30() ext-real set
(len (G1,G2,W2,y)) - 0 is non empty V28() V29() V30() ext-real positive non negative set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
dom G2 is finite Element of K32(NAT)
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len (G1,(G1,G2,W1),W2,y)) - 0 is non empty V28() V29() V30() ext-real positive non negative set
(G1,(G1,G2,W1),W2,y) . vs is set
(G1,G2,W1) . (W2 + vs) is set
(G1,G2,W2,y) . vs is set
G2 . (W2 + vs) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,1,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,1,W1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
dom (G1,G2,1,W1) is finite Element of K32(NAT)
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,1,W1) . W2 is set
G2 . W2 is set
len (G1,G2,1,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,1,W1)) - 0 is non empty V28() V29() V30() ext-real positive non negative set
W2 - 1 is V28() V29() V30() ext-real set
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W1,W2)) + W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len G2) + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1,G2,1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,W2,(len G2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,1,W1),(G1,G2,W2,(len G2))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,W2,(len G2)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W2,(len G2))) + W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len G2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1,(G1,G2,W2,(len G2))) is Element of the_Vertices_of G1
(G1,G2,W2,(len G2)) . 1 is set
len (G1,G2,1,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,1,W1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1,(G1,G2,1,W1)) is Element of the_Vertices_of G1
(G1,G2,1,W1) . (len (G1,G2,1,W1)) is set
len (G1,(G1,G2,1,W1),(G1,G2,W2,(len G2))) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,(G1,G2,1,W1),(G1,G2,W2,(len G2)))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
- W2 is V28() V29() V30() ext-real non positive set
((len G2) + 1) + (- W2) is V28() V29() V30() ext-real set
W1 + (((len G2) + 1) + (- W2)) is V28() V29() V30() ext-real set
((len G2) + W1) + (- W2) is V28() V29() V30() ext-real set
(((len G2) + W1) + (- W2)) + 1 is V28() V29() V30() ext-real set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
y is set
vs is set
(G1,G2,1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W2,(len G2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G2 . W1 is set
G2 . W2 is set
(G1,(G1,G2,W2,(len G2))) is Element of the_Vertices_of G1
len (G1,G2,W2,(len G2)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W2,(len G2)) . (len (G1,G2,W2,(len G2))) is set
(G1,G2) is Element of the_Vertices_of G1
G2 . (len G2) is set
(G1,(G1,G2,1,W1),(G1,G2,W2,(len G2))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,1,W1)) is Element of the_Vertices_of G1
(G1,G2,1,W1) . 1 is set
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,(G1,G2,1,W1)) is Element of the_Vertices_of G1
len (G1,G2,1,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,1,W1) . (len (G1,G2,1,W1)) is set
(G1,(G1,G2,W2,(len G2))) is Element of the_Vertices_of G1
(G1,G2,W2,(len G2)) . 1 is set
G2 . W1 is set
G2 . W2 is set
G2 . W1 is set
G2 . W2 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
(len (G1,G2,W1,W2)) + W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len G2) + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
((len (G1,G2,W1,W2)) + W2) - W2 is V28() V29() V30() ext-real set
((len G2) + W1) - W1 is V28() V29() V30() ext-real set
G2 . W1 is set
G2 . W2 is set
G2 . W1 is set
G2 . W2 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
(G1,G2,1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,W1,(len G2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,1,W1),(G1,G2,W1,(len G2))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,1,(len G2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
(G1,G2,1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,1,W1)) is Element of the_Vertices_of G1
len (G1,G2,1,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,1,W1) . (len (G1,G2,1,W1)) is set
(G1,G2,W2,(len G2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W2,(len G2))) is Element of the_Vertices_of G1
(G1,G2,W2,(len G2)) . 1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . y is set
G2 . vs is set
Seg y is non empty finite y -element Element of K32(NAT)
(G1,G2,y,vs) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,y,vs) . vs is set
G2 . vs is set
(G1,G2,1,y) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,1,y) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
dom (G1,G2,1,y) is finite Element of K32(NAT)
(G1,G2,vs,(len G2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,1,y),(G1,G2,vs,(len G2))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,1,y) . vs is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,W2,(len G2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,1,W1)) is Element of the_Vertices_of G1
len (G1,G2,1,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,1,W1) . (len (G1,G2,1,W1)) is set
(G1,(G1,G2,W2,(len G2))) is Element of the_Vertices_of G1
(G1,G2,W2,(len G2)) . 1 is set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) . vs is set
vs - W1 is V28() V29() V30() ext-real set
(vs - W1) + W2 is V28() V29() V30() ext-real set
G2 . ((vs - W1) + W2) is set
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
(len (G1,G2,1,W1)) + n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len (G1,G2,W1,W2)) + W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len G2) + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W1 + n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(W1 + n) + W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W1 + (len G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
n + W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(n + W2) + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
((n + W2) + W1) - W1 is V28() V29() V30() ext-real set
((len G2) + W1) - W1 is non empty V28() V29() V30() ext-real non even set
len (G1,G2,W2,(len G2)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W2,(len G2))) + W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len G2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(n + W2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
n + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(n + 1) + W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
((n + 1) + W2) - W2 is V28() V29() V30() ext-real set
((len (G1,G2,W2,(len G2))) + W2) - W2 is non empty V28() V29() V30() ext-real non even set
(len (G1,G2,W2,(len G2))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((len (G1,G2,W2,(len G2))) + 1) - 1 is non empty V28() V29() V30() ext-real non even set
(n + 1) - 1 is V28() V29() V30() ext-real set
(G1,(G1,G2,1,W1),(G1,G2,W2,(len G2))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,W2,(len G2)) . (n + 1) is set
G2 . (n + W2) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((len G2) + W1) - W2 is non empty V28() V29() V30() ext-real non even set
(len (G1,G2,W1,W2)) + W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G2 . W1 is set
(G1,G2,1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,W1,(len G2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,1,1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,1,1),(G1,G2,W1,(len G2))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,1,1)) is Element of the_Vertices_of G1
len (G1,G2,1,1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,1,1) . (len (G1,G2,1,1)) is set
(G1,(G1,G2,W1,(len G2))) is Element of the_Vertices_of G1
(G1,G2,W1,(len G2)) . 1 is set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
len (G1,G2,1,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
dom (G1,G2,1,W1) is finite Element of K32(NAT)
dom (G1,G2,1,1) is finite Element of K32(NAT)
(G1,G2,1,W1) . W2 is set
(G1,G2,1,1) . W2 is set
(G1,G2,1) is Element of the_Vertices_of G1
<*(G1,G2,1)*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
<*(G1,G2,1)*> . 1 is set
(G1,G2,W1,(len G2)) . W2 is set
len (G1,G2,W1,(len G2)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(len (G1,G2,1,1)) + y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(len (G1,G2,1,1)) + y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(G1,G2,1,W1) . W2 is set
(G1,G2,W1,(len G2)) . W2 is set
dom (G1,G2,1,1) is finite Element of K32(NAT)
len (G1,G2,W1,(len G2)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,1,W1) . W2 is set
(G1,G2,W1,(len G2)) . W2 is set
(G1,G2,1,W1) . W2 is set
(G1,G2,W1,(len G2)) . W2 is set
(len (G1,G2,1,W1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
len (G1,G2,W1,(len G2)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,1,1)) + (len (G1,G2,W1,(len G2))) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len (G1,G2,W1,(len G2))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1,W2)) is Element of the_Vertices_of G1
(G1,G2,W1,W2) . 1 is set
(G1,(G1,G2,W1,W2)) is Element of the_Vertices_of G1
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) . (len (G1,G2,W1,W2)) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
dom (G1,G2,W1,W2) is finite Element of K32(NAT)
Seg W1 is non empty finite W1 -element Element of K32(NAT)
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W2 is set
W1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
<*W1,W2*> is non empty Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like set
G2 ^ <*W1,W2*> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
vs is Element of the_Vertices_of G1
<*(G1,G2),W1,W2*> is non empty Relation-like NAT -defined Function-like finite 3 -element FinSequence-like FinSubsequence-like set
len (G1,(G1,G2),((G1,G2) .adj W1),W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,(G1,G2),((G1,G2) .adj W1),W1) . 3 is set
(G1,(G1,G2),((G1,G2) .adj W1),W1) . 2 is set
(2,2) -cut (G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
<*W1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
((2 + 1),3) -cut (G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
<*W1*> ^ (((2 + 1),3) -cut (G1,(G1,G2),((G1,G2) .adj W1),W1)) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
((1 + 1),3) -cut (G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
<*W2*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
<*W1*> ^ <*W2*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like set
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(2,3) -cut (G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
(G1,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) . 1 is set
G2 ^' (G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
(2,(len (G1,(G1,G2),((G1,G2) .adj W1),W1))) -cut (G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
G2 ^ ((2,(len (G1,(G1,G2),((G1,G2) .adj W1),W1))) -cut (G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
G2 ^ ((2,3) -cut (G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
W2 is set
W1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1)) is Element of the_Vertices_of G1
(G1,G2,W1) . 1 is set
(G1,(G1,G2,W1)) is Element of the_Vertices_of G1
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) . (len (G1,G2,W1)) is set
vs is Element of the_Vertices_of G1
(G1,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Element of the_Vertices_of G1
len (G1,(G1,G2),((G1,G2) .adj W1),W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,(G1,G2),((G1,G2) .adj W1),W1) . (len (G1,(G1,G2),((G1,G2) .adj W1),W1)) is set
(G1,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) . 1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(len G2) + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is set
W1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is Element of the_Vertices_of G1
(G1,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) . 1 is set
(len (G1,G2,W1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
len (G1,(G1,G2),((G1,G2) .adj W1),W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + (len (G1,(G1,G2),((G1,G2) .adj W1),W1)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
<*(G1,G2),W1,W2*> is non empty Relation-like NAT -defined Function-like finite 3 -element FinSequence-like FinSubsequence-like set
(len G2) + 3 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(len G2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len G2) + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
dom G2 is finite Element of K32(NAT)
W2 is set
W1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,W1) . ((len G2) + 1) is set
(G1,G2,W1) . ((len G2) + 2) is set
<*W1,W2*> is non empty Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like set
<*W1,W2*> . 1 is set
G2 ^ <*W1,W2*> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom <*W1,W2*> is non empty finite 2 -element Element of K32(NAT)
<*W1,W2*> . 2 is set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1) . vs is set
G2 . vs is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is set
y is set
vs is set
W1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
dom (G1,G2) is finite Element of K32(NAT)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W1 div 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G2 . W1 is set
(G1,G2) . (W1 div 2) is set
2 * (W1 div 2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
0 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
2 * 0 is empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V21() V22() V23() V25() V26() V27() V28() V29() V30() ext-real non positive non negative finite finite-yielding V49() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V86() even Element of NAT
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len (G1,G2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(2 * (len (G1,G2))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
0 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
dom (G1,G2) is finite Element of K32(NAT)
dom G2 is finite Element of K32(NAT)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(len (G1,G2)) * 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
((len (G1,G2)) * 2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 + W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(2 * W1) div 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) - 1 is V28() V29() V30() ext-real even set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W2 div 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (W2 div 2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
2 * (len (G1,G2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len (G1,G2))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,1,W1)) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y is set
vs is set
vs is set
[vs,vs] is V1() set
(G1,(G1,G2,1,W1)) . vs is set
dom (G1,(G1,G2,1,W1)) is finite Element of K32(NAT)
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
len (G1,(G1,G2,1,W1)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
dom (G1,G2,1,W1) is finite Element of K32(NAT)
len (G1,G2,1,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
dom G2 is finite Element of K32(NAT)
dom (G1,G2) is finite Element of K32(NAT)
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,1,W1) . (2 * vs) is set
G2 . (2 * vs) is set
(G1,G2) . vs is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is set
W1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1)) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
<*W1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
(G1,G2) ^ <*W1*> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len (G1,(G1,G2,W1)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len (G1,(G1,G2,W1))) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len (G1,(G1,G2,W1)))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len (G1,G2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len (G1,G2))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
2 + ((2 * (len (G1,G2))) + 1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
2 * ((len (G1,G2)) + 1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
len ((G1,G2) ^ <*W1*>) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
len <*W1*> is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len (G1,G2)) + (len <*W1*>) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
2 * (len ((G1,G2) ^ <*W1*>)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
(G1,(G1,G2,W1)) . vs is set
2 * vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(G1,G2,W1) . (2 * vs) is set
dom ((G1,G2) ^ <*W1*>) is non empty finite Element of K32(NAT)
dom (G1,G2) is finite Element of K32(NAT)
dom G2 is finite Element of K32(NAT)
((G1,G2) ^ <*W1*>) . vs is set
(G1,G2) . vs is set
G2 . (2 * vs) is set
dom <*W1*> is non empty trivial finite 1 -element Element of K32(NAT)
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
(len (G1,G2)) + vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(len (G1,G2)) + vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
{1} is non empty trivial finite V49() 1 -element Element of K32(NAT)
((2 * (len (G1,G2))) + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len G2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((G1,G2) ^ <*W1*>) . vs is set
<*W1*> . 1 is set
dom (G1,G2) is finite Element of K32(NAT)
dom <*W1*> is non empty trivial finite 1 -element Element of K32(NAT)
((G1,G2) ^ <*W1*>) . vs is set
((G1,G2) ^ <*W1*>) . vs is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is set
dom (G1,G2) is finite Element of K32(NAT)
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
(G1,G2) . y is set
2 * y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even set
vs - 1 is non empty V28() V29() V30() ext-real non even set
y + y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
y * 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(len (G1,G2)) * 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(len G2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((len G2) + 1) - 1 is non empty V28() V29() V30() ext-real non even set
n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . n is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . y is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . y is set
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs div 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (vs div 2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
2 * (len (G1,G2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(G1,G2) . n is set
(2 * n) - 1 is non empty V28() V29() V30() ext-real non even set
G2 . ((2 * n) - 1) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is set
dom (G1,G2) is finite Element of K32(NAT)
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
(G1,G2) . y is set
2 * y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
y + y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
y * 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(len (G1,G2)) * 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
((len (G1,G2)) * 2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . vs is set
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
G2 . y is set
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
G2 . y is set
y div 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (y div 2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
2 * (len (G1,G2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len (G1,G2))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) . vs is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is set
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
G2 . y is set
y - 1 is non empty V28() V29() V30() ext-real non even set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . vs is set
vs + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (vs + 2) is set
(len G2) - 0 is non empty V28() V29() V30() ext-real positive non negative set
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(vs + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
n is Element of the_Vertices_of G1
n is Element of the_Vertices_of G1
G2 . (vs + 1) is set
(vs + 1) - 1 is non empty V28() V29() V30() ext-real non even set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
W1 is set
W2 is set
y is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is Element of the_Vertices_of G1
G2 . vs is set
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (vs + 1) is set
vs is Element of the_Vertices_of G1
G2 . (vs + 2) is set
(vs + 2) - 2 is V28() V29() V30() ext-real set
(len G2) - 0 is non empty V28() V29() V30() ext-real positive non negative set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W2 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W2 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
the_Source_of G1 is Relation-like Function-like V18( the_Edges_of G1, the_Vertices_of G1) Element of K32(K33((the_Edges_of G1),(the_Vertices_of G1)))
K33((the_Edges_of G1),(the_Vertices_of G1)) is Relation-like set
K32(K33((the_Edges_of G1),(the_Vertices_of G1))) is non empty set
W1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (W1 + 1) is set
(the_Source_of G1) . (G2 . (W1 + 1)) is set
W1 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (W1 + 2) is set
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
W1 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (W1 + 2) is set
W1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (W1 + 1) is set
(the_Source_of G1) . (G2 . (W1 + 1)) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is set
y is set
vs is set
W2 is set
(G1,G2,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) .adj W2 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W2),W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W2),W2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1,G2,W2) . ((len G2) + 1) is set
dom G2 is finite Element of K32(NAT)
(G1,G2,W2) . (len G2) is set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
((len G2) + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W2) . vs is set
the_Source_of G1 is Relation-like Function-like V18( the_Edges_of G1, the_Vertices_of G1) Element of K32(K33((the_Edges_of G1),(the_Vertices_of G1)))
K33((the_Edges_of G1),(the_Vertices_of G1)) is Relation-like set
K32(K33((the_Edges_of G1),(the_Vertices_of G1))) is non empty set
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1,G2,W2) . (vs + 1) is set
(the_Source_of G1) . ((G1,G2,W2) . (vs + 1)) is set
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1,G2,W2) . vs is set
G2 . vs is set
(G1,G2,W2) . (vs + 1) is set
G2 . (vs + 1) is set
the_Source_of G1 is Relation-like Function-like V18( the_Edges_of G1, the_Vertices_of G1) Element of K32(K33((the_Edges_of G1),(the_Vertices_of G1)))
K33((the_Edges_of G1),(the_Vertices_of G1)) is Relation-like set
K32(K33((the_Edges_of G1),(the_Vertices_of G1))) is non empty set
(the_Source_of G1) . ((G1,G2,W2) . (vs + 1)) is set
(G1,G2,W2) . vs is set
the_Source_of G1 is Relation-like Function-like V18( the_Edges_of G1, the_Vertices_of G1) Element of K32(K33((the_Edges_of G1),(the_Vertices_of G1)))
K33((the_Edges_of G1),(the_Vertices_of G1)) is Relation-like set
K32(K33((the_Edges_of G1),(the_Vertices_of G1))) is non empty set
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1,G2,W2) . (vs + 1) is set
(the_Source_of G1) . ((G1,G2,W2) . (vs + 1)) is set
(G1,G2,W2) . vs is set
the_Source_of G1 is Relation-like Function-like V18( the_Edges_of G1, the_Vertices_of G1) Element of K32(K33((the_Edges_of G1),(the_Vertices_of G1)))
K33((the_Edges_of G1),(the_Vertices_of G1)) is Relation-like set
K32(K33((the_Edges_of G1),(the_Vertices_of G1))) is non empty set
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1,G2,W2) . (vs + 1) is set
(the_Source_of G1) . ((G1,G2,W2) . (vs + 1)) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs - 1 is V28() V29() V30() ext-real even set
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W1 + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
dom G2 is finite Element of K32(NAT)
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len G2) - 0 is non empty V28() V29() V30() ext-real positive non negative set
(vs + vs) - 1 is non empty V28() V29() V30() ext-real non even set
(len (G1,G2,W1,W2)) - 0 is non empty V28() V29() V30() ext-real positive non negative set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) . (vs + 1) is set
W1 + vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G2 . (W1 + vs) is set
vs + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) . (vs + 2) is set
(vs + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) . ((vs + 1) + 1) is set
(vs - 1) + 1 is non empty V28() V29() V30() ext-real non even set
((vs - 1) + 1) + 1 is V28() V29() V30() ext-real even set
W1 + (((vs - 1) + 1) + 1) is V28() V29() V30() ext-real set
G2 . (W1 + (((vs - 1) + 1) + 1)) is set
(W1 + vs) + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G2 . ((W1 + vs) + 2) is set
(G1,G2,W1,W2) . (vs + 1) is set
(W1 + vs) - 1 is V28() V29() V30() ext-real set
((W1 + vs) - 1) + 1 is V28() V29() V30() ext-real set
G2 . (((W1 + vs) - 1) + 1) is set
(W1 + vs) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G2 . ((W1 + vs) + 1) is set
(G1,G2,W1,W2) . vs is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
0 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
2 * (len (G1,G2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(2 * (len (G1,G2))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(2 * 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is Element of the_Vertices_of G1
(G1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
<*W1*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
W1 is Element of the_Vertices_of G1
(G1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
<*W1*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W2 div 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
dom (G1,G2) is finite Element of K32(NAT)
G2 . W1 is set
W1 div 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2) . (W1 div 2) is set
2 * (W1 div 2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
G2 . W2 is set
(G1,G2) . (W2 div 2) is set
W1 is set
W2 is set
(G1,G2) . W1 is set
(G1,G2) . W2 is set
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
G2 . (2 * y) is set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
G2 . (2 * vs) is set
dom G2 is finite Element of K32(NAT)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(G1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
len (G1,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len W1) - y is non empty V28() V29() V30() ext-real non even set
(len W1) - vs is non empty V28() V29() V30() ext-real non even set
((len W1) - y) + 1 is V28() V29() V30() ext-real even set
((len W1) - vs) + 1 is V28() V29() V30() ext-real even set
dom (G1,W1) is finite Element of K32(NAT)
dom W1 is finite Element of K32(NAT)
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 - y is non empty V28() V29() V30() ext-real non even set
(W2 - y) + 1 is V28() V29() V30() ext-real even set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(G1,W1) . vs is set
W1 . (((len W1) - vs) + 1) is set
W2 - vs is non empty V28() V29() V30() ext-real non even set
(W2 - vs) + 1 is V28() V29() V30() ext-real even set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(G1,W1) . y is set
W1 . (((len W1) - y) + 1) is set
(G1,(G1,G2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev (G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs - 1 is non empty V28() V29() V30() ext-real non even set
vs - 1 is non empty V28() V29() V30() ext-real non even set
n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
n + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len (G1,G2,W1,W2)) - 0 is non empty V28() V29() V30() ext-real positive non negative set
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1,G2,W1,W2) . (vs + 1) is set
W1 + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G2 . (W1 + vs) is set
n + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1,G2,W1,W2) . (n + 1) is set
W1 + n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G2 . (W1 + n) is set
dom G2 is finite Element of K32(NAT)
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (y + vs) is set
y + n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (y + n) is set
(G1,G2,W1,W2) . vs is set
(G1,G2,W1,W2) . vs is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) .edgesInOut() is Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is finite Element of K32((the_Edges_of G1))
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
W1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
dom G2 is finite Element of K32(NAT)
(G1,G2,W1) . vs is set
G2 . vs is set
(G1,G2,W1) . vs is set
G2 . vs is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(vs + 1) - 1 is V28() V29() V30() ext-real even set
(len (G1,G2,W1)) - 1 is V28() V29() V30() ext-real even set
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len G2) + (1 + 1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
((len G2) + (1 + 1)) - 1 is V28() V29() V30() ext-real set
(len G2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1,G2,W1) . vs is set
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(vs + 1) - 1 is V28() V29() V30() ext-real even set
((len G2) + 1) - 1 is non empty V28() V29() V30() ext-real non even set
dom G2 is finite Element of K32(NAT)
(G1,G2,W1) . vs is set
G2 . vs is set
(G1,G2,W1) . vs is set
(G1,G2,W1) . vs is set
(G1,G2,W1) . vs is set
(G1,G2,W1) . vs is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is Element of the_Vertices_of G1
(G1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
<*W1*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
1 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
2 * 0 is empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V21() V22() V23() V25() V26() V27() V28() V29() V30() ext-real non positive non negative finite finite-yielding V49() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V86() even Element of NAT
(2 * 0) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G2 . W1 is set
G2 . W2 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
G2 is set
W2 is set
W1 is set
(G1,G2,W2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
len (G1,G2,W2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W2,W1) . vs is set
(G1,G2,W2,W1) . vs is set
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W2,W1) . vs is set
(G1,G2,W2,W1) . vs is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
len (G1,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,W1) . y is set
(G1,W1) . vs is set
dom (G1,W1) is finite Element of K32(NAT)
(len W1) - y is V28() V29() V30() ext-real even set
((len W1) - y) + 1 is non empty V28() V29() V30() ext-real non even set
dom W1 is finite Element of K32(NAT)
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 - y is V28() V29() V30() ext-real even set
(W2 - y) + 1 is non empty V28() V29() V30() ext-real non even set
(len W1) - vs is V28() V29() V30() ext-real even set
((len W1) - vs) + 1 is non empty V28() V29() V30() ext-real non even set
W2 - vs is V28() V29() V30() ext-real even set
(W2 - vs) + 1 is non empty V28() V29() V30() ext-real non even set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (((len W1) - vs) + 1) is set
W1 . vs is set
W1 . vs is set
- y is V28() V29() V30() ext-real non positive set
1 + (- y) is V28() V29() V30() ext-real set
(len W1) + (1 + (- y)) is V28() V29() V30() ext-real set
(G1,(G1,G2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev (G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) . vs is set
(G1,G2,W1,W2) . vs is set
vs - 1 is V28() V29() V30() ext-real even set
vs - 1 is V28() V29() V30() ext-real even set
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
n + W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs + W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(len (G1,G2,W1,W2)) - 0 is non empty V28() V29() V30() ext-real positive non negative set
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) . (vs + 1) is set
W1 + vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G2 . (W1 + vs) is set
n + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) . (n + 1) is set
W1 + n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G2 . (W1 + n) is set
dom G2 is finite Element of K32(NAT)
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y + n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
1 + 0 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(W1 + 1) - 1 is V28() V29() V30() ext-real set
(len (G1,G2,W1,W2)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
y + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
W2 is set
W1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .edgesInOut() is Element of K32((the_Edges_of G1))
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) . vs is set
(G1,G2,W1) . vs is set
dom G2 is finite Element of K32(NAT)
G2 . vs is set
G2 . vs is set
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(y + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len G2) + (1 + 1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len G2) + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) . ((len G2) + 2) is set
(len G2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((len G2) + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
dom G2 is finite Element of K32(NAT)
G2 . vs is set
n is Element of the_Vertices_of G1
(G1,n) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
<*n*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
1 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(vs + 1) - 1 is non empty V28() V29() V30() ext-real non even set
3 - 1 is V28() V29() V30() ext-real set
2 - 1 is V28() V29() V30() ext-real set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
dom G2 is finite Element of K32(NAT)
G2 . W1 is set
G2 . W2 is set
W2 - 1 is non empty V28() V29() V30() ext-real non even set
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (W2 + 1) is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . y is set
W1 - 1 is non empty V28() V29() V30() ext-real non even set
W1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (W1 + 1) is set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . vs is set
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
(G1,G2,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
W2 is set
W1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . y is set
(G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is Element of the_Vertices_of G1
(G1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
<*W1*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
1 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(W1 + 2) - 2 is V28() V29() V30() ext-real set
3 - 2 is V28() V29() V30() ext-real set
2 * 0 is empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V21() V22() V23() V25() V26() V27() V28() V29() V30() ext-real non positive non negative finite finite-yielding V49() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V86() even Element of NAT
(2 * 0) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len (G1,G2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len (G1,G2))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
0 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
the Element of the_Vertices_of G1 is Element of the_Vertices_of G1
(G1, the Element of the_Vertices_of G1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
<* the Element of the_Vertices_of G1*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
G2 is Element of the_Vertices_of G1
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
<*G2*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
G2 is set
W2 is set
W1 is set
(G1,G2,W2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
choose (the_Vertices_of G1) is Element of the_Vertices_of G1
(G1,(choose (the_Vertices_of G1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1) (G1) (G1)
<*(choose (the_Vertices_of G1))*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
G2 is set
W1 is set
(G1,G2,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
(G1,(G1,G2,G2,W1)) is Element of the_Vertices_of G1
len (G1,G2,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,G2,W1) . (len (G1,G2,G2,W1)) is set
(G1,(G1,G2,G2,W1)) is Element of the_Vertices_of G1
(G1,G2,G2,W1) . 1 is set
choose (the_Vertices_of G1) is Element of the_Vertices_of G1
(G1,(choose (the_Vertices_of G1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1) (G1) (G1)
<*(choose (the_Vertices_of G1))*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,(G1,G2)) is Element of the_Vertices_of G1
len (G1,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) . (len (G1,G2)) is set
(G1,(G1,G2)) is Element of the_Vertices_of G1
(G1,G2) . 1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1)
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len (G1,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
Rev G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(G1,W1) is Element of the_Vertices_of G1
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (len W1) is set
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,(G1,G2,W1)) is Element of the_Vertices_of G1
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) . (len (G1,G2,W1)) is set
(G1,(G1,G2,W1)) is Element of the_Vertices_of G1
(G1,G2,W1) . 1 is set
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
dom (G1,G2,W1) is finite Element of K32(NAT)
dom G2 is finite Element of K32(NAT)
(G1,G2,W1) . y is set
G2 . y is set
y + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) . (y + 2) is set
G2 . (y + 2) is set
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1,G2,W1) . (y + 1) is set
G2 . (y + 1) is set
(len (G1,G2,W1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len W1) + y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
1 + y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
2 * 0 is empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V21() V22() V23() V25() V26() V27() V28() V29() V30() ext-real non positive non negative finite finite-yielding V49() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V86() even Element of NAT
(2 * 0) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . ((2 * 0) + 1) is set
((2 * 0) + 1) + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (((2 * 0) + 1) + 2) is set
((2 * 0) + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W1 . (((2 * 0) + 1) + 1) is set
(len G2) + 0 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
y + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) . (y + 2) is set
2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W1 . (2 + 1) is set
(G1,G2,W1) . (y + 1) is set
W1 . (1 + 1) is set
y + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) . (y + 2) is set
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1,G2,W1) . (y + 1) is set
y + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) . (y + 2) is set
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1,G2,W1) . (y + 1) is set
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(len G2) + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(len G2) + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(G1,G2,W1) . y is set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (vs + 1) is set
(len (G1,G2,W1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len W1) + (len G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
vs + (len G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
1 + (vs + (len G2)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((len W1) + (len G2)) - (len G2) is non empty V28() V29() V30() ext-real non even set
(vs + 1) + (len G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((vs + 1) + (len G2)) - (len G2) is non empty V28() V29() V30() ext-real non even set
(vs + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(y + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + ((vs + 1) + 1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(vs + 1) + (1 + 1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W1 . ((vs + 1) + (1 + 1)) is set
((vs + 1) + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (((vs + 1) + 1) + 1) is set
y + (1 + 1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(G1,G2,W1) . (y + (1 + 1)) is set
(G1,G2,W1) . (y + 1) is set
W1 . ((vs + 1) + 1) is set
y + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) . (y + 2) is set
dom G2 is finite Element of K32(NAT)
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) . y is set
y + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) . (y + 2) is set
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1,G2,W1) . (y + 1) is set
(G1,G2,W1) . y is set
y + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) . (y + 2) is set
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1,G2,W1) . (y + 1) is set
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1)
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1)
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + (len W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len G2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W1,W2)) + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len (G1,G2,W1,W2)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) . vs is set
(G1,G2,W1,W2) . vs is set
vs - 1 is V28() V29() V30() ext-real even set
vs - 1 is V28() V29() V30() ext-real even set
(len (G1,G2,W1,W2)) - 0 is non empty V28() V29() V30() ext-real positive non negative set
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
n + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) . (n + 1) is set
W1 + n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G2 . (W1 + n) is set
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W1 + n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
dom G2 is finite Element of K32(NAT)
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs + n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs + n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
n + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) . (n + 1) is set
G2 . (W1 + n) is set
n + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
n + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1,W2)) is Element of the_Vertices_of G1
(G1,G2,W1,W2) . 1 is set
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,(G1,G2,W1,W2)) is Element of the_Vertices_of G1
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) . (len (G1,G2,W1,W2)) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
(G1,G2,1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
(G1,G2,W2,(len G2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
(G1,(G1,G2,1,W1),(G1,G2,W2,(len G2))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
(G1,G2,1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1)
(G1,G2,W2,(len G2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1)
(G1,(G1,G2,1,W1),(G1,G2,W2,(len G2))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(G1,G2,W1,W2) . vs is set
(G1,G2,W1,W2) . n is set
dom (G1,G2,W1,W2) is finite Element of K32(NAT)
Seg W1 is finite W1 -element Element of K32(NAT)
G2 . vs is set
G2 . n is set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
n - vs is non empty V28() V29() V30() ext-real non even set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(n - vs) + vs is V28() V29() V30() ext-real even set
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
G2 . n is set
W1 - W1 is V28() V29() V30() ext-real set
W2 - W1 is V28() V29() V30() ext-real set
n - n is V28() V29() V30() ext-real even set
vs - n is V28() V29() V30() ext-real even set
(W2 - W1) + n is V28() V29() V30() ext-real set
((W2 - W1) + n) - n is V28() V29() V30() ext-real set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs - vs is non empty V28() V29() V30() ext-real non even set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(vs - vs) + vs is V28() V29() V30() ext-real even set
vs - vs is V28() V29() V30() ext-real even set
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
G2 . n is set
Seg W1 is finite W1 -element Element of K32(NAT)
n - vs is non empty V28() V29() V30() ext-real non even set
(n - vs) + vs is V28() V29() V30() ext-real even set
xaa1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
G2 . xaa1 is set
x is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs + x is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
x is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
n + x is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs + x is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
Seg W1 is finite W1 -element Element of K32(NAT)
Seg W1 is finite W1 -element Element of K32(NAT)
G2 . W1 is set
G2 . W2 is set
G2 . W1 is set
G2 . W2 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) . vs is set
(G1,G2,W1,W2) . n is set
dom (G1,G2,W1,W2) is finite Element of K32(NAT)
Seg W1 is finite W1 -element Element of K32(NAT)
G2 . vs is set
G2 . n is set
n - W1 is V28() V29() V30() ext-real set
(n - W1) + W2 is V28() V29() V30() ext-real set
G2 . ((n - W1) + W2) is set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
n - vs is V28() V29() V30() ext-real even set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(n - vs) + vs is non empty V28() V29() V30() ext-real non even set
(n - W1) + W1 is V28() V29() V30() ext-real set
n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W1,W2)) + W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
((n - W1) + W2) + W1 is V28() V29() V30() ext-real set
n + W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs - vs is V28() V29() V30() ext-real even set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(vs - vs) + vs is non empty V28() V29() V30() ext-real non even set
vs - W1 is V28() V29() V30() ext-real set
(vs - W1) + W2 is V28() V29() V30() ext-real set
G2 . ((vs - W1) + W2) is set
Seg W1 is finite W1 -element Element of K32(NAT)
n - vs is V28() V29() V30() ext-real even set
(n - vs) + vs is non empty V28() V29() V30() ext-real non even set
W2 - W1 is V28() V29() V30() ext-real set
n + (W2 - W1) is V28() V29() V30() ext-real set
vs + (W2 - W1) is V28() V29() V30() ext-real set
x is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
n - W1 is V28() V29() V30() ext-real set
(n - W1) + W2 is V28() V29() V30() ext-real set
G2 . ((n - W1) + W2) is set
(len (G1,G2,W1,W2)) + W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
((n - W1) + W2) + W1 is V28() V29() V30() ext-real set
n + W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
n - vs is V28() V29() V30() ext-real even set
1 - 1 is V28() V29() V30() ext-real set
xaa1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
Seg W1 is finite W1 -element Element of K32(NAT)
Seg W1 is finite W1 -element Element of K32(NAT)
G2 . W1 is set
G2 . W2 is set
G2 . W1 is set
G2 . W2 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
K32((G1,G2)) is non empty finite V49() set
W1 is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSubsequence-like Element of K32((G1,G2))
Seq W1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
K32((G1,G2)) is non empty finite V49() set
W1 is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSubsequence-like Element of K32((G1,G2))
Seq W1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,G2)
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,W1)
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
K32((G1,W1)) is non empty finite V49() set
vs is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSubsequence-like Element of K32((G1,W1))
Seq vs is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
K32((G1,G2)) is non empty finite V49() set
n is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSubsequence-like Element of K32((G1,G2))
Seq n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom n is finite Element of K32(NAT)
Sgm (dom n) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
dom vs is finite Element of K32(NAT)
(Sgm (dom n)) | (dom vs) is Relation-like NAT -defined dom vs -defined NAT -defined NAT -valued Function-like finite FinSubsequence-like Element of K32(K33(NAT,NAT))
K33(NAT,NAT) is non empty non trivial Relation-like non finite set
K32(K33(NAT,NAT)) is non empty non trivial non finite set
rng ((Sgm (dom n)) | (dom vs)) is finite Element of K32(NAT)
n | (rng ((Sgm (dom n)) | (dom vs))) is Relation-like NAT -defined rng ((Sgm (dom n)) | (dom vs)) -defined NAT -defined the_Edges_of G1 -valued Function-like finite FinSubsequence-like set
x is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSubsequence-like Element of K32((G1,G2))
Seq x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,W1) is Element of the_Vertices_of G1
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (len W1) is set
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,W1) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
K32((G1,W1)) is non empty finite V49() set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len (G1,G2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
len (G1,W1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len (G1,W1)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W2 is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSubsequence-like Element of K32((G1,W1))
Seq W2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(2 * (len (G1,G2))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(2 * (len (G1,W1))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1,W2)) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) - vs is V28() V29() V30() ext-real even set
len (G1,(G1,G2,W1,W2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
Seg (len (G1,(G1,G2,W1,W2))) is finite len (G1,(G1,G2,W1,W2)) -element Element of K32(NAT)
dom (G1,(G1,G2,W1,W2)) is finite Element of K32(NAT)
(len G2) - 1 is V28() V29() V30() ext-real even set
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs - 1 is V28() V29() V30() ext-real even set
xaa1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
xaa1 div 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
{ b₁ where b₁ is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT : ( 1 <= b₁ & b₁ <= xaa1 div 2 ) } is set
x is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
x div 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
n div 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
{ b₁ where b₁ is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT : ( x div 2 <= b₁ & b₁ <= n div 2 ) } is set
{ b₁ where b₁ is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT : ( 1 <= b₁ & b₁ <= xaa1 div 2 ) } \/ { b₁ where b₁ is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT : ( x div 2 <= b₁ & b₁ <= n div 2 ) } is set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) | ( { b₁ where b₁ is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT : ( 1 <= b₁ & b₁ <= xaa1 div 2 ) } \/ { b₁ where b₁ is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT : ( x div 2 <= b₁ & b₁ <= n div 2 ) } ) is Relation-like NAT -defined { b₁ where b₁ is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT : ( 1 <= b₁ & b₁ <= xaa1 div 2 ) } \/ { b₁ where b₁ is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT : ( x div 2 <= b₁ & b₁ <= n div 2 ) } -defined NAT -defined the_Edges_of G1 -valued Function-like finite FinSubsequence-like Element of K32(K33(NAT,(the_Edges_of G1)))
K33(NAT,(the_Edges_of G1)) is Relation-like set
K32(K33(NAT,(the_Edges_of G1))) is non empty set
2 * (xaa1 div 2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
2 * (x div 2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
2 - 1 is V28() V29() V30() ext-real set
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(W2 + 1) - 1 is V28() V29() V30() ext-real set
(x div 2) - 1 is V28() V29() V30() ext-real set
2 * (n div 2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W2 is set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
xaa1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 + W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
dom G2 is finite Element of K32(NAT)
dom (G1,G2) is finite Element of K32(NAT)
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
n + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
dom G2 is finite Element of K32(NAT)
dom (G1,G2) is finite Element of K32(NAT)
dom (G1,G2) is finite Element of K32(NAT)
dom (G1,G2) is finite Element of K32(NAT)
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
Seg (len (G1,G2)) is finite len (G1,G2) -element Element of K32(NAT)
W2 is finite set
0 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
0 + (xaa1 div 2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
{ b₁ where b₁ is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT : ( 0 + 1 <= b₁ & b₁ <= 0 + (xaa1 div 2) ) } is set
(dom (G1,G2)) /\ ( { b₁ where b₁ is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT : ( 1 <= b₁ & b₁ <= xaa1 div 2 ) } \/ { b₁ where b₁ is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT : ( x div 2 <= b₁ & b₁ <= n div 2 ) } ) is finite Element of K32(NAT)
dom ((G1,G2) | ( { b₁ where b₁ is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT : ( 1 <= b₁ & b₁ <= xaa1 div 2 ) } \/ { b₁ where b₁ is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT : ( x div 2 <= b₁ & b₁ <= n div 2 ) } )) is finite Element of K32(( { b₁ where b₁ is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT : ( 1 <= b₁ & b₁ <= xaa1 div 2 ) } \/ { b₁ where b₁ is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT : ( x div 2 <= b₁ & b₁ <= n div 2 ) } ))
K32(( { b₁ where b₁ is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT : ( 1 <= b₁ & b₁ <= xaa1 div 2 ) } \/ { b₁ where b₁ is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT : ( x div 2 <= b₁ & b₁ <= n div 2 ) } )) is non empty set
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
n div 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (n div 2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
n + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is finite set
W2 is set
xa is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
card W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(n div 2) - (x div 2) is V28() V29() V30() ext-real set
W2 is finite set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(x div 2) + W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
{ b₁ where b₁ is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT : ( x div 2 <= b₁ & b₁ <= (x div 2) + W2 ) } is set
card W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W2 is finite set
card W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is finite set
card W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
K32((G1,G2)) is non empty finite V49() set
xa is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSubsequence-like Element of K32((G1,G2))
Seq xa is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom xa is finite Element of K32(NAT)
Sgm (dom xa) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom xa)) * xa is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite set
es is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(n div 2) - es is V28() V29() V30() ext-real set
2 * es is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
((W2 + 1) - 1) - 1 is V28() V29() V30() ext-real set
es + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
xb is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
es + xb is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
{ b₁ where b₁ is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT : ( es + 1 <= b₁ & b₁ <= es + xb ) } is set
x9 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
x is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
k is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
k is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * k is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
xaa1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(2 * k) + 0 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * k is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
x9 is set
x is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
card W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
x9 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
x9 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
x is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
x + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
card W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
card W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
card W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
Sgm W2 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
dom (Sgm W2) is finite Element of K32(NAT)
Seg (xaa1 div 2) is finite xaa1 div 2 -element Element of K32(NAT)
len (Sgm W2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
2 * (len (G1,(G1,G2,W1,W2))) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len (G1,(G1,G2,W1,W2)))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
((len G2) + W1) - W2 is V28() V29() V30() ext-real set
W2 /\ W2 is finite set
x9 is set
x is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
k is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * k is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
2 * x is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * x) + 0 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is finite set
card W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(xaa1 div 2) + (n div 2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
rng (Sgm (dom xa)) is finite Element of K32(NAT)
dom (Seq xa) is finite Element of K32(NAT)
Sgm W2 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
dom (Sgm W2) is finite Element of K32(NAT)
Seg (card W2) is finite card W2 -element Element of K32(NAT)
Sgm W2 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
dom (Sgm W2) is finite Element of K32(NAT)
Seg (n div 2) is finite n div 2 -element Element of K32(NAT)
x9 is set
x is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,(G1,G2,W1,W2)) . x is set
2 * x is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(G1,G2,W1,W2) . (2 * x) is set
(2 * x) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
x + x is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W1 - 0 is V28() V29() V30() ext-real non negative set
((2 * x) + 1) - 1 is V28() V29() V30() ext-real even set
Seg W1 is finite W1 -element Element of K32(NAT)
(G1,(G1,G2,W1,W2)) . x9 is set
G2 . (2 * x) is set
(Sgm W2) . x is set
(Sgm W2) ^ (Sgm W2) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
((Sgm W2) ^ (Sgm W2)) . x is set
(Sgm W2) . x is set
0 + x is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(Seq xa) . x is set
xa . x is set
(G1,G2) . x is set
(Seq xa) . x9 is set
(2 * x) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
k is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
(xaa1 div 2) + k is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(Sgm W2) . x is set
(Sgm W2) ^ (Sgm W2) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
((Sgm W2) ^ (Sgm W2)) . x is set
k is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
es + k is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (es + k) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * x) - W1 is V28() V29() V30() ext-real set
((2 * x) - W1) + W2 is V28() V29() V30() ext-real set
(2 * x) - vs is non empty V28() V29() V30() ext-real non even set
((2 * x) - vs) + vs is V28() V29() V30() ext-real even set
k + es is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
x - (xaa1 div 2) is V28() V29() V30() ext-real set
(x - (xaa1 div 2)) + es is V28() V29() V30() ext-real set
2 * ((x - (xaa1 div 2)) + es) is V28() V29() V30() ext-real even set
(((2 * x) - W1) + W2) + 1 is V28() V29() V30() ext-real set
n + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
z is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
k + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
xa . (es + k) is set
(G1,G2) . (es + k) is set
2 * (x - (xaa1 div 2)) is V28() V29() V30() ext-real even set
((2 * x) - W1) + 1 is V28() V29() V30() ext-real set
(((2 * x) - W1) + 1) + W2 is V28() V29() V30() ext-real set
n + W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
z is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
z + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(Sgm W2) . k is set
(Seq xa) . x is set
G2 . (2 * (es + k)) is set
z is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
z div 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,(G1,G2,W1,W2)) . x9 is set
(Seq xa) . x9 is set
(2 * x) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,(G1,G2,W1,W2)) . x9 is set
(Seq xa) . x9 is set
(G1,(G1,G2,W1,W2)) . x9 is set
(Seq xa) . x9 is set
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,G2) is Element of the_Vertices_of G1
G2 . (len G2) is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
y is set
vs is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * W2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,vs,((2 * W2) + 1)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,vs,((2 * W2) + 1)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,vs,(G1,vs,((2 * W2) + 1)),(G1,vs,((2 * W2) + 1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,vs)
vs is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,vs,((2 * W2) + 1)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,vs,((2 * W2) + 1)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,vs,(G1,vs,((2 * W2) + 1)),(G1,vs,((2 * W2) + 1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,vs)
y is set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * W2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y is set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * W2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
y is set
2 * W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * W2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
vs is set
(G1,vs,((2 * W2) + 1)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,vs,((2 * W2) + 1)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,vs,(G1,vs,((2 * W2) + 1)),(G1,vs,((2 * W2) + 1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,vs)
vs is set
W2 is Relation-like Function-like set
dom W2 is set
W2 . 0 is set
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 . y is set
2 * y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * y) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,G2)
len vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,G2)
len vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,vs,((2 * y) + 1)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,vs,((2 * y) + 1)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,vs,(G1,vs,((2 * y) + 1)),(G1,vs,((2 * y) + 1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,vs)
n is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,G2)
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W2 . (y + 1) is set
x is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,G2)
xaa1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,xaa1,((2 * y) + 1)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,xaa1,((2 * y) + 1)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,xaa1,(G1,xaa1,((2 * y) + 1)),(G1,xaa1,((2 * y) + 1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,xaa1)
len x is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
2 * (y + 1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (y + 1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
xaa1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,vs,1,(G1,vs,((2 * y) + 1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,vs,(G1,vs,((2 * y) + 1)),(len vs)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
((2 * y) + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
vs . (G1,vs,((2 * y) + 1)) is set
vs . ((2 * y) + 1) is set
(G1,vs,(G1,vs,((2 * y) + 1))) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs . (G1,vs,((2 * y) + 1)) is set
(G1,x,xaa1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
x . (G1,x,xaa1) is set
x . xaa1 is set
(G1,(G1,vs,1,(G1,vs,((2 * y) + 1)))) is Element of the_Vertices_of G1
len (G1,vs,1,(G1,vs,((2 * y) + 1))) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,vs,1,(G1,vs,((2 * y) + 1))) . (len (G1,vs,1,(G1,vs,((2 * y) + 1)))) is set
(G1,(G1,vs,(G1,vs,((2 * y) + 1)),(len vs))) is Element of the_Vertices_of G1
(G1,vs,(G1,vs,((2 * y) + 1)),(len vs)) . 1 is set
(G1,(G1,vs,1,(G1,vs,((2 * y) + 1))),(G1,vs,(G1,vs,((2 * y) + 1)),(len vs))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,x,1,xaa1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,vs,1,(G1,vs,((2 * y) + 1))),1,xaa1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,vs,1,xaa1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
xaa1 - 1 is V28() V29() V30() ext-real even set
es is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
es + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
xaa1 - 0 is non empty V28() V29() V30() ext-real positive non negative set
len (G1,vs,1,xaa1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len (G1,x,1,xaa1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,vs,1,xaa1) . xaa1 is set
vs . xaa1 is set
(G1,vs,xaa1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,x,xaa1) - 1 is V28() V29() V30() ext-real even set
(G1,x,xaa1) - 0 is non empty V28() V29() V30() ext-real positive non negative set
es is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,x,1,(G1,x,xaa1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,x,1,(G1,x,xaa1)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,vs,1,(G1,x,xaa1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,vs,1,(G1,x,xaa1)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,(G1,vs,1,(G1,vs,((2 * y) + 1))),1,(G1,x,xaa1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
es + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(G1,vs,1,(G1,x,xaa1)) . (es + 1) is set
vs . (G1,x,xaa1) is set
(G1,x,xaa1) - (G1,vs,((2 * y) + 1)) is V28() V29() V30() ext-real even set
((G1,x,xaa1) - (G1,vs,((2 * y) + 1))) + (G1,vs,((2 * y) + 1)) is non empty V28() V29() V30() ext-real non even set
vs . (((G1,x,xaa1) - (G1,vs,((2 * y) + 1))) + (G1,vs,((2 * y) + 1))) is set
(G1,x,xaa1) + (G1,vs,((2 * y) + 1)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1,x,xaa1) + (G1,vs,((2 * y) + 1)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((G1,x,xaa1) + (G1,vs,((2 * y) + 1))) - (G1,vs,((2 * y) + 1)) is non empty V28() V29() V30() ext-real non even set
((G1,x,xaa1) + (G1,vs,((2 * y) + 1))) - (G1,vs,((2 * y) + 1)) is non empty V28() V29() V30() ext-real non even set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,x,1,xaa1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,vs,1,(G1,vs,((2 * y) + 1))),1,xaa1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,vs,1,xaa1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
xaa1 - 1 is V28() V29() V30() ext-real even set
es is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
es + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
xaa1 - 0 is non empty V28() V29() V30() ext-real positive non negative set
len (G1,vs,1,xaa1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len (G1,x,1,xaa1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,vs,1,xaa1) . xaa1 is set
vs . xaa1 is set
(G1,x,xaa1) - (G1,vs,((2 * y) + 1)) is V28() V29() V30() ext-real even set
((G1,x,xaa1) - (G1,vs,((2 * y) + 1))) + (G1,vs,((2 * y) + 1)) is non empty V28() V29() V30() ext-real non even set
vs . (((G1,x,xaa1) - (G1,vs,((2 * y) + 1))) + (G1,vs,((2 * y) + 1))) is set
(((G1,x,xaa1) - (G1,vs,((2 * y) + 1))) + (G1,vs,((2 * y) + 1))) - (G1,vs,((2 * y) + 1)) is V28() V29() V30() ext-real even set
(G1,vs,((2 * y) + 1)) - (G1,vs,((2 * y) + 1)) is V28() V29() V30() ext-real even set
((G1,x,xaa1) - (G1,vs,((2 * y) + 1))) + (G1,vs,((2 * y) + 1)) is non empty V28() V29() V30() ext-real non even set
0 + (G1,vs,((2 * y) + 1)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(G1,x,xaa1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,x,xaa1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,x,xaa1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,G2)
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 . y is set
len vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
2 * y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * y) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W2 . (y + 1) is set
2 * (y + 1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (y + 1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
2 * 0 is empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V21() V22() V23() V25() V26() V27() V28() V29() V30() ext-real non positive non negative finite finite-yielding V49() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V86() even Element of NAT
(2 * 0) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,G2)
len y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,y,vs) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 . ((len G2) + 1) is set
2 * ((len G2) + 1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * ((len G2) + 1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,G2)
len vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len vs) + 0 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
((len G2) + 1) + ((len G2) + 1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1,vs,vs) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
(G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
2 * W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * W1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,W2,1,((2 * W1) + 1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
((2 * W1) + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W2 . (((2 * W1) + 1) + 1) is set
((2 * W1) + 1) + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 . (((2 * W1) + 1) + 2) is set
(G1,W2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,W2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,W2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
len W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
2 * (W1 + 1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (W1 + 1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len W2) - 0 is non empty V28() V29() V30() ext-real positive non negative set
(((2 * W1) + 1) + 2) - 2 is V28() V29() V30() ext-real set
W2 . ((2 * W1) + 1) is set
len (G1,W2,1,((2 * W1) + 1)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,(G1,W2,1,((2 * W1) + 1))) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,(G1,W2,1,((2 * W1) + 1))) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,(G1,W2,1,((2 * W1) + 1))) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (G1,(G1,W2,1,((2 * W1) + 1))) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (G1,(G1,W2,1,((2 * W1) + 1)))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,W2,1,((2 * W1) + 1)))
(G1,(G1,W2,1,((2 * W1) + 1))) is Element of the_Vertices_of G1
(G1,W2,1,((2 * W1) + 1)) . 1 is set
(G1,(G1,W2,1,((2 * W1) + 1))) is Element of the_Vertices_of G1
(G1,W2,1,((2 * W1) + 1)) . (len (G1,W2,1,((2 * W1) + 1))) is set
W2 . 1 is set
(G1,vs) is Element of the_Vertices_of G1
vs . 1 is set
(G1,vs) is Element of the_Vertices_of G1
len vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs . (len vs) is set
(G1,W2,1,((2 * W1) + 1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1,W2)
(G1,W2) is Element of the_Vertices_of G1
(G1,W2,((2 * W1) + 1),(((2 * W1) + 1) + 2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
len (G1,W2,1,((2 * W1) + 1)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,W2,1,((2 * W1) + 1))) + ((2 * W1) + 1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(((2 * W1) + 1) + 2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
((2 * W1) + 1) + (2 + 1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
n is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,W2)
x is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,W2)
K32((G1,(G1,W2,1,((2 * W1) + 1)))) is non empty finite V49() set
(G1,vs) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
n is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSubsequence-like Element of K32((G1,(G1,W2,1,((2 * W1) + 1))))
Seq n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom n is finite Element of K32(NAT)
Sgm (dom n) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom n)) * n is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite set
n is set
n . n is set
[n,(n . n)] is V1() set
dom (G1,(G1,W2,1,((2 * W1) + 1))) is finite Element of K32(NAT)
Seg W1 is finite W1 -element Element of K32(NAT)
rng (Sgm (dom n)) is finite Element of K32(NAT)
(G1,vs) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,vs) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,vs) is finite Element of K32((the_Vertices_of G1))
dom (Sgm (dom n)) is finite Element of K32(NAT)
dom (G1,vs) is finite Element of K32(NAT)
len (G1,vs) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
Seg (len (G1,vs)) is finite len (G1,vs) -element Element of K32(NAT)
x is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs . x is set
n is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1)
(G1,n,1,x) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1)
len (G1,n,1,x) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
x - 1 is V28() V29() V30() ext-real even set
(G1,(G1,n,1,x)) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,(G1,n,1,x)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W2 div 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * 0 is empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V21() V22() V23() V25() V26() V27() V28() V29() V30() ext-real non positive non negative finite finite-yielding V49() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V86() even Element of NAT
(2 * 0) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,W2) is Element of the_Vertices_of G1
(G1,W2) is Element of the_Vertices_of G1
W2 . (len W2) is set
2 * (W2 div 2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
2 * (len (G1,vs)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(2 * (len (G1,vs))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
Seg (W2 div 2) is finite W2 div 2 -element Element of K32(NAT)
(Sgm (dom n)) | (Seg (W2 div 2)) is Relation-like NAT -defined Seg (W2 div 2) -defined NAT -defined NAT -valued Function-like finite FinSubsequence-like Element of K32(K33(NAT,NAT))
K33(NAT,NAT) is non empty non trivial Relation-like non finite set
K32(K33(NAT,NAT)) is non empty non trivial non finite set
dom ((Sgm (dom n)) | (Seg (W2 div 2))) is finite Element of K32(NAT)
g is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng ((Sgm (dom n)) | (Seg (W2 div 2))) is finite Element of K32(NAT)
n | (rng ((Sgm (dom n)) | (Seg (W2 div 2)))) is Relation-like NAT -defined rng ((Sgm (dom n)) | (Seg (W2 div 2))) -defined NAT -defined the_Edges_of G1 -valued Function-like finite FinSubsequence-like set
es is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSubsequence-like Element of K32((G1,(G1,W2,1,((2 * W1) + 1))))
es is set
K32((G1,W2)) is non empty finite V49() set
es is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSubsequence-like Element of K32((G1,W2))
n \ es is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSubsequence-like Element of K32((G1,(G1,W2,1,((2 * W1) + 1))))
W2 is set
dom es is finite Element of K32(NAT)
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is Relation-like Function-like set
dom W2 is set
dom g is finite Element of K32(NAT)
xa is set
g . xa is set
xa is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 . W2 is set
[W2,(W2 . W2)] is V1() set
xb is set
(Sgm (dom n)) . xb is set
xb is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
[xb,W2] is V1() Element of K33(NAT,NAT)
rng g is finite set
dom (Seq n) is finite Element of K32(NAT)
len (Sgm (dom n)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(Sgm (dom n)) . xa is set
len g is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
card (dom es) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
card es is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
Seq es is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (Seq es) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is set
es \/ (n \ es) is Relation-like finite set
es \/ (n \ es) is Relation-like finite set
es \/ (n \ es) is Relation-like finite set
es \/ (n \ es) is Relation-like finite set
dom (n \ es) is finite Element of K32(NAT)
(dom es) \/ (dom (n \ es)) is finite Element of K32(NAT)
Sgm (dom es) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
Sgm (dom (n \ es)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom es)) ^ (Sgm (dom (n \ es))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
dom (G1,(G1,n,1,x)) is finite Element of K32(NAT)
(Sgm (dom es)) * es is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
(Sgm (dom n)) . W2 is set
[W2,((Sgm (dom n)) . W2)] is V1() set
n . ((Sgm (dom n)) . W2) is set
[((Sgm (dom n)) . W2),(n . ((Sgm (dom n)) . W2))] is V1() set
(G1,(G1,n,1,x)) . W2 is set
[W2,((G1,(G1,n,1,x)) . W2)] is V1() set
(Seq n) . W2 is set
dom (Seq es) is finite Element of K32(NAT)
dom (Sgm (dom es)) is finite Element of K32(NAT)
(Sgm (dom es)) . W2 is set
es . ((Sgm (dom es)) . W2) is set
(Seq es) . W2 is set
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,W2)
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,W2)
(G1,vs) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,vs) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,vs) is finite Element of K32((the_Vertices_of G1))
(W1 + 1) .--> (W2 . (((2 * W1) + 1) + 1)) is Relation-like NAT -defined {(W1 + 1)} -defined Function-like one-to-one finite set
{(W1 + 1)} is non empty trivial finite V49() 1 -element set
{(W1 + 1)} --> (W2 . (((2 * W1) + 1) + 1)) is non empty Relation-like {(W1 + 1)} -defined Function-like constant V17({(W1 + 1)}) V18({(W1 + 1)},{(W2 . (((2 * W1) + 1) + 1))}) finite Element of K32(K33({(W1 + 1)},{(W2 . (((2 * W1) + 1) + 1))}))
{(W2 . (((2 * W1) + 1) + 1))} is non empty trivial finite 1 -element set
K33({(W1 + 1)},{(W2 . (((2 * W1) + 1) + 1))}) is non empty Relation-like finite set
K32(K33({(W1 + 1)},{(W2 . (((2 * W1) + 1) + 1))})) is non empty finite V49() set
n +* ((W1 + 1) .--> (W2 . (((2 * W1) + 1) + 1))) is Relation-like Function-like finite set
(G1,vs,(W2 . (((2 * W1) + 1) + 1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,vs) .adj (W2 . (((2 * W1) + 1) + 1)) is Element of the_Vertices_of G1
(G1,(G1,vs),((G1,vs) .adj (W2 . (((2 * W1) + 1) + 1))),(W2 . (((2 * W1) + 1) + 1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,vs,(G1,(G1,vs),((G1,vs) .adj (W2 . (((2 * W1) + 1) + 1))),(W2 . (((2 * W1) + 1) + 1)))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
xaa1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
{(W1 + 1)} is non empty trivial finite V49() 1 -element Element of K32(NAT)
dom ((W1 + 1) .--> (W2 . (((2 * W1) + 1) + 1))) is trivial finite V49() Element of K32({(W1 + 1)})
K32({(W1 + 1)}) is non empty finite V49() set
dom (n +* ((W1 + 1) .--> (W2 . (((2 * W1) + 1) + 1)))) is finite set
(dom n) \/ {(W1 + 1)} is non empty finite Element of K32(NAT)
xaa1 is set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
Seg (W1 + 1) is non empty finite W1 + 1 -element Element of K32(NAT)
Seg (W1 + 1) is non empty finite W1 + 1 -element Element of K32(NAT)
Seg (W1 + 1) is non empty finite W1 + 1 -element Element of K32(NAT)
Seg (W1 + 1) is non empty finite W1 + 1 -element Element of K32(NAT)
W2 is set
xaa1 is Relation-like NAT -defined Function-like FinSubsequence-like set
g is set
es is set
[g,es] is V1() set
dom xaa1 is Element of K32(NAT)
xaa1 . g is set
es is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
dom (G1,W2) is finite Element of K32(NAT)
((W1 + 1) .--> (W2 . (((2 * W1) + 1) + 1))) . g is set
(G1,W2) . g is set
W2 . (2 * (W1 + 1)) is set
n . g is set
K32((G1,W2)) is non empty finite V49() set
W2 is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSubsequence-like Element of K32((G1,W2))
dom W2 is finite Element of K32(NAT)
Sgm (dom W2) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
Sgm {(W1 + 1)} is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom n)) ^ (Sgm {(W1 + 1)}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
<*(W1 + 1)*> is non empty trivial Relation-like NAT -defined NAT -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom n)) ^ <*(W1 + 1)*> is non empty Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
(dom n) /\ (dom ((W1 + 1) .--> (W2 . (((2 * W1) + 1) + 1)))) is trivial finite V49() Element of K32({(W1 + 1)})
g is set
W1 + 0 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,(G1,vs,(W2 . (((2 * W1) + 1) + 1)))) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
<*(W2 . (((2 * W1) + 1) + 1))*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
(Seq n) ^ <*(W2 . (((2 * W1) + 1) + 1))*> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (G1,(G1,vs,(W2 . (((2 * W1) + 1) + 1)))) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
len (Seq n) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
len <*(W2 . (((2 * W1) + 1) + 1))*> is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len (Seq n)) + (len <*(W2 . (((2 * W1) + 1) + 1))*>) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len (Seq n)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
card n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(card n) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
Seq W2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (Seq W2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
card W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
card ((W1 + 1) .--> (W2 . (((2 * W1) + 1) + 1))) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(card n) + (card ((W1 + 1) .--> (W2 . (((2 * W1) + 1) + 1)))) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
[(W1 + 1),(W2 . (((2 * W1) + 1) + 1))] is V1() set
{[(W1 + 1),(W2 . (((2 * W1) + 1) + 1))]} is non empty trivial Relation-like Function-like constant finite 1 -element set
card {[(W1 + 1),(W2 . (((2 * W1) + 1) + 1))]} is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(card n) + (card {[(W1 + 1),(W2 . (((2 * W1) + 1) + 1))]}) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(Sgm (dom W2)) * W2 is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite set
g is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
dom (Seq W2) is finite Element of K32(NAT)
(Seq W2) . g is set
(Sgm (dom W2)) . g is set
W2 . ((Sgm (dom W2)) . g) is set
dom (G1,(G1,vs,(W2 . (((2 * W1) + 1) + 1)))) is finite Element of K32(NAT)
dom (Seq n) is finite Element of K32(NAT)
dom (Sgm (dom n)) is finite Element of K32(NAT)
(Sgm (dom n)) . g is set
(G1,(G1,vs,(W2 . (((2 * W1) + 1) + 1)))) . g is set
(Seq n) . g is set
n . ((Sgm (dom n)) . g) is set
dom <*(W2 . (((2 * W1) + 1) + 1))*> is non empty trivial finite 1 -element Element of K32(NAT)
es is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
(len (Seq n)) + es is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
es is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
(len (Seq n)) + es is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
{1} is non empty trivial finite V49() 1 -element Element of K32(NAT)
(dom n) \/ (dom ((W1 + 1) .--> (W2 . (((2 * W1) + 1) + 1)))) is finite set
len (Sgm (dom n)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
card (dom n) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 . (W1 + 1) is set
((W1 + 1) .--> (W2 . (((2 * W1) + 1) + 1))) . (W1 + 1) is set
(G1,(G1,vs,(W2 . (((2 * W1) + 1) + 1)))) . g is set
<*(W2 . (((2 * W1) + 1) + 1))*> . 1 is set
dom (Seq n) is finite Element of K32(NAT)
dom <*(W2 . (((2 * W1) + 1) + 1))*> is non empty trivial finite 1 -element Element of K32(NAT)
(G1,(G1,vs,(W2 . (((2 * W1) + 1) + 1)))) . g is set
(G1,(G1,vs,(W2 . (((2 * W1) + 1) + 1)))) . g is set
(G1,W2) is Element of the_Vertices_of G1
(G1,W2) is Element of the_Vertices_of G1
W2 . (len W2) is set
g is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,W2)
es is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,W2)
(G1,vs) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,vs) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,vs) is finite Element of K32((the_Vertices_of G1))
n is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,W2)
n is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,W2)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
(G1,W2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,W2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,W2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,W1)
(G1,W1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,W1) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,W1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
2 * 0 is empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V21() V22() V23() V25() V26() V27() V28() V29() V30() ext-real non positive non negative finite finite-yielding V49() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V86() even Element of NAT
(2 * 0) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,W1)
len y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is Element of the_Vertices_of G1
(G1,vs) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1) (G1) (G1)
<*vs*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
(G1,W1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,W1) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,W1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) : verum } is set
((the_Vertices_of G1) \/ (the_Edges_of G1)) * is non empty functional FinSequence-membered set
K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *)) is non empty set
W1 is set
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
choose (the_Vertices_of G1) is Element of the_Vertices_of G1
(G1,(choose (the_Vertices_of G1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1) (G1) (G1)
<*(choose (the_Vertices_of G1))*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) : verum } is set
(G1) is non empty functional FinSequence-membered Element of K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *))
((the_Vertices_of G1) \/ (the_Edges_of G1)) * is non empty functional FinSequence-membered set
K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) : verum } is set
K32((G1)) is non empty set
W1 is set
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
choose (the_Vertices_of G1) is Element of the_Vertices_of G1
(G1,(choose (the_Vertices_of G1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1) (G1) (G1)
<*(choose (the_Vertices_of G1))*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) : verum } is set
(G1) is non empty functional FinSequence-membered Element of K32((G1))
(G1) is non empty functional FinSequence-membered Element of K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *))
((the_Vertices_of G1) \/ (the_Edges_of G1)) * is non empty functional FinSequence-membered set
K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) : verum } is set
K32((G1)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) : verum } is set
K32((G1)) is non empty set
W1 is set
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
choose (the_Vertices_of G1) is Element of the_Vertices_of G1
(G1,(choose (the_Vertices_of G1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1) (G1) (G1)
<*(choose (the_Vertices_of G1))*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) : verum } is set
(G1) is non empty functional FinSequence-membered Element of K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *))
((the_Vertices_of G1) \/ (the_Edges_of G1)) * is non empty functional FinSequence-membered set
K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) : verum } is set
K32((G1)) is non empty set
W1 is set
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
choose (the_Vertices_of G1) is Element of the_Vertices_of G1
(G1,(choose (the_Vertices_of G1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1) (G1) (G1)
<*(choose (the_Vertices_of G1))*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) : verum } is set
(G1) is non empty functional FinSequence-membered Element of K32((G1))
(G1) is non empty functional FinSequence-membered Element of K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *))
((the_Vertices_of G1) \/ (the_Edges_of G1)) * is non empty functional FinSequence-membered set
K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) : verum } is set
K32((G1)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) : verum } is set
K32((G1)) is non empty set
W1 is set
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
choose (the_Vertices_of G1) is Element of the_Vertices_of G1
(G1,(choose (the_Vertices_of G1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1) (G1) (G1)
<*(choose (the_Vertices_of G1))*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) : verum } is set
(G1) is non empty functional FinSequence-membered Element of K32((G1))
(G1) is non empty functional FinSequence-membered Element of K32((G1))
(G1) is non empty functional FinSequence-membered Element of K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *))
((the_Vertices_of G1) \/ (the_Edges_of G1)) * is non empty functional FinSequence-membered set
K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) : verum } is set
K32((G1)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) : verum } is set
K32((G1)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) : verum } is set
K32((G1)) is non empty set
W1 is set
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1)
choose (the_Vertices_of G1) is Element of the_Vertices_of G1
(G1,(choose (the_Vertices_of G1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1) (G1) (G1)
<*(choose (the_Vertices_of G1))*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
G1 is Relation-like NAT -defined Function-like finite [Graph-like] finite set
(G1) is non empty functional FinSequence-membered Element of K32((G1))
(G1) is non empty functional FinSequence-membered Element of K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *))
the_Vertices_of G1 is non empty finite set
the_Edges_of G1 is finite set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty finite set
((the_Vertices_of G1) \/ (the_Edges_of G1)) * is non empty functional FinSequence-membered set
K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) : verum } is set
K32((G1)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) : verum } is set
G1 .size() is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (G1 .size()) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (G1 .size())) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
{ b₁ where b₁ is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of ((the_Vertices_of G1) \/ (the_Edges_of G1)) * : len b₁ <= (2 * (G1 .size())) + 1 } is set
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
(G1,W2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
y is Relation-like Function-like set
dom y is set
vs is set
vs is set
y . vs is set
y . vs is set
vs is set
n is set
[vs,n] is V1() set
dom (G1,W2) is finite Element of K32(NAT)
vs `2 is set
(G1,W2) . vs is set
n is set
x is set
[n,x] is V1() set
[vs,n] `2 is set
[n,x] `2 is set
vs `2 is set
(G1,W2) . n is set
vs is set
rng y is set
vs is set
y . vs is set
vs is set
n is set
[vs,n] is V1() set
[vs,n] `2 is set
vs `2 is set
rng (G1,W2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty finite V49() set
card (G1,W2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
card (the_Edges_of G1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
len (G1,W2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len (G1,W2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len (G1,W2))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is set
y is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
len y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
(G1) is non empty functional FinSequence-membered Element of K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *))
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
((the_Vertices_of G1) \/ (the_Edges_of G1)) * is non empty functional FinSequence-membered set
K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) : verum } is set
K32((G1)) is non empty set
G2 is non empty functional FinSequence-membered Element of K32((G1))
W1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of G2
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
(G1) is non empty functional FinSequence-membered Element of K32((G1))
(G1) is non empty functional FinSequence-membered Element of K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *))
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
((the_Vertices_of G1) \/ (the_Edges_of G1)) * is non empty functional FinSequence-membered set
K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) : verum } is set
K32((G1)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) : verum } is set
K32((G1)) is non empty set
G2 is non empty functional FinSequence-membered Element of K32((G1))
W1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of G2
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
(G1) is non empty functional FinSequence-membered Element of K32((G1))
(G1) is non empty functional FinSequence-membered Element of K32((G1))
(G1) is non empty functional FinSequence-membered Element of K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *))
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
((the_Vertices_of G1) \/ (the_Edges_of G1)) * is non empty functional FinSequence-membered set
K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) : verum } is set
K32((G1)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) : verum } is set
K32((G1)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) : verum } is set
K32((G1)) is non empty set
G2 is non empty functional FinSequence-membered Element of K32((G1))
W1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of G2
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
(G1) is non empty functional FinSequence-membered Element of K32((G1))
(G1) is non empty functional FinSequence-membered Element of K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *))
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
((the_Vertices_of G1) \/ (the_Edges_of G1)) * is non empty functional FinSequence-membered set
K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) : verum } is set
K32((G1)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) : verum } is set
K32((G1)) is non empty set
G2 is non empty functional FinSequence-membered Element of K32((G1))
W1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of G2
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
(G1) is non empty functional FinSequence-membered Element of K32((G1))
(G1) is non empty functional FinSequence-membered Element of K32((G1))
(G1) is non empty functional FinSequence-membered Element of K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *))
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
((the_Vertices_of G1) \/ (the_Edges_of G1)) * is non empty functional FinSequence-membered set
K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) : verum } is set
K32((G1)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) : verum } is set
K32((G1)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) : verum } is set
K32((G1)) is non empty set
G2 is non empty functional FinSequence-membered Element of K32((G1))
W1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of G2
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
(G1) is non empty functional FinSequence-membered Element of K32((G1))
(G1) is non empty functional FinSequence-membered Element of K32((G1))
(G1) is non empty functional FinSequence-membered Element of K32((G1))
(G1) is non empty functional FinSequence-membered Element of K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *))
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
((the_Vertices_of G1) \/ (the_Edges_of G1)) * is non empty functional FinSequence-membered set
K32((((the_Vertices_of G1) \/ (the_Edges_of G1)) *)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) : verum } is set
K32((G1)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) : verum } is set
K32((G1)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) : verum } is set
K32((G1)) is non empty set
{ b₁ where b₁ is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) : verum } is set
K32((G1)) is non empty set
G2 is non empty functional FinSequence-membered Element of K32((G1))
W1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of G2
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
dom G2 is finite Element of K32(NAT)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
G2 . W1 is set
W1 - 1 is non empty V28() V29() V30() ext-real non even set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) - 0 is non empty V28() V29() V30() ext-real positive non negative set
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W2 is set
W2 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (W2 + 2) is set
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (W2 + 1) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
dom G2 is finite Element of K32(NAT)
W1 - 1 is non empty V28() V29() V30() ext-real non even set
W1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (W1 + 1) is set
G2 . W1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (W1 + 1) is set
(G1,G2,W1) is Element of the_Vertices_of G1
(G1,G2,W1) .edgesInOut() is Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
G2 . W1 is set
W1 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (W1 + 2) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 - 1 is V28() V29() V30() ext-real even set
G2 . (W1 - 1) is set
(G1,G2,W1) is Element of the_Vertices_of G1
(G1,G2,W1) .edgesInOut() is Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(1 + 1) - 1 is V28() V29() V30() ext-real set
(len G2) - 0 is non empty V28() V29() V30() ext-real positive non negative set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
dom G2 is finite Element of K32(NAT)
W2 - 1 is non empty V28() V29() V30() ext-real non even set
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (W2 + 1) is set
G2 . W2 is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . y is set
(G1,G2,y) is Element of the_Vertices_of G1
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
dom G2 is finite Element of K32(NAT)
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W1 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
G2 is Element of the_Vertices_of G1
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1) (G1) (G1)
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
<*G2*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
len (G1,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) . 1 is set
(G1,(G1,G2)) is Element of the_Vertices_of G1
(G1,(G1,G2)) is Element of the_Vertices_of G1
(G1,G2) . (len (G1,G2)) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
G2 is set
W1 is set
W2 is set
(G1,W1,W2,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
len (G1,W1,W2,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
<*W1,G2,W2*> is non empty Relation-like NAT -defined Function-like finite 3 -element FinSequence-like FinSubsequence-like set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
G2 is set
W1 is set
W2 is set
(G1,W1,W2,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
(G1,(G1,W1,W2,G2)) is Element of the_Vertices_of G1
(G1,W1,W2,G2) . 1 is set
(G1,(G1,W1,W2,G2)) is Element of the_Vertices_of G1
len (G1,W1,W2,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,W1,W2,G2) . (len (G1,W1,W2,G2)) is set
<*W1,G2,W2*> is non empty Relation-like NAT -defined Function-like finite 3 -element FinSequence-like FinSubsequence-like set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(G2,W2) is Element of the_Vertices_of G2
W2 . 1 is set
(G1,W1) is Element of the_Vertices_of G1
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (len W1) is set
(G2,W2) is Element of the_Vertices_of G2
len W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 . (len W2) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G2 . 1 is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W1 is set
W2 is set
(G1,G2) is Element of the_Vertices_of G1
(G1,G2) is Element of the_Vertices_of G1
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is set
W2 is set
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is set
W2 is set
y is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
vs is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
(G1,y) is Element of the_Vertices_of G1
y . 1 is set
(G1,y) is Element of the_Vertices_of G1
len y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y . (len y) is set
(G2,vs) is Element of the_Vertices_of G2
vs . 1 is set
(G2,vs) is Element of the_Vertices_of G2
len vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs . (len vs) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,W1,y) is Element of the_Vertices_of G1
(G2,W2,y) is Element of the_Vertices_of G2
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 . y is set
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(G2,W2) is Element of the_Vertices_of G2
W2 . 1 is set
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of W1 is non empty set
the_Edges_of W1 is set
(the_Vertices_of W1) \/ (the_Edges_of W1) is non empty set
y is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of y is non empty set
the_Edges_of y is set
(the_Vertices_of y) \/ (the_Edges_of y) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
len (G1,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is Relation-like NAT -defined (the_Vertices_of W1) \/ (the_Edges_of W1) -valued Function-like finite FinSequence-like FinSubsequence-like (W1)
dom W2 is finite Element of K32(NAT)
(W1,W2) is Relation-like NAT -defined (the_Vertices_of W1) \/ (the_Edges_of W1) -valued Function-like finite FinSequence-like FinSubsequence-like (W1)
Rev W2 is Relation-like NAT -defined (the_Vertices_of W1) \/ (the_Edges_of W1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of W1) \/ (the_Edges_of W1)
dom (W1,W2) is finite Element of K32(NAT)
vs is Relation-like NAT -defined (the_Vertices_of y) \/ (the_Edges_of y) -valued Function-like finite FinSequence-like FinSubsequence-like (y)
rng vs is finite Element of K32(((the_Vertices_of y) \/ (the_Edges_of y)))
K32(((the_Vertices_of y) \/ (the_Edges_of y))) is non empty set
(y,vs) is Relation-like NAT -defined (the_Vertices_of y) \/ (the_Edges_of y) -valued Function-like finite FinSequence-like FinSubsequence-like (y)
Rev vs is Relation-like NAT -defined (the_Vertices_of y) \/ (the_Edges_of y) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of y) \/ (the_Edges_of y)
rng (y,vs) is finite Element of K32(((the_Vertices_of y) \/ (the_Edges_of y)))
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
(G1,(G1,G2)) is Element of the_Vertices_of G1
len (G1,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) . (len (G1,G2)) is set
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,(G1,G2)) is Element of the_Vertices_of G1
(G1,G2) . 1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
W1 is set
W2 is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len (G1,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) . 1 is set
G2 . 1 is set
(G1,G2) . (len G2) is set
(G1,G2) . (len (G1,G2)) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
dom G2 is finite Element of K32(NAT)
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
dom (G1,G2) is finite Element of K32(NAT)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G2 . W1 is set
(len G2) - W1 is V28() V29() V30() ext-real set
((len G2) - W1) + 1 is V28() V29() V30() ext-real set
(G1,G2) . (((len G2) - W1) + 1) is set
Seg (len G2) is non empty finite len G2 -element Element of K32(NAT)
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
len (G1,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
Seg (len (G1,G2)) is non empty finite len (G1,G2) -element Element of K32(NAT)
(G1,G2) . y is set
(len G2) - y is V28() V29() V30() ext-real set
((len G2) - y) + 1 is V28() V29() V30() ext-real set
G2 . (((len G2) - y) + 1) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
dom (G1,G2) is finite Element of K32(NAT)
(G1,G2) . W1 is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) - W1 is V28() V29() V30() ext-real set
((len G2) - W1) + 1 is V28() V29() V30() ext-real set
G2 . (((len G2) - W1) + 1) is set
dom G2 is finite Element of K32(NAT)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
(G1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
(G2,W2) is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
Rev W2 is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G2) \/ (the_Edges_of G2)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + (len W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1)) is Element of the_Vertices_of G1
(G1,G2,W1) . 1 is set
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,(G1,G2,W1)) is Element of the_Vertices_of G1
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) . (len (G1,G2,W1)) is set
(G1,W1) is Element of the_Vertices_of G1
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (len W1) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is set
y is set
vs is set
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,W1) is Element of the_Vertices_of G1
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (len W1) is set
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
dom G2 is finite Element of K32(NAT)
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,W1) . W2 is set
G2 . W2 is set
dom (G1,G2,W1) is finite Element of K32(NAT)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(len G2) + W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(G1,G2,W1) . ((len G2) + W2) is set
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W1 . (W2 + 1) is set
dom (G1,G2,W1) is finite Element of K32(NAT)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
dom (G1,G2,W1) is finite Element of K32(NAT)
dom G2 is finite Element of K32(NAT)
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
y is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
vs is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
(G2,y,vs) is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
(G1,W1) is Element of the_Vertices_of G1
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (len W1) is set
(G1,W2) is Element of the_Vertices_of G1
W2 . 1 is set
(G2,y) is Element of the_Vertices_of G2
len y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y . (len y) is set
(G2,vs) is Element of the_Vertices_of G2
vs . 1 is set
W1 ^' W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
(G1,W1) is Element of the_Vertices_of G1
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (len W1) is set
(G1,W2) is Element of the_Vertices_of G1
W2 . 1 is set
(G2,y) is Element of the_Vertices_of G2
len y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y . (len y) is set
(G2,vs) is Element of the_Vertices_of G2
vs . 1 is set
(G1,W1) is Element of the_Vertices_of G1
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (len W1) is set
(G1,W2) is Element of the_Vertices_of G1
W2 . 1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W1,W2)) + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(G1,G2,W1,W2) . (y + 1) is set
W1 + y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G2 . (W1 + y) is set
dom G2 is finite Element of K32(NAT)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1,W2)) is Element of the_Vertices_of G1
(G1,G2,W1,W2) . 1 is set
G2 . W1 is set
(G1,(G1,G2,W1,W2)) is Element of the_Vertices_of G1
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) . (len (G1,G2,W1,W2)) is set
G2 . W2 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,W2,y) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1,W2),(G1,G2,W2,y)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,W1,y) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,1,(len G2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
W1 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (W1 + 2) is set
W1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (W1 + 1) is set
(G1,(G2 . W1),(G2 . (W1 + 2)),(G2 . (W1 + 1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,G2,W1,(W1 + 2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,W1,(W1 + 2)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W1,(W1 + 2))) + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
2 + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
1 + (2 + W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
<*(G2 . W1),(G2 . (W1 + 1)),(G2 . (W1 + 2))*> is non empty Relation-like NAT -defined Function-like finite 3 -element FinSequence-like FinSubsequence-like set
len (G1,(G2 . W1),(G2 . (W1 + 2)),(G2 . (W1 + 1))) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
dom (G1,(G2 . W1),(G2 . (W1 + 2)),(G2 . (W1 + 1))) is finite Element of K32(NAT)
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
n - 1 is V28() V29() V30() ext-real set
3 - 0 is non empty V28() V29() V30() ext-real positive non negative set
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
n + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(G1,G2,W1,(W1 + 2)) . n is set
W1 + n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G2 . (W1 + n) is set
(G1,(G2 . W1),(G2 . (W1 + 2)),(G2 . (W1 + 1))) . n is set
(G1,(G2 . W1),(G2 . (W1 + 2)),(G2 . (W1 + 1))) . n is set
(G1,(G2 . W1),(G2 . (W1 + 2)),(G2 . (W1 + 1))) . n is set
(G1,(G2 . W1),(G2 . (W1 + 2)),(G2 . (W1 + 1))) . n is set
(G1,(G2 . W1),(G2 . (W1 + 2)),(G2 . (W1 + 1))) . n is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (W2 + 1) is set
(G1,(G1,G2,W1,W2),(G2 . (W2 + 1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1,W2)) is Element of the_Vertices_of G1
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) . (len (G1,G2,W1,W2)) is set
(G1,(G1,G2,W1,W2)) .adj (G2 . (W2 + 1)) is Element of the_Vertices_of G1
(G1,(G1,(G1,G2,W1,W2)),((G1,(G1,G2,W1,W2)) .adj (G2 . (W2 + 1))),(G2 . (W2 + 1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,(G1,G2,W1,W2),(G1,(G1,(G1,G2,W1,W2)),((G1,(G1,G2,W1,W2)) .adj (G2 . (W2 + 1))),(G2 . (W2 + 1)))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,(W2 + 2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G2 . W2 is set
G2 . (W2 + 2) is set
(G1,G2,(W2 + 2)) is Element of the_Vertices_of G1
(G1,G2,W2,(W2 + 2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,W1) is Element of the_Vertices_of G1
<*(G1,G2,W1)*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,1,W2),1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) is Element of the_Vertices_of G1
G2 . (len G2) is set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1),W2,y) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,W2,y) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,1,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
dom (G1,G2,1,W1) is finite Element of K32(NAT)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,1,W1) . W2 is set
G2 . W2 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
dom G2 is finite Element of K32(NAT)
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
dom (G1,G2,W1,W2) is finite Element of K32(NAT)
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) . y is set
W1 + y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(W1 + y) - 1 is V28() V29() V30() ext-real set
G2 . ((W1 + y) - 1) is set
y - 1 is V28() V29() V30() ext-real set
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W1,W2)) - 0 is non empty V28() V29() V30() ext-real positive non negative set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W1 + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G2 . (W1 + vs) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,W1,y,vs) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G2,W2,y,vs) is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(y,vs) -cut W2 is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G2) \/ (the_Edges_of G2)
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,G2)
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W1,W2)) + W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len G2) + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is set
W2 is set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,y,vs) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,G2)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,G2)
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,G2)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
(G1,G2,1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,1,W1)) is Element of the_Vertices_of G1
len (G1,G2,1,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,1,W1) . (len (G1,G2,1,W1)) is set
(G1,G2,W2,(len G2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W2,(len G2))) is Element of the_Vertices_of G1
(G1,G2,W2,(len G2)) . 1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
Seg W1 is non empty finite W1 -element Element of K32(NAT)
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,G2)
(G1,G2,W1,W2) . y is set
G2 . y is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,G2)
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) . y is set
y - W1 is V28() V29() V30() ext-real set
(y - W1) + W2 is V28() V29() V30() ext-real set
G2 . ((y - W1) + W2) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,G2)
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((len G2) + W1) - W2 is non empty V28() V29() V30() ext-real non even set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G2 . W1 is set
(G1,G2,W1,(len G2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,G2)
(G1,G2,1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,W1,(len G2)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W1,(len G2))) + (len G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len G2) + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
len (G1,G2,1,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
dom (G1,G2,1,W1) is finite Element of K32(NAT)
Seg W1 is finite W1 -element Element of K32(NAT)
(G1,G2,W1,(len G2)) . W2 is set
G2 . W2 is set
(G1,G2,1,W1) . W2 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G2 . W1 is set
(G1,G2,1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,G2)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,(len G2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
y is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of y is non empty set
the_Edges_of y is set
(the_Vertices_of y) \/ (the_Edges_of y) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,G2)
(G1,(G1,G2,W1,W2)) is Element of the_Vertices_of G1
(G1,G2,W1,W2) . 1 is set
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
vs is Relation-like NAT -defined (the_Vertices_of y) \/ (the_Edges_of y) -valued Function-like finite FinSequence-like FinSubsequence-like (y)
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(y,vs,vs,vs) is Relation-like NAT -defined (the_Vertices_of y) \/ (the_Edges_of y) -valued Function-like finite FinSequence-like FinSubsequence-like (y,vs)
(y,(y,vs,vs,vs)) is Element of the_Vertices_of y
len (y,vs,vs,vs) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(y,vs,vs,vs) . (len (y,vs,vs,vs)) is set
(y,vs) is Element of the_Vertices_of y
len vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs . (len vs) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,G2)
dom (G1,G2,W1,W2) is finite Element of K32(NAT)
Seg W1 is non empty finite W1 -element Element of K32(NAT)
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,W1,y,vs) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,W1)
(G2,W2,y,vs) is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2,W2)
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . y is set
W1 . vs is set
(G1,W1,vs,(len W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G2,W2,vs,(len W2)) is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
(G1,W1,1,y) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G2,W2,1,y) is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
(G1,(G1,W1,1,y),(G1,W1,vs,(len W1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G2,(G2,W2,1,y),(G2,W2,vs,(len W2))) is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . y is set
W1 . vs is set
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . y is set
W1 . vs is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W2 is set
W1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
<*W1,W2*> is non empty Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like set
G2 ^ <*W1,W2*> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W2 is set
W1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1)) is Element of the_Vertices_of G1
(G1,G2,W1) . 1 is set
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,(G1,G2,W1)) is Element of the_Vertices_of G1
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) . (len (G1,G2,W1)) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W2 is set
W1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W2 is set
W1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(len G2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1,G2,W1) . ((len G2) + 1) is set
(len G2) + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) . ((len G2) + 2) is set
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
dom G2 is finite Element of K32(NAT)
(G1,G2,W1) . y is set
G2 . y is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is set
W2 is set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
vs is set
y is set
(G1,G2,y) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) .adj y is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj y),y) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj y),y)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
0 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
2 * 0 is empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V21() V22() V23() V25() V26() V27() V28() V29() V30() ext-real non positive non negative finite finite-yielding V49() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V86() even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(W1 + 1) div 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * ((W1 + 1) div 2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * ((W1 + 1) div 2)) - 1 is non empty V28() V29() V30() ext-real non even set
0 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
((W1 + 1) div 2) - 1 is V28() V29() V30() ext-real set
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
2 * (len (G1,G2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
2 * y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(len G2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * ((W1 + 1) div 2)) - (2 * 1) is V28() V29() V30() ext-real even set
((len G2) + 1) + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(W1 + 1) - 2 is V28() V29() V30() ext-real set
((W1 + 1) - 2) + 2 is V28() V29() V30() ext-real set
(W1 + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(W1 + 2) - 2 is V28() V29() V30() ext-real set
(len G2) + 3 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
((len G2) + 3) - 3 is V28() V29() V30() ext-real set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
G2 is Element of the_Vertices_of G1
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1) (G1) (G1)
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
<*G2*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
(G1,(G1,G2)) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
len (G1,(G1,G2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len (G1,(G1,G2))) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(G1,(G1,G2)) . 1 is set
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * 1) - 1 is non empty V28() V29() V30() ext-real non even set
(G1,G2) . ((2 * 1) - 1) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
G2 is set
W1 is set
W2 is set
(G1,W1,W2,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
(G1,(G1,W1,W2,G2)) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
<*W1,W2*> is non empty Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like set
<*W1,G2,W2*> is non empty Relation-like NAT -defined Function-like finite 3 -element FinSequence-like FinSubsequence-like set
len (G1,W1,W2,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,W1,W2,G2)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
len (G1,(G1,W1,W2,G2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len (G1,(G1,W1,W2,G2))) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
3 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(G1,(G1,W1,W2,G2)) . 2 is set
2 * 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * 2) - 1 is non empty V28() V29() V30() ext-real non even set
(G1,W1,W2,G2) . ((2 * 2) - 1) is set
(G1,(G1,W1,W2,G2)) . 1 is set
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * 1) - 1 is non empty V28() V29() V30() ext-real non even set
(G1,W1,W2,G2) . ((2 * 1) - 1) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) . 1 is set
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2) . (len (G1,G2)) is set
(len G2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
2 * (len (G1,G2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * 1) - 1 is non empty V28() V29() V30() ext-real non even set
G2 . ((2 * 1) - 1) is set
(2 * (len (G1,G2))) - 1 is non empty V28() V29() V30() ext-real non even set
G2 . ((2 * (len (G1,G2))) - 1) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) is Element of the_Vertices_of G1
W1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(W1 + 1) div 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2) . ((W1 + 1) div 2) is set
2 * ((W1 + 1) div 2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * ((W1 + 1) div 2)) - 1 is non empty V28() V29() V30() ext-real non even set
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G2 . W1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
dom (G1,G2) is finite Element of K32(NAT)
dom G2 is finite Element of K32(NAT)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * W1) - 1 is non empty V28() V29() V30() ext-real non even set
W1 + W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len (G1,G2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((len G2) + 1) - 1 is non empty V28() V29() V30() ext-real non even set
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
2 - 1 is V28() V29() V30() ext-real set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
((2 * W1) - 1) + 1 is V28() V29() V30() ext-real even set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,1,W1)) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y is set
vs is set
vs is set
[vs,vs] is V1() set
(G1,(G1,G2,1,W1)) . vs is set
dom (G1,(G1,G2,1,W1)) is finite Element of K32(NAT)
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
len (G1,(G1,G2,1,W1)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * vs) - 1 is non empty V28() V29() V30() ext-real non even set
dom (G1,G2,1,W1) is finite Element of K32(NAT)
len (G1,G2,1,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
dom G2 is finite Element of K32(NAT)
dom (G1,G2) is finite Element of K32(NAT)
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,1,W1) . ((2 * vs) - 1) is set
G2 . ((2 * vs) - 1) is set
(G1,G2) . vs is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1)) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is set
<*W2*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
(G1,G2) ^ <*W2*> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
((len G2) + 2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
len (G1,(G1,G2,W1)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len (G1,(G1,G2,W1))) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
len ((G1,G2) ^ <*W2*>) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
len <*W2*> is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len (G1,G2)) + (len <*W2*>) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len (G1,G2)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
2 * (len ((G1,G2) ^ <*W2*>)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
2 * (len (G1,G2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len (G1,G2))) + (2 * 1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(len G2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((len G2) + 1) + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
(G1,(G1,G2,W1)) . vs is set
2 * vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * vs) - 1 is non empty V28() V29() V30() ext-real non even set
(G1,G2,W1) . ((2 * vs) - 1) is set
dom ((G1,G2) ^ <*W2*>) is non empty finite Element of K32(NAT)
dom (G1,G2) is finite Element of K32(NAT)
dom G2 is finite Element of K32(NAT)
((G1,G2) ^ <*W2*>) . vs is set
(G1,G2) . vs is set
G2 . ((2 * vs) - 1) is set
dom <*W2*> is non empty trivial finite 1 -element Element of K32(NAT)
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
(len (G1,G2)) + vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
(len (G1,G2)) + vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
((G1,G2) ^ <*W2*>) . vs is set
<*W2*> . 1 is set
dom (G1,G2) is finite Element of K32(NAT)
dom <*W2*> is non empty trivial finite 1 -element Element of K32(NAT)
((G1,G2) ^ <*W2*>) . vs is set
((G1,G2) ^ <*W2*>) . vs is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
(G2,W2) is Relation-like NAT -defined the_Vertices_of G2 -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
len (G1,W1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len (G1,W1)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
len W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len W2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
len (G2,W2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len (G2,W2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
dom (G1,W1) is finite Element of K32(NAT)
(G1,W1) . vs is set
2 * vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * vs) - 1 is non empty V28() V29() V30() ext-real non even set
W2 . ((2 * vs) - 1) is set
(G2,W2) . vs is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 div 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
dom (G1,G2) is finite Element of K32(NAT)
G2 . W1 is set
(G1,G2) . (W1 div 2) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W2 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of W2 is non empty set
the_Edges_of W2 is set
(the_Vertices_of W2) \/ (the_Edges_of W2) is non empty set
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
dom (G1,G2) is finite Element of K32(NAT)
2 * W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
dom G2 is finite Element of K32(NAT)
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
y is Relation-like NAT -defined (the_Vertices_of W2) \/ (the_Edges_of W2) -valued Function-like finite FinSequence-like FinSubsequence-like (W2)
dom y is finite Element of K32(NAT)
(W2,y) is Relation-like NAT -defined the_Edges_of W2 -valued Function-like finite FinSequence-like FinSubsequence-like (W2)
dom (W2,y) is finite Element of K32(NAT)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
dom (G1,G2) is finite Element of K32(NAT)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2) . W1 is set
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) - 1 is V28() V29() V30() ext-real even set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,1,W1)) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W2 is set
W1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1)) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
<*W1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
(G1,G2) ^ <*W1*> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
G2 is set
<*G2*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
W1 is set
W2 is set
(G1,W1,W2,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
(G1,(G1,W1,W2,G2)) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,W1,W2,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
len (G1,(G1,W1,W2,G2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len (G1,(G1,W1,W2,G2))) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len (G1,(G1,W1,W2,G2)))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
<*W1,G2,W2*> is non empty Relation-like NAT -defined Function-like finite 3 -element FinSequence-like FinSubsequence-like set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
(G1,(G1,W1,W2,G2)) . vs is set
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(G1,W1,W2,G2) . (2 * 1) is set
<*G2*> . vs is set
len <*G2*> is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(2 * 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
choose (the_Vertices_of G1) is Element of the_Vertices_of G1
(G1,(choose (the_Vertices_of G1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1) (G1) (G1)
<*(choose (the_Vertices_of G1))*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
(G1,(G1,G2)) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev (G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the_Edges_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len (G1,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len (G1,G2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len (G1,G2))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len (G1,(G1,G2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len (G1,(G1,G2))) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len (G1,(G1,G2)))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
(G1,(G1,G2)) . y is set
2 * y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(G1,G2) . (2 * y) is set
(len (G1,G2)) - y is V28() V29() V30() ext-real set
((len (G1,G2)) - y) + 1 is V28() V29() V30() ext-real set
Seg (len (G1,G2)) is finite len (G1,G2) -element Element of K32(NAT)
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
dom (G1,G2) is finite Element of K32(NAT)
dom G2 is finite Element of K32(NAT)
(len G2) - (2 * y) is non empty V28() V29() V30() ext-real non even set
((len G2) - (2 * y)) + 1 is V28() V29() V30() ext-real even set
((2 * (len (G1,G2))) + 1) - (2 * y) is non empty V28() V29() V30() ext-real non even set
(((2 * (len (G1,G2))) + 1) - (2 * y)) + 1 is V28() V29() V30() ext-real even set
2 * vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
dom (G1,G2) is finite Element of K32(NAT)
(Rev (G1,G2)) . y is set
(G1,G2) . vs is set
G2 . (2 * vs) is set
len (Rev (G1,G2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1)) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) ^ (G1,W1) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the_Edges_of G1
len ((G1,G2) ^ (G1,W1)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
len (G1,W1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(len (G1,G2)) + (len (G1,W1)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + (len W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
2 * (len (G1,W1)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len (G1,W1))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + ((2 * (len (G1,W1))) + 1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len G2) + (2 * (len (G1,W1))) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
((len G2) + (2 * (len (G1,W1)))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
len (G1,(G1,G2,W1)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len (G1,(G1,G2,W1))) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len (G1,(G1,G2,W1)))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(2 * (len (G1,W1))) + (len G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
2 * (len (G1,G2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len (G1,G2))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(2 * (len (G1,W1))) + ((2 * (len (G1,G2))) + 1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(2 * (len (G1,W1))) + (2 * (len (G1,G2))) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
((2 * (len (G1,W1))) + (2 * (len (G1,G2)))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 ^' W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,(G1,G2,W1)) . vs is set
2 * vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(G1,G2,W1) . (2 * vs) is set
dom ((G1,G2) ^ (G1,W1)) is finite Element of K32(NAT)
dom (G1,G2) is finite Element of K32(NAT)
2 * vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
dom G2 is finite Element of K32(NAT)
((G1,G2) ^ (G1,W1)) . vs is set
(G1,G2) . vs is set
G2 . (2 * vs) is set
(G1,(G1,G2,W1)) . vs is set
dom (G1,W1) is finite Element of K32(NAT)
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
(len (G1,G2)) + vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
(len (G1,G2)) + vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * vs) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
2 * vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * vs) + ((2 * (len (G1,G2))) + 1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(2 * vs) + (len G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(2 * vs) - 1 is non empty V28() V29() V30() ext-real non even set
(len G2) + ((2 * vs) - 1) is V28() V29() V30() ext-real even set
vs + vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
(len W1) - 0 is non empty V28() V29() V30() ext-real positive non negative set
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(1 + 1) - 1 is V28() V29() V30() ext-real set
(G1,G2,W1) . (2 * vs) is set
n + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W1 . (n + 1) is set
W1 . (2 * vs) is set
((G1,G2) ^ (G1,W1)) . vs is set
(G1,W1) . vs is set
(G1,(G1,G2,W1)) . vs is set
dom (G1,G2) is finite Element of K32(NAT)
dom (G1,W1) is finite Element of K32(NAT)
(G1,(G1,G2,W1)) . vs is set
((G1,G2) ^ (G1,W1)) . vs is set
(G1,(G1,G2,W1)) . vs is set
((G1,G2) ^ (G1,W1)) . vs is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
(G2,W2) is Relation-like NAT -defined the_Edges_of G2 -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
len (G1,W1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len (G1,W1)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len (G1,W1))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len (G2,W2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len (G2,W2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len (G2,W2))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
dom (G1,W1) is finite Element of K32(NAT)
(G1,W1) . vs is set
2 * vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W2 . (2 * vs) is set
(G2,W2) . vs is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W2 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of W2 is non empty set
the_Edges_of W2 is set
(the_Vertices_of W2) \/ (the_Edges_of W2) is non empty set
W1 is set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y is Relation-like NAT -defined (the_Vertices_of W2) \/ (the_Edges_of W2) -valued Function-like finite FinSequence-like FinSubsequence-like (W2)
len y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y . vs is set
vs is set
(W2,y) is finite Element of K32((the_Vertices_of W2))
K32((the_Vertices_of W2)) is non empty set
(W2,y) is Relation-like NAT -defined the_Vertices_of W2 -valued Function-like finite FinSequence-like FinSubsequence-like (W2)
rng (W2,y) is finite Element of K32((the_Vertices_of W2))
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) is Element of the_Vertices_of G1
G2 . W1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
G2 is Element of the_Vertices_of G1
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1) (G1) (G1)
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
<*G2*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
(G1,(G1,G2)) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,(G1,G2)) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,(G1,G2)) is finite Element of K32((the_Vertices_of G1))
{G2} is non empty trivial finite 1 -element Element of K32((the_Vertices_of G1))
len (G1,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is set
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) . W2 is set
(G1,G2) . 1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
G2 is set
W1 is set
W2 is set
(G1,W1,W2,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
(G1,(G1,W1,W2,G2)) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,(G1,W1,W2,G2)) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,(G1,W1,W2,G2)) is finite Element of K32((the_Vertices_of G1))
{W1,W2} is non empty finite set
<*W1,W2*> is non empty Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
(G1,(G1,G2)) is finite Element of K32((the_Vertices_of G1))
(G1,(G1,G2)) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,(G1,G2)) is finite Element of K32((the_Vertices_of G1))
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . vs is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y - vs is V28() V29() V30() ext-real even set
(y - vs) + 1 is non empty V28() V29() V30() ext-real non even set
dom G2 is finite Element of K32(NAT)
Seg (len G2) is non empty finite len G2 -element Element of K32(NAT)
len (G1,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) - vs is V28() V29() V30() ext-real even set
((len G2) - vs) + 1 is non empty V28() V29() V30() ext-real non even set
(G1,G2) . (((len G2) - vs) + 1) is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) . y is set
dom (G1,G2) is finite Element of K32(NAT)
(len G2) - y is V28() V29() V30() ext-real even set
((len G2) - y) + 1 is non empty V28() V29() V30() ext-real non even set
G2 . (((len G2) - y) + 1) is set
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 - y is V28() V29() V30() ext-real even set
(W1 - y) + 1 is non empty V28() V29() V30() ext-real non even set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1)) is finite Element of K32((the_Vertices_of G1))
(G1,(G1,G2,W1)) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,(G1,G2,W1)) is finite Element of K32((the_Vertices_of G1))
(G1,W1) is finite Element of K32((the_Vertices_of G1))
(G1,W1) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,W1) is finite Element of K32((the_Vertices_of G1))
(G1,G2) \/ (G1,W1) is finite Element of K32((the_Vertices_of G1))
G2 ^' W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
y is set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . vs is set
dom G2 is finite Element of K32(NAT)
dom (G1,G2,W1) is finite Element of K32(NAT)
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) . vs is set
vs is Element of the_Vertices_of G1
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) . vs is set
G2 . vs is set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
(len G2) + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
0 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len G2) + n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
((len G2) + n) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len (G1,G2,W1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
n + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(n + 1) + (len G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len W1) + (len G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((n + 1) + (len G2)) - (len G2) is non empty V28() V29() V30() ext-real non even set
((len W1) + (len G2)) - (len G2) is non empty V28() V29() V30() ext-real non even set
(G1,W1,(n + 1)) is Element of the_Vertices_of G1
(len W1) - 1 is V28() V29() V30() ext-real even set
((len W1) - 1) + 1 is non empty V28() V29() V30() ext-real non even set
W1 . (n + 1) is set
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . vs is set
vs - 1 is V28() V29() V30() ext-real even set
(len W1) - 0 is non empty V28() V29() V30() ext-real positive non negative set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(len G2) + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) . ((len G2) + vs) is set
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (vs + 1) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1,W2)) is finite Element of K32((the_Vertices_of G1))
(G1,(G1,G2,W1,W2)) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,(G1,G2,W1,W2)) is finite Element of K32((the_Vertices_of G1))
vs is set
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) . vs is set
vs - 1 is V28() V29() V30() ext-real even set
(len (G1,G2,W1,W2)) - 0 is non empty V28() V29() V30() ext-real positive non negative set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W1 + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
dom G2 is finite Element of K32(NAT)
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) . (vs + 1) is set
G2 . (W1 + vs) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
W1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1)) is finite Element of K32((the_Vertices_of G1))
(G1,(G1,G2,W1)) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,(G1,G2,W1)) is finite Element of K32((the_Vertices_of G1))
W2 is set
{W2} is non empty trivial finite 1 -element set
(G1,G2) \/ {W2} is non empty finite set
vs is Element of the_Vertices_of G1
(G1,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) . 1 is set
(G1,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is finite Element of K32((the_Vertices_of G1))
(G1,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is finite Element of K32((the_Vertices_of G1))
(G1,G2) \/ (G1,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is finite Element of K32((the_Vertices_of G1))
n is set
{(G1,G2),W2} is non empty finite set
(G1,G2) \/ {(G1,G2),W2} is non empty finite set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] finite set
the_Vertices_of G1 is non empty finite set
the_Edges_of G1 is finite set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty finite set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty finite V49() set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
card (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(card (G1,G2)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W2 is set
W1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1)) is finite Element of K32((the_Vertices_of G1))
(G1,(G1,G2,W1)) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,(G1,G2,W1)) is finite Element of K32((the_Vertices_of G1))
card (G1,(G1,G2,W1)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
{W2} is non empty trivial finite 1 -element set
(G1,G2) \/ {W2} is non empty finite set
card ((G1,G2) \/ {W2}) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
W1 is set
W2 is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . y is set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . vs is set
(G1,G2,y,vs) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2,vs,y) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,vs,y)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev (G1,G2,vs,y) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
vs is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
(G1,W1) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,W1) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,W1) is finite Element of K32((the_Vertices_of G1))
(G2,W2) is finite Element of K32((the_Vertices_of G2))
K32((the_Vertices_of G2)) is non empty set
(G2,W2) is Relation-like NAT -defined the_Vertices_of G2 -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
rng (G2,W2) is finite Element of K32((the_Vertices_of G2))
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W2 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of W2 is non empty set
the_Edges_of W2 is set
(the_Vertices_of W2) \/ (the_Edges_of W2) is non empty set
W1 is set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
y is Relation-like NAT -defined (the_Vertices_of W2) \/ (the_Edges_of W2) -valued Function-like finite FinSequence-like FinSubsequence-like (W2)
len y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y . vs is set
vs is set
(W2,y) is finite Element of K32((the_Edges_of W2))
K32((the_Edges_of W2)) is non empty set
(W2,y) is Relation-like NAT -defined the_Edges_of W2 -valued Function-like finite FinSequence-like FinSubsequence-like (W2)
rng (W2,y) is finite Element of K32((the_Edges_of W2))
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
G2 . W2 is set
W2 - 1 is non empty V28() V29() V30() ext-real non even set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) - 0 is non empty V28() V29() V30() ext-real positive non negative set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (vs + 1) is set
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (W2 + 1) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng G2 is finite Element of K32(((the_Vertices_of G1) \/ (the_Edges_of G1)))
K32(((the_Vertices_of G1) \/ (the_Edges_of G1))) is non empty set
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
(G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
(G1,G2) \/ (G1,G2) is finite set
W1 is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W2 is set
dom G2 is finite Element of K32(NAT)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
G2 . W2 is set
dom G2 is finite Element of K32(NAT)
W1 is set
dom G2 is finite Element of K32(NAT)
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
G2 . W2 is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1)) is finite Element of K32((the_Edges_of G1))
(G1,(G1,G2,W1)) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,(G1,G2,W1)) is finite Element of K32((the_Edges_of G1))
(G1,W1) is finite Element of K32((the_Edges_of G1))
(G1,W1) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,W1) is finite Element of K32((the_Edges_of G1))
(G1,G2) \/ (G1,W1) is finite Element of K32((the_Edges_of G1))
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 ^' W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
xaa1 is set
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(G1,G2,W1) . W2 is set
G2 . W2 is set
n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 - n is non empty V28() V29() V30() ext-real non even set
g is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
g + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len (G1,G2,W1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(W2 - n) + (len G2) is V28() V29() V30() ext-real even set
x is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
x + (len G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(W2 - n) + n is V28() V29() V30() ext-real even set
(x + (len G2)) - (len G2) is non empty V28() V29() V30() ext-real non even set
W1 . (g + 1) is set
(len G2) + g is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1,G2,W1) . ((len G2) + g) is set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
G2 . W2 is set
(G1,G2,W1) . W2 is set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W1 . W2 is set
W2 - 1 is non empty V28() V29() V30() ext-real non even set
g is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
n + g is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(G1,G2,W1) . (n + g) is set
g + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W1 . (g + 1) is set
(g + 1) + n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len W1) + (len G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(n + g) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
dom (G1,G2) is finite Element of K32(NAT)
W1 is set
W2 is set
(G1,G2) . W2 is set
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2) . vs is set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2) . W2 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
W2 is set
y is set
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1,W2)) is finite Element of K32((the_Edges_of G1))
(G1,(G1,G2,W1,W2)) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,(G1,G2,W1,W2)) is finite Element of K32((the_Edges_of G1))
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is set
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(G1,G2,W1,W2) . vs is set
vs - 1 is non empty V28() V29() V30() ext-real non even set
(len (G1,G2,W1,W2)) - 0 is non empty V28() V29() V30() ext-real positive non negative set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
dom G2 is finite Element of K32(NAT)
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y + vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (W1 + vs) is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
(G1,(G1,G2)) is finite Element of K32((the_Edges_of G1))
(G1,(G1,G2)) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,(G1,G2)) is finite Element of K32((the_Edges_of G1))
W1 is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
G2 . W2 is set
dom G2 is finite Element of K32(NAT)
(len G2) - W2 is non empty V28() V29() V30() ext-real non even set
((len G2) - W2) + 1 is V28() V29() V30() ext-real even set
dom (G1,G2) is finite Element of K32(NAT)
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
len (G1,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) . (((len G2) - W2) + 1) is set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(G1,G2) . W2 is set
(len (G1,G2)) - W2 is non empty V28() V29() V30() ext-real non even set
((len (G1,G2)) - W2) + 1 is V28() V29() V30() ext-real even set
(G1,(G1,G2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev (G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
dom (G1,(G1,G2)) is finite Element of K32(NAT)
(G1,(G1,G2)) . (((len (G1,G2)) - W2) + 1) is set
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
G2 . y is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
G2 is set
{G2} is non empty trivial finite 1 -element set
W1 is set
W2 is set
(G1,W1,W2,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
(G1,(G1,W1,W2,G2)) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,(G1,W1,W2,G2)) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,(G1,W1,W2,G2)) is finite Element of K32((the_Edges_of G1))
<*G2*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
len (G1,W1,W2,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(G1,W1,W2,G2) . vs is set
2 * 0 is empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V21() V22() V23() V25() V26() V27() V28() V29() V30() ext-real non positive non negative finite finite-yielding V49() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V86() even Element of NAT
(2 * 0) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
choose (the_Vertices_of G1) is Element of the_Vertices_of G1
(G1,(choose (the_Vertices_of G1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1) (G1) (G1)
<*(choose (the_Vertices_of G1))*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
G1 .edgesBetween (G1,G2) is Element of K32((the_Edges_of G1))
W1 is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is Element of the_Vertices_of G1
G2 . vs is set
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (vs + 1) is set
y is Element of the_Vertices_of G1
G2 . (vs + 2) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
(G1,W1) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,W1) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,W1) is finite Element of K32((the_Edges_of G1))
(G2,W2) is finite Element of K32((the_Edges_of G2))
K32((the_Edges_of G2)) is non empty set
(G2,W2) is Relation-like NAT -defined the_Edges_of G2 -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
rng (G2,W2) is finite Element of K32((the_Edges_of G2))
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
W1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,W1)) is finite Element of K32((the_Edges_of G1))
(G1,(G1,G2,W1)) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,(G1,G2,W1)) is finite Element of K32((the_Edges_of G1))
{W1} is non empty trivial finite 1 -element set
(G1,G2) \/ {W1} is non empty finite set
W2 is set
(G1,G2) .edgesInOut() is Element of K32((the_Edges_of G1))
(G1,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) . 1 is set
(G1,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is finite Element of K32((the_Edges_of G1))
(G1,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is finite Element of K32((the_Edges_of G1))
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (G1,G2)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,W1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,W1) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,W1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (G1,G2)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
2 * (G1,W1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (G1,W1)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
(G1,W1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,W1) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,W1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G2,W2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G2,W2) is Relation-like NAT -defined the_Edges_of G2 -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
len (G2,W2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
(G1,G2,(G2 . W1)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,(G2 . W1)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
y is set
(G1,W1,y) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G2,W2,y) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,W1,y) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G2,W2,y) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,W1) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,W1) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,W1) is finite Element of K32((the_Vertices_of G1))
W2 . (G1,W1,y) is set
(G2,W2) is finite Element of K32((the_Vertices_of G2))
K32((the_Vertices_of G2)) is non empty set
(G2,W2) is Relation-like NAT -defined the_Vertices_of G2 -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
rng (G2,W2) is finite Element of K32((the_Vertices_of G2))
len W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even set
W2 . vs is set
W2 . (G1,W1,y) is set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 . vs is set
(G1,W1) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,W1) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,W1) is finite Element of K32((the_Vertices_of G1))
(G2,W2) is finite Element of K32((the_Vertices_of G2))
K32((the_Vertices_of G2)) is non empty set
(G2,W2) is Relation-like NAT -defined the_Vertices_of G2 -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
rng (G2,W2) is finite Element of K32((the_Vertices_of G2))
len W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,W1) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,W1) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,W1) is finite Element of K32((the_Vertices_of G1))
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G2 . 1 is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) is Element of the_Vertices_of G1
(G1,G2) is Element of the_Vertices_of G1
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,(G1,G2)) is Element of the_Vertices_of G1
len (G1,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2) . (len (G1,G2)) is set
(G1,(G1,G2)) is Element of the_Vertices_of G1
(G1,G2) . 1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
W2 . 1 is set
len W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 . (len W2) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W2 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of W2 is non empty set
the_Edges_of W2 is set
(the_Vertices_of W2) \/ (the_Edges_of W2) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
W1 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (W1 + 2) is set
W1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (W1 + 1) is set
y is Relation-like NAT -defined (the_Vertices_of W2) \/ (the_Edges_of W2) -valued Function-like finite FinSequence-like FinSubsequence-like (W2)
len y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is set
W2 is set
vs is set
y is set
(G1,G2,y) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) .adj y is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj y),y) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj y),y)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of W1 is non empty set
the_Edges_of W1 is set
(the_Vertices_of W1) \/ (the_Edges_of W1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is Relation-like NAT -defined (the_Vertices_of W1) \/ (the_Edges_of W1) -valued Function-like finite FinSequence-like FinSubsequence-like (W1)
len W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of W1 is non empty set
the_Edges_of W1 is set
(the_Vertices_of W1) \/ (the_Edges_of W1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is Relation-like NAT -defined (the_Vertices_of W1) \/ (the_Edges_of W1) -valued Function-like finite FinSequence-like FinSubsequence-like (W1)
len W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of W1 is non empty set
the_Edges_of W1 is set
(the_Vertices_of W1) \/ (the_Edges_of W1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is Relation-like NAT -defined (the_Vertices_of W1) \/ (the_Edges_of W1) -valued Function-like finite FinSequence-like FinSubsequence-like (W1)
y is Element of the_Vertices_of W1
(W1,y) is Relation-like NAT -defined (the_Vertices_of W1) \/ (the_Edges_of W1) -valued Function-like finite FinSequence-like FinSubsequence-like (W1) (W1) (W1) (W1) (W1) (W1) (W1)
<*y*> is non empty trivial Relation-like NAT -defined the_Vertices_of W1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of W1
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
len (G1,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,W1) is Element of the_Vertices_of G1
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (len W1) is set
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
W1 ^' G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
len (G1,W1,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,W1,G2)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len W1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
(G1,W1,G2) . W2 is set
W1 . W2 is set
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,W1,G2) . y is set
W1 . y is set
(G1,W1) is Element of the_Vertices_of G1
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (len W1) is set
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,W1) is Element of the_Vertices_of G1
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (len W1) is set
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,W1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W1,W2)) + W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W2 - W1 is V28() V29() V30() ext-real even set
(W2 - W1) + 1 is non empty V28() V29() V30() ext-real non even set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is set
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
1 + 0 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) - 2 is V28() V29() V30() ext-real set
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(len G2) - (2 * 1) is non empty V28() V29() V30() ext-real non even set
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (W2 + 1) is set
(G1,(G1,G2,1,W2),(G2 . (W2 + 1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,1,W2)) is Element of the_Vertices_of G1
len (G1,G2,1,W2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,1,W2) . (len (G1,G2,1,W2)) is set
(G1,(G1,G2,1,W2)) .adj (G2 . (W2 + 1)) is Element of the_Vertices_of G1
(G1,(G1,(G1,G2,1,W2)),((G1,(G1,G2,1,W2)) .adj (G2 . (W2 + 1))),(G2 . (W2 + 1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,(G1,G2,1,W2),(G1,(G1,(G1,G2,1,W2)),((G1,(G1,G2,1,W2)) .adj (G2 . (W2 + 1))),(G2 . (W2 + 1)))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(len G2) - 0 is non empty V28() V29() V30() ext-real positive non negative set
W2 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,1,(W2 + 2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is finite Element of K32((the_Edges_of G1))
(G1,W1) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,W1) is finite Element of K32((the_Edges_of G1))
(G1,W1) is finite Element of K32((the_Vertices_of G1))
(G1,W1) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,W1) is finite Element of K32((the_Vertices_of G1))
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . y is set
y - 0 is non empty V28() V29() V30() ext-real positive non negative set
3 - 1 is V28() V29() V30() ext-real set
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
y - (2 * 1) is non empty V28() V29() V30() ext-real non even set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . vs is set
vs + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (vs + 2) is set
G2 . (vs + 1) is set
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W1 . vs is set
vs - 1 is non empty V28() V29() V30() ext-real non even set
(len W1) - 0 is non empty V28() V29() V30() ext-real positive non negative set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . vs is set
vs + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (vs + 2) is set
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W1 . (vs + 1) is set
(G1,W1,vs) is Element of the_Vertices_of G1
(G1,W1,(vs + 2)) is Element of the_Vertices_of G1
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (y + 1) is set
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W1 . vs is set
y + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (y + 2) is set
vs - 1 is non empty V28() V29() V30() ext-real non even set
(len W1) - 0 is non empty V28() V29() V30() ext-real positive non negative set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . vs is set
vs + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (vs + 2) is set
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W1 . (vs + 1) is set
(G1,W1,vs) is Element of the_Vertices_of G1
(G1,W1,(vs + 2)) is Element of the_Vertices_of G1
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is Element of the_Vertices_of G1
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W2 is set
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(len G2) - (2 * 1) is non empty V28() V29() V30() ext-real non even set
(len G2) - 0 is non empty V28() V29() V30() ext-real positive non negative set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . y is set
y + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (y + 2) is set
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (y + 1) is set
W1 .edgesInOut() is Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
W2 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (W2 + 2) is set
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (W2 + 1) is set
W1 .edgesInOut() is Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
W1 .edgesInOut() is Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
W1 .edgesInOut() is Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
y is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
(G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
len W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
y is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of y is non empty set
the_Edges_of y is set
(the_Vertices_of y) \/ (the_Edges_of y) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
vs is Relation-like NAT -defined (the_Vertices_of y) \/ (the_Edges_of y) -valued Function-like finite FinSequence-like FinSubsequence-like (y)
len vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of W1 is non empty set
the_Edges_of W1 is set
(the_Vertices_of W1) \/ (the_Edges_of W1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
W2 is Relation-like NAT -defined (the_Vertices_of W1) \/ (the_Edges_of W1) -valued Function-like finite FinSequence-like FinSubsequence-like (W1)
(W1,W2) is Relation-like NAT -defined (the_Vertices_of W1) \/ (the_Edges_of W1) -valued Function-like finite FinSequence-like FinSubsequence-like (W1)
Rev W2 is Relation-like NAT -defined (the_Vertices_of W1) \/ (the_Edges_of W1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of W1) \/ (the_Edges_of W1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) .edgesInOut() is Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is finite Element of K32((the_Edges_of G1))
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W1 is Element of the_Vertices_of G1
W1 .edgesInOut() is Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
W2 is set
{W2} is non empty trivial finite 1 -element set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . y is set
(G1,G2,y) is Element of the_Vertices_of G1
y - 1 is V28() V29() V30() ext-real even set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(1 + 1) - 1 is V28() V29() V30() ext-real set
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (y + 1) is set
G2 . (y - 1) is set
G2 . vs is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] finite set
the_Vertices_of G1 is non empty finite set
the_Edges_of G1 is finite set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty finite set
G1 .size() is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W1 is Relation-like Function-like set
dom W1 is set
W2 is set
y is set
W1 . W2 is set
W1 . y is set
vs is set
vs is set
[vs,vs] is V1() set
dom (G1,G2) is finite Element of K32(NAT)
y `2 is set
(G1,G2) . vs is set
vs is set
n is set
[vs,n] is V1() set
[vs,vs] `2 is set
[vs,n] `2 is set
W2 `2 is set
(G1,G2) . vs is set
W2 is set
rng W1 is set
y is set
W1 . y is set
vs is set
vs is set
[vs,vs] is V1() set
[vs,vs] `2 is set
y `2 is set
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty finite V49() set
card (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
card (the_Edges_of G1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
W1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of W1 is non empty set
the_Edges_of W1 is set
(the_Vertices_of W1) \/ (the_Edges_of W1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
W2 is Relation-like NAT -defined (the_Vertices_of W1) \/ (the_Edges_of W1) -valued Function-like finite FinSequence-like FinSubsequence-like (W1)
(W1,W2) is Relation-like NAT -defined (the_Vertices_of W1) \/ (the_Edges_of W1) -valued Function-like finite FinSequence-like FinSubsequence-like (W1)
Rev W2 is Relation-like NAT -defined (the_Vertices_of W1) \/ (the_Edges_of W1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of W1) \/ (the_Edges_of W1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2,W1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
W2 is set
W1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .edgesInOut() is Element of K32((the_Edges_of G1))
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) . vs is set
(G1,G2,W1) . vs is set
dom G2 is finite Element of K32(NAT)
G2 . vs is set
G2 . vs is set
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(y + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len G2) + (1 + 1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len G2) + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) . ((len G2) + 2) is set
(len G2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((len G2) + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
dom G2 is finite Element of K32(NAT)
G2 . vs is set
n is Element of the_Vertices_of G1
(G1,n) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1) (G1) (G1)
<*n*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
1 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(vs + 1) - 1 is non empty V28() V29() V30() ext-real non even set
3 - 1 is V28() V29() V30() ext-real set
2 - 1 is V28() V29() V30() ext-real set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W2 is set
W1 is set
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
(G1,G2,(G2 . W1)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,(G2 . W1)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
dom G2 is finite Element of K32(NAT)
W2 - 1 is non empty V28() V29() V30() ext-real non even set
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (W2 + 1) is set
G2 . W2 is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . y is set
W1 - 1 is non empty V28() V29() V30() ext-real non even set
W1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (W1 + 1) is set
G2 . W1 is set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . vs is set
(G1,G2,(G2 . vs)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs - 1 is V28() V29() V30() ext-real even set
(vs - 1) + 1 is non empty V28() V29() V30() ext-real non even set
(W1 - 1) + 1 is V28() V29() V30() ext-real even set
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W1 is set
G2 . W2 is set
(G1,G2,(G2 . W1)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] finite set
the_Vertices_of G1 is non empty finite set
the_Edges_of G1 is finite set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty finite set
G1 .order() is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(G1 .order()) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
2 * (len (G1,G2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) - 2 is V28() V29() V30() ext-real set
W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,1,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
W1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (W1 + 1) is set
(G1,(G1,G2,1,W1),(G2 . (W1 + 1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,1,W1)) is Element of the_Vertices_of G1
len (G1,G2,1,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,1,W1) . (len (G1,G2,1,W1)) is set
(G1,(G1,G2,1,W1)) .adj (G2 . (W1 + 1)) is Element of the_Vertices_of G1
(G1,(G1,(G1,G2,1,W1)),((G1,(G1,G2,1,W1)) .adj (G2 . (W1 + 1))),(G2 . (W1 + 1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,(G1,G2,1,W1),(G1,(G1,(G1,G2,1,W1)),((G1,(G1,G2,1,W1)) .adj (G2 . (W1 + 1))),(G2 . (W1 + 1)))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,1,W1)) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
vs is Relation-like Function-like set
dom vs is set
(len G2) - 0 is non empty V28() V29() V30() ext-real positive non negative set
vs is set
vs is set
vs . vs is set
vs . vs is set
n is set
n is set
[n,n] is V1() set
(G1,(G1,G2,1,W1)) . n is set
[n,n] `2 is set
vs `2 is set
x is set
xaa1 is set
[x,xaa1] is V1() set
dom (G1,(G1,G2,1,W1)) is finite Element of K32(NAT)
(G1,(G1,G2,1,W1)) . x is set
[x,xaa1] `2 is set
vs `2 is set
es is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
es is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,(G1,G2,1,W1)) . es is set
(G1,(G1,G2,1,W1)) . es is set
2 * es is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * es) - 1 is non empty V28() V29() V30() ext-real non even set
dom (G1,G2,1,W1) is finite Element of K32(NAT)
2 * es is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * es) - 1 is non empty V28() V29() V30() ext-real non even set
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,1,W1) . W2 is set
G2 . W2 is set
len (G1,(G1,G2,1,W1)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
es is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,1,W1) . es is set
G2 . es is set
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
g is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
vs is set
rng vs is set
vs is set
vs . vs is set
n is set
n is set
[n,n] is V1() set
[n,n] `2 is set
vs `2 is set
(G1,(G1,G2,1,W1)) . n is set
rng (G1,(G1,G2,1,W1)) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty finite V49() set
card (G1,(G1,G2,1,W1)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
card (the_Vertices_of G1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len (G1,(G1,G2,1,W1))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G2 . W1 is set
W1 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (W1 + 2) is set
<*(G2 . (W1 + 2))*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
(G1,(G1,G2,1,W1)) ^ <*(G2 . (W1 + 2))*> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len <*(G2 . (W1 + 2))*> is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len (G1,(G1,G2,1,W1))) + (len <*(G2 . (W1 + 2))*>) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1)
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
W2 is set
W1 is set
(G1,G2,W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) .adj W1 is Element of the_Vertices_of G1
(G1,(G1,G2),((G1,G2) .adj W1),W1) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,G2,(G1,(G1,G2),((G1,G2) .adj W1),W1)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,G2,W1) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len G2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
((len G2) + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) . vs is set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,W1) . vs is set
(G1,G2,W1) . vs is set
dom G2 is finite Element of K32(NAT)
G2 . vs is set
G2 . vs is set
dom G2 is finite Element of K32(NAT)
G2 . vs is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
G2 is set
W1 is set
(G1,W1,W1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1)
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
len (G1,W1,W1,G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
W1 is set
W2 is set
y is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is Element of the_Vertices_of G1
G2 . vs is set
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (vs + 1) is set
vs is Element of the_Vertices_of G1
G2 . (vs + 2) is set
(G1,G2,(vs + 2),(len G2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
2 * 0 is empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V21() V22() V23() V25() V26() V27() V28() V29() V30() ext-real non positive non negative finite finite-yielding V49() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V86() even Element of NAT
(2 * 0) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,((2 * 0) + 1),vs) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,G2,(vs + 2),(len G2))) is Element of the_Vertices_of G1
len (G1,G2,(vs + 2),(len G2)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,G2,(vs + 2),(len G2)) . (len (G1,G2,(vs + 2),(len G2))) is set
(G1,G2) is Element of the_Vertices_of G1
G2 . (len G2) is set
(len G2) - 0 is non empty V28() V29() V30() ext-real positive non negative set
(vs + 2) - 2 is V28() V29() V30() ext-real set
(G1,(G1,G2,((2 * 0) + 1),vs)) is finite Element of K32((the_Edges_of G1))
(G1,(G1,G2,((2 * 0) + 1),vs)) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,(G1,G2,((2 * 0) + 1),vs)) is finite Element of K32((the_Edges_of G1))
len (G1,G2,((2 * 0) + 1),vs) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
x is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(G1,G2,((2 * 0) + 1),vs) . x is set
dom (G1,G2,((2 * 0) + 1),vs) is finite Element of K32(NAT)
G2 . x is set
x + 0 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,(G1,G2,(vs + 2),(len G2)),(G1,G2,((2 * 0) + 1),vs)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,(G1,(G1,G2,(vs + 2),(len G2)),(G1,G2,((2 * 0) + 1),vs))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
Rev (G1,(G1,G2,(vs + 2),(len G2)),(G1,G2,((2 * 0) + 1),vs)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G1) \/ (the_Edges_of G1)
(G1,(G1,G2,(vs + 2),(len G2))) is finite Element of K32((the_Edges_of G1))
(G1,(G1,G2,(vs + 2),(len G2))) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,(G1,G2,(vs + 2),(len G2))) is finite Element of K32((the_Edges_of G1))
x is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(G1,G2,(vs + 2),(len G2)) . x is set
x - 1 is non empty V28() V29() V30() ext-real non even set
(len (G1,G2,(vs + 2),(len G2))) - 0 is non empty V28() V29() V30() ext-real positive non negative set
xaa1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(vs + 2) + xaa1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
dom G2 is finite Element of K32(NAT)
xaa1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . ((vs + 2) + xaa1) is set
(vs + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(vs + 1) + 0 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(G1,(G1,G2,((2 * 0) + 1),vs)) is Element of the_Vertices_of G1
(G1,G2,((2 * 0) + 1),vs) . 1 is set
(G1,(G1,(G1,G2,(vs + 2),(len G2)),(G1,G2,((2 * 0) + 1),vs))) is finite Element of K32((the_Edges_of G1))
(G1,(G1,(G1,G2,(vs + 2),(len G2)),(G1,G2,((2 * 0) + 1),vs))) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,(G1,(G1,G2,(vs + 2),(len G2)),(G1,G2,((2 * 0) + 1),vs))) is finite Element of K32((the_Edges_of G1))
(G1,(G1,G2,(vs + 2),(len G2))) \/ (G1,(G1,G2,((2 * 0) + 1),vs)) is finite Element of K32((the_Edges_of G1))
(G1,(G1,(G1,(G1,G2,(vs + 2),(len G2)),(G1,G2,((2 * 0) + 1),vs)))) is finite Element of K32((the_Edges_of G1))
(G1,(G1,(G1,(G1,G2,(vs + 2),(len G2)),(G1,G2,((2 * 0) + 1),vs)))) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,(G1,(G1,(G1,G2,(vs + 2),(len G2)),(G1,G2,((2 * 0) + 1),vs)))) is finite Element of K32((the_Edges_of G1))
x is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,x) is finite Element of K32((the_Edges_of G1))
(G1,x) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,x) is finite Element of K32((the_Edges_of G1))
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,G2)
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1,W1)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is set
y is set
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(G1,W1) is Element of the_Vertices_of G1
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (len W1) is set
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,G2) is Element of the_Vertices_of G1
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (len G2) is set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(G1,W1) is Element of the_Vertices_of G1
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (len W1) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is finite Element of K32((the_Edges_of G1))
(G1,W1) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,W1) is finite Element of K32((the_Edges_of G1))
(G1,W1) is finite Element of K32((the_Vertices_of G1))
(G1,W1) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,W1) is finite Element of K32((the_Vertices_of G1))
K32((G1,W1)) is non empty finite V49() set
W2 is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSubsequence-like Element of K32((G1,W1))
Seq W2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
y is set
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
G2 . vs is set
vs div 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(Seq W2) . (vs div 2) is set
dom (Seq W2) is finite Element of K32(NAT)
dom (G1,W1) is finite Element of K32(NAT)
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,W1) . vs is set
y is set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . vs is set
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . W2 is set
(G1,W1) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
K32((G1,W1)) is non empty finite V49() set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (W2 + 2) is set
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (W2 + 1) is set
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
G2 . y is set
y div 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2) . (y div 2) is set
dom (G1,G2) is finite Element of K32(NAT)
dom (G1,W1) is finite Element of K32(NAT)
vs is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSubsequence-like Element of K32((G1,W1))
Seq vs is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,W1) . vs is set
2 * vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
2 * (y div 2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
y - 1 is non empty V28() V29() V30() ext-real non even set
(2 * vs) - 1 is non empty V28() V29() V30() ext-real non even set
len (G1,W1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
dom W1 is finite Element of K32(NAT)
(len W1) - 0 is non empty V28() V29() V30() ext-real positive non negative set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . vs is set
vs + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (vs + 2) is set
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W1 . (vs + 1) is set
n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . n is set
(G1,G2) is Element of the_Vertices_of G1
G2 . (len G2) is set
(G1,W1) is Element of the_Vertices_of G1
W1 . (len W1) is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . y is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,W1) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
K32((G1,W1)) is non empty finite V49() set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
G2 . W2 is set
W2 div 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2) . (W2 div 2) is set
dom (G1,G2) is finite Element of K32(NAT)
dom (G1,W1) is finite Element of K32(NAT)
y is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSubsequence-like Element of K32((G1,W1))
Seq y is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,W1) . y is set
len (G1,W1) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (W2 div 2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
2 * y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
dom W1 is finite Element of K32(NAT)
W1 . (2 * y) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,G2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,G2)
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,G2)
(G1,W2) is Element of the_Vertices_of G1
W2 . 1 is set
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
(G1,W2) is Element of the_Vertices_of G1
len W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 . (len W2) is set
(G1,G2) is Element of the_Vertices_of G1
G2 . (len G2) is set
G2 . (len G2) is set
W1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
G2 . W1 is set
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W2 - (2 * 1) is non empty V28() V29() V30() ext-real non even set
(G1,G2,W2,(len G2)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1,G2)
2 * 0 is empty Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V21() V22() V23() V25() V26() V27() V28() V29() V30() ext-real non positive non negative finite finite-yielding V49() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V86() even Element of NAT
(2 * 0) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y))
(G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y)) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
K32((G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y))) is non empty finite V49() set
(G1, the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y))) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
n is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSubsequence-like Element of K32((G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y)))
Seq n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(G1,(G1,G2,W2,(len G2))) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
G2 . W2 is set
(G1,G2) is Element of the_Vertices_of G1
(G1,G2,1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1)
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
K32((G1,G2)) is non empty finite V49() set
(G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y)) is Element of the_Vertices_of G1
(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y) . 1 is set
(G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y)) is Element of the_Vertices_of G1
len (G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y) . (len (G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y)) is set
len (G1,G2,W2,(len G2)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len (G1,G2,W2,(len G2))) + (len G2) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len G2) + W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
(len (G1,G2,W2,(len G2))) - 0 is non empty V28() V29() V30() ext-real positive non negative set
(G1,G2,W2,(len G2)) . y is set
(G1, the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y))) is Element of the_Vertices_of G1
len the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y)) is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y)) . (len the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y))) is set
dom (G1,G2,W2,(len G2)) is finite Element of K32(NAT)
G2 . y is set
(G1,G2,W2,(len G2)) . 1 is set
(G1, the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y))) is Element of the_Vertices_of G1
the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y)) . 1 is set
G2 . 1 is set
W2 - 0 is non empty V28() V29() V30() ext-real positive non negative set
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (y + 1) is set
(G1, the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y)),(G2 . (y + 1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1, the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y))) .adj (G2 . (y + 1)) is Element of the_Vertices_of G1
(G1,(G1, the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y))),((G1, the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y))) .adj (G2 . (y + 1))),(G2 . (y + 1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1, the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y)),(G1,(G1, the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y))),((G1, the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y))) .adj (G2 . (y + 1))),(G2 . (y + 1)))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(len G2) - 0 is non empty V28() V29() V30() ext-real positive non negative set
y + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (y + 2) is set
W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y)) . W2 is set
g is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y) . g is set
dom (G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y) is finite Element of K32(NAT)
(G1,G2,W2,(len G2)) . g is set
g + 0 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
G2 . g is set
(G1, the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y))) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
rng (G1, the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y))) is finite Element of K32((the_Edges_of G1))
(G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y)) is finite Element of K32((the_Edges_of G1))
rng (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y)) is finite Element of K32((the_Edges_of G1))
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y) . W2 is set
(G1,G2,W2,(len G2)) . W2 is set
G2 . W2 is set
(y + 1) div 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
((y + 1) div 2) .--> (G2 . (y + 1)) is Relation-like NAT -defined {((y + 1) div 2)} -defined Function-like one-to-one finite set
{((y + 1) div 2)} is non empty trivial finite V49() 1 -element set
{((y + 1) div 2)} --> (G2 . (y + 1)) is non empty Relation-like {((y + 1) div 2)} -defined Function-like constant V17({((y + 1) div 2)}) V18({((y + 1) div 2)},{(G2 . (y + 1))}) finite Element of K32(K33({((y + 1) div 2)},{(G2 . (y + 1))}))
{(G2 . (y + 1))} is non empty trivial finite 1 -element set
K33({((y + 1) div 2)},{(G2 . (y + 1))}) is non empty Relation-like finite set
K32(K33({((y + 1) div 2)},{(G2 . (y + 1))})) is non empty finite V49() set
n is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSubsequence-like Element of K32((G1,G2))
n +* (((y + 1) div 2) .--> (G2 . (y + 1))) is Relation-like Function-like finite set
dom (n +* (((y + 1) div 2) .--> (G2 . (y + 1)))) is finite set
dom n is finite Element of K32(NAT)
dom (((y + 1) div 2) .--> (G2 . (y + 1))) is trivial finite V49() Element of K32({((y + 1) div 2)})
K32({((y + 1) div 2)}) is non empty finite V49() set
(dom n) \/ (dom (((y + 1) div 2) .--> (G2 . (y + 1)))) is finite set
{((y + 1) div 2)} is non empty trivial finite V49() 1 -element Element of K32(NAT)
(((y + 1) div 2) .--> (G2 . (y + 1))) . ((y + 1) div 2) is set
es is set
es is set
W2 is set
[es,W2] is V1() set
(n +* (((y + 1) div 2) .--> (G2 . (y + 1)))) . es is set
(G1,G2) . es is set
dom (G1,G2) is finite Element of K32(NAT)
n . es is set
dom (G1,G2) is finite Element of K32(NAT)
len (G1,G2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
Seg (len (G1,G2)) is finite len (G1,G2) -element Element of K32(NAT)
es is Relation-like NAT -defined Function-like FinSubsequence-like set
dom (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y)) is finite Element of K32(NAT)
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
len (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
2 * (len (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y))) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * W2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(2 * (len (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y)))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
2 * W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * W2) - 0 is V28() V29() V30() ext-real non negative set
((2 * W2) + 1) - 1 is V28() V29() V30() ext-real even set
es is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSubsequence-like Element of K32((G1,G2))
dom es is finite Element of K32(NAT)
Sgm (dom es) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
Sgm (dom n) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
Sgm (dom (((y + 1) div 2) .--> (G2 . (y + 1)))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom n)) ^ (Sgm (dom (((y + 1) div 2) .--> (G2 . (y + 1))))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
(dom n) /\ (dom (((y + 1) div 2) .--> (G2 . (y + 1)))) is trivial finite V49() Element of K32({((y + 1) div 2)})
W2 is set
2 * ((y + 1) div 2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(y + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(1 + 1) + y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
0 + y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
len W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(len the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y))) + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(G1,W2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
len (G1,W2) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
2 * (len (G1,W2)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len (G1,W2))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len (Sgm (dom n)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
card (dom n) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
card n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
len (G1, the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y))) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
Sgm {((y + 1) div 2)} is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
<*((y + 1) div 2)*> is non empty trivial Relation-like NAT -defined NAT -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of NAT
len (Sgm (dom (((y + 1) div 2) .--> (G2 . (y + 1))))) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(Sgm (dom (((y + 1) div 2) .--> (G2 . (y + 1))))) . 1 is set
Seq es is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(Sgm (dom es)) * es is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite set
len (Seq es) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
card es is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
card (dom es) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
card (dom (((y + 1) div 2) .--> (G2 . (y + 1)))) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(card (dom n)) + (card (dom (((y + 1) div 2) .--> (G2 . (y + 1))))) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(card (dom n)) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(card n) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
(len (G1, the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y)))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
2 * (len (Seq es)) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len (Seq es))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
2 * (len (G1, the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y)))) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
(2 * (len (G1, the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y))))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
((2 * (len (G1, the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y))))) + 1) + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal set
dom (Seq es) is finite Element of K32(NAT)
(Sgm (dom es)) . W2 is set
dom (Sgm (dom es)) is finite Element of K32(NAT)
(len (Sgm (dom n))) + (len (Sgm (dom (((y + 1) div 2) .--> (G2 . (y + 1)))))) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
Seg ((len (Sgm (dom n))) + (len (Sgm (dom (((y + 1) div 2) .--> (G2 . (y + 1))))))) is finite (len (Sgm (dom n))) + (len (Sgm (dom (((y + 1) div 2) .--> (G2 . (y + 1)))))) -element Element of K32(NAT)
(Seq es) . W2 is set
es . ((Sgm (dom es)) . W2) is set
dom (Sgm (dom n)) is finite Element of K32(NAT)
(Sgm (dom n)) . W2 is set
rng (Sgm (dom n)) is finite Element of K32(NAT)
n . ((Sgm (dom n)) . W2) is set
dom (G1, the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y))) is finite Element of K32(NAT)
2 * W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
dom the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y)) is finite Element of K32(NAT)
(G1, the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y))) . W2 is set
the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y)) . (2 * W2) is set
W2 . (2 * W2) is set
(Sgm (dom n)) * n is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite set
((Sgm (dom n)) * n) . W2 is set
dom ((Sgm (dom n)) * n) is finite Element of K32(NAT)
(len (Sgm (dom n))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
dom (Sgm (dom (((y + 1) div 2) .--> (G2 . (y + 1))))) is finite Element of K32(NAT)
(len the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y))) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W2 . ((len the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y))) + 1) is set
2 * W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
((2 * (len (G1, the Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,(G1,(G1,G2,W2,(len G2)),((2 * 0) + 1),y))))) + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W2 . (2 * W2) is set
2 * W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W2 . (2 * W2) is set
2 * W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W2 . (2 * W2) is set
(G1,W2) . W2 is set
(G1,G2) is Element of the_Vertices_of G1
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,G2)
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,G2)
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1,G2)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G1
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
the_Vertices_of G2 is non empty Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
the_Edges_of G2 is Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . 1 is set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . vs is set
vs + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (vs + 2) is set
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W1 . (vs + 1) is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
rng W1 is finite Element of K32(((the_Vertices_of G2) \/ (the_Edges_of G2)))
K32(((the_Vertices_of G2) \/ (the_Edges_of G2))) is non empty set
vs is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G1
the_Vertices_of G2 is non empty Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
W2 is Element of the_Vertices_of G1
(G1,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1) (G1) (G1)
<*W2*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
y is Element of the_Vertices_of G2
(G2,y) is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2) (G2) (G2) (G2) (G2) (G2) (G2)
<*y*> is non empty trivial Relation-like NAT -defined the_Vertices_of G2 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G2
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G1
the_Edges_of G2 is Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is finite Element of K32((the_Edges_of G1))
(G1,W1) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,W1) is finite Element of K32((the_Edges_of G1))
the_Vertices_of G2 is non empty Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,W1) is finite Element of K32((the_Vertices_of G1))
(G1,W1) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,W1) is finite Element of K32((the_Vertices_of G1))
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
1 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
2 * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs - (2 * 1) is non empty V28() V29() V30() ext-real non even set
n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
n + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
2 - 1 is V28() V29() V30() ext-real set
vs - (2 - 1) is V28() V29() V30() ext-real set
(len W1) - 0 is non empty V28() V29() V30() ext-real positive non negative set
W1 . n is set
n + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (n + 2) is set
W1 . (n + 1) is set
W1 . vs is set
W1 . vs is set
vs + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (vs + 2) is set
vs + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W1 . (vs + 1) is set
W1 . vs is set
W1 . vs is set
vs is set
rng W1 is finite Element of K32(((the_Vertices_of G1) \/ (the_Edges_of G1)))
K32(((the_Vertices_of G1) \/ (the_Edges_of G1))) is non empty set
(G1,W1) \/ (G1,W1) is finite set
n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . n is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . 1 is set
n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
n + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W1 . n is set
n + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (n + 2) is set
W1 . (n + 1) is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G1
the_Vertices_of G2 is non empty Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
the_Edges_of G2 is Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is finite Element of K32((the_Vertices_of G1))
(G1,W1) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,W1) is finite Element of K32((the_Vertices_of G1))
(G1,W1) is finite Element of K32((the_Edges_of G1))
(G1,W1) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,W1) is finite Element of K32((the_Edges_of G1))
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] non trivial set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
W1 is Element of the_Vertices_of G1
{W1} is non empty trivial finite 1 -element set
(the_Vertices_of G1) \ {W1} is Element of K32((the_Vertices_of G1))
G1 .edgesBetween ((the_Vertices_of G1) \ {W1}) is Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
W2 is Relation-like NAT -defined Function-like finite [Graph-like] inducedSubgraph of G1,(the_Vertices_of G1) \ {W1},G1 .edgesBetween ((the_Vertices_of G1) \ {W1})
the_Vertices_of W2 is non empty set
the_Edges_of W2 is set
(the_Vertices_of W2) \/ (the_Edges_of W2) is non empty set
W1 .edgesInOut() is Element of K32((the_Edges_of G1))
(the_Edges_of G1) \ (W1 .edgesInOut()) is Element of K32((the_Edges_of G1))
{W1} is non empty trivial finite 1 -element Element of K32((the_Vertices_of G1))
(the_Vertices_of G1) \ {W1} is Element of K32((the_Vertices_of G1))
G1 .edgesInOut {W1} is Element of K32((the_Edges_of G1))
G1 .edgesBetween ((the_Vertices_of G1) \ {W1}) is Element of K32((the_Edges_of G1))
vs is set
rng G2 is finite Element of K32(((the_Vertices_of G1) \/ (the_Edges_of G1)))
K32(((the_Vertices_of G1) \/ (the_Edges_of G1))) is non empty set
dom G2 is finite Element of K32(NAT)
n is set
G2 . n is set
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
len G2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
((the_Vertices_of G1) \ {W1}) \/ ((the_Edges_of G1) \ (W1 .edgesInOut())) is set
x is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
x - 1 is non empty V28() V29() V30() ext-real non even set
x + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (x + 1) is set
G2 . x is set
xaa1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . xaa1 is set
W1 .edgesIn() is Element of K32((the_Edges_of G1))
W1 .edgesOut() is Element of K32((the_Edges_of G1))
(W1 .edgesIn()) \/ (W1 .edgesOut()) is Element of K32((the_Edges_of G1))
the_Target_of G1 is Relation-like Function-like V18( the_Edges_of G1, the_Vertices_of G1) Element of K32(K33((the_Edges_of G1),(the_Vertices_of G1)))
K33((the_Edges_of G1),(the_Vertices_of G1)) is Relation-like set
K32(K33((the_Edges_of G1),(the_Vertices_of G1))) is non empty set
(the_Target_of G1) . vs is set
the_Source_of G1 is Relation-like Function-like V18( the_Edges_of G1, the_Vertices_of G1) Element of K32(K33((the_Edges_of G1),(the_Vertices_of G1)))
K33((the_Edges_of G1),(the_Vertices_of G1)) is Relation-like set
K32(K33((the_Edges_of G1),(the_Vertices_of G1))) is non empty set
(the_Source_of G1) . vs is set
(G1,G2,xaa1) is Element of the_Vertices_of G1
(G1,G2,(x + 1)) is Element of the_Vertices_of G1
((the_Vertices_of G1) \ {W1}) \/ ((the_Edges_of G1) \ (W1 .edgesInOut())) is set
((the_Vertices_of G1) \ {W1}) \/ ((the_Edges_of G1) \ (W1 .edgesInOut())) is set
((the_Vertices_of G1) \ {W1}) \/ ((the_Edges_of G1) \ (W1 .edgesInOut())) is set
the_Vertices_of W2 is non empty Element of K32((the_Vertices_of G1))
(the_Vertices_of W2) \/ ((the_Edges_of G1) \ (W1 .edgesInOut())) is non empty set
the_Edges_of W2 is Element of K32((the_Edges_of G1))
(the_Vertices_of W2) \/ (the_Edges_of W2) is non empty set
vs is Relation-like NAT -defined (the_Vertices_of W2) \/ (the_Edges_of W2) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of W2) \/ (the_Edges_of W2)
len vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(G1,G2) is Element of the_Vertices_of G1
G2 . 1 is set
vs . 1 is set
n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . n is set
n + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G2 . (n + 2) is set
n + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
G2 . (n + 1) is set
n is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
(n + 1) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,G2) is finite Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
(G1,G2) is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Edges_of G1))
W1 is set
{W1} is non empty trivial finite 1 -element set
(the_Edges_of G1) \ {W1} is Element of K32((the_Edges_of G1))
W2 is Relation-like NAT -defined Function-like finite [Graph-like] spanning inducedSubgraph of G1, the_Vertices_of G1,(the_Edges_of G1) \ {W1}
the_Vertices_of W2 is non empty set
the_Edges_of W2 is set
(the_Vertices_of W2) \/ (the_Edges_of W2) is non empty set
the_Edges_of W2 is Element of K32((the_Edges_of G1))
y is set
the_Vertices_of W2 is non empty Element of K32((the_Vertices_of G1))
K32((the_Vertices_of G1)) is non empty set
(G1,G2) is finite Element of K32((the_Vertices_of G1))
(G1,G2) is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
rng (G1,G2) is finite Element of K32((the_Vertices_of G1))
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G1
W1 is set
W2 is set
y is set
(G1,W1,W2,y) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
(G2,W1,W2,y) is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2) (G2) (G2)
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
<*W1,y,W2*> is non empty Relation-like NAT -defined Function-like finite 3 -element FinSequence-like FinSubsequence-like set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G1
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
(G2,W2) is Element of the_Vertices_of G2
len W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 . (len W2) is set
(G2,W2) .edgesInOut() is Element of K32((the_Edges_of G2))
K32((the_Edges_of G2)) is non empty set
y is set
(G1,W1,y) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W1) is Element of the_Vertices_of G1
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (len W1) is set
(G1,W1) .adj y is Element of the_Vertices_of G1
(G1,(G1,W1),((G1,W1) .adj y),y) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
(G1,W1,(G1,(G1,W1),((G1,W1) .adj y),y)) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G2,W2,y) is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
(G2,W2) .adj y is Element of the_Vertices_of G2
(G2,(G2,W2),((G2,W2) .adj y),y) is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2) (G2) (G2)
(G2,W2,(G2,(G2,W2),((G2,W2) .adj y),y)) is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G1
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
(G2,W1) is Element of the_Vertices_of G2
W1 . 1 is set
(G2,W1) is Element of the_Vertices_of G2
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (len W1) is set
W2 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
(G1,W2) is Element of the_Vertices_of G1
W2 . 1 is set
(G1,W2) is Element of the_Vertices_of G1
len W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 . (len W2) is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
dom W2 is finite Element of K32(NAT)
W2 . (y + 1) is set
the_Edges_of G2 is Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
the_Source_of G2 is Relation-like Function-like V18( the_Edges_of G2, the_Vertices_of G2) Element of K32(K33((the_Edges_of G2),(the_Vertices_of G2)))
K33((the_Edges_of G2),(the_Vertices_of G2)) is Relation-like set
K32(K33((the_Edges_of G2),(the_Vertices_of G2))) is non empty set
(the_Source_of G2) . (W2 . (y + 1)) is set
W2 . y is set
the_Source_of G1 is Relation-like Function-like V18( the_Edges_of G1, the_Vertices_of G1) Element of K32(K33((the_Edges_of G1),(the_Vertices_of G1)))
K33((the_Edges_of G1),(the_Vertices_of G1)) is Relation-like set
K32(K33((the_Edges_of G1),(the_Vertices_of G1))) is non empty set
(the_Source_of G1) . (W2 . (y + 1)) is set
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W2 . y is set
W2 . vs is set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 . y is set
W2 . vs is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 . y is set
W2 . vs is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] Subgraph of G1
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)
(G1,W1) is Element of the_Vertices_of G1
len W1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W1 . (len W1) is set
(G2,W2) is Element of the_Vertices_of G2
len W2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 . (len W2) is set
(G1,W1) is Element of the_Vertices_of G1
W1 . 1 is set
(G2,W2) is Element of the_Vertices_of G2
W2 . 1 is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
dom W2 is finite Element of K32(NAT)
W2 . (y + 1) is set
the_Edges_of G2 is Element of K32((the_Edges_of G1))
K32((the_Edges_of G1)) is non empty set
the_Source_of G2 is Relation-like Function-like V18( the_Edges_of G2, the_Vertices_of G2) Element of K32(K33((the_Edges_of G2),(the_Vertices_of G2)))
K33((the_Edges_of G2),(the_Vertices_of G2)) is Relation-like set
K32(K33((the_Edges_of G2),(the_Vertices_of G2))) is non empty set
(the_Source_of G2) . (W2 . (y + 1)) is set
the_Source_of G1 is Relation-like Function-like V18( the_Edges_of G1, the_Vertices_of G1) Element of K32(K33((the_Edges_of G1),(the_Vertices_of G1)))
K33((the_Edges_of G1),(the_Vertices_of G1)) is Relation-like set
K32(K33((the_Edges_of G1),(the_Vertices_of G1))) is non empty set
(the_Source_of G1) . (W2 . (y + 1)) is set
W2 . y is set
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W2 . y is set
W2 . vs is set
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal even Element of NAT
W2 . y is set
W2 . vs is set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 . y is set
W2 . vs is set
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 . y is set
W2 . vs is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 . y is set
W2 . vs is set
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
vs is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 . y is set
W2 . vs is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G2 is non empty set
W1 is set
y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 is Relation-like NAT -defined the_Vertices_of G2 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G2
len W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
W2 . y is set
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
W2 . (y + 1) is set
vs is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Edges_of G1 is set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Edges_of G2 is set
W1 is set
W2 is Relation-like NAT -defined the_Edges_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
the_Vertices_of G1 is non empty set
len W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
(len W2) + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
vs is Relation-like NAT -defined the_Vertices_of G1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
len vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
the_Vertices_of G2 is non empty set
vs is Relation-like NAT -defined the_Vertices_of G2 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G2
vs is Relation-like NAT -defined the_Vertices_of G2 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G2
len vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
n is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
y is Relation-like NAT -defined the_Edges_of G2 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the_Edges_of G2
len y is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
vs . n is set
n + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal Element of NAT
vs . (n + 1) is set
y . n is set
vs is Relation-like NAT -defined the_Vertices_of G2 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G2
len vs is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is set
W2 is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of (the_Vertices_of G2) \/ (the_Edges_of G2)
len W2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative finite cardinal Element of NAT
y is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 . y is set
y + 2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal non even Element of NAT
W2 . (y + 2) is set
y + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real positive non negative finite cardinal even Element of NAT
W2 . (y + 1) is set
W2 . 1 is set
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] set
W1 is set
W2 is set
y is set
(G1,W1,y,W2) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1)
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
(G2,W1,y,W2) is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2) (G2) (G2)
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
<*W1,W2,y*> is non empty Relation-like NAT -defined Function-like finite 3 -element FinSequence-like FinSubsequence-like set
choose (the_Vertices_of G1) is Element of the_Vertices_of G1
(G1,(choose (the_Vertices_of G1))) is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1) (G1) (G1) (G1) (G1) (G1) (G1)
<*(choose (the_Vertices_of G1))*> is non empty trivial Relation-like NAT -defined the_Vertices_of G1 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G1
choose (the_Vertices_of G2) is Element of the_Vertices_of G2
(G2,(choose (the_Vertices_of G2))) is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2) (G2) (G2) (G2) (G2) (G2) (G2)
<*(choose (the_Vertices_of G2))*> is non empty trivial Relation-like NAT -defined the_Vertices_of G2 -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the_Vertices_of G2
G1 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G1 is non empty set
the_Edges_of G1 is set
(the_Vertices_of G1) \/ (the_Edges_of G1) is non empty set
G2 is Relation-like NAT -defined Function-like finite [Graph-like] set
the_Vertices_of G2 is non empty set
the_Edges_of G2 is set
(the_Vertices_of G2) \/ (the_Edges_of G2) is non empty set
W1 is Relation-like NAT -defined (the_Vertices_of G1) \/ (the_Edges_of G1) -valued Function-like finite FinSequence-like FinSubsequence-like (G1)
W2 is Relation-like NAT -defined (the_Vertices_of G2) \/ (the_Edges_of G2) -valued Function-like finite FinSequence-like FinSubsequence-like (G2)