:: GRAPH_2 semantic presentation

REAL is non empty non trivial non finite V81() V82() V83() V87() V90() V91() V93() set
NAT is ordinal non empty non trivial non finite cardinal limit_cardinal V81() V82() V83() V84() V85() V86() V87() V88() V90() Element of bool REAL
bool REAL is non empty non trivial non finite set
omega is ordinal non empty non trivial non finite cardinal limit_cardinal V81() V82() V83() V84() V85() V86() V87() V88() V90() set
bool omega is non empty non trivial non finite set
bool NAT is non empty non trivial non finite set
COMPLEX is non empty non trivial non finite V81() V87() set
RAT is non empty non trivial non finite V81() V82() V83() V84() V87() set
{} is Relation-like non-empty empty-yielding NAT -defined RAT -valued ordinal natural Function-like one-to-one constant functional empty trivial ext-real non positive non negative V31() V32() V33() V34() V35() V36() V37() V38() V39() finite finite-yielding V46() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V81() V82() V83() V84() V85() V86() V87() V90() V91() V92() V93() V94() integer set
the Relation-like non-empty empty-yielding NAT -defined RAT -valued ordinal natural Function-like one-to-one constant functional empty trivial ext-real non positive non negative V31() V32() V33() V34() V35() V36() V37() V38() V39() finite finite-yielding V46() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V81() V82() V83() V84() V85() V86() V87() V90() V91() V92() V93() V94() integer set is Relation-like non-empty empty-yielding NAT -defined RAT -valued ordinal natural Function-like one-to-one constant functional empty trivial ext-real non positive non negative V31() V32() V33() V34() V35() V36() V37() V38() V39() finite finite-yielding V46() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V81() V82() V83() V84() V85() V86() V87() V90() V91() V92() V93() V94() integer set
1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
INT is non empty non trivial non finite V81() V82() V83() V84() V85() V87() set
2 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
3 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
0 is Relation-like non-empty empty-yielding NAT -defined RAT -valued ordinal natural Function-like one-to-one constant functional empty trivial ext-real non positive non negative V31() V32() V33() V34() V35() V36() V37() V38() V39() finite finite-yielding V46() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V81() V82() V83() V84() V85() V86() V87() V90() V91() V92() V93() V94() integer Element of NAT
Seg 1 is non empty trivial finite 1 -element V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= 1 ) } is set
card {} is Relation-like non-empty empty-yielding NAT -defined RAT -valued ordinal natural Function-like one-to-one constant functional empty trivial ext-real non positive non negative V31() V32() V33() V34() V35() V36() V37() V38() V39() finite finite-yielding V46() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V81() V82() V83() V84() V85() V86() V87() V90() V91() V92() V93() V94() integer set
f is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
f + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
m is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
n is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
j is ext-real V31() V94() integer set
i is ext-real V31() V94() integer set
j - i is ext-real V31() V94() integer set
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(f + 1) - 1 is ext-real V31() V94() integer set
m - 1 is ext-real V31() V94() integer set
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(m + 1) - 1 is ext-real V31() V94() integer set
j + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
Seg n is finite n -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= n ) } is set
m | (Seg n) is Relation-like NAT -defined Seg n -defined NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . i is set
f . i is set
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . i is set
f . i is set
f is set
Sgm f is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
dom (Sgm f) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
m is set
Sgm m is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm f) * (Sgm m) is Relation-like NAT -defined NAT -valued RAT -valued Function-like V32() V33() V34() V35() finite Element of bool [:NAT,NAT:]
[:NAT,NAT:] is Relation-like RAT -valued INT -valued non empty non trivial V32() V33() V34() V35() non finite set
bool [:NAT,NAT:] is non empty non trivial non finite set
(Sgm f) | m is Relation-like NAT -defined m -defined NAT -defined NAT -valued RAT -valued Function-like V32() V33() V34() V35() finite FinSubsequence-like Element of bool [:NAT,NAT:]
rng ((Sgm f) | m) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() set
Sgm (rng ((Sgm f) | m)) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
Seg n is finite n -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= n ) } is set
len (Sgm f) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
Seg (len (Sgm f)) is finite len (Sgm f) -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len (Sgm f) ) } is set
rng (Sgm m) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() set
i is finite set
Sgm i is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
dom (Sgm i) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
card i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of omega
Seg (card i) is finite card i -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= card i ) } is set
dom ((Sgm f) * (Sgm m)) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
rng (Sgm f) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() set
j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng j is finite set
rX is set
X is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
rng X is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() set
dom X is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
qm is set
X . qm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom (Sgm m) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
(Sgm m) . qm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm f) . ((Sgm m) . qm) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom ((Sgm f) | m) is finite Element of bool m
bool m is set
qm is set
((Sgm f) | m) . qm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(dom (Sgm f)) /\ m is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
q1 is set
(Sgm m) . q1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm f) . qm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
X . q1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rX is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
qm is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
len X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
q1 is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
X . rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mX is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
X . qm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm m) . rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm f) . ((Sgm m) . rX) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm m) . qm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm f) . ((Sgm m) . qm) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len (Sgm m) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mXC is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm m) . mXC is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mXC1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm m) . mXC1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mXCm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
fvs is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( f <= b₁ & b₁ <= f + a₁ ) } is set
m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( f <= b₁ & b₁ <= f + m ) } is set
m + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
f + (m + 1) is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( f <= b₁ & b₁ <= f + (m + 1) ) } is set
(m + 1) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : b₁ <= f + m } is set
n is finite set
j is set
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is finite set
card j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of omega
(f + m) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(f + m) + 0 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is set
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(f + m) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j is finite set
{(f + (m + 1))} is non empty trivial finite V46() 1 -element V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() set
j \/ {(f + (m + 1))} is non empty finite set
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( f <= b₁ & b₁ <= f + m ) } \/ {(f + (m + 1))} is non empty set
card j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of omega
f + 0 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( f <= b₁ & b₁ <= f + 0 ) } is set
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
m is finite set
card m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of omega
n is set
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
{f} is non empty trivial finite V46() 1 -element V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() set
n is finite set
m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( f <= b₁ & b₁ <= f + m ) } is set
card n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of omega
m + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( f <= b₁ & b₁ <= f + m ) } is set
card { b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( f <= b₁ & b₁ <= f + m ) } is ordinal cardinal set
m + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
{ H₁(b₁) where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( f <= b₁ & b₁ <= f + m & S₁[b₁] ) } is set
i is finite set
{ H₁(b₁) where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( f <= b₁ & b₁ <= f + m ) } is set
j is set
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is set
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is finite set
card j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of omega
f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
m + f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( m + 1 <= b₁ & b₁ <= m + f ) } is set
Sgm { b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( m + 1 <= b₁ & b₁ <= m + f ) } is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
Seg (m + f) is finite m + f -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= m + f ) } is set
j is set
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm { b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( m + 1 <= b₁ & b₁ <= m + f ) } ) . j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m + j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
(Sgm { b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( m + 1 <= b₁ & b₁ <= m + f ) } ) . j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m + j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m + j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm { b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( m + 1 <= b₁ & b₁ <= m + f ) } ) . j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is finite set
card j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of omega
rX is set
m + 0 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
qm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
1 - 1 is ext-real V31() V94() integer set
f - 1 is ext-real V31() V94() integer set
f -' 1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(m + 1) + rX is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
rX + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
Sgm j is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
len (Sgm j) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rng (Sgm { b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( m + 1 <= b₁ & b₁ <= m + f ) } ) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() set
rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm { b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( m + 1 <= b₁ & b₁ <= m + f ) } ) . rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m + rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rX + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(Sgm { b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( m + 1 <= b₁ & b₁ <= m + f ) } ) . (rX + 1) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m + (rX + 1) is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
qm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
q1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(m + rX) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
dom (Sgm { b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( m + 1 <= b₁ & b₁ <= m + f ) } ) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
(Sgm { b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( m + 1 <= b₁ & b₁ <= m + f ) } ) . 1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
q1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm { b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( m + 1 <= b₁ & b₁ <= m + f ) } ) . 0 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m + 0 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rng (Sgm j) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() set
dom (Sgm j) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
rX is set
(Sgm j) . rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
Seg f is finite f -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= f ) } is set
qm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm { b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( m + 1 <= b₁ & b₁ <= m + f ) } ) . qm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m + qm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
n is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(n + 1) -' m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom i is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
m - m is ext-real V31() V94() integer set
(n + 1) - m is ext-real V31() V94() integer set
j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len j) + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
((n + 1) - m) + m is ext-real V31() V94() integer set
j is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
j + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
j . (j + 1) is set
(j + 1) - 1 is ext-real V31() V94() integer set
m + ((j + 1) - 1) is ext-real V31() V94() integer set
f . (m + ((j + 1) - 1)) is set
m + j is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
f . (m + j) is set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len i) + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len j) + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
dom i is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
Seg (len i) is finite len i -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len i ) } is set
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
i . j is set
m + j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f . (m + j) is set
j . j is set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(f,m,n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (f,m,n) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len (f,m,n)) + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(f,m,n) . (i + 1) is set
m + i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f . (m + i) is set
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(f,m,n) . (i + 1) is set
m + i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f . (m + i) is set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(f,m,m) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
f . m is set
<*(f . m)*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
[1,(f . m)] is non empty set
{1,(f . m)} is non empty finite set
{1} is non empty trivial finite V46() 1 -element V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() set
{{1,(f . m)},{1}} is non empty finite V46() set
{[1,(f . m)]} is Relation-like Function-like constant non empty trivial finite 1 -element set
len (f,m,m) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len (f,m,m)) + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(f,m,m) . (0 + 1) is set
m + 0 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f . (m + 0) is set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(f,1,(len f)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(len f) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len (f,1,(len f)) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len (f,1,(len f))) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
n is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
dom (f,1,(len f)) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
Seg (len f) is finite len f -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len f ) } is set
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(f,1,(len f)) . n is set
f . n is set
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(f,(m + 1),n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
n + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(f,(n + 1),i) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(f,(m + 1),n) ^ (f,(n + 1),i) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(f,(m + 1),i) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len ((f,(m + 1),n) ^ (f,(n + 1),i)) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom ((f,(m + 1),n) ^ (f,(n + 1),i)) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
Seg (len ((f,(m + 1),n) ^ (f,(n + 1),i))) is finite len ((f,(m + 1),n) ^ (f,(n + 1),i)) -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len ((f,(m + 1),n) ^ (f,(n + 1),i)) ) } is set
rX is ext-real V31() V94() integer set
qm is ext-real V31() V94() integer set
rX - qm is ext-real V31() V94() integer set
i + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len (f,(m + 1),i) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len (f,(m + 1),i)) + (m + 1) is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len (f,(m + 1),n) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len (f,(m + 1),n)) + (m + 1) is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len (f,(n + 1),i) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len (f,(n + 1),i)) + (n + 1) is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
n - m is ext-real V31() V94() integer set
- n is ext-real non positive V31() V94() integer set
i + (- n) is ext-real V31() V94() integer set
(n - m) + (i + (- n)) is ext-real V31() V94() integer set
i - m is ext-real V31() V94() integer set
mX is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
q1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
mXC is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mXC + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
dom (f,(m + 1),n) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
((f,(m + 1),n) ^ (f,(n + 1),i)) . mX is set
(f,(m + 1),n) . mX is set
(m + 1) + mXC is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
f . ((m + 1) + mXC) is set
(f,(m + 1),i) . mX is set
q1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
q1 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
mXC is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mXC + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
mXC1 is ext-real V31() V94() integer set
mXC1 - q1 is ext-real V31() V94() integer set
mXCm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mXCm + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len (f,(n + 1),i)) + (len (f,(m + 1),n)) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len ((f,(m + 1),n) ^ (f,(n + 1),i))) - (len (f,(m + 1),n)) is ext-real V31() V94() integer set
dom (f,(n + 1),i) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
(n + 1) + mXCm is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(m + 1) + mXC is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
q1 + (mXCm + 1) is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
((f,(m + 1),n) ^ (f,(n + 1),i)) . mX is set
(f,(n + 1),i) . (mXCm + 1) is set
f . ((n + 1) + mXCm) is set
(f,(m + 1),i) . mX is set
q1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
q1 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(f,1,m) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
m + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(f,(m + 1),(len f)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(f,1,m) ^ (f,(m + 1),(len f)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(f,1,(len f)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(f,1,m) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
m + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(f,(m + 1),n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(f,1,m) ^ (f,(m + 1),n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
n + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(f,(n + 1),(len f)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((f,1,m) ^ (f,(m + 1),n)) ^ (f,(n + 1),(len f)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(f,1,n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(f,1,n) ^ (f,(n + 1),(len f)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(f,1,(len f)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng f is finite set
m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(f,m,n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng (f,m,n) is finite set
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j is set
dom (f,m,n) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
j is set
(f,m,n) . j is set
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len (f,m,n) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
X + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len (f,m,n)) + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m + X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom f is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
(f,m,n) . j is set
f . (m + X) is set
f is set
m is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
n is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
i is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
(m,n,i) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng m is finite set
rng (m,n,i) is finite set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f . m is set
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(f,m,n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(f,m,n) . 1 is set
len (f,m,n) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(f,m,n) . (len (f,m,n)) is set
f . n is set
n + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len (f,m,n)) + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n + 0 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
m + 0 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f . (m + 0) is set
m + j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
m is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(m,2,(len m)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
f ^ (m,2,(len m)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(m,f) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(f,2,(len f)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
m ^ (f,2,(len f)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (m,f) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len (m,f)) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len m) + (len f) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
1 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len f) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len (f,2,(len f)) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len (f,2,(len f))) + (1 + 1) is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len m) + (len (f,2,(len f))) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
((len m) + (len (f,2,(len f)))) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(f,m) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(m,2,(len m)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
f ^ (m,2,(len m)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(f,m) . n is set
f . n is set
dom f is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(m,f) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(f,2,(len f)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
m ^ (f,2,(len f)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len m) + n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(m,f) . ((len m) + n) is set
n + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
f . (n + 1) is set
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
1 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len f) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len (f,2,(len f)) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len (f,2,(len f))) + (1 + 1) is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len (f,2,(len f))) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
((len (f,2,(len f))) + 1) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
dom (f,2,(len f)) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
(f,2,(len f)) . n is set
(1 + 1) + j is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
f . ((1 + 1) + j) is set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f . (len f) is set
m is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(m,f) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(f,2,(len f)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
m ^ (f,2,(len f)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (m,f) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(m,f) . (len (m,f)) is set
1 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(1 + 1) - 1 is ext-real V31() V94() integer set
(len f) - 1 is ext-real V31() V94() integer set
(len (m,f)) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
((len (m,f)) + 1) - 1 is ext-real V31() V94() integer set
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len m) + (len f) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
((len m) + (len f)) - 1 is ext-real V31() V94() integer set
(len m) + ((len f) - 1) is ext-real V31() V94() integer set
(len f) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len (f,2,(len f)) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len (f,2,(len f))) + (1 + 1) is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len (f,2,(len f))) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
((len (f,2,(len f))) + 1) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng f is finite set
m is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(f,m) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(m,2,(len m)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
f ^ (m,2,(len m)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng (f,m) is finite set
rng m is finite set
(rng f) \/ (rng m) is finite set
j is set
rng (m,2,(len m)) is finite set
(rng f) \/ (rng (m,2,(len m))) is finite set
f is set
m is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
n is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
(m,n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(n,2,(len n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
m ^ (n,2,(len n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng (m,n) is finite set
rng m is finite set
rng n is finite set
(rng m) \/ (rng n) is finite set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f . (len f) is set
rng f is finite set
m is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
m . 1 is set
(f,m) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(m,2,(len m)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
f ^ (m,2,(len m)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng (f,m) is finite set
rng m is finite set
(rng f) \/ (rng m) is finite set
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
1 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len m) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len (m,2,(len m)) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len (m,2,(len m))) + (1 + 1) is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len (m,2,(len m))) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
((len (m,2,(len m))) + 1) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j is set
rng (m,2,(len m)) is finite set
(rng f) \/ (rng (m,2,(len m))) is finite set
dom m is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
j is set
m . j is set
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom f is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
X + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
dom (m,2,(len m)) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rX + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(m,2,(len m)) . (rX + 1) is set
(1 + 1) + rX is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
m . ((1 + 1) + rX) is set
m . j is set
<*1,2*> is Relation-like NAT -defined NAT -valued Function-like non empty V32() V33() V34() V35() finite 2 -element FinSequence-like FinSubsequence-like FinSequence of NAT
<*1*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
[1,1] is non empty set
{1,1} is non empty finite V46() V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() set
{1} is non empty trivial finite V46() 1 -element V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() set
{{1,1},{1}} is non empty finite V46() set
{[1,1]} is Relation-like Function-like constant non empty trivial finite 1 -element set
<*2*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
[1,2] is non empty set
{1,2} is non empty finite V46() V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() set
{{1,2},{1}} is non empty finite V46() set
{[1,2]} is Relation-like Function-like constant non empty trivial finite 1 -element set
<*1*> ^ <*2*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like set
1 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len <*1,2*> is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
rng <*1,2*> is non empty finite V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() set
<*1*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial V32() V33() V34() V35() V36() V37() V38() V39() finite 1 -element FinSequence-like FinSubsequence-like FinSequence of NAT
rng <*1*> is non empty trivial finite 1 -element V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() set
<*2*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial V32() V33() V34() V35() V36() V37() V38() V39() finite 1 -element FinSequence-like FinSubsequence-like FinSequence of NAT
rng <*2*> is non empty trivial finite 1 -element V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() set
(rng <*1*>) \/ (rng <*2*>) is non empty finite V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() set
{1} \/ (rng <*2*>) is non empty finite V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() set
{2} is non empty trivial finite V46() 1 -element V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() set
{1} \/ {2} is non empty finite V46() V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rng f is finite set
card (rng f) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of omega
m is set
n is set
{m,n} is non empty finite set
dom f is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
j is set
[1,j] is non empty set
{1,j} is non empty finite set
{{1,j},{1}} is non empty finite V46() set
f . 1 is set
<*j*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
{[1,j]} is Relation-like Function-like constant non empty trivial finite 1 -element set
{j} is non empty trivial finite 1 -element set
m is set
n is set
{m,n} is non empty finite set
f is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
f + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
1 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
<*1,2*> . f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
<*1,2*> . (f + 1) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like () () set
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rng f is finite set
f . 1 is set
m is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like () () set
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rng m is finite set
m . 1 is set
n is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
f . n is set
m . n is set
n + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
f . (n + 1) is set
m . (n + 1) is set
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
dom f is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
dom m is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
Seg (len m) is finite len m -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len m ) } is set
i is set
j is set
{i,j} is non empty finite set
Seg (len f) is finite len f -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len f ) } is set
f . 0 is set
m . 0 is set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like () () set
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rng f is finite set
m is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like () () set
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rng m is finite set
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f . n is set
m . n is set
n + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
f . (n + 1) is set
m . (n + 1) is set
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
dom f is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
dom m is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
Seg (len m) is finite len m -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len m ) } is set
i is set
j is set
{i,j} is non empty finite set
Seg (len f) is finite len f -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len f ) } is set
f . 0 is set
m . 0 is set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like () () set
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rng f is finite set
m is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like () () set
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rng m is finite set
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like () () set
len n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rng n is finite set
i is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
j is set
j is set
{j,j} is non empty finite set
dom n is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
n . i is set
Seg (len n) is finite len n -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len n ) } is set
dom f is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
Seg (len f) is finite len f -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len f ) } is set
f . i is set
dom m is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
Seg (len m) is finite len m -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len m ) } is set
m . i is set
f is set
m is set
{f,m} is non empty finite set
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
<*f,m*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like set
<*f*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
[1,f] is non empty set
{1,f} is non empty finite set
{{1,f},{1}} is non empty finite V46() set
{[1,f]} is Relation-like Function-like constant non empty trivial finite 1 -element set
<*m*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
[1,m] is non empty set
{1,m} is non empty finite set
{{1,m},{1}} is non empty finite V46() set
{[1,m]} is Relation-like Function-like constant non empty trivial finite 1 -element set
<*f*> ^ <*m*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like set
<*f,m*> . 1 is set
3 -' 2 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
1 + 2 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(1 + 2) - 2 is ext-real V31() V94() integer set
<*f,m*> . 2 is set
[:NAT,NAT:] is Relation-like RAT -valued INT -valued non empty non trivial V32() V33() V34() V35() non finite set
bool [:NAT,NAT:] is non empty non trivial non finite set
j is Relation-like NAT -defined NAT -valued Function-like V25( NAT , NAT ) V32() V33() V34() V35() Element of bool [:NAT,NAT:]
j . 0 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
3 -' 1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
2 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(2 + 1) - 1 is ext-real V31() V94() integer set
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j . j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j . (j + 1) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(j + 1) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j . ((j + 1) + 1) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j . (0 + 1) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
j . (1 + 1) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is set
j . 1 is set
j . 2 is set
X is set
j . X is set
Seg (len j) is finite len j -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len j ) } is set
rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j . rX is set
j . rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
<*f,m*> . (j . rX) is set
rng j is finite set
X is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
X + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like () set
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
j . (X + 1) is set
j . (X + 1) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
<*f,m*> . (j . (X + 1)) is set
j . X is set
j . X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
<*f,m*> . (j . X) is set
X is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like () () set
rng X is finite set
len X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
X . 1 is set
dom X is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
f is set
m is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
bool m is finite V46() set
n is Relation-like NAT -defined f -valued Function-like finite Element of bool m
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom n is finite set
Seg (len m) is finite len m -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len m ) } is set
dom n is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
dom m is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
f is Relation-like NAT -defined Function-like FinSubsequence-like set
dom f is V81() V82() V83() V84() V85() V86() V90() Element of bool NAT
m is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng m is finite set
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng n is finite set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
m * f is Relation-like NAT -defined Function-like finite set
j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
n * f is Relation-like NAT -defined Function-like finite set
j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
m ^ n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(m ^ n) * f is Relation-like NAT -defined Function-like finite set
i ^ j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng (m ^ n) is finite set
(rng m) \/ (rng n) is finite set
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len (m ^ n) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len m) + (len n) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
Seg ((len m) + (len n)) is finite (len m) + (len n) -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= (len m) + (len n) ) } is set
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
dom n is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
dom i is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
dom m is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
len i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len (i ^ j) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
j . j is set
(m ^ n) . j is set
f . ((m ^ n) . j) is set
m . j is set
f . (m . j) is set
i . j is set
(i ^ j) . j is set
(len m) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j - (len m) is ext-real V31() V94() integer set
j -' (len m) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len m) + X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j . j is set
(m ^ n) . j is set
f . ((m ^ n) . j) is set
n . X is set
f . (n . X) is set
j . X is set
(i ^ j) . j is set
f is set
m is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
bool m is finite V46() set
i is set
j is Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of i
bool j is finite V46() set
n is Relation-like NAT -defined f -valued Function-like finite FinSubsequence-like Element of bool m
dom n is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
dom m is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
j is Relation-like NAT -defined i -valued Function-like finite FinSubsequence-like Element of bool j
rng j is finite set
rng j is finite set
f is set
m is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
bool m is finite V46() set
f is set
m is set
n is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
bool n is finite V46() set
i is Relation-like NAT -defined f -valued Function-like finite FinSubsequence-like Element of bool n
i | m is Relation-like NAT -defined m -defined NAT -defined f -valued Function-like finite FinSubsequence-like set
j is Relation-like NAT -defined Function-like FinSubsequence-like set
f is set
m is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
bool m is finite V46() set
n is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
bool n is finite V46() set
i is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
j is Relation-like NAT -defined f -valued Function-like finite FinSubsequence-like Element of bool m
Seq j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom j is finite set
Sgm (dom j) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom j)) * j is Relation-like NAT -defined f -valued Function-like finite set
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
Sgm (dom j) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
j is Relation-like NAT -defined f -valued Function-like finite FinSubsequence-like Element of bool m
Seq j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom j is finite set
Sgm (dom j) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom j)) * j is Relation-like NAT -defined f -valued Function-like finite set
j is Relation-like NAT -defined f -valued Function-like finite FinSubsequence-like Element of bool n
Seq j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom j is finite set
Sgm (dom j) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom j)) * j is Relation-like NAT -defined f -valued Function-like finite set
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
(Sgm (dom j)) | (dom j) is Relation-like NAT -defined dom j -defined NAT -defined NAT -valued RAT -valued Function-like V32() V33() V34() V35() finite FinSubsequence-like Element of bool [:NAT,NAT:]
[:NAT,NAT:] is Relation-like RAT -valued INT -valued non empty non trivial V32() V33() V34() V35() non finite set
bool [:NAT,NAT:] is non empty non trivial non finite set
rng ((Sgm (dom j)) | (dom j)) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() set
j | (rng ((Sgm (dom j)) | (dom j))) is Relation-like NAT -defined rng ((Sgm (dom j)) | (dom j)) -defined NAT -defined f -valued Function-like finite FinSubsequence-like set
dom m is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
X is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
Seg X is finite X -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= X ) } is set
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
dom n is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
qm is finite set
Sgm qm is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
dom (Sgm qm) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
card qm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of omega
Seg (card qm) is finite card qm -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= card qm ) } is set
q1 is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
Seg q1 is finite q1 -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= q1 ) } is set
q1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
Seg q1 is finite q1 -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= q1 ) } is set
rng (Sgm (dom j)) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() set
dom (Sgm (dom j)) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
Sgm (dom j) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
rng (Sgm (dom j)) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() set
dom ((Sgm (dom j)) | (dom j)) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
mX is Relation-like NAT -defined dom j -defined NAT -valued RAT -valued Function-like V32() V33() V34() V35() finite FinSubsequence-like Element of bool [:NAT,NAT:]
dom mX is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
mXC is set
mX . mXC is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mXC1 is set
mXCm is set
rX is finite set
[mXC,mXCm] is non empty set
{mXC,mXCm} is non empty finite set
{mXC} is non empty trivial finite 1 -element set
{{mXC,mXCm},{mXC}} is non empty finite V46() set
mXC is set
mXC1 is set
mX . mXC1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mXCm is set
[mXCm,mXC] is non empty set
{mXCm,mXC} is non empty finite set
{mXCm} is non empty trivial finite 1 -element set
{{mXCm,mXC},{mXCm}} is non empty finite V46() set
mXC is set
mXC1 is set
[mXC,mXC1] is non empty set
{mXC,mXC1} is non empty finite set
{mXC} is non empty trivial finite 1 -element set
{{mXC,mXC1},{mXC}} is non empty finite V46() set
mXCm is set
fvs is set
[mXCm,fvs] is non empty set
{mXCm,fvs} is non empty finite set
{mXCm} is non empty trivial finite 1 -element set
{{mXCm,fvs},{mXCm}} is non empty finite V46() set
mX . mXCm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm (dom j)) . mXCm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mX . mXC is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm (dom j)) . mXC is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
fvs is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len (Sgm (dom j)) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
fvs is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mX is Relation-like NAT -defined dom j -defined NAT -valued RAT -valued Function-like V32() V33() V34() V35() finite FinSubsequence-like Element of bool [:NAT,NAT:]
card rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of omega
Sgm rX is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
dom (Sgm rX) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
Sgm (dom j) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
rng (Sgm (dom j)) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() set
mX is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
Seg mX is finite mX -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= mX ) } is set
mX is set
dom i is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
dom (Sgm (dom j)) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
(Sgm (dom j)) . mX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom (Seq j) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
dom (Sgm (dom j)) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
(Sgm (dom j)) . mX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mX is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
(Sgm (dom j)) . mX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm (dom j)) . mX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j . ((Sgm (dom j)) . mX) is set
(Seq j) . ((Sgm (dom j)) . mX) is set
(Sgm (dom j)) * (Sgm (dom j)) is Relation-like NAT -defined NAT -valued RAT -valued Function-like V32() V33() V34() V35() finite Element of bool [:NAT,NAT:]
((Sgm (dom j)) * (Sgm (dom j))) . mX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom ((Sgm (dom j)) * (Sgm (dom j))) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
(Sgm (dom j)) . ((Sgm (dom j)) . mX) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom (Seq j) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
(Seq j) . mX is set
j . ((Sgm (dom j)) . mX) is set
j . ((Sgm (dom j)) . ((Sgm (dom j)) . mX)) is set
i . mX is set
f is non empty V67() MultiGraphStruct
the carrier of f is non empty set
m is Element of the carrier of f
n is Element of the carrier of f
i is set
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
the carrier' of f is set
[: the carrier' of f, the carrier of f:] is Relation-like set
bool [: the carrier' of f, the carrier of f:] is set
the Source of f . i is set
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
the Target of f . i is set
f is non empty V67() MultiGraphStruct
the carrier of f is non empty set
m is Element of the carrier of f
n is Element of the carrier of f
i is Element of the carrier of f
j is Element of the carrier of f
j is set
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
the carrier' of f is set
[: the carrier' of f, the carrier of f:] is Relation-like set
bool [: the carrier' of f, the carrier of f:] is set
the Source of f . j is set
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
the Target of f . j is set
f is non empty V67() MultiGraphStruct
the carrier of f is non empty set
the carrier' of f is set
m is set
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is Relation-like set
bool [: the carrier' of f, the carrier of f:] is set
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
{ b₁ where b₁ is Element of the carrier of f : ex b₂ being Element of the carrier' of f st
( b₂ in m & ( b₁ = the Source of f . b₂ or b₁ = the Target of f . b₂ ) ) } is set
f is non empty V67() MultiGraphStruct
the carrier of f is non empty set
f is non empty V67() MultiGraphStruct
the carrier of f is non empty set
the carrier' of f is set
m is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
rng m is finite set
n is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
rng n is finite set
(f,(rng n)) is set
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is Relation-like set
bool [: the carrier' of f, the carrier of f:] is set
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
{ b₁ where b₁ is Element of the carrier of f : ex b₂ being Element of the carrier' of f st
( b₂ in rng n & ( b₁ = the Source of f . b₂ or b₁ = the Target of f . b₂ ) ) } is set
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len n) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
i is set
j is Element of the carrier of f
j is Element of the carrier' of f
the Source of f . j is set
the Target of f . j is set
j is Element of the carrier' of f
the Source of f . j is set
the Target of f . j is set
dom n is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
j is set
n . j is set
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
X + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
m /. (X + 1) is Element of the carrier of f
m /. X is Element of the carrier of f
dom m is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
n . X is set
m . X is set
m . (X + 1) is set
j is set
m . j is set
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n . j is set
j is Element of the carrier' of f
j + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
m /. (j + 1) is Element of the carrier of f
m /. j is Element of the carrier of f
the Source of f . j is set
the Target of f . j is set
m . j is set
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
n . (len n) is set
m /. ((len n) + 1) is Element of the carrier of f
m /. (len n) is Element of the carrier of f
X is Element of the carrier' of f
the Source of f . X is set
the Target of f . X is set
m . ((len n) + 1) is set
f is non empty V67() MultiGraphStruct
the carrier of f is non empty set
m is Element of the carrier of f
<*m*> is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of f
[1,m] is non empty set
{1,m} is non empty finite set
{{1,m},{1}} is non empty finite V46() set
{[1,m]} is Relation-like Function-like constant non empty trivial finite 1 -element set
len <*m*> is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len {} is Relation-like non-empty empty-yielding NAT -defined RAT -valued ordinal natural Function-like one-to-one constant functional empty trivial ext-real non positive non negative V31() V32() V33() V34() V35() V36() V37() V38() V39() finite finite-yielding V46() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V81() V82() V83() V84() V85() V86() V87() V90() V91() V92() V93() V94() integer Element of NAT
(len {}) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
<*m*> /. n is Element of the carrier of f
n + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
<*m*> /. (n + 1) is Element of the carrier of f
{} . n is Relation-like non-empty empty-yielding NAT -defined RAT -valued ordinal natural Function-like one-to-one constant functional empty trivial ext-real non positive non negative V31() V32() V33() V34() V35() V36() V37() V38() V39() finite finite-yielding V46() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V81() V82() V83() V84() V85() V86() V87() V90() V91() V92() V93() V94() integer set
f is non empty V67() MultiGraphStruct
the carrier' of f is set
the carrier of f is non empty set
m is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len m) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rng n is finite set
i is set
dom n is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
j is set
n . j is set
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i /. j is Element of the carrier of f
j + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
i /. (j + 1) is Element of the carrier of f
m . j is set
i . (j + 1) is set
i . j is set
j is Element of the carrier of f
j is Element of the carrier of f
f is non empty V67() MultiGraphStruct
the carrier of f is non empty set
the carrier' of f is set
m is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
m . 1 is set
n is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
n . 1 is set
i is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len i) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
dom m is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is Relation-like set
bool [: the carrier' of f, the carrier of f:] is set
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
Seg (len m) is finite len m -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len m ) } is set
len n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
Seg (len n) is finite len n -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len n ) } is set
dom n is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
j is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
m . j is set
n . j is set
n /. 1 is Element of the carrier of f
m /. (1 + 1) is Element of the carrier of f
m /. 1 is Element of the carrier of f
q1 is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
q1 /. 1 is Element of the carrier of f
q1 /. (1 + 1) is Element of the carrier of f
len q1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
i . 1 is set
n /. (1 + 1) is Element of the carrier of f
dom q1 is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
mXC1 is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
q1 . mXC1 is set
m . mXC1 is set
mXC1 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
q1 . (mXC1 + 1) is set
m . (mXC1 + 1) is set
mXCm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mXCm + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
m /. (mXCm + 1) is Element of the carrier of f
m /. mXCm is Element of the carrier of f
q1 /. (mXCm + 1) is Element of the carrier of f
q1 . (mXCm + 1) is set
q1 /. mXCm is Element of the carrier of f
i . mXCm is set
q1 . mXCm is set
m . mXCm is set
q1 . 0 is set
m . 0 is set
dom q1 is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
mXC1 is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
q1 . mXC1 is set
n . mXC1 is set
mXC1 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
q1 . (mXC1 + 1) is set
n . (mXC1 + 1) is set
mXCm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mXCm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mXCm + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
n /. (mXCm + 1) is Element of the carrier of f
n /. mXCm is Element of the carrier of f
q1 /. (mXCm + 1) is Element of the carrier of f
q1 . (mXCm + 1) is set
q1 /. mXCm is Element of the carrier of f
i . mXCm is set
q1 . mXCm is set
n . mXCm is set
mXCm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
q1 . 0 is set
n . 0 is set
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
X + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
m /. X is Element of the carrier of f
m . X is set
n /. j is Element of the carrier of f
m /. j is Element of the carrier of f
m /. (X + 1) is Element of the carrier of f
i . X is set
the Source of f . (i . X) is set
the Target of f . (i . X) is set
n /. X is Element of the carrier of f
n /. (X + 1) is Element of the carrier of f
n . X is set
rX is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
f is non empty V67() MultiGraphStruct
the carrier of f is non empty set
the carrier' of f is set
m is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
n is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
dom n is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is Relation-like set
bool [: the carrier' of f, the carrier of f:] is set
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . j is set
j + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
m . (j + 1) is set
m /. j is Element of the carrier of f
m /. (j + 1) is Element of the carrier of f
len n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n . j is set
the Target of f . (n . j) is set
the Source of f . (n . j) is set
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len n) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
f is non empty V67() MultiGraphStruct
the carrier of f is non empty set
the carrier' of f is set
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is Relation-like set
bool [: the carrier' of f, the carrier of f:] is set
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
m is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
rng m is finite set
n is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
n . 1 is set
the Source of f . (n . 1) is set
the Target of f . (n . 1) is set
{( the Source of f . (n . 1)),( the Target of f . (n . 1))} is non empty finite set
m /. (1 + 1) is Element of the carrier of f
m /. 1 is Element of the carrier of f
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len n) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
m . 1 is set
rng n is finite set
(f,(rng n)) is set
{ b₁ where b₁ is Element of the carrier of f : ex b₂ being Element of the carrier' of f st
( b₂ in rng n & ( b₁ = the Source of f . b₂ or b₁ = the Target of f . b₂ ) ) } is set
card (rng m) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of omega
X is set
rX is set
{X,rX} is non empty finite set
dom m is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
dom n is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
m . (1 + 1) is set
f is non empty V67() MultiGraphStruct
the carrier of f is non empty set
the carrier' of f is set
m is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
n is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len n) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
i is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
i + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
dom n is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
m . i is set
m . (i + 1) is set
rng n is finite set
(f,(rng n)) is set
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is Relation-like set
bool [: the carrier' of f, the carrier of f:] is set
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
{ b₁ where b₁ is Element of the carrier of f : ex b₂ being Element of the carrier' of f st
( b₂ in rng n & ( b₁ = the Source of f . b₂ or b₁ = the Target of f . b₂ ) ) } is set
card (f,(rng n)) is ordinal cardinal set
rng m is finite set
card (rng m) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of omega
f is non empty V67() MultiGraphStruct
the carrier' of f is set
the carrier of f is non empty set
m is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is Relation-like set
bool [: the carrier' of f, the carrier of f:] is set
m . 1 is set
the Source of f . (m . 1) is set
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
the Target of f . (m . 1) is set
j is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom m is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
j . 1 is set
j . 2 is set
rng j is finite set
{( the Source of f . (m . 1)),( the Target of f . (m . 1))} is non empty finite set
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len m) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
{(j . 2),(j . 1)} is non empty finite set
j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like () () set
rng j is finite set
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j . 1 is set
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
j is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j /. X is Element of the carrier of f
j . X is set
j /. X is Element of the carrier of f
X + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j /. (X + 1) is Element of the carrier of f
m . X is set
j /. (X + 1) is Element of the carrier of f
j . (X + 1) is set
j . X is set
j . (X + 1) is set
X is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rng X is finite set
rX is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like () () set
f is non empty set
card f is ordinal non empty cardinal set
the Element of f is Element of f
n is set
i is set
{ the Element of f} is non empty trivial finite 1 -element set
f is non empty V67() MultiGraphStruct
the carrier of f is non empty set
the carrier' of f is set
card the carrier of f is ordinal non empty cardinal set
m is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
n is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
i is finite set
j is set
{j} is non empty trivial finite 1 -element set
rng m is finite set
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len n) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
Seg (len m) is finite len m -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len m ) } is set
dom m is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
j is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
j . j is set
m . j is set
rng j is finite set
Seg (len j) is finite len j -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len j ) } is set
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is Relation-like set
bool [: the carrier' of f, the carrier of f:] is set
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
j is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len n) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom m is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
j is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
j . j is set
m . j is set
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
dom n is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
n . 1 is set
the Target of f . (n . 1) is set
the Source of f . (n . 1) is set
m /. j is Element of the carrier of f
j /. j is Element of the carrier of f
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j /. X is Element of the carrier of f
m /. X is Element of the carrier of f
X + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j /. (X + 1) is Element of the carrier of f
m /. (X + 1) is Element of the carrier of f
n . X is set
the Target of f . (n . X) is set
the Source of f . (n . X) is set
(X + 1) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j /. ((X + 1) + 1) is Element of the carrier of f
m /. ((X + 1) + 1) is Element of the carrier of f
n . (X + 1) is set
the Target of f . (n . (X + 1)) is set
the Source of f . (n . (X + 1)) is set
m /. 1 is Element of the carrier of f
m /. (1 + 1) is Element of the carrier of f
j /. 1 is Element of the carrier of f
j /. (1 + 1) is Element of the carrier of f
j /. 0 is Element of the carrier of f
m /. 0 is Element of the carrier of f
j /. (0 + 1) is Element of the carrier of f
m /. (0 + 1) is Element of the carrier of f
n . 0 is set
the Target of f . (n . 0) is set
the Source of f . (n . 0) is set
X is set
rng n is finite set
(f,(rng n)) is set
{ b₁ where b₁ is Element of the carrier of f : ex b₂ being Element of the carrier' of f st
( b₂ in rng n & ( b₁ = the Source of f . b₂ or b₁ = the Target of f . b₂ ) ) } is set
rX is Element of the carrier of f
qm is Element of the carrier' of f
the Source of f . qm is set
the Target of f . qm is set
qm is set
the Source of f . qm is set
the Target of f . qm is set
q1 is set
n . q1 is set
mX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n . mX is set
the Target of f . (n . mX) is set
the Source of f . (n . mX) is set
{( the Source of f . (n . 1)),( the Target of f . (n . 1))} is non empty finite set
rX is Element of the carrier' of f
the Target of f . rX is set
the Source of f . rX is set
q1 is Element of the carrier of f
qm is Element of the carrier of f
j + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j /. (j + 1) is Element of the carrier of f
n . j is set
j /. 1 is Element of the carrier of f
m /. (j + 1) is Element of the carrier of f
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n . X is set
the Target of f . (n . X) is set
the Source of f . (n . X) is set
m /. 1 is Element of the carrier of f
card (f,(rng n)) is ordinal cardinal set
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
X + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j /. X is Element of the carrier of f
j /. (X + 1) is Element of the carrier of f
n . X is set
the Source of f . (n . X) is set
the Target of f . (n . X) is set
j /. j is Element of the carrier of f
j . X is set
m /. X is Element of the carrier of f
m /. (X + 1) is Element of the carrier of f
m /. j is Element of the carrier of f
m . X is set
i is set
j is set
j is Element of the carrier of f
<*j*> is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of f
[1,j] is non empty set
{1,j} is non empty finite set
{{1,j},{1}} is non empty finite V46() set
{[1,j]} is Relation-like Function-like constant non empty trivial finite 1 -element set
m . 1 is set
j is Element of the carrier of f
<*j*> is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of f
[1,j] is non empty set
{1,j} is non empty finite set
{{1,j},{1}} is non empty finite V46() set
{[1,j]} is Relation-like Function-like constant non empty trivial finite 1 -element set
X is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
rX is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
f is non empty V67() MultiGraphStruct
the carrier' of f is set
the carrier of f is non empty set
card the carrier of f is ordinal non empty cardinal set
m is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
n is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
i is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
Seg f is finite f -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= f ) } is set
f + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
Seg (f + 1) is non empty finite f + 1 -element V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= f + 1 ) } is set
m is non empty V67() MultiGraphStruct
the carrier of m is non empty set
the carrier' of m is set
n is Relation-like NAT -defined the carrier of m -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of m
n | (Seg (f + 1)) is Relation-like NAT -defined Seg (f + 1) -defined NAT -defined the carrier of m -valued Function-like finite FinSequence-like FinSubsequence-like Element of bool [:NAT, the carrier of m:]
[:NAT, the carrier of m:] is Relation-like non empty non trivial non finite set
bool [:NAT, the carrier of m:] is non empty non trivial non finite set
i is Relation-like NAT -defined the carrier of m -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of m
j is Relation-like NAT -defined the carrier' of m -valued Function-like finite FinSequence-like FinSubsequence-like Chain of m
j | (Seg f) is Relation-like NAT -defined Seg f -defined NAT -defined the carrier' of m -valued Function-like finite FinSequence-like FinSubsequence-like Element of bool [:NAT, the carrier' of m:]
[:NAT, the carrier' of m:] is Relation-like set
bool [:NAT, the carrier' of m:] is set
j is Relation-like NAT -defined the carrier' of m -valued Function-like finite FinSequence-like FinSubsequence-like Chain of m
len n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len j) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len j) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
i /. (j + 1) is Element of the carrier of m
i . (j + 1) is set
n . (j + 1) is set
n /. j is Element of the carrier of m
n . j is set
i /. j is Element of the carrier of m
i . j is set
j . j is set
j . j is set
n /. (j + 1) is Element of the carrier of m
len i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len j) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i /. j is Element of the carrier of m
j + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
i /. (j + 1) is Element of the carrier of m
j . j is set
len i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len j) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len j) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i is non empty V67() MultiGraphStruct
the carrier' of i is set
j is Relation-like NAT -defined the carrier' of i -valued Function-like finite FinSequence-like FinSubsequence-like Chain of i
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
( the carrier' of i,j,m,n) is Relation-like NAT -defined the carrier' of i -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of i
n + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
the carrier of i is non empty set
j is Relation-like NAT -defined the carrier of i -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of i
( the carrier of i,j,m,(n + 1)) is Relation-like NAT -defined the carrier of i -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of i
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len ( the carrier of i,j,m,(n + 1)) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom ( the carrier of i,j,m,(n + 1)) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
( the carrier of i,j,m,(n + 1)) . X is set
rng ( the carrier of i,j,m,(n + 1)) is finite set
rng j is finite set
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len f) + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
((len f) + m) - m is ext-real V31() V94() integer set
(n + 1) - m is ext-real V31() V94() integer set
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len j) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len ( the carrier of i,j,m,(n + 1))) + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
((len ( the carrier of i,j,m,(n + 1))) + m) - m is ext-real V31() V94() integer set
(n + 1) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
((n + 1) + 1) - m is ext-real V31() V94() integer set
n - m is ext-real V31() V94() integer set
(n - m) + 1 is ext-real V31() V94() integer set
((n - m) + 1) + 1 is ext-real V31() V94() integer set
1 - 1 is ext-real V31() V94() integer set
m - 1 is ext-real V31() V94() integer set
m -' 1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
X + rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
q1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
q1 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
qm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
qm + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
m + (q1 + 1) is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
rX + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
( the carrier of i,j,m,(n + 1)) . (rX + 1) is set
j . (qm + 1) is set
j /. (qm + 1) is Element of the carrier of i
j /. qm is Element of the carrier of i
m + q1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
( the carrier of i,j,m,(n + 1)) . rX is set
j . qm is set
n - (m - 1) is ext-real V31() V94() integer set
(m - 1) + (n - (m - 1)) is ext-real V31() V94() integer set
(m - 1) + rX is ext-real V31() V94() integer set
mXC1 is Element of the carrier of i
mXCm is Element of the carrier of i
j . qm is set
f . rX is set
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom f is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
f . X is set
rng f is finite set
rng j is finite set
(len f) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
( the carrier of i,j,m,(n + 1)) . X is set
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
( the carrier of i,j,m,(n + 1)) . X is set
X + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
( the carrier of i,j,m,(n + 1)) . (X + 1) is set
f . X is set
f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
n is non empty V67() MultiGraphStruct
the carrier of n is non empty set
the carrier' of n is set
i is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of n
( the carrier of n,i,f,(m + 1)) is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of n
j is Relation-like NAT -defined the carrier of n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of n
j is Relation-like NAT -defined the carrier' of n -valued Function-like finite FinSequence-like FinSubsequence-like Chain of n
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
( the carrier' of n,j,f,m) is Relation-like NAT -defined the carrier' of n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of n
j is Relation-like NAT -defined the carrier' of n -valued Function-like finite FinSequence-like FinSubsequence-like Chain of n
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len j) + f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len j) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len j) + f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(m + 1) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len j) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j /. X is Element of the carrier of n
X + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j /. (X + 1) is Element of the carrier of n
j . X is set
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rX + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
f + rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j . X is set
i . (f + rX) is set
f + X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(f + rX) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
((f + rX) + 1) - 1 is ext-real V31() V94() integer set
((len j) + f) - 1 is ext-real V31() V94() integer set
i /. (f + rX) is Element of the carrier of n
j . (X + 1) is set
i /. ((f + rX) + 1) is Element of the carrier of n
f + (rX + 1) is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j . (f + rX) is set
i . ((f + rX) + 1) is set
f is non empty V67() MultiGraphStruct
the carrier of f is non empty set
the carrier' of f is set
m is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . (len m) is set
n is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
n . 1 is set
i is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
j is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
i ^ j is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of f
( the carrier of f,m,n) is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(n,2,(len n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
m ^ (n,2,(len n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len j) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len ( the carrier of f,m,n) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len ( the carrier of f,m,n)) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len m) + (len n) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom m is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
( the carrier of f,m,n) . X is set
m . X is set
rX is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
(len m) + rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
qm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len m) + qm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len n) - 1 is ext-real V31() V94() integer set
(len m) + ((len n) - 1) is ext-real V31() V94() integer set
qm + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
((len n) - 1) + 1 is ext-real V31() V94() integer set
dom n is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
( the carrier of f,m,n) . ((len m) + qm) is set
n . (qm + 1) is set
( the carrier of f,m,n) . X is set
len i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len i) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len (i ^ j) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom (i ^ j) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
dom i is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
X + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
m /. (X + 1) is Element of the carrier of f
m /. X is Element of the carrier of f
(i ^ j) . X is set
i . X is set
m . (X + 1) is set
m . X is set
( the carrier of f,m,n) . (X + 1) is set
( the carrier of f,m,n) . X is set
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
rX is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
(len i) + rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rX is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
(len i) + rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(i ^ j) . X is set
j . rX is set
rX + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
qm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
qm + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
n /. (qm + 1) is Element of the carrier of f
n . (qm + 1) is set
q1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
q1 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
( the carrier of f,m,n) . X is set
n . qm is set
(len m) + q1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
( the carrier of f,m,n) . ((len m) + q1) is set
n /. qm is Element of the carrier of f
j . qm is set
X + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
( the carrier of f,m,n) . (X + 1) is set
((len i) + 1) + qm is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
( the carrier of f,m,n) . (((len i) + 1) + qm) is set
dom i is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
(len i) + (len j) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
((len i) + (len j)) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len (i ^ j)) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom i is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
(i ^ j) . X is set
i . X is set
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
rX is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
(len i) + rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rX is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
(len i) + rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(i ^ j) . X is set
j . rX is set
dom i is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
f is non empty V67() MultiGraphStruct
the carrier of f is non empty set
the carrier' of f is set
m is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . (len m) is set
n is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
n . 1 is set
( the carrier of f,m,n) is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(n,2,(len n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
m ^ (n,2,(len n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
i is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
j is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
j is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
j ^ j is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of f
j is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len j) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len j) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len ( the carrier of f,m,n) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len ( the carrier of f,m,n)) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len m) + (len n) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len j) + (len j) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
((len j) + (len j)) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len (j ^ j) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len (j ^ j)) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
q1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom (j ^ j) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
qm is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len qm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
qm /. q1 is Element of the carrier of f
qm . q1 is set
q1 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
qm /. (q1 + 1) is Element of the carrier of f
qm . (q1 + 1) is set
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
m /. (q1 + 1) is Element of the carrier of f
m /. q1 is Element of the carrier of f
m . (q1 + 1) is set
m . q1 is set
j . q1 is set
(j ^ j) . q1 is set
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
mX is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
(len j) + mX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len j) + mX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
mX + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
n /. (mX + 1) is Element of the carrier of f
n /. mX is Element of the carrier of f
j . mX is set
mXCm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mXCm + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
n . mX is set
(len m) + mXCm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
qm . ((len m) + mXCm) is set
n . (mX + 1) is set
((len j) + 1) + mX is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
qm . (((len j) + 1) + mX) is set
(j ^ j) . q1 is set
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
f is non empty V67() MultiGraphStruct
the carrier of f is non empty set
m is Element of the carrier of f
<*m*> is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of f
[1,m] is non empty set
{1,m} is non empty finite set
{{1,m},{1}} is non empty finite V46() set
{[1,m]} is Relation-like Function-like constant non empty trivial finite 1 -element set
len {} is Relation-like non-empty empty-yielding NAT -defined RAT -valued ordinal natural Function-like one-to-one constant functional empty trivial ext-real non positive non negative V31() V32() V33() V34() V35() V36() V37() V38() V39() finite finite-yielding V46() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V81() V82() V83() V84() V85() V86() V87() V90() V91() V92() V93() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
<*m*> /. j is Element of the carrier of f
j + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
<*m*> /. (j + 1) is Element of the carrier of f
{} . j is Relation-like non-empty empty-yielding NAT -defined RAT -valued ordinal natural Function-like one-to-one constant functional empty trivial ext-real non positive non negative V31() V32() V33() V34() V35() V36() V37() V38() V39() finite finite-yielding V46() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V81() V82() V83() V84() V85() V86() V87() V90() V91() V92() V93() V94() integer Element of NAT
len <*m*> is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len {}) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
f is non empty V67() MultiGraphStruct
the carrier' of f is set
f is non empty V67() MultiGraphStruct
the carrier' of f is set
the carrier of f is non empty set
the Element of the carrier of f is Element of the carrier of f
the Relation-like non-empty empty-yielding NAT -defined the carrier' of f -valued ordinal natural Function-like one-to-one constant functional empty trivial ext-real non positive non negative V31() V32() V33() V34() V35() V36() V37() V38() V39() finite finite-yielding V46() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered oriented cyclic V81() V82() V83() V84() V85() V86() V87() V90() V91() V92() V93() V94() integer Chain of f is Relation-like non-empty empty-yielding NAT -defined the carrier' of f -valued ordinal natural Function-like one-to-one constant functional empty trivial ext-real non positive non negative V31() V32() V33() V34() V35() V36() V37() V38() V39() finite finite-yielding V46() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered oriented cyclic V81() V82() V83() V84() V85() V86() V87() V90() V91() V92() V93() V94() integer Chain of f
<* the Element of the carrier of f*> is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of f
[1, the Element of the carrier of f] is non empty set
{1, the Element of the carrier of f} is non empty finite set
{{1, the Element of the carrier of f},{1}} is non empty finite V46() set
{[1, the Element of the carrier of f]} is Relation-like Function-like constant non empty trivial finite 1 -element set
i is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i . j is set
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i . j is set
f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
Seg f is finite f -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= f ) } is set
m is non empty V67() MultiGraphStruct
the carrier' of m is set
n is Relation-like NAT -defined the carrier' of m -valued Function-like finite FinSequence-like FinSubsequence-like (m) Chain of m
n | (Seg f) is Relation-like NAT -defined Seg f -defined NAT -defined the carrier' of m -valued Function-like finite FinSequence-like FinSubsequence-like Element of bool [:NAT, the carrier' of m:]
[:NAT, the carrier' of m:] is Relation-like set
bool [:NAT, the carrier' of m:] is set
the carrier of m is non empty set
j is Relation-like NAT -defined the carrier of m -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of m
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
Seg (f + 1) is non empty finite f + 1 -element V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= f + 1 ) } is set
j | (Seg (f + 1)) is Relation-like NAT -defined Seg (f + 1) -defined NAT -defined the carrier of m -valued Function-like finite FinSequence-like FinSubsequence-like Element of bool [:NAT, the carrier of m:]
[:NAT, the carrier of m:] is Relation-like non empty non trivial non finite set
bool [:NAT, the carrier of m:] is non empty non trivial non finite set
j is Relation-like NAT -defined the carrier of m -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of m
j is Relation-like NAT -defined the carrier of m -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of m
i is Relation-like NAT -defined the carrier' of m -valued Function-like finite FinSequence-like FinSubsequence-like Chain of m
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j . X is set
j . rX is set
j . X is set
j . rX is set
j is Relation-like NAT -defined the carrier of m -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of m
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f is non empty V67() MultiGraphStruct
the carrier of f is non empty set
the carrier' of f is set
m is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
n is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
i is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like (f) Chain of f
len i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len i) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
dom m is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is Relation-like set
bool [: the carrier' of f, the carrier of f:] is set
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
Seg (len m) is finite len m -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len m ) } is set
len n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
Seg (len n) is finite len n -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len n ) } is set
dom n is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
j is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
m . j is set
n . j is set
(1 + 1) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
n /. ((1 + 1) + 1) is Element of the carrier of f
n /. (1 + 1) is Element of the carrier of f
n /. 1 is Element of the carrier of f
m /. ((1 + 1) + 1) is Element of the carrier of f
m /. (1 + 1) is Element of the carrier of f
m /. 1 is Element of the carrier of f
m . ((1 + 1) + 1) is set
m . 1 is set
i . 1 is set
n . 1 is set
mXC1 is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len mXC1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n . ((1 + 1) + 1) is set
i . 2 is set
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
X + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
m /. X is Element of the carrier of f
m . X is set
n /. j is Element of the carrier of f
m /. j is Element of the carrier of f
m /. (X + 1) is Element of the carrier of f
i . X is set
the Source of f . (i . X) is set
the Target of f . (i . X) is set
n /. X is Element of the carrier of f
n /. (X + 1) is Element of the carrier of f
n . X is set
f is non empty V67() MultiGraphStruct
the carrier of f is non empty set
the carrier' of f is set
m is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like (f) Chain of f
i is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . j is set
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . j is set
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . j is set
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . j is set
j + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
i /. (1 + 1) is Element of the carrier of f
m /. (1 + 1) is Element of the carrier of f
i /. 1 is Element of the carrier of f
n . 1 is set
m /. 1 is Element of the carrier of f
(1 + 1) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
m . (1 + 1) is set
m /. ((1 + 1) + 1) is Element of the carrier of f
i /. ((1 + 1) + 1) is Element of the carrier of f
n . 2 is set
i . 1 is set
i . ((1 + 1) + 1) is set
i . (1 + 1) is set
q1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . q1 is set
mX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . mX is set
q1 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
m . ((1 + 1) + 1) is set
m . 1 is set
len n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . j is set
m . j is set
len n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f is non empty V67() MultiGraphStruct
the carrier of f is non empty set
the carrier' of f is set
m is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
bool m is finite V46() set
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . 1 is set
m . (len m) is set
n is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
bool n is finite V46() set
len n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . i is set
m . j is set
j - i is ext-real V31() V94() integer set
i - i is ext-real V31() V94() integer set
(len n) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
i -' 1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
1 - 1 is ext-real V31() V94() integer set
i - 1 is ext-real V31() V94() integer set
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( j <= b₁ & b₁ <= len n ) } is set
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= j ) } is set
j + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( ( 1 <= b₁ & b₁ <= i ) or ( j + 1 <= b₁ & b₁ <= len m ) ) } is set
( the carrier of f,m,j,((len n) + 1)) is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
( the carrier of f,m,1,i) is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
( the carrier of f,m,(j + 1),((len n) + 1)) is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
j - 1 is ext-real V31() V94() integer set
j -' 1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
( the carrier' of f,n,j,(len n)) is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of f
mXC1 is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
len mXC1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len mXC1) + j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( ( 1 <= b₁ & b₁ <= j ) or ( j <= b₁ & b₁ <= len n ) ) } is set
fvs is Relation-like Function-like set
dom fvs is set
((len n) + 1) - 1 is ext-real V31() V94() integer set
Seg (len n) is finite len n -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len n ) } is set
fvs is set
fvs is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
fvs is Relation-like NAT -defined Function-like FinSubsequence-like set
fvs is set
domfvs is set
c9 is set
[domfvs,c9] is non empty set
{domfvs,c9} is non empty finite set
{domfvs} is non empty trivial finite 1 -element set
{{domfvs,c9},{domfvs}} is non empty finite V46() set
dom fvs is V81() V82() V83() V84() V85() V86() V90() Element of bool NAT
p1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom n is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
fvs . domfvs is set
n . p1 is set
(1 + 1) - 1 is ext-real V31() V94() integer set
( the carrier' of f,n,1,j) is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of f
domfvs is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSubsequence-like Element of bool n
Seq domfvs is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom domfvs is finite set
Sgm (dom domfvs) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom domfvs)) * domfvs is Relation-like NAT -defined the carrier' of f -valued Function-like finite set
q1 is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
fvs is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
len q1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len fvs is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len fvs) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
c9 is set
p1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= j ) } \/ { b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( j <= b₁ & b₁ <= len n ) } is set
p1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
{ b₂ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( ( 1 <= b₂ & b₂ <= j ) or ( j <= b₂ & b₂ <= len n ) ) } is set
p1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
{ b₂ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( ( 1 <= b₂ & b₂ <= j ) or ( j <= b₂ & b₂ <= len n ) ) } is set
{ b₂ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( ( 1 <= b₂ & b₂ <= j ) or ( j <= b₂ & b₂ <= len n ) ) } is set
c9 is set
p1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
c9 is set
p1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
c9 is finite set
Sgm c9 is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
rng (Sgm c9) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() set
dom domfvs is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
p1 is finite set
Sgm p1 is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
len (Sgm c9) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
card c9 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of omega
j - j is ext-real V31() V94() integer set
(len n) - j is ext-real V31() V94() integer set
(len mXC1) -' 1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len mXC1) - 1 is ext-real V31() V94() integer set
- (j - i) is ext-real V31() V94() integer set
- (- (j - i)) is ext-real V31() V94() integer set
mXC is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mXC + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
qm is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
( the carrier of f,m,(mXC + 1),j) is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
( the carrier of f,m,(mXC + 1),j) ^ ( the carrier of f,m,(j + 1),((len n) + 1)) is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len qm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len mXC1) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len qm) - 1 is ext-real V31() V94() integer set
(len qm) -' 1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
((len n) - j) + 1 is ext-real V31() V94() integer set
y is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
y -' 1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
y - 1 is ext-real V31() V94() integer set
k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(j + 1) + k is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j + y is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
x is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j + x is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
- 1 is ext-real non positive V31() V94() integer set
(len mXC1) + (- 1) is ext-real V31() V94() integer set
((len mXC1) + (- 1)) + 1 is ext-real V31() V94() integer set
mXC + (len mXC1) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i is set
x is set
y is set
[x,y] is non empty set
{x,y} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,y},{x}} is non empty finite V46() set
mXC1 . x is set
dom mXC1 is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mXC + k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm c9) . k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
dom (Sgm c9) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
(Sgm c9) * domfvs is Relation-like NAT -defined the carrier' of f -valued Function-like finite set
dom ((Sgm c9) * domfvs) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
((Sgm c9) * domfvs) . x is set
domfvs . (mXC + k) is set
j + i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n . (j + i) is set
x is set
y is set
[x,y] is non empty set
{x,y} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,y},{x}} is non empty finite V46() set
((Sgm c9) * domfvs) . x is set
k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mXC + k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm c9) . k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm c9) . x is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
mXC1 . k is set
(mXC + 1) + i is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
n . ((mXC + 1) + i) is set
domfvs . ((Sgm c9) . k) is set
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
y is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
x is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
p1 \/ c9 is finite set
Sgm (p1 \/ c9) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm p1) ^ (Sgm c9) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( j + 1 <= b₁ & b₁ <= len m ) } is set
x is Relation-like Function-like set
dom x is set
Seg (len m) is finite len m -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len m ) } is set
y is set
k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
y is Relation-like NAT -defined Function-like FinSubsequence-like set
k is set
i is set
p1 is set
[i,p1] is non empty set
{i,p1} is non empty finite set
{i} is non empty trivial finite 1 -element set
{{i,p1},{i}} is non empty finite V46() set
dom y is V81() V82() V83() V84() V85() V86() V90() Element of bool NAT
DL is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom m is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
y . i is set
m . DL is set
qm . 1 is set
q1 . (len q1) is set
fvs ^ mXC1 is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of f
k is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSubsequence-like Element of bool m
Seq k is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom k is finite set
Sgm (dom k) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom k)) * k is Relation-like NAT -defined the carrier of f -valued Function-like finite set
i is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
len i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
( the carrier of f,q1,qm) is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
(qm,2,(len qm)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
q1 ^ (qm,2,(len qm)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
p1 is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len p1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
p1 . 1 is set
p1 . (len p1) is set
i + (- 1) is ext-real V31() V94() integer set
- j is ext-real non positive V31() V94() integer set
(- j) + 1 is ext-real V31() V94() integer set
(len n) + ((- j) + 1) is ext-real V31() V94() integer set
(i + (- 1)) + ((len n) + ((- j) + 1)) is ext-real V31() V94() integer set
i + (- j) is ext-real V31() V94() integer set
(len n) + (i + (- j)) is ext-real V31() V94() integer set
idseq j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
Seg j is finite j -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
id (Seg j) is Relation-like Seg j -defined Seg j -valued RAT -valued INT -valued Function-like one-to-one total V32() V33() V34() V35() finite Element of bool [:(Seg j),(Seg j):]
[:(Seg j),(Seg j):] is Relation-like RAT -valued INT -valued V32() V33() V34() V35() finite set
bool [:(Seg j),(Seg j):] is finite V46() set
dom (Sgm p1) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
DL is set
DR is set
DL is set
[DR,DL] is non empty set
{DR,DL} is non empty finite set
{DR} is non empty trivial finite 1 -element set
{{DR,DL},{DR}} is non empty finite V46() set
fvs . DR is set
dom fvs is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
SL is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
SR is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
SR + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(Sgm p1) . SL is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm p1) * domfvs is Relation-like NAT -defined the carrier' of f -valued Function-like finite set
dom ((Sgm p1) * domfvs) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
((Sgm p1) * domfvs) . DR is set
domfvs . SL is set
1 + SR is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
n . (1 + SR) is set
DR is set
DL is set
[DR,DL] is non empty set
{DR,DL} is non empty finite set
{DR} is non empty trivial finite 1 -element set
{{DR,DL},{DR}} is non empty finite V46() set
((Sgm p1) * domfvs) . DR is set
(Sgm p1) . DR is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
domfvs . ((Sgm p1) . DR) is set
SL is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm p1) . SL is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
fvs . SL is set
n . SL is set
SR is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
SR + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len i) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
1 + (len fvs) is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
q1 . 1 is set
qm . (len qm) is set
m . ((len n) + 1) is set
( the carrier of f,qm,(0 + 1),(len qm)) is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
( the carrier of f,qm,(0 + 1),1) is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
( the carrier of f,qm,(1 + 1),(len qm)) is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
( the carrier of f,qm,(0 + 1),1) ^ ( the carrier of f,qm,(1 + 1),(len qm)) is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
rng (Sgm p1) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() set
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= i ) } is set
DR is set
DL is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
DR is set
DL is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
DR is set
DL is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= i ) } \/ { b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( j + 1 <= b₁ & b₁ <= len m ) } is set
DL is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
{ b₂ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( ( 1 <= b₂ & b₂ <= i ) or ( j + 1 <= b₂ & b₂ <= len m ) ) } is set
DL is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
{ b₂ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( ( 1 <= b₂ & b₂ <= i ) or ( j + 1 <= b₂ & b₂ <= len m ) ) } is set
{ b₂ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( ( 1 <= b₂ & b₂ <= i ) or ( j + 1 <= b₂ & b₂ <= len m ) ) } is set
DR is finite set
Sgm DR is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
rng (Sgm DR) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() set
dom k is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
((len n) + 1) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len qm) + j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len ( the carrier of f,m,(j + 1),((len n) + 1)) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len ( the carrier of f,m,(j + 1),((len n) + 1))) + (j + 1) is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len ( the carrier of f,m,(j + 1),((len n) + 1))) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
((len ( the carrier of f,m,(j + 1),((len n) + 1))) + 1) + j is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
DL is finite set
Sgm DL is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
idseq i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
Seg i is finite i -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
id (Seg i) is Relation-like Seg i -defined Seg i -valued RAT -valued INT -valued Function-like one-to-one total V32() V33() V34() V35() finite Element of bool [:(Seg i),(Seg i):]
[:(Seg i),(Seg i):] is Relation-like RAT -valued INT -valued V32() V33() V34() V35() finite set
bool [:(Seg i),(Seg i):] is finite V46() set
dom (Sgm DL) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
SR is set
i is set
j is set
[i,j] is non empty set
{i,j} is non empty finite set
{i} is non empty trivial finite 1 -element set
{{i,j},{i}} is non empty finite V46() set
q1 . i is set
dom q1 is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
l is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
l + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(Sgm DL) . k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm DL) * k is Relation-like NAT -defined the carrier of f -valued Function-like finite set
dom ((Sgm DL) * k) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
((Sgm DL) * k) . i is set
k . k is set
1 + l is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
m . (1 + l) is set
i is set
j is set
[i,j] is non empty set
{i,j} is non empty finite set
{i} is non empty trivial finite 1 -element set
{{i,j},{i}} is non empty finite V46() set
((Sgm DL) * k) . i is set
(Sgm DL) . i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
k . ((Sgm DL) . i) is set
k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm DL) . k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
q1 . k is set
m . k is set
l is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
l + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len (Sgm DR) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
card DR is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of omega
(y - 1) + 1 is ext-real V31() V94() integer set
j + ((y - 1) + 1) is ext-real V31() V94() integer set
(((len n) - j) + 1) + 1 is ext-real V31() V94() integer set
((((len n) - j) + 1) + 1) - 1 is ext-real V31() V94() integer set
j + (((((len n) - j) + 1) + 1) - 1) is ext-real V31() V94() integer set
i is set
j is set
k is set
[j,k] is non empty set
{j,k} is non empty finite set
{j} is non empty trivial finite 1 -element set
{{j,k},{j}} is non empty finite V46() set
( the carrier of f,m,(j + 1),((len n) + 1)) . j is set
dom ( the carrier of f,m,(j + 1),((len n) + 1)) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
l is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j + l is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm DR) . l is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
dom (Sgm DR) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
(Sgm DR) * k is Relation-like NAT -defined the carrier of f -valued Function-like finite set
dom ((Sgm DR) * k) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
((Sgm DR) * k) . j is set
k . (j + l) is set
(j + 1) + i is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
m . ((j + 1) + i) is set
j is set
k is set
[j,k] is non empty set
{j,k} is non empty finite set
{j} is non empty trivial finite 1 -element set
{{j,k},{j}} is non empty finite V46() set
((Sgm DR) * k) . j is set
l is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j + l is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm DR) . l is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm DR) . j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
( the carrier of f,m,(j + 1),((len n) + 1)) . l is set
(j + 1) + i is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
m . ((j + 1) + i) is set
k . ((Sgm DR) . l) is set
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
l is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
DL \/ DR is finite set
Sgm (DL \/ DR) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm DL) ^ (Sgm DR) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
( the carrier of f,qm,1,1) is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
qm . (0 + 1) is set
<*(qm . (0 + 1))*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
[1,(qm . (0 + 1))] is non empty set
{1,(qm . (0 + 1))} is non empty finite set
{{1,(qm . (0 + 1))},{1}} is non empty finite V46() set
{[1,(qm . (0 + 1))]} is Relation-like Function-like constant non empty trivial finite 1 -element set
j + 0 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . (j + 0) is set
<*(m . (j + 0))*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
[1,(m . (j + 0))] is non empty set
{1,(m . (j + 0))} is non empty finite set
{{1,(m . (j + 0))},{1}} is non empty finite V46() set
{[1,(m . (j + 0))]} is Relation-like Function-like constant non empty trivial finite 1 -element set
( the carrier of f,m,j,j) is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
q1 ^ ( the carrier of f,m,(j + 1),((len n) + 1)) is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
rng (Sgm DL) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() set
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( j <= b₁ & b₁ <= len m ) } is set
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( j <= b₁ & b₁ <= len n ) } is set
( the carrier of f,m,j,((len n) + 1)) is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
qm is Relation-like Function-like set
dom qm is set
j - 1 is ext-real V31() V94() integer set
- (j - 1) is ext-real V31() V94() integer set
- (- (j - 1)) is ext-real V31() V94() integer set
j -' 1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
q1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
q1 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
Seg (len n) is finite len n -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len n ) } is set
mX is set
mXC is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mX is Relation-like NAT -defined Function-like FinSubsequence-like set
mXC is set
mXC1 is set
mXCm is set
[mXC1,mXCm] is non empty set
{mXC1,mXCm} is non empty finite set
{mXC1} is non empty trivial finite 1 -element set
{{mXC1,mXCm},{mXC1}} is non empty finite V46() set
dom mX is V81() V82() V83() V84() V85() V86() V90() Element of bool NAT
fvs is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom n is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
mX . mXC1 is set
n . fvs is set
mXC is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSubsequence-like Element of bool n
Seq mXC is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom mXC is finite set
Sgm (dom mXC) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom mXC)) * mXC is Relation-like NAT -defined the carrier' of f -valued Function-like finite set
mXC1 is Relation-like Function-like set
dom mXC1 is set
Seg (len m) is finite len m -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len m ) } is set
mXCm is set
fvs is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mXCm is Relation-like NAT -defined Function-like FinSubsequence-like set
fvs is set
fvs is set
fvs is set
[fvs,fvs] is non empty set
{fvs,fvs} is non empty finite set
{fvs} is non empty trivial finite 1 -element set
{{fvs,fvs},{fvs}} is non empty finite V46() set
dom mXCm is V81() V82() V83() V84() V85() V86() V90() Element of bool NAT
domfvs is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom m is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
mXCm . fvs is set
m . domfvs is set
( the carrier' of f,n,j,(len n)) is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of f
fvs is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSubsequence-like Element of bool m
Seq fvs is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom fvs is finite set
Sgm (dom fvs) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom fvs)) * fvs is Relation-like NAT -defined the carrier of f -valued Function-like finite set
fvs is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
fvs is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
len fvs is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
domfvs is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len domfvs is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
domfvs . 1 is set
domfvs . (len domfvs) is set
len fvs is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len fvs) + j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
- j is ext-real non positive V31() V94() integer set
(- j) + 1 is ext-real V31() V94() integer set
(len n) + ((- j) + 1) is ext-real V31() V94() integer set
(len fvs) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
c9 is set
p1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
c9 is set
p1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
c9 is finite set
Sgm c9 is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
len (Sgm c9) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
card c9 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of omega
p1 is finite set
Sgm p1 is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
rng (Sgm p1) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() set
dom fvs is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
j - j is ext-real V31() V94() integer set
(len n) - j is ext-real V31() V94() integer set
(len fvs) -' 1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len fvs) - 1 is ext-real V31() V94() integer set
p is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j + p is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
q1 + (len fvs) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
x is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j + x is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
- 1 is ext-real non positive V31() V94() integer set
(len fvs) + (- 1) is ext-real V31() V94() integer set
((len fvs) + (- 1)) + 1 is ext-real V31() V94() integer set
rng (Sgm c9) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() set
dom mXC is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
y is set
k is set
i is set
[k,i] is non empty set
{k,i} is non empty finite set
{k} is non empty trivial finite 1 -element set
{{k,i},{k}} is non empty finite V46() set
fvs . k is set
dom fvs is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
x is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
q1 + x is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm c9) . x is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
y is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
y + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
dom (Sgm c9) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
(Sgm c9) * mXC is Relation-like NAT -defined the carrier' of f -valued Function-like finite set
dom ((Sgm c9) * mXC) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
((Sgm c9) * mXC) . k is set
mXC . (q1 + x) is set
j + y is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n . (j + y) is set
k is set
i is set
[k,i] is non empty set
{k,i} is non empty finite set
{k} is non empty trivial finite 1 -element set
{{k,i},{k}} is non empty finite V46() set
((Sgm c9) * mXC) . k is set
x is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
q1 + x is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm c9) . x is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm c9) . k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
y is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
y + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
fvs . x is set
(q1 + 1) + y is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
n . ((q1 + 1) + y) is set
mXC . ((Sgm c9) . x) is set
len (Sgm p1) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
card p1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of omega
((len n) + 1) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len ( the carrier of f,m,j,((len n) + 1)) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len ( the carrier of f,m,j,((len n) + 1))) + j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
((len n) - j) + 1 is ext-real V31() V94() integer set
(((len n) - j) + 1) + 1 is ext-real V31() V94() integer set
(len ( the carrier of f,m,j,((len n) + 1))) - 1 is ext-real V31() V94() integer set
(len ( the carrier of f,m,j,((len n) + 1))) -' 1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j + k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len ( the carrier of f,m,j,((len n) + 1))) + (- 1) is ext-real V31() V94() integer set
((len ( the carrier of f,m,j,((len n) + 1))) + (- 1)) + 1 is ext-real V31() V94() integer set
q1 + (len ( the carrier of f,m,j,((len n) + 1))) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i is set
x is set
y is set
[x,y] is non empty set
{x,y} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,y},{x}} is non empty finite V46() set
( the carrier of f,m,j,((len n) + 1)) . x is set
dom ( the carrier of f,m,j,((len n) + 1)) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
q1 + k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm p1) . k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
dom (Sgm p1) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
(Sgm p1) * fvs is Relation-like NAT -defined the carrier of f -valued Function-like finite set
dom ((Sgm p1) * fvs) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
((Sgm p1) * fvs) . x is set
fvs . (q1 + k) is set
j + i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . (j + i) is set
x is set
y is set
[x,y] is non empty set
{x,y} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,y},{x}} is non empty finite V46() set
((Sgm p1) * fvs) . x is set
k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
q1 + k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm p1) . k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm p1) . x is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
( the carrier of f,m,j,((len n) + 1)) . k is set
(q1 + 1) + i is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
m . ((q1 + 1) + i) is set
fvs . ((Sgm p1) . k) is set
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= i ) } is set
( the carrier of f,m,1,i) is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= j ) } is set
rX is set
qm is Relation-like Function-like set
dom qm is set
((len n) + 1) - 1 is ext-real V31() V94() integer set
Seg (len n) is finite len n -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len n ) } is set
q1 is set
mX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(1 + 1) - 1 is ext-real V31() V94() integer set
( the carrier' of f,n,1,j) is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of f
mX is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
len mX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len mX) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
q1 is Relation-like NAT -defined Function-like FinSubsequence-like set
mXC is set
mXC1 is set
mXCm is set
[mXC1,mXCm] is non empty set
{mXC1,mXCm} is non empty finite set
{mXC1} is non empty trivial finite 1 -element set
{{mXC1,mXCm},{mXC1}} is non empty finite V46() set
dom q1 is V81() V82() V83() V84() V85() V86() V90() Element of bool NAT
fvs is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom n is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
q1 . mXC1 is set
n . fvs is set
mXC is set
mXC1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mXC is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSubsequence-like Element of bool n
Seq mXC is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom mXC is finite set
Sgm (dom mXC) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom mXC)) * mXC is Relation-like NAT -defined the carrier' of f -valued Function-like finite set
mXC1 is finite set
Sgm mXC1 is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
fvs is Relation-like Function-like set
dom fvs is set
Seg (len m) is finite len m -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len m ) } is set
fvs is set
fvs is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
fvs is Relation-like NAT -defined Function-like FinSubsequence-like set
fvs is set
domfvs is set
c9 is set
[domfvs,c9] is non empty set
{domfvs,c9} is non empty finite set
{domfvs} is non empty trivial finite 1 -element set
{{domfvs,c9},{domfvs}} is non empty finite V46() set
dom fvs is V81() V82() V83() V84() V85() V86() V90() Element of bool NAT
p1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom m is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
fvs . domfvs is set
m . p1 is set
domfvs is set
c9 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
fvs is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSubsequence-like Element of bool m
Seq fvs is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom fvs is finite set
Sgm (dom fvs) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom fvs)) * fvs is Relation-like NAT -defined the carrier of f -valued Function-like finite set
c9 is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
len c9 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
p1 is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len p1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
p1 . 1 is set
p1 . (len p1) is set
len ( the carrier of f,m,1,i) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
idseq j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
Seg j is finite j -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
id (Seg j) is Relation-like Seg j -defined Seg j -valued RAT -valued INT -valued Function-like one-to-one total V32() V33() V34() V35() finite Element of bool [:(Seg j),(Seg j):]
[:(Seg j),(Seg j):] is Relation-like RAT -valued INT -valued V32() V33() V34() V35() finite set
bool [:(Seg j),(Seg j):] is finite V46() set
dom (Sgm mXC1) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
SL is set
p is set
x is set
[p,x] is non empty set
{p,x} is non empty finite set
{p} is non empty trivial finite 1 -element set
{{p,x},{p}} is non empty finite V46() set
mX . p is set
dom mX is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
y is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm mXC1) . y is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
k + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(Sgm mXC1) * mXC is Relation-like NAT -defined the carrier' of f -valued Function-like finite set
dom ((Sgm mXC1) * mXC) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
((Sgm mXC1) * mXC) . p is set
mXC . y is set
1 + k is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
n . (1 + k) is set
p is set
x is set
[p,x] is non empty set
{p,x} is non empty finite set
{p} is non empty trivial finite 1 -element set
{{p,x},{p}} is non empty finite V46() set
((Sgm mXC1) * mXC) . p is set
(Sgm mXC1) . p is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mXC . ((Sgm mXC1) . p) is set
y is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom mXC is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
(Sgm mXC1) . y is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mX . y is set
n . y is set
k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
k + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
domfvs is finite set
Sgm domfvs is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
idseq i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
Seg i is finite i -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
id (Seg i) is Relation-like Seg i -defined Seg i -valued RAT -valued INT -valued Function-like one-to-one total V32() V33() V34() V35() finite Element of bool [:(Seg i),(Seg i):]
[:(Seg i),(Seg i):] is Relation-like RAT -valued INT -valued V32() V33() V34() V35() finite set
bool [:(Seg i),(Seg i):] is finite V46() set
dom (Sgm domfvs) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
p is set
x is set
y is set
[x,y] is non empty set
{x,y} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,y},{x}} is non empty finite V46() set
( the carrier of f,m,1,i) . x is set
dom ( the carrier of f,m,1,i) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(Sgm domfvs) . k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(Sgm domfvs) * fvs is Relation-like NAT -defined the carrier of f -valued Function-like finite set
dom ((Sgm domfvs) * fvs) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
((Sgm domfvs) * fvs) . x is set
fvs . k is set
1 + i is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
m . (1 + i) is set
x is set
y is set
[x,y] is non empty set
{x,y} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,y},{x}} is non empty finite V46() set
((Sgm domfvs) * fvs) . x is set
(Sgm domfvs) . x is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
fvs . ((Sgm domfvs) . x) is set
k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom fvs is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
(Sgm domfvs) . k is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
( the carrier of f,m,1,i) . k is set
m . k is set
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
f is non empty V67() MultiGraphStruct
the carrier of f is non empty set
the carrier' of f is set
m is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
bool m is finite V46() set
m . 1 is set
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . (len m) is set
n is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
bool n is finite V46() set
j is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSubsequence-like Element of bool n
Seq j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom j is finite set
Sgm (dom j) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom j)) * j is Relation-like NAT -defined the carrier' of f -valued Function-like finite set
j is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSubsequence-like Element of bool m
Seq j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom j is finite set
Sgm (dom j) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom j)) * j is Relation-like NAT -defined the carrier of f -valued Function-like finite set
i is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like (f) Chain of f
len n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSubsequence-like Element of bool n
Seq j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom j is finite set
Sgm (dom j) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom j)) * j is Relation-like NAT -defined the carrier' of f -valued Function-like finite set
i is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSubsequence-like Element of bool m
Seq i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom i is finite set
Sgm (dom i) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom i)) * i is Relation-like NAT -defined the carrier of f -valued Function-like finite set
i is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSubsequence-like Element of bool n
Seq i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom i is finite set
Sgm (dom i) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom i)) * i is Relation-like NAT -defined the carrier' of f -valued Function-like finite set
j is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
j is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSubsequence-like Element of bool m
Seq j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom j is finite set
Sgm (dom j) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom j)) * j is Relation-like NAT -defined the carrier of f -valued Function-like finite set
j is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
j . 1 is set
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j . (len j) is set
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i is ordinal natural ext-real non negative V31() finite cardinal V94() integer set
j is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSubsequence-like Element of bool n
Seq j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom j is finite set
Sgm (dom j) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom j)) * j is Relation-like NAT -defined the carrier' of f -valued Function-like finite set
j is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
j is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSubsequence-like Element of bool m
Seq j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom j is finite set
Sgm (dom j) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom j)) * j is Relation-like NAT -defined the carrier of f -valued Function-like finite set
X is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
X . 1 is set
len X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
X . (len X) is set
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSubsequence-like Element of bool n
Seq j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom j is finite set
Sgm (dom j) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom j)) * j is Relation-like NAT -defined the carrier' of f -valued Function-like finite set
j is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
j is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSubsequence-like Element of bool m
Seq j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom j is finite set
Sgm (dom j) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom j)) * j is Relation-like NAT -defined the carrier of f -valued Function-like finite set
X is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
X . 1 is set
len X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
X . (len X) is set
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
bool j is finite V46() set
bool X is finite V46() set
q1 is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
len q1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mX is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len mX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mX . 1 is set
mX . (len mX) is set
rX is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSubsequence-like Element of bool j
Seq rX is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom rX is finite set
Sgm (dom rX) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom rX)) * rX is Relation-like NAT -defined the carrier' of f -valued Function-like finite set
qm is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSubsequence-like Element of bool X
Seq qm is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom qm is finite set
Sgm (dom qm) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom qm)) * qm is Relation-like NAT -defined the carrier of f -valued Function-like finite set
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
Sgm (dom j) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
dom rX is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
(Sgm (dom j)) | (dom rX) is Relation-like NAT -defined dom rX -defined NAT -defined NAT -valued RAT -valued Function-like V32() V33() V34() V35() finite FinSubsequence-like Element of bool [:NAT,NAT:]
[:NAT,NAT:] is Relation-like RAT -valued INT -valued non empty non trivial V32() V33() V34() V35() non finite set
bool [:NAT,NAT:] is non empty non trivial non finite set
rng ((Sgm (dom j)) | (dom rX)) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() set
j | (rng ((Sgm (dom j)) | (dom rX))) is Relation-like NAT -defined rng ((Sgm (dom j)) | (dom rX)) -defined NAT -defined the carrier' of f -valued Function-like finite FinSubsequence-like set
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
Sgm (dom j) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
dom qm is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
(Sgm (dom j)) | (dom qm) is Relation-like NAT -defined dom qm -defined NAT -defined NAT -valued RAT -valued Function-like V32() V33() V34() V35() finite FinSubsequence-like Element of bool [:NAT,NAT:]
rng ((Sgm (dom j)) | (dom qm)) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() set
j | (rng ((Sgm (dom j)) | (dom qm))) is Relation-like NAT -defined rng ((Sgm (dom j)) | (dom qm)) -defined NAT -defined the carrier of f -valued Function-like finite FinSubsequence-like set
mXC1 is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSubsequence-like Element of bool m
Seq mXC1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom mXC1 is finite set
Sgm (dom mXC1) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom mXC1)) * mXC1 is Relation-like NAT -defined the carrier of f -valued Function-like finite set
mXC is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSubsequence-like Element of bool n
Seq mXC is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom mXC is finite set
Sgm (dom mXC) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom mXC)) * mXC is Relation-like NAT -defined the carrier' of f -valued Function-like finite set
mXCm is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSubsequence-like Element of bool n
Seq mXCm is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom mXCm is finite set
Sgm (dom mXCm) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom mXCm)) * mXCm is Relation-like NAT -defined the carrier' of f -valued Function-like finite set
fvs is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like (f) Chain of f
fvs is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSubsequence-like Element of bool m
Seq fvs is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom fvs is finite set
Sgm (dom fvs) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom fvs)) * fvs is Relation-like NAT -defined the carrier of f -valued Function-like finite set
fvs is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
fvs . 1 is set
len fvs is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
fvs . (len fvs) is set
domfvs is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSubsequence-like Element of bool n
Seq domfvs is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom domfvs is finite set
Sgm (dom domfvs) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom domfvs)) * domfvs is Relation-like NAT -defined the carrier' of f -valued Function-like finite set
p1 is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
c9 is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSubsequence-like Element of bool m
Seq c9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom c9 is finite set
Sgm (dom c9) is Relation-like NAT -defined NAT -valued Function-like V32() V33() V34() V35() finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (dom c9)) * c9 is Relation-like NAT -defined the carrier of f -valued Function-like finite set
SL is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
SL . 1 is set
len SL is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
SL . (len SL) is set
len p1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f is non empty V67() MultiGraphStruct
the carrier' of f is set
m is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
Seg m is finite m -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
f | (Seg m) is Relation-like NAT -defined Seg m -defined NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
n is non empty V67() MultiGraphStruct
the carrier' of n is set
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom i is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
i . j is set
f . j is set
i . j is set
f . j is set
dom f is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
Seg (len f) is finite len f -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len f ) } is set
Seg (len i) is finite len i -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len i ) } is set
f is non empty V67() MultiGraphStruct
the carrier' of f is set
the carrier of f is non empty set
the Element of the carrier of f is Element of the carrier of f
the Relation-like non-empty empty-yielding NAT -defined the carrier' of f -valued ordinal natural Function-like one-to-one constant functional empty trivial ext-real non positive non negative V31() V32() V33() V34() V35() V36() V37() V38() V39() finite finite-yielding V46() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered oriented cyclic V81() V82() V83() V84() V85() V86() V87() V90() V91() V92() V93() V94() integer Chain of f is Relation-like non-empty empty-yielding NAT -defined the carrier' of f -valued ordinal natural Function-like one-to-one constant functional empty trivial ext-real non positive non negative V31() V32() V33() V34() V35() V36() V37() V38() V39() finite finite-yielding V46() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered oriented cyclic V81() V82() V83() V84() V85() V86() V87() V90() V91() V92() V93() V94() integer Chain of f
i is Relation-like NAT -defined the carrier' of f -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like Chain of f
<* the Element of the carrier of f*> is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of f
[1, the Element of the carrier of f] is non empty set
{1, the Element of the carrier of f} is non empty finite set
{{1, the Element of the carrier of f},{1}} is non empty finite V46() set
{[1, the Element of the carrier of f]} is Relation-like Function-like constant non empty trivial finite 1 -element set
j is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j . j is set
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j . j is set
f is non empty V67() MultiGraphStruct
the carrier' of f is set
m is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like (f) Chain of f
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . n is set
m . i is set
the carrier of f is non empty set
j is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len m) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
i + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j /. (i + 1) is Element of the carrier of f
j /. i is Element of the carrier of f
j . i is set
j /. n is Element of the carrier of f
n + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j /. (n + 1) is Element of the carrier of f
j . (i + 1) is set
j . n is set
j . (n + 1) is set
f is non empty V67() MultiGraphStruct
the carrier' of f is set
m is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like (f) Chain of f
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . 1 is set
m . 2 is set
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . n is set
m . i is set
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . n is set
m . i is set
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . n is set
m . i is set
the carrier of f is non empty set
j is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j /. (i + 1) is Element of the carrier of f
(len m) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j . (i + 1) is set
n + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j /. (n + 1) is Element of the carrier of f
j /. n is Element of the carrier of f
j . (n + 1) is set
j . n is set
j /. i is Element of the carrier of f
j . i is set
n + 0 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f is non empty V67() MultiGraphStruct
the carrier' of f is set
m is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like Chain of f
f is non empty V67() MultiGraphStruct
the carrier' of f is set
m is Relation-like NAT -defined the carrier' of f -valued Function-like finite FinSequence-like FinSubsequence-like oriented Chain of f
the carrier of f is non empty set
the Source of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
[: the carrier' of f, the carrier of f:] is Relation-like set
bool [: the carrier' of f, the carrier of f:] is set
m . 1 is set
the Source of f . (m . 1) is set
the Target of f is Relation-like the carrier' of f -defined the carrier of f -valued Function-like V25( the carrier' of f, the carrier of f) Element of bool [: the carrier' of f, the carrier of f:]
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
m . (len m) is set
the Target of f . (m . (len m)) is set
<*( the Target of f . (m . (len m)))*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
[1,( the Target of f . (m . (len m)))] is non empty set
{1,( the Target of f . (m . (len m)))} is non empty finite set
{{1,( the Target of f . (m . (len m)))},{1}} is non empty finite V46() set
{[1,( the Target of f . (m . (len m)))]} is Relation-like Function-like constant non empty trivial finite 1 -element set
j ^ <*( the Target of f . (m . (len m)))*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
len (j ^ <*( the Target of f . (m . (len m)))*>) is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len <*( the Target of f . (m . (len m)))*> is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len m) + (len <*( the Target of f . (m . (len m)))*>) is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len m) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
Seg (len j) is finite len j -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len j ) } is set
Seg (len m) is finite len m -element V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
{ b₁ where b₁ is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT : ( 1 <= b₁ & b₁ <= len m ) } is set
dom m is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
rng (j ^ <*( the Target of f . (m . (len m)))*>) is non empty finite set
j is set
dom (j ^ <*( the Target of f . (m . (len m)))*>) is non empty finite V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() Element of bool NAT
X is set
(j ^ <*( the Target of f . (m . (len m)))*>) . X is set
rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rng m is finite set
m . rX is set
qm is Element of the carrier' of f
the Source of f . qm is set
rng the Source of f is set
(j ^ <*( the Target of f . (m . (len m)))*>) . rX is set
j . rX is set
rng m is finite set
rng the Target of f is set
qm is Element of the carrier' of f
the Target of f . qm is set
j is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
j . 1 is set
len j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
X + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
dom j is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
j . (X + 1) is set
rX is Element of the carrier of f
j /. (X + 1) is Element of the carrier of f
m . X is set
the Target of f . (m . X) is set
j . (X + 1) is set
m . (X + 1) is set
the Source of f . (m . (X + 1)) is set
j . X is set
qm is Element of the carrier of f
j /. X is Element of the carrier of f
j . X is set
the Source of f . (m . X) is set
j . 1 is set
n is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
n . 1 is set
i is Relation-like NAT -defined the carrier of f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
i . 1 is set
f is non empty set
m is Relation-like NAT -defined f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of f
m /. 1 is Element of f
n is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
(f,m,n) is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
len n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(n,2,(len n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
m ^ (n,2,(len n)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
(f,m,n) /. 1 is Element of f
dom m is non empty finite V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() Element of bool NAT
(f,n,2,(len n)) is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
m ^ (f,n,2,(len n)) is Relation-like NAT -defined f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of f
dom (m ^ (f,n,2,(len n))) is non empty finite V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() Element of bool NAT
(m ^ (f,n,2,(len n))) . 1 is set
m . 1 is set
f is non empty set
m is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
n is Relation-like NAT -defined f -valued Function-like non empty non trivial finite FinSequence-like FinSubsequence-like FinSequence of f
(f,m,n) is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
len n is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(n,2,(len n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
m ^ (n,2,(len n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (f,m,n) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(f,m,n) /. (len (f,m,n)) is Element of f
n /. (len n) is Element of f
(len (f,m,n)) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len m) + (len n) is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
1 + 0 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(f,m,n) . (len (f,m,n)) is set
n . (len n) is set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(f,{}) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len {} is Relation-like non-empty empty-yielding NAT -defined RAT -valued ordinal natural Function-like one-to-one constant functional empty trivial ext-real non positive non negative V31() V32() V33() V34() V35() V36() V37() V38() V39() finite finite-yielding V46() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V81() V82() V83() V84() V85() V86() V87() V90() V91() V92() V93() V94() integer Element of NAT
({},2,(len {})) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
f ^ ({},2,(len {})) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
f ^ {} is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
f is set
<*f*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
[1,f] is non empty set
{1,f} is non empty finite set
{{1,f},{1}} is non empty finite V46() set
{[1,f]} is Relation-like Function-like constant non empty trivial finite 1 -element set
m is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(m,<*f*>) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len <*f*> is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(<*f*>,2,(len <*f*>)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
m ^ (<*f*>,2,(len <*f*>)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
f is non empty set
m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
len n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
(f,n,i) is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
len i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(i,2,(len i)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
n ^ (i,2,(len i)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(f,n,i) /. m is Element of f
n /. m is Element of f
(len n) + (len i) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len n) + 0 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len (f,n,i) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len (f,n,i)) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(f,n,i) . m is set
n . m is set
f is non empty set
m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
i is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
len i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
(f,n,i) is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
(i,2,(len i)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
n ^ (i,2,(len i)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len n) + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(f,n,i) /. ((len n) + m) is Element of f
i /. (m + 1) is Element of f
(len n) + (len i) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len (f,n,i) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len (f,n,i)) + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
len (f,n,i) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len (f,n,i) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len (f,n,i) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(f,n,i) . ((len n) + m) is set
i . (m + 1) is set
m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f is Relation-like NAT -defined INT -valued Function-like V32() V33() V34() finite FinSequence-like FinSubsequence-like FinSequence of INT
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
bool INT is non empty non trivial non finite set
(INT,f,m,n) is Relation-like NAT -defined INT -valued Function-like V32() V33() V34() finite FinSequence-like FinSubsequence-like FinSequence of INT
rng (INT,f,m,n) is finite V81() V82() V83() V84() V85() V90() V91() V92() set
n + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(n + 1) - m is ext-real V31() V94() integer set
m - m is ext-real V31() V94() integer set
len (INT,f,m,n) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len (INT,f,m,n)) + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rng (INT,f,m,n) is finite V81() V82() V83() V84() V85() V90() V91() V92() Element of bool INT
j is non empty finite V81() V82() V83() V84() V85() V88() V89() V90() V91() V92() Element of bool INT
min j is ext-real V31() V94() integer set
(min j) .. (INT,f,m,n) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
((min j) .. (INT,f,m,n)) + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(((min j) .. (INT,f,m,n)) + m) - 1 is ext-real V31() V94() integer set
1 - 1 is ext-real V31() V94() integer set
m - 1 is ext-real V31() V94() integer set
0 + 0 is Relation-like non-empty empty-yielding NAT -defined RAT -valued ordinal natural Function-like one-to-one constant functional empty trivial ext-real non positive non negative V31() V32() V33() V34() V35() V36() V37() V38() V39() finite finite-yielding V46() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V81() V82() V83() V84() V85() V86() V87() V90() V91() V92() V93() V94() integer Element of NAT
((min j) .. (INT,f,m,n)) + (m - 1) is ext-real V31() V94() integer set
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
X + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j is non empty finite V81() V82() V83() V84() V85() V88() V89() V90() V91() V92() Element of bool INT
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
min j is ext-real V31() V94() integer set
(min j) .. (INT,f,m,n) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
((min j) .. (INT,f,m,n)) + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is non empty finite V81() V82() V83() V84() V85() V88() V89() V90() V91() V92() Element of bool INT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
min j is ext-real V31() V94() integer set
(min j) .. (INT,f,m,n) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
((min j) .. (INT,f,m,n)) + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f is Relation-like NAT -defined INT -valued Function-like V32() V33() V34() finite FinSequence-like FinSubsequence-like FinSequence of INT
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(f,m,n) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f . i is ext-real V31() V94() integer set
(INT,f,m,n) is Relation-like NAT -defined INT -valued Function-like V32() V33() V34() finite FinSequence-like FinSubsequence-like FinSequence of INT
len (INT,f,m,n) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(len (INT,f,m,n)) + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
n - m is ext-real V31() V94() integer set
(n - m) + 1 is ext-real V31() V94() integer set
rng (INT,f,m,n) is finite V81() V82() V83() V84() V85() V90() V91() V92() set
i + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
j is non empty finite V81() V82() V83() V84() V85() V88() V89() V90() V91() V92() Element of bool INT
min j is ext-real V31() V94() integer set
(min j) .. (INT,f,m,n) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
((min j) .. (INT,f,m,n)) + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
((min j) .. (INT,f,m,n)) - 1 is ext-real V31() V94() integer set
(((min j) .. (INT,f,m,n)) - 1) + m is ext-real V31() V94() integer set
(((min j) .. (INT,f,m,n)) + m) - 1 is ext-real V31() V94() integer set
1 - 1 is ext-real V31() V94() integer set
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(INT,f,m,n) . (j + 1) is ext-real V31() V94() integer set
(i + 1) - m is ext-real V31() V94() integer set
(INT,f,m,n) . ((i + 1) - m) is ext-real V31() V94() integer set
((len (INT,f,m,n)) + m) - 1 is ext-real V31() V94() integer set
m + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(m + 1) - 1 is ext-real V31() V94() integer set
(INT,f,m,n) . ((min j) .. (INT,f,m,n)) is ext-real V31() V94() integer set
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f . X is ext-real V31() V94() integer set
m - m is ext-real V31() V94() integer set
X - m is ext-real V31() V94() integer set
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rX + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
dom (INT,f,m,n) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
(INT,f,m,n) . (rX + 1) is ext-real V31() V94() integer set
m + rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f . (m + rX) is ext-real V31() V94() integer set
X is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f . X is ext-real V31() V94() integer set
m - m is ext-real V31() V94() integer set
X - m is ext-real V31() V94() integer set
rX is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
rX + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(len (INT,f,m,n)) - 1 is ext-real V31() V94() integer set
((len (INT,f,m,n)) - 1) + m is ext-real V31() V94() integer set
qm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
0 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
dom (INT,f,m,n) is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
i - m is ext-real V31() V94() integer set
(i - m) + 1 is ext-real V31() V94() integer set
rX + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f . (rX + m) is ext-real V31() V94() integer set
(INT,f,m,n) . qm is ext-real V31() V94() integer set
(n + 1) - m is ext-real V31() V94() integer set
rng (INT,f,m,n) is finite V81() V82() V83() V84() V85() V90() V91() V92() Element of bool INT
X is non empty finite V81() V82() V83() V84() V85() V88() V89() V90() V91() V92() Element of bool INT
qm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
qm + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
q1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
qm + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mX is ext-real set
mXC is set
(INT,f,m,n) . mXC is ext-real V31() V94() integer set
mXC1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mXC1 - 1 is ext-real V31() V94() integer set
mXC1 + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(mXC1 + m) - 1 is ext-real V31() V94() integer set
mXCm is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mXCm + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f . (mXCm + m) is ext-real V31() V94() integer set
mXCm + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(INT,f,m,n) . (mXCm + 1) is ext-real V31() V94() integer set
(INT,f,m,n) . mXC1 is ext-real V31() V94() integer set
rX is non empty finite V81() V82() V83() V88() V89() V90() V91() V92() Element of bool REAL
min rX is ext-real V31() V94() set
min X is ext-real V31() V94() integer set
(min X) .. (INT,f,m,n) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
((min X) .. (INT,f,m,n)) - 1 is ext-real V31() V94() integer set
mXC1 is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mXC1 + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
mXC1 + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
f . (mXC1 + m) is ext-real V31() V94() integer set
(INT,f,m,n) . ((min X) .. (INT,f,m,n)) is ext-real V31() V94() integer set
((min X) .. (INT,f,m,n)) + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(((min X) .. (INT,f,m,n)) + m) - 1 is ext-real V31() V94() integer set
((min X) .. (INT,f,m,n)) + m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f is Relation-like NAT -defined INT -valued Function-like V32() V33() V34() finite FinSequence-like FinSubsequence-like FinSequence of INT
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
(f,m,m) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f . m is ext-real V31() V94() integer set
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f . n is ext-real V31() V94() integer set
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f . n is ext-real V31() V94() integer set
f is Relation-like NAT -defined INT -valued Function-like V32() V33() V34() finite FinSequence-like FinSubsequence-like FinSequence of INT
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m is Relation-like NAT -defined INT -valued Function-like V32() V33() V34() finite FinSequence-like FinSubsequence-like FinSequence of INT
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(f,(n + 1),(len f)) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f . (n + 1) is ext-real V31() V94() integer set
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f . i is ext-real V31() V94() integer set
f +* ((n + 1),(f . i)) is Relation-like Function-like set
(f +* ((n + 1),(f . i))) +* (i,(f . (n + 1))) is Relation-like Function-like set
dom m is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
dom (f +* ((n + 1),(f . i))) is set
dom f is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . j is ext-real V31() V94() integer set
m . j is ext-real V31() V94() integer set
(f +* ((n + 1),(f . i))) . j is set
f . j is ext-real V31() V94() integer set
(f +* ((n + 1),(f . i))) . j is set
f . j is ext-real V31() V94() integer set
(f +* ((n + 1),(f . i))) . j is set
f . j is ext-real V31() V94() integer set
(f +* ((n + 1),(f . i))) . j is set
f is Relation-like NAT -defined INT -valued Function-like V32() V33() V34() finite FinSequence-like FinSubsequence-like FinSequence of INT
len f is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m is Relation-like NAT -defined INT -valued Function-like V32() V33() V34() finite FinSequence-like FinSubsequence-like FinSequence of INT
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
n + 1 is ordinal natural non empty ext-real positive non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V88() V89() V90() V91() V92() V94() integer Element of NAT
(f,(n + 1),(len f)) is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f . (n + 1) is ext-real V31() V94() integer set
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f . i is ext-real V31() V94() integer set
f +* ((n + 1),(f . i)) is Relation-like Function-like set
(f +* ((n + 1),(f . i))) +* (i,(f . (n + 1))) is Relation-like Function-like set
dom m is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
dom (f +* ((n + 1),(f . i))) is set
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
len m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m . j is ext-real V31() V94() integer set
m . j is ext-real V31() V94() integer set
dom f is finite V81() V82() V83() V84() V85() V86() V90() V91() V92() Element of bool NAT
(f +* ((n + 1),(f . i))) . j is set
f . j is ext-real V31() V94() integer set
(f +* ((n + 1),(f . i))) . j is set
f . j is ext-real V31() V94() integer set
(f +* ((n + 1),(f . i))) . j is set
(f +* ((n + 1),(f . i))) . j is set
f . j is ext-real V31() V94() integer set
f is Relation-like NAT -defined INT -valued Function-like V32() V33() V34() finite FinSequence-like FinSubsequence-like FinSequence of INT
n is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
m is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
i is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
j is ordinal natural ext-real non negative V31() finite cardinal V81() V82() V83() V84() V85() V86() V90() V91() V92() V94() integer Element of NAT
f . i is ext-real V31() V94() integer set
f . j is ext-real V31() V94() integer set