:: NEWTON semantic presentation

REAL is non empty V12() non finite V61() V62() V63() V67() set
NAT is non empty V12() epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal V61() V62() V63() V64() V65() V66() V67() Element of K19(REAL)
K19(REAL) is V12() non finite set
COMPLEX is non empty V12() non finite V61() V67() set
RAT is non empty V12() non finite V61() V62() V63() V64() V67() set
INT is non empty V12() non finite V61() V62() V63() V64() V65() V67() set
K20(COMPLEX,COMPLEX) is V12() non finite complex-valued set
K19(K20(COMPLEX,COMPLEX)) is V12() non finite set
K20(K20(COMPLEX,COMPLEX),COMPLEX) is V12() non finite complex-valued set
K19(K20(K20(COMPLEX,COMPLEX),COMPLEX)) is V12() non finite set
K20(REAL,REAL) is V12() non finite complex-valued ext-real-valued real-valued set
K19(K20(REAL,REAL)) is V12() non finite set
K20(K20(REAL,REAL),REAL) is V12() non finite complex-valued ext-real-valued real-valued set
K19(K20(K20(REAL,REAL),REAL)) is V12() non finite set
K20(RAT,RAT) is V5( RAT ) V12() non finite complex-valued ext-real-valued real-valued set
K19(K20(RAT,RAT)) is V12() non finite set
K20(K20(RAT,RAT),RAT) is V5( RAT ) V12() non finite complex-valued ext-real-valued real-valued set
K19(K20(K20(RAT,RAT),RAT)) is V12() non finite set
K20(INT,INT) is V5( RAT ) V5( INT ) V12() non finite complex-valued ext-real-valued real-valued set
K19(K20(INT,INT)) is V12() non finite set
K20(K20(INT,INT),INT) is V5( RAT ) V5( INT ) V12() non finite complex-valued ext-real-valued real-valued set
K19(K20(K20(INT,INT),INT)) is V12() non finite set
K20(NAT,NAT) is V5( RAT ) V5( INT ) V12() non finite complex-valued ext-real-valued real-valued natural-valued set
K20(K20(NAT,NAT),NAT) is V5( RAT ) V5( INT ) V12() non finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20(K20(NAT,NAT),NAT)) is V12() non finite set
omega is non empty V12() epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal V61() V62() V63() V64() V65() V66() V67() set
K19(omega) is V12() non finite set
K19(NAT) is V12() non finite set
K232(NAT) is V39() set
{} is set
the functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative integer finite V44() cardinal {} -element FinSequence-membered V61() V62() V63() V64() V65() V66() V67() set is functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative integer finite V44() cardinal {} -element FinSequence-membered V61() V62() V63() V64() V65() V66() V67() set
1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
2 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
3 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
0 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
<*> REAL is V1() V4( NAT ) V5( REAL ) Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative integer finite finite-yielding V44() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-valued ext-real-valued real-valued natural-valued V61() V62() V63() V64() V65() V66() V67() FinSequence of REAL
Product (<*> REAL) is complex real ext-real Element of REAL
K207() is V1() V4(K20(REAL,REAL)) V5( REAL ) Function-like V30(K20(REAL,REAL), REAL ) complex-valued ext-real-valued real-valued Element of K19(K20(K20(REAL,REAL),REAL))
K258(REAL,(<*> REAL),K207()) is complex real ext-real Element of REAL
Seg 1 is non empty V12() finite 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= 1 ) } is set
{1} is non empty V12() finite V44() 1 -element V61() V62() V63() V64() V65() V66() set
Seg 2 is non empty finite 2 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= 2 ) } is set
{1,2} is finite V44() V61() V62() V63() V64() V65() V66() set
idseq 1 is V1() V4( NAT ) Function-like non empty V12() finite 1 -element FinSequence-like FinSubsequence-like set
id (Seg 1) is V1() V4( Seg 1) V5( RAT ) V5( INT ) V5( Seg 1) non empty total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg 1),(Seg 1)))
K20((Seg 1),(Seg 1)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg 1),(Seg 1))) is finite V44() set
<*1*> is V1() V4( NAT ) V5( NAT ) Function-like one-to-one non empty V12() finite 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued V55() decreasing non-decreasing non-increasing FinSequence of NAT
[1,1] is set
{1,1} is finite V44() V61() V62() V63() V64() V65() V66() set
{{1,1},{1}} is finite V44() set
{[1,1]} is non empty V12() finite 1 -element set
idseq 2 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like set
id (Seg 2) is V1() V4( Seg 2) V5( RAT ) V5( INT ) V5( Seg 2) non empty total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg 2),(Seg 2)))
K20((Seg 2),(Seg 2)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg 2),(Seg 2))) is finite V44() set
<*1,2*> is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
<*1*> is V1() V4( NAT ) Function-like one-to-one non empty V12() finite 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued V55() decreasing non-decreasing non-increasing set
<*2*> is V1() V4( NAT ) Function-like one-to-one non empty V12() finite 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued V55() decreasing non-decreasing non-increasing set
[1,2] is set
{{1,2},{1}} is finite V44() set
{[1,2]} is non empty V12() finite 1 -element set
<*1*> ^ <*2*> is V1() V4( NAT ) Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
card {} is epsilon-transitive epsilon-connected ordinal cardinal set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( not b₁ <= 1 & not m <= b₁ ) } is set
{1} \/ { b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( not b₁ <= 1 & not m <= b₁ ) } is set
{m} is non empty V12() finite V44() 1 -element V61() V62() V63() V64() V65() V66() set
({1} \/ { b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( not b₁ <= 1 & not m <= b₁ ) } ) \/ {m} is set
k is set
n is set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is complex real ext-real set
k is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
m * k is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K337(m) is V1() V4( REAL ) V5( REAL ) Function-like V30( REAL , REAL ) complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
id REAL is V1() V4( REAL ) V5( REAL ) non empty total complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
K207() [;] (m,(id REAL)) is set
K337(m) * k is V1() finite FinSequence-like complex-valued ext-real-valued real-valued set
len (m * k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
len k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(len k) -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
REAL * is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = len k } is set
n is V1() V4( NAT ) V5( REAL ) Function-like finite len k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of (len k) -tuples_on REAL
m * n is V1() V4( NAT ) V5( REAL ) Function-like finite len k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of (len k) -tuples_on REAL
K337(m) * n is V1() finite FinSequence-like complex-valued ext-real-valued real-valued set
len (m * n) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
len n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
dom k is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
m is complex real ext-real set
m * k is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K337(m) is V1() V4( REAL ) V5( REAL ) Function-like V30( REAL , REAL ) complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
id REAL is V1() V4( REAL ) V5( REAL ) non empty total complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
K207() [;] (m,(id REAL)) is set
K337(m) * k is V1() finite FinSequence-like complex-valued ext-real-valued real-valued set
dom (m * k) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m is complex set
k |-> m is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
(Seg k) --> m is V1() V4( Seg k) V5({m}) Function-like V30( Seg k,{m}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg k),{m}))
{m} is non empty V12() finite 1 -element V61() set
K20((Seg k),{m}) is finite complex-valued set
K19(K20((Seg k),{m})) is finite V44() set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m is complex set
k |-> m is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
(Seg k) --> m is V1() V4( Seg k) V5({m}) Function-like V30( Seg k,{m}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg k),{m}))
{m} is non empty V12() finite 1 -element V61() set
K20((Seg k),{m}) is finite complex-valued set
K19(K20((Seg k),{m})) is finite V44() set
Product (k |-> m) is complex set
m is complex real ext-real set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m,k) is set
k |-> m is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
(Seg k) --> m is V1() V4( Seg k) V5({m}) Function-like V30( Seg k,{m}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg k),{m}))
{m} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg k),{m}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg k),{m})) is finite V44() set
Product (k |-> m) is complex real ext-real set
m is complex real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m,k) is complex real ext-real set
k |-> m is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
(Seg k) --> m is V1() V4( Seg k) V5({m}) Function-like V30( Seg k,{m}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg k),{m}))
{m} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg k),{m}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg k),{m})) is finite V44() set
Product (k |-> m) is complex real ext-real set
m is complex set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m,k) is set
k |-> m is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
(Seg k) --> m is V1() V4( Seg k) V5({m}) Function-like V30( Seg k,{m}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg k),{m}))
{m} is non empty V12() finite 1 -element V61() set
K20((Seg k),{m}) is finite complex-valued set
K19(K20((Seg k),{m})) is finite V44() set
Product (k |-> m) is complex set
m is complex set
(m,0) is complex set
0 |-> m is V1() V4( NAT ) V5( RAT ) Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative integer finite finite-yielding V44() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered complex-valued ext-real-valued real-valued natural-valued V61() V62() V63() V64() V65() V66() V67() set
Seg 0 is functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative integer finite V44() cardinal 0 -element FinSequence-membered V61() V62() V63() V64() V65() V66() V67() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= 0 ) } is set
(Seg 0) --> m is V1() V4( Seg 0) V5({m}) Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative V30( Seg 0,{m}) integer finite finite-yielding V44() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-valued ext-real-valued real-valued natural-valued V61() V62() V63() V64() V65() V66() V67() Element of K19(K20((Seg 0),{m}))
{m} is non empty V12() finite 1 -element V61() set
K20((Seg 0),{m}) is finite complex-valued set
K19(K20((Seg 0),{m})) is finite V44() set
Product (0 |-> m) is complex real ext-real set
m is complex set
(m,1) is complex set
1 |-> m is V1() V4( NAT ) Function-like non empty V12() finite 1 -element FinSequence-like FinSubsequence-like complex-valued set
(Seg 1) --> m is V1() V4( Seg 1) V5({m}) Function-like V30( Seg 1,{m}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg 1),{m}))
{m} is non empty V12() finite 1 -element V61() set
K20((Seg 1),{m}) is finite complex-valued set
K19(K20((Seg 1),{m})) is finite V44() set
Product (1 |-> m) is complex set
<*m*> is V1() V4( NAT ) Function-like non empty V12() finite 1 -element FinSequence-like FinSubsequence-like complex-valued set
[1,m] is set
{1,m} is finite V61() set
{{1,m},{1}} is finite V44() set
{[1,m]} is non empty V12() finite 1 -element set
Product <*m*> is complex set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is complex set
(k,(m + 1)) is complex set
(m + 1) |-> k is V1() V4( NAT ) Function-like finite m + 1 -element FinSequence-like FinSubsequence-like complex-valued set
Seg (m + 1) is non empty finite m + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m + 1 ) } is set
(Seg (m + 1)) --> k is V1() V4( Seg (m + 1)) V5({k}) Function-like V30( Seg (m + 1),{k}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg (m + 1)),{k}))
{k} is non empty V12() finite 1 -element V61() set
K20((Seg (m + 1)),{k}) is finite complex-valued set
K19(K20((Seg (m + 1)),{k})) is finite V44() set
Product ((m + 1) |-> k) is complex set
(k,m) is complex set
m |-> k is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
(Seg m) --> k is V1() V4( Seg m) V5({k}) Function-like V30( Seg m,{k}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg m),{k}))
K20((Seg m),{k}) is finite complex-valued set
K19(K20((Seg m),{k})) is finite V44() set
Product (m |-> k) is complex set
(k,m) * k is complex set
<*k*> is V1() V4( NAT ) Function-like non empty V12() finite 1 -element FinSequence-like FinSubsequence-like complex-valued set
[1,k] is set
{1,k} is finite V61() set
{{1,k},{1}} is finite V44() set
{[1,k]} is non empty V12() finite 1 -element set
(m |-> k) ^ <*k*> is V1() V4( NAT ) Function-like non empty finite m + 1 -element FinSequence-like FinSubsequence-like complex-valued set
Product ((m |-> k) ^ <*k*>) is complex set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m,k) is complex real ext-real set
k |-> m is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
(Seg k) --> m is V1() V4( Seg k) V5( INT ) V5({m}) Function-like V30( Seg k,{m}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg k),{m}))
{m} is non empty V12() finite V44() 1 -element V61() V62() V63() V64() V65() V66() set
K20((Seg k),{m}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg k),{m})) is finite V44() set
Product (k |-> m) is complex real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m,n) is complex real ext-real set
n |-> m is V1() V4( NAT ) Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg n is finite n -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= n ) } is set
(Seg n) --> m is V1() V4( Seg n) V5( INT ) V5({m}) Function-like V30( Seg n,{m}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg n),{m}))
K20((Seg n),{m}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg n),{m})) is finite V44() set
Product (n |-> m) is complex real ext-real set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m,(n + 1)) is complex real ext-real set
(n + 1) |-> m is V1() V4( NAT ) Function-like finite n + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg (n + 1) is non empty finite n + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= n + 1 ) } is set
(Seg (n + 1)) --> m is V1() V4( Seg (n + 1)) V5( INT ) V5({m}) Function-like V30( Seg (n + 1),{m}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg (n + 1)),{m}))
K20((Seg (n + 1)),{m}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg (n + 1)),{m})) is finite V44() set
Product ((n + 1) |-> m) is complex real ext-real set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t * m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m,0) is complex real ext-real set
0 |-> m is V1() V4( NAT ) V5( RAT ) Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative integer finite finite-yielding V44() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered complex-valued ext-real-valued real-valued natural-valued V61() V62() V63() V64() V65() V66() V67() set
Seg 0 is functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative integer finite V44() cardinal 0 -element FinSequence-membered V61() V62() V63() V64() V65() V66() V67() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= 0 ) } is set
(Seg 0) --> m is V1() V4( Seg 0) V5( INT ) V5({m}) Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative V30( Seg 0,{m}) integer finite finite-yielding V44() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-valued ext-real-valued real-valued natural-valued V61() V62() V63() V64() V65() V66() V67() Element of K19(K20((Seg 0),{m}))
K20((Seg 0),{m}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg 0),{m})) is finite V44() set
Product (0 |-> m) is complex real ext-real set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is complex set
(k,m) is complex set
m |-> k is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
(Seg m) --> k is V1() V4( Seg m) V5({k}) Function-like V30( Seg m,{k}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg m),{k}))
{k} is non empty V12() finite 1 -element V61() set
K20((Seg m),{k}) is finite complex-valued set
K19(K20((Seg m),{k})) is finite V44() set
Product (m |-> k) is complex set
n is complex set
k * n is complex set
((k * n),m) is complex set
m |-> (k * n) is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued set
(Seg m) --> (k * n) is V1() V4( Seg m) V5({(k * n)}) Function-like V30( Seg m,{(k * n)}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg m),{(k * n)}))
{(k * n)} is non empty V12() finite 1 -element V61() set
K20((Seg m),{(k * n)}) is finite complex-valued set
K19(K20((Seg m),{(k * n)})) is finite V44() set
Product (m |-> (k * n)) is complex set
(n,m) is complex set
m |-> n is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued set
(Seg m) --> n is V1() V4( Seg m) V5({n}) Function-like V30( Seg m,{n}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg m),{n}))
{n} is non empty V12() finite 1 -element V61() set
K20((Seg m),{n}) is finite complex-valued set
K19(K20((Seg m),{n})) is finite V44() set
Product (m |-> n) is complex set
(k,m) * (n,m) is complex set
t is complex Element of COMPLEX
(t,m) is complex set
m |-> t is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued set
(Seg m) --> t is V1() V4( Seg m) V5({t}) Function-like V30( Seg m,{t}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg m),{t}))
{t} is non empty V12() finite 1 -element V61() set
K20((Seg m),{t}) is finite complex-valued set
K19(K20((Seg m),{t})) is finite V44() set
Product (m |-> t) is complex set
t is complex Element of COMPLEX
(t,m) is complex set
m |-> t is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued set
(Seg m) --> t is V1() V4( Seg m) V5({t}) Function-like V30( Seg m,{t}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg m),{t}))
{t} is non empty V12() finite 1 -element V61() set
K20((Seg m),{t}) is finite complex-valued set
K19(K20((Seg m),{t})) is finite V44() set
Product (m |-> t) is complex set
(t,m) * (t,m) is complex set
t * t is complex set
m |-> (t * t) is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued set
(Seg m) --> (t * t) is V1() V4( Seg m) V5({(t * t)}) Function-like V30( Seg m,{(t * t)}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg m),{(t * t)}))
{(t * t)} is non empty V12() finite 1 -element V61() set
K20((Seg m),{(t * t)}) is finite complex-valued set
K19(K20((Seg m),{(t * t)})) is finite V44() set
Product (m |-> (t * t)) is complex set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m + k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n is complex set
(n,(m + k)) is complex set
(m + k) |-> n is V1() V4( NAT ) Function-like finite m + k -element FinSequence-like FinSubsequence-like complex-valued set
Seg (m + k) is finite m + k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m + k ) } is set
(Seg (m + k)) --> n is V1() V4( Seg (m + k)) V5({n}) Function-like V30( Seg (m + k),{n}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg (m + k)),{n}))
{n} is non empty V12() finite 1 -element V61() set
K20((Seg (m + k)),{n}) is finite complex-valued set
K19(K20((Seg (m + k)),{n})) is finite V44() set
Product ((m + k) |-> n) is complex set
(n,m) is complex set
m |-> n is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
(Seg m) --> n is V1() V4( Seg m) V5({n}) Function-like V30( Seg m,{n}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg m),{n}))
K20((Seg m),{n}) is finite complex-valued set
K19(K20((Seg m),{n})) is finite V44() set
Product (m |-> n) is complex set
(n,k) is complex set
k |-> n is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
(Seg k) --> n is V1() V4( Seg k) V5({n}) Function-like V30( Seg k,{n}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg k),{n}))
K20((Seg k),{n}) is finite complex-valued set
K19(K20((Seg k),{n})) is finite V44() set
Product (k |-> n) is complex set
(n,m) * (n,k) is complex set
t is complex Element of COMPLEX
(t,m) is complex set
m |-> t is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued set
(Seg m) --> t is V1() V4( Seg m) V5({t}) Function-like V30( Seg m,{t}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg m),{t}))
{t} is non empty V12() finite 1 -element V61() set
K20((Seg m),{t}) is finite complex-valued set
K19(K20((Seg m),{t})) is finite V44() set
Product (m |-> t) is complex set
(t,k) is complex set
k |-> t is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued set
(Seg k) --> t is V1() V4( Seg k) V5({t}) Function-like V30( Seg k,{t}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg k),{t}))
K20((Seg k),{t}) is finite complex-valued set
K19(K20((Seg k),{t})) is finite V44() set
Product (k |-> t) is complex set
(t,m) * (t,k) is complex set
(m + k) |-> t is V1() V4( NAT ) V5( COMPLEX ) Function-like finite m + k -element FinSequence-like FinSubsequence-like complex-valued Element of (m + k) -tuples_on COMPLEX
(m + k) -tuples_on COMPLEX is functional non empty FinSequence-membered FinSequenceSet of COMPLEX
COMPLEX * is functional non empty FinSequence-membered FinSequenceSet of COMPLEX
{ b₁ where b₁ is V1() V4( NAT ) V5( COMPLEX ) Function-like finite FinSequence-like FinSubsequence-like Element of COMPLEX * : len b₁ = m + k } is set
(Seg (m + k)) --> t is V1() V4( Seg (m + k)) V5({t}) Function-like V30( Seg (m + k),{t}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg (m + k)),{t}))
K20((Seg (m + k)),{t}) is finite complex-valued set
K19(K20((Seg (m + k)),{t})) is finite V44() set
Product ((m + k) |-> t) is complex Element of COMPLEX
K201() is V1() V4(K20(COMPLEX,COMPLEX)) V5( COMPLEX ) Function-like V30(K20(COMPLEX,COMPLEX), COMPLEX ) complex-valued Element of K19(K20(K20(COMPLEX,COMPLEX),COMPLEX))
K258(COMPLEX,((m + k) |-> t),K201()) is complex Element of COMPLEX
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m * k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n is complex set
(n,m) is complex set
m |-> n is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
(Seg m) --> n is V1() V4( Seg m) V5({n}) Function-like V30( Seg m,{n}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg m),{n}))
{n} is non empty V12() finite 1 -element V61() set
K20((Seg m),{n}) is finite complex-valued set
K19(K20((Seg m),{n})) is finite V44() set
Product (m |-> n) is complex set
((n,m),k) is complex set
k |-> (n,m) is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
(Seg k) --> (n,m) is V1() V4( Seg k) V5({(n,m)}) Function-like V30( Seg k,{(n,m)}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg k),{(n,m)}))
{(n,m)} is non empty V12() finite 1 -element V61() set
K20((Seg k),{(n,m)}) is finite complex-valued set
K19(K20((Seg k),{(n,m)})) is finite V44() set
Product (k |-> (n,m)) is complex set
(n,(m * k)) is complex set
(m * k) |-> n is V1() V4( NAT ) Function-like finite m * k -element FinSequence-like FinSubsequence-like complex-valued set
Seg (m * k) is finite m * k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m * k ) } is set
(Seg (m * k)) --> n is V1() V4( Seg (m * k)) V5({n}) Function-like V30( Seg (m * k),{n}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg (m * k)),{n}))
K20((Seg (m * k)),{n}) is finite complex-valued set
K19(K20((Seg (m * k)),{n})) is finite V44() set
Product ((m * k) |-> n) is complex set
t is complex Element of COMPLEX
(t,(m * k)) is complex set
(m * k) |-> t is V1() V4( NAT ) Function-like finite m * k -element FinSequence-like FinSubsequence-like complex-valued set
(Seg (m * k)) --> t is V1() V4( Seg (m * k)) V5({t}) Function-like V30( Seg (m * k),{t}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg (m * k)),{t}))
{t} is non empty V12() finite 1 -element V61() set
K20((Seg (m * k)),{t}) is finite complex-valued set
K19(K20((Seg (m * k)),{t})) is finite V44() set
Product ((m * k) |-> t) is complex set
(t,m) is complex set
m |-> t is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued set
(Seg m) --> t is V1() V4( Seg m) V5({t}) Function-like V30( Seg m,{t}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg m),{t}))
K20((Seg m),{t}) is finite complex-valued set
K19(K20((Seg m),{t})) is finite V44() set
Product (m |-> t) is complex set
k |-> (t,m) is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued set
(Seg k) --> (t,m) is V1() V4( Seg k) V5({(t,m)}) Function-like V30( Seg k,{(t,m)}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg k),{(t,m)}))
{(t,m)} is non empty V12() finite 1 -element V61() set
K20((Seg k),{(t,m)}) is finite complex-valued set
K19(K20((Seg k),{(t,m)})) is finite V44() set
Product (k |-> (t,m)) is complex set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(1,m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
m |-> 1 is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
(Seg m) --> 1 is V1() V4( Seg m) V5( RAT ) V5( INT ) V5({1}) Function-like V30( Seg m,{1}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),{1}))
K20((Seg m),{1}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),{1})) is finite V44() set
Product (m |-> 1) is complex real ext-real set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(1,k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
k |-> 1 is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
(Seg k) --> 1 is V1() V4( Seg k) V5( RAT ) V5( INT ) V5({1}) Function-like V30( Seg k,{1}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg k),{1}))
K20((Seg k),{1}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg k),{1})) is finite V44() set
Product (k |-> 1) is complex real ext-real set
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(1,(k + 1)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
(k + 1) |-> 1 is V1() V4( NAT ) Function-like finite k + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg (k + 1) is non empty finite k + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k + 1 ) } is set
(Seg (k + 1)) --> 1 is V1() V4( Seg (k + 1)) V5( RAT ) V5( INT ) V5({1}) Function-like V30( Seg (k + 1),{1}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg (k + 1)),{1}))
K20((Seg (k + 1)),{1}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg (k + 1)),{1})) is finite V44() set
Product ((k + 1) |-> 1) is complex real ext-real set
1 * 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(1,0) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
0 |-> 1 is V1() V4( NAT ) V5( RAT ) Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative integer finite finite-yielding V44() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered complex-valued ext-real-valued real-valued natural-valued V61() V62() V63() V64() V65() V66() V67() set
Seg 0 is functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative integer finite V44() cardinal 0 -element FinSequence-membered V61() V62() V63() V64() V65() V66() V67() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= 0 ) } is set
(Seg 0) --> 1 is V1() V4( Seg 0) V5( RAT ) V5( INT ) V5({1}) Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative V30( Seg 0,{1}) integer finite finite-yielding V44() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-valued ext-real-valued real-valued natural-valued V61() V62() V63() V64() V65() V66() V67() Element of K19(K20((Seg 0),{1}))
K20((Seg 0),{1}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg 0),{1})) is finite V44() set
Product (0 |-> 1) is complex real ext-real set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(0,m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
m |-> 0 is V1() empty-yielding V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
(Seg m) --> 0 is V1() V4( Seg m) V5( RAT ) V5( INT ) V5({0}) Function-like V30( Seg m,{0}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),{0}))
{0} is non empty V12() finite V44() 1 -element V61() V62() V63() V64() V65() V66() set
K20((Seg m),{0}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),{0})) is finite V44() set
Product (m |-> 0) is complex real ext-real set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(0,k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
k |-> 0 is V1() empty-yielding V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
(Seg k) --> 0 is V1() V4( Seg k) V5( RAT ) V5( INT ) V5({0}) Function-like V30( Seg k,{0}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg k),{0}))
K20((Seg k),{0}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg k),{0})) is finite V44() set
Product (k |-> 0) is complex real ext-real set
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(0,(k + 1)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
(k + 1) |-> 0 is V1() empty-yielding V4( NAT ) Function-like finite k + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg (k + 1) is non empty finite k + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k + 1 ) } is set
(Seg (k + 1)) --> 0 is V1() V4( Seg (k + 1)) V5( RAT ) V5( INT ) V5({0}) Function-like V30( Seg (k + 1),{0}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg (k + 1)),{0}))
K20((Seg (k + 1)),{0}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg (k + 1)),{0})) is finite V44() set
Product ((k + 1) |-> 0) is complex real ext-real set
(0,k) * 0 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(0,1) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
1 |-> 0 is V1() empty-yielding V4( NAT ) Function-like one-to-one non empty V12() finite 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued V55() decreasing non-decreasing non-increasing set
(Seg 1) --> 0 is V1() V4( Seg 1) V5( RAT ) V5( INT ) V5({0}) Function-like V30( Seg 1,{0}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg 1),{0}))
K20((Seg 1),{0}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg 1),{0})) is finite V44() set
Product (1 |-> 0) is complex real ext-real set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
idseq m is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
id (Seg m) is V1() V4( Seg m) V5( RAT ) V5( INT ) V5( Seg m) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),(Seg m)))
K20((Seg m),(Seg m)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),(Seg m))) is finite V44() set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
idseq m is V1() V4( NAT ) V5( RAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
id (Seg m) is V1() V4( Seg m) V5( RAT ) V5( INT ) V5( Seg m) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),(Seg m)))
K20((Seg m),(Seg m)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),(Seg m))) is finite V44() set
Product (idseq m) is complex real ext-real set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m) is complex real ext-real Element of REAL
idseq m is V1() V4( NAT ) V5( RAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
id (Seg m) is V1() V4( Seg m) V5( RAT ) V5( INT ) V5( Seg m) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),(Seg m)))
K20((Seg m),(Seg m)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),(Seg m))) is finite V44() set
Product (idseq m) is complex real ext-real set
(0) is complex real ext-real Element of REAL
idseq 0 is V1() V4( NAT ) V5( RAT ) Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative integer finite finite-yielding V44() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered complex-valued ext-real-valued real-valued natural-valued V61() V62() V63() V64() V65() V66() V67() set
Seg 0 is functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative integer finite V44() cardinal 0 -element FinSequence-membered V61() V62() V63() V64() V65() V66() V67() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= 0 ) } is set
id (Seg 0) is V1() V4( Seg 0) V5( RAT ) V5( INT ) V5( Seg 0) functional empty total epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative integer finite finite-yielding V44() cardinal {} -element FinSequence-like FinSequence-membered complex-valued ext-real-valued real-valued natural-valued V61() V62() V63() V64() V65() V66() V67() Element of K19(K20((Seg 0),(Seg 0)))
K20((Seg 0),(Seg 0)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg 0),(Seg 0))) is finite V44() set
Product (idseq 0) is complex real ext-real set
(1) is complex real ext-real Element of REAL
Product (idseq 1) is complex real ext-real set
(2) is complex real ext-real Element of REAL
Product (idseq 2) is complex real ext-real set
1 * 2 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((m + 1)) is complex real ext-real Element of REAL
idseq (m + 1) is V1() V4( NAT ) V5( RAT ) Function-like finite m + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg (m + 1) is non empty finite m + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m + 1 ) } is set
id (Seg (m + 1)) is V1() V4( Seg (m + 1)) V5( RAT ) V5( INT ) V5( Seg (m + 1)) non empty total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg (m + 1)),(Seg (m + 1))))
K20((Seg (m + 1)),(Seg (m + 1))) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg (m + 1)),(Seg (m + 1)))) is finite V44() set
Product (idseq (m + 1)) is complex real ext-real set
(m) is complex real ext-real Element of REAL
idseq m is V1() V4( NAT ) V5( RAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
id (Seg m) is V1() V4( Seg m) V5( RAT ) V5( INT ) V5( Seg m) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),(Seg m)))
K20((Seg m),(Seg m)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),(Seg m))) is finite V44() set
Product (idseq m) is complex real ext-real set
(m) * (m + 1) is complex real ext-real Element of REAL
<*(m + 1)*> is V1() V4( NAT ) V5( NAT ) Function-like one-to-one non empty V12() finite 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued V55() decreasing non-decreasing non-increasing FinSequence of NAT
[1,(m + 1)] is set
{1,(m + 1)} is finite V44() V61() V62() V63() V64() V65() V66() set
{{1,(m + 1)},{1}} is finite V44() set
{[1,(m + 1)]} is non empty V12() finite 1 -element set
(idseq m) ^ <*(m + 1)*> is V1() V4( NAT ) Function-like non empty finite m + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m) is complex real ext-real Element of REAL
idseq m is V1() V4( NAT ) V5( RAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
id (Seg m) is V1() V4( Seg m) V5( RAT ) V5( INT ) V5( Seg m) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),(Seg m)))
K20((Seg m),(Seg m)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),(Seg m))) is finite V44() set
Product (idseq m) is complex real ext-real set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(k) is complex real ext-real Element of REAL
idseq k is V1() V4( NAT ) V5( RAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
id (Seg k) is V1() V4( Seg k) V5( RAT ) V5( INT ) V5( Seg k) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg k),(Seg k)))
K20((Seg k),(Seg k)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg k),(Seg k))) is finite V44() set
Product (idseq k) is complex real ext-real set
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((k + 1)) is complex real ext-real Element of REAL
idseq (k + 1) is V1() V4( NAT ) V5( RAT ) Function-like finite k + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg (k + 1) is non empty finite k + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k + 1 ) } is set
id (Seg (k + 1)) is V1() V4( Seg (k + 1)) V5( RAT ) V5( INT ) V5( Seg (k + 1)) non empty total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg (k + 1)),(Seg (k + 1))))
K20((Seg (k + 1)),(Seg (k + 1))) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg (k + 1)),(Seg (k + 1)))) is finite V44() set
Product (idseq (k + 1)) is complex real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(k + 1) * n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m) is complex real ext-real Element of REAL
idseq m is V1() V4( NAT ) V5( RAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
id (Seg m) is V1() V4( Seg m) V5( RAT ) V5( INT ) V5( Seg m) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),(Seg m)))
K20((Seg m),(Seg m)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),(Seg m))) is finite V44() set
Product (idseq m) is complex real ext-real set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
idseq m is V1() V4( NAT ) V5( RAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
id (Seg m) is V1() V4( Seg m) V5( RAT ) V5( INT ) V5( Seg m) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),(Seg m)))
K20((Seg m),(Seg m)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),(Seg m))) is finite V44() set
Product (idseq m) is complex real ext-real set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
idseq k is V1() V4( NAT ) V5( RAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
id (Seg k) is V1() V4( Seg k) V5( RAT ) V5( INT ) V5( Seg k) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg k),(Seg k)))
K20((Seg k),(Seg k)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg k),(Seg k))) is finite V44() set
Product (idseq k) is complex real ext-real set
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(k + 1) * (k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(k + 1) * 0 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((k + 1)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
idseq (k + 1) is V1() V4( NAT ) V5( RAT ) Function-like finite k + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg (k + 1) is non empty finite k + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k + 1 ) } is set
id (Seg (k + 1)) is V1() V4( Seg (k + 1)) V5( RAT ) V5( INT ) V5( Seg (k + 1)) non empty total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg (k + 1)),(Seg (k + 1))))
K20((Seg (k + 1)),(Seg (k + 1))) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg (k + 1)),(Seg (k + 1)))) is finite V44() set
Product (idseq (k + 1)) is complex real ext-real set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
idseq m is V1() V4( NAT ) V5( RAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
id (Seg m) is V1() V4( Seg m) V5( RAT ) V5( INT ) V5( Seg m) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),(Seg m)))
K20((Seg m),(Seg m)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),(Seg m))) is finite V44() set
Product (idseq m) is complex real ext-real set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
idseq m is V1() V4( NAT ) V5( RAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
id (Seg m) is V1() V4( Seg m) V5( RAT ) V5( INT ) V5( Seg m) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),(Seg m)))
K20((Seg m),(Seg m)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),(Seg m))) is finite V44() set
Product (idseq m) is complex real ext-real set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(k) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
idseq k is V1() V4( NAT ) V5( RAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
id (Seg k) is V1() V4( Seg k) V5( RAT ) V5( INT ) V5( Seg k) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg k),(Seg k)))
K20((Seg k),(Seg k)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg k),(Seg k))) is finite V44() set
Product (idseq k) is complex real ext-real set
(m) * (k) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k - m is complex real ext-real integer set
(k) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
idseq k is V1() V4( NAT ) V5( RAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
id (Seg k) is V1() V4( Seg k) V5( RAT ) V5( INT ) V5( Seg k) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg k),(Seg k)))
K20((Seg k),(Seg k)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg k),(Seg k))) is finite V44() set
Product (idseq k) is complex real ext-real set
(m) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
idseq m is V1() V4( NAT ) V5( RAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
id (Seg m) is V1() V4( Seg m) V5( RAT ) V5( INT ) V5( Seg m) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),(Seg m)))
K20((Seg m),(Seg m)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),(Seg m))) is finite V44() set
Product (idseq m) is complex real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(n) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
idseq n is V1() V4( NAT ) V5( RAT ) Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg n is finite n -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= n ) } is set
id (Seg n) is V1() V4( Seg n) V5( RAT ) V5( INT ) V5( Seg n) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg n),(Seg n)))
K20((Seg n),(Seg n)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg n),(Seg n))) is finite V44() set
Product (idseq n) is complex real ext-real set
(m) * (n) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
(k) / ((m) * (n)) is non empty complex real ext-real positive non negative Element of REAL
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(t) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
idseq t is V1() V4( NAT ) V5( RAT ) Function-like finite t -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg t is finite t -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= t ) } is set
id (Seg t) is V1() V4( Seg t) V5( RAT ) V5( INT ) V5( Seg t) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg t),(Seg t)))
K20((Seg t),(Seg t)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg t),(Seg t))) is finite V44() set
Product (idseq t) is complex real ext-real set
(m) * (t) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
(k) / ((m) * (t)) is non empty complex real ext-real positive non negative Element of REAL
n is set
t is set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(t) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
idseq t is V1() V4( NAT ) V5( RAT ) Function-like finite t -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg t is finite t -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= t ) } is set
id (Seg t) is V1() V4( Seg t) V5( RAT ) V5( INT ) V5( Seg t) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg t),(Seg t)))
K20((Seg t),(Seg t)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg t),(Seg t))) is finite V44() set
Product (idseq t) is complex real ext-real set
(m) * (t) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
(k) / ((m) * (t)) is non empty complex real ext-real positive non negative Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m,k) is set
k - m is complex real ext-real integer set
(k) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
idseq k is V1() V4( NAT ) V5( RAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
id (Seg k) is V1() V4( Seg k) V5( RAT ) V5( INT ) V5( Seg k) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg k),(Seg k)))
K20((Seg k),(Seg k)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg k),(Seg k))) is finite V44() set
Product (idseq k) is complex real ext-real set
(m) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
idseq m is V1() V4( NAT ) V5( RAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
id (Seg m) is V1() V4( Seg m) V5( RAT ) V5( INT ) V5( Seg m) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),(Seg m)))
K20((Seg m),(Seg m)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),(Seg m))) is finite V44() set
Product (idseq m) is complex real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(n) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
idseq n is V1() V4( NAT ) V5( RAT ) Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg n is finite n -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= n ) } is set
id (Seg n) is V1() V4( Seg n) V5( RAT ) V5( INT ) V5( Seg n) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg n),(Seg n)))
K20((Seg n),(Seg n)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg n),(Seg n))) is finite V44() set
Product (idseq n) is complex real ext-real set
(m) * (n) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
(k) / ((m) * (n)) is non empty complex real ext-real positive non negative Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m,k) is complex real ext-real set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(0,m) is complex real ext-real Element of REAL
m - 0 is complex real ext-real integer Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
idseq m is V1() V4( NAT ) V5( RAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
id (Seg m) is V1() V4( Seg m) V5( RAT ) V5( INT ) V5( Seg m) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),(Seg m)))
K20((Seg m),(Seg m)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),(Seg m))) is finite V44() set
Product (idseq m) is complex real ext-real set
1 * (m) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m) / (1 * (m)) is non empty complex real ext-real positive non negative Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m - k is complex real ext-real integer set
(k,m) is complex real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(n,m) is complex real ext-real Element of REAL
0 - m is complex real ext-real integer Element of REAL
k - m is complex real ext-real integer set
- (k - m) is complex real ext-real integer set
- m is complex real ext-real non positive integer set
- (- m) is complex real ext-real non negative integer set
m - n is complex real ext-real integer set
(m) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
idseq m is V1() V4( NAT ) V5( RAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
id (Seg m) is V1() V4( Seg m) V5( RAT ) V5( INT ) V5( Seg m) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),(Seg m)))
K20((Seg m),(Seg m)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),(Seg m))) is finite V44() set
Product (idseq m) is complex real ext-real set
(n) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
idseq n is V1() V4( NAT ) V5( RAT ) Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg n is finite n -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= n ) } is set
id (Seg n) is V1() V4( Seg n) V5( RAT ) V5( INT ) V5( Seg n) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg n),(Seg n)))
K20((Seg n),(Seg n)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg n),(Seg n))) is finite V44() set
Product (idseq n) is complex real ext-real set
(k) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
idseq k is V1() V4( NAT ) V5( RAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
id (Seg k) is V1() V4( Seg k) V5( RAT ) V5( INT ) V5( Seg k) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg k),(Seg k)))
K20((Seg k),(Seg k)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg k),(Seg k))) is finite V44() set
Product (idseq k) is complex real ext-real set
(n) * (k) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
(m) / ((n) * (k)) is non empty complex real ext-real positive non negative Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m,m) is complex real ext-real Element of REAL
m - m is complex real ext-real integer set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(0,m) is complex real ext-real Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((k + 1),(m + 1)) is complex real ext-real Element of REAL
((k + 1),m) is complex real ext-real Element of REAL
(k,m) is complex real ext-real Element of REAL
((k + 1),m) + (k,m) is complex real ext-real Element of REAL
m - k is complex real ext-real integer set
m - (k + 1) is complex real ext-real integer Element of REAL
(m + 1) - (k + 1) is complex real ext-real integer Element of REAL
(m) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
idseq m is V1() V4( NAT ) V5( RAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
id (Seg m) is V1() V4( Seg m) V5( RAT ) V5( INT ) V5( Seg m) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),(Seg m)))
K20((Seg m),(Seg m)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),(Seg m))) is finite V44() set
Product (idseq m) is complex real ext-real set
((k + 1)) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
idseq (k + 1) is V1() V4( NAT ) V5( RAT ) Function-like finite k + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg (k + 1) is non empty finite k + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k + 1 ) } is set
id (Seg (k + 1)) is V1() V4( Seg (k + 1)) V5( RAT ) V5( INT ) V5( Seg (k + 1)) non empty total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg (k + 1)),(Seg (k + 1))))
K20((Seg (k + 1)),(Seg (k + 1))) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg (k + 1)),(Seg (k + 1)))) is finite V44() set
Product (idseq (k + 1)) is complex real ext-real set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(t) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
idseq t is V1() V4( NAT ) V5( RAT ) Function-like finite t -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg t is finite t -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= t ) } is set
id (Seg t) is V1() V4( Seg t) V5( RAT ) V5( INT ) V5( Seg t) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg t),(Seg t)))
K20((Seg t),(Seg t)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg t),(Seg t))) is finite V44() set
Product (idseq t) is complex real ext-real set
((k + 1)) * (t) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
(m) / (((k + 1)) * (t)) is non empty complex real ext-real positive non negative Element of REAL
(k) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
idseq k is V1() V4( NAT ) V5( RAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
id (Seg k) is V1() V4( Seg k) V5( RAT ) V5( INT ) V5( Seg k) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg k),(Seg k)))
K20((Seg k),(Seg k)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg k),(Seg k))) is finite V44() set
Product (idseq k) is complex real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(n) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
idseq n is V1() V4( NAT ) V5( RAT ) Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg n is finite n -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= n ) } is set
id (Seg n) is V1() V4( Seg n) V5( RAT ) V5( INT ) V5( Seg n) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg n),(Seg n)))
K20((Seg n),(Seg n)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg n),(Seg n))) is finite V44() set
Product (idseq n) is complex real ext-real set
(k) * (n) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
(m) / ((k) * (n)) is non empty complex real ext-real positive non negative Element of REAL
((m) / (((k + 1)) * (t))) + ((m) / ((k) * (n))) is non empty complex real ext-real positive non negative Element of REAL
(m) * ((k) * (n)) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
(m) * (((k + 1)) * (t)) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
((m) * ((k) * (n))) + ((m) * (((k + 1)) * (t))) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
(((k + 1)) * (t)) * ((k) * (n)) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
(((m) * ((k) * (n))) + ((m) * (((k + 1)) * (t)))) / ((((k + 1)) * (t)) * ((k) * (n))) is non empty complex real ext-real positive non negative Element of REAL
(k) * (k + 1) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((k) * (k + 1)) * (t) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m) * (((k) * (k + 1)) * (t)) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((m) * ((k) * (n))) + ((m) * (((k) * (k + 1)) * (t))) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(((m) * ((k) * (n))) + ((m) * (((k) * (k + 1)) * (t)))) / ((((k + 1)) * (t)) * ((k) * (n))) is non empty complex real ext-real positive non negative Element of REAL
(k + 1) * (t) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(n) + ((k + 1) * (t)) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m) * ((n) + ((k + 1) * (t))) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(k) * ((m) * ((n) + ((k + 1) * (t)))) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(n) * (((k + 1)) * (t)) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
(k) * ((n) * (((k + 1)) * (t))) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
((k) * ((m) * ((n) + ((k + 1) * (t))))) / ((k) * ((n) * (((k + 1)) * (t)))) is non empty complex real ext-real positive non negative Element of REAL
t + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((t + 1)) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
idseq (t + 1) is V1() V4( NAT ) V5( RAT ) Function-like finite t + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg (t + 1) is non empty finite t + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= t + 1 ) } is set
id (Seg (t + 1)) is V1() V4( Seg (t + 1)) V5( RAT ) V5( INT ) V5( Seg (t + 1)) non empty total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg (t + 1)),(Seg (t + 1))))
K20((Seg (t + 1)),(Seg (t + 1))) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg (t + 1)),(Seg (t + 1)))) is finite V44() set
Product (idseq (t + 1)) is complex real ext-real set
((t + 1)) + ((k + 1) * (t)) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m) * (((t + 1)) + ((k + 1) * (t))) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((m) * (((t + 1)) + ((k + 1) * (t)))) / ((n) * (((k + 1)) * (t))) is non empty complex real ext-real positive non negative Element of REAL
(t) * (t + 1) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(t) * (k + 1) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((t) * (t + 1)) + ((t) * (k + 1)) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m) * (((t) * (t + 1)) + ((t) * (k + 1))) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((m) * (((t) * (t + 1)) + ((t) * (k + 1)))) / ((n) * (((k + 1)) * (t))) is non empty complex real ext-real positive non negative Element of REAL
(t + 1) + (k + 1) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m) * ((t + 1) + (k + 1)) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(t) * ((m) * ((t + 1) + (k + 1))) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((k + 1)) * (n) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
(t) * (((k + 1)) * (n)) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
((t) * ((m) * ((t + 1) + (k + 1)))) / ((t) * (((k + 1)) * (n))) is non empty complex real ext-real positive non negative Element of REAL
k - (k + 1) is complex real ext-real integer Element of REAL
m - (k - (k + 1)) is complex real ext-real integer Element of REAL
(m) * (m - (k - (k + 1))) is complex real ext-real integer Element of REAL
((m) * (m - (k - (k + 1)))) / (((k + 1)) * (n)) is complex real ext-real Element of REAL
((m + 1)) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
idseq (m + 1) is V1() V4( NAT ) V5( RAT ) Function-like finite m + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg (m + 1) is non empty finite m + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m + 1 ) } is set
id (Seg (m + 1)) is V1() V4( Seg (m + 1)) V5( RAT ) V5( INT ) V5( Seg (m + 1)) non empty total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg (m + 1)),(Seg (m + 1))))
K20((Seg (m + 1)),(Seg (m + 1))) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg (m + 1)),(Seg (m + 1)))) is finite V44() set
Product (idseq (m + 1)) is complex real ext-real set
((m + 1)) / (((k + 1)) * (n)) is non empty complex real ext-real positive non negative Element of REAL
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m + 0 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(1,m) is complex real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(1,k) is complex real ext-real Element of REAL
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(1,(k + 1)) is complex real ext-real Element of REAL
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((0 + 1),(k + 1)) is complex real ext-real Element of REAL
(0,k) is complex real ext-real Element of REAL
k + (0,k) is complex real ext-real Element of REAL
(1,1) is complex real ext-real Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m - 1 is complex real ext-real integer Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(k,m) is complex real ext-real Element of REAL
(1,m) is complex real ext-real Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(k,m) is complex real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(t,(n + 1)) is complex real ext-real Element of REAL
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(k,n) is complex real ext-real Element of REAL
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((k + 1),n) is complex real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k + k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(k,n) + ((k + 1),n) is complex real ext-real Element of REAL
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(t,(n + 1)) is complex real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(n,0) is complex real ext-real Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m + k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
((m + 1),(m + k)) is complex real ext-real Element of REAL
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m + (k + 1) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal set
((m + 1),(m + (k + 1))) is complex real ext-real Element of REAL
n is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
dom n is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
Sum n is complex real ext-real Element of REAL
K205() is V1() V4(K20(REAL,REAL)) V5( REAL ) Function-like V30(K20(REAL,REAL), REAL ) complex-valued ext-real-valued real-valued Element of K19(K20(K20(REAL,REAL),REAL))
K258(REAL,n,K205()) is complex real ext-real Element of REAL
t is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
t is complex real ext-real Element of REAL
<*t*> is V1() V4( NAT ) V5( REAL ) Function-like one-to-one non empty V12() finite 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued V55() decreasing non-decreasing non-increasing FinSequence of REAL
[1,t] is set
{1,t} is finite V61() V62() V63() set
{{1,t},{1}} is finite V44() set
{[1,t]} is non empty V12() finite 1 -element set
t ^ <*t*> is V1() V4( NAT ) V5( REAL ) Function-like non empty finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(len t) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m + 1) - 1 is complex real ext-real integer Element of REAL
n . 1 is complex real ext-real set
(m,m) is complex real ext-real Element of REAL
<*(m,m)*> is V1() V4( NAT ) V5( REAL ) Function-like one-to-one non empty V12() finite 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued V55() decreasing non-decreasing non-increasing FinSequence of REAL
[1,(m,m)] is set
{1,(m,m)} is finite V61() V62() V63() set
{{1,(m,m)},{1}} is finite V44() set
{[1,(m,m)]} is non empty V12() finite 1 -element set
Sum <*(m,m)*> is complex real ext-real Element of REAL
K258(REAL,<*(m,m)*>,K205()) is complex real ext-real Element of REAL
m + (k + 1) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((m + 1),(m + (k + 1))) is complex real ext-real Element of REAL
m + (k + 1) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m + (k + 1)) - 1 is complex real ext-real integer Element of REAL
dom t is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m + k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m + k) - 1 is complex real ext-real integer Element of REAL
t . k is complex real ext-real set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m,k) is complex real ext-real Element of REAL
n . k is complex real ext-real set
Seg (k + 1) is non empty finite k + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k + 1 ) } is set
(m,(m + k)) is complex real ext-real Element of REAL
(t ^ <*t*>) . ((len t) + 1) is complex real ext-real set
Sum t is complex real ext-real Element of REAL
K258(REAL,t,K205()) is complex real ext-real Element of REAL
(Sum t) + t is complex real ext-real Element of REAL
((m + 1),(m + k)) + (m,(m + k)) is complex real ext-real Element of REAL
(m + k) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((m + 1),((m + k) + 1)) is complex real ext-real Element of REAL
((m + 1),(m + (k + 1))) is complex real ext-real Element of REAL
m + 0 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
((m + 1),(m + 0)) is complex real ext-real Element of REAL
k is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
dom k is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
Sum k is complex real ext-real Element of REAL
K205() is V1() V4(K20(REAL,REAL)) V5( REAL ) Function-like V30(K20(REAL,REAL), REAL ) complex-valued ext-real-valued real-valued Element of K19(K20(K20(REAL,REAL),REAL))
K258(REAL,k,K205()) is complex real ext-real Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m,k) is complex real ext-real Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m,k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is complex real ext-real set
k is complex real ext-real set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
t + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
Seg (t + 1) is non empty finite t + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= t + 1 ) } is set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t - 1 is complex real ext-real integer Element of REAL
(t + 1) - 1 is complex real ext-real integer Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
t - k is complex real ext-real integer Element of REAL
(k,t) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m,k) is complex real ext-real set
k |-> m is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
(Seg k) --> m is V1() V4( Seg k) V5({m}) Function-like V30( Seg k,{m}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg k),{m}))
{m} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg k),{m}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg k),{m})) is finite V44() set
Product (k |-> m) is complex real ext-real set
(k,t) * (m,k) is complex real ext-real Element of REAL
(k,k) is complex real ext-real set
k |-> k is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
(Seg k) --> k is V1() V4( Seg k) V5({k}) Function-like V30( Seg k,{k}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg k),{k}))
{k} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg k),{k}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg k),{k})) is finite V44() set
Product (k |-> k) is complex real ext-real set
((k,t) * (m,k)) * (k,k) is complex real ext-real Element of REAL
k1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t - k1 is complex real ext-real integer Element of REAL
(k1,t) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m,k) is complex real ext-real set
k |-> m is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
(Seg k) --> m is V1() V4( Seg k) V5({m}) Function-like V30( Seg k,{m}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg k),{m}))
K20((Seg k),{m}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg k),{m})) is finite V44() set
Product (k |-> m) is complex real ext-real set
(k1,t) * (m,k) is complex real ext-real Element of REAL
(k,k1) is complex real ext-real set
k1 |-> k is V1() V4( NAT ) Function-like finite k1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg k1 is finite k1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k1 ) } is set
(Seg k1) --> k is V1() V4( Seg k1) V5({k}) Function-like V30( Seg k1,{k}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg k1),{k}))
K20((Seg k1),{k}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg k1),{k})) is finite V44() set
Product (k1 |-> k) is complex real ext-real set
((k1,t) * (m,k)) * (k,k1) is complex real ext-real Element of REAL
t is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
dom t is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
rng t is finite set
k is set
k is set
t . k is set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k - 1 is complex real ext-real integer Element of REAL
(t + 1) - 1 is complex real ext-real integer Element of REAL
k1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
t - k1 is complex real ext-real integer Element of REAL
t . k is set
(k1,t) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m,m1) is complex real ext-real set
m1 |-> m is V1() V4( NAT ) Function-like finite m1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg m1 is finite m1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m1 ) } is set
(Seg m1) --> m is V1() V4( Seg m1) V5({m}) Function-like V30( Seg m1,{m}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg m1),{m}))
{m} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg m1),{m}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg m1),{m})) is finite V44() set
Product (m1 |-> m) is complex real ext-real set
(k1,t) * (m,m1) is complex real ext-real Element of REAL
(k,k1) is complex real ext-real set
k1 |-> k is V1() V4( NAT ) Function-like finite k1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg k1 is finite k1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k1 ) } is set
(Seg k1) --> k is V1() V4( Seg k1) V5({k}) Function-like V30( Seg k1,{k}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg k1),{k}))
{k} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg k1),{k}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg k1),{k})) is finite V44() set
Product (k1 |-> k) is complex real ext-real set
((k1,t) * (m,m1)) * (k,k1) is complex real ext-real Element of REAL
c₁₁ is complex real ext-real Element of REAL
k is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
dom k is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k - 1 is complex real ext-real integer Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n - k1 is complex real ext-real integer set
k . k is complex real ext-real set
(k1,n) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m,k) is complex real ext-real set
k |-> m is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
(Seg k) --> m is V1() V4( Seg k) V5({m}) Function-like V30( Seg k,{m}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg k),{m}))
{m} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg k),{m}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg k),{m})) is finite V44() set
Product (k |-> m) is complex real ext-real set
(k1,n) * (m,k) is complex real ext-real Element of REAL
(k,k1) is complex real ext-real set
k1 |-> k is V1() V4( NAT ) Function-like finite k1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg k1 is finite k1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k1 ) } is set
(Seg k1) --> k is V1() V4( Seg k1) V5({k}) Function-like V30( Seg k1,{k}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg k1),{k}))
{k} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg k1),{k}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg k1),{k})) is finite V44() set
Product (k1 |-> k) is complex real ext-real set
((k1,n) * (m,k)) * (k,k1) is complex real ext-real Element of REAL
t is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
dom t is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
t is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
dom t is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t . k is complex real ext-real set
t . k is complex real ext-real set
Seg (n + 1) is non empty finite n + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= n + 1 ) } is set
k - 1 is complex real ext-real integer Element of REAL
(n + 1) - 1 is complex real ext-real integer Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
n - k is complex real ext-real integer Element of REAL
(k,n) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m,k) is complex real ext-real set
k |-> m is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
(Seg k) --> m is V1() V4( Seg k) V5({m}) Function-like V30( Seg k,{m}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg k),{m}))
{m} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg k),{m}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg k),{m})) is finite V44() set
Product (k |-> m) is complex real ext-real set
(k,n) * (m,k) is complex real ext-real Element of REAL
(k,k) is complex real ext-real set
k |-> k is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
(Seg k) --> k is V1() V4( Seg k) V5({k}) Function-like V30( Seg k,{k}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg k),{k}))
{k} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg k),{k}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg k),{k})) is finite V44() set
Product (k |-> k) is complex real ext-real set
((k,n) * (m,k)) * (k,k) is complex real ext-real Element of REAL
m is complex real ext-real set
k is complex real ext-real set
(m,k,0) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len (m,k,0) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
dom (m,k,0) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
t is set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
t - 1 is complex real ext-real integer Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
0 - k is complex real ext-real integer Element of REAL
(m,k,0) . 1 is complex real ext-real set
(0,0) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m,k) is complex real ext-real set
k |-> m is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
(Seg k) --> m is V1() V4( Seg k) V5({m}) Function-like V30( Seg k,{m}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg k),{m}))
{m} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg k),{m}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg k),{m})) is finite V44() set
Product (k |-> m) is complex real ext-real set
(0,0) * (m,k) is complex real ext-real Element of REAL
(k,k) is complex real ext-real set
k |-> k is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
(Seg k) --> k is V1() V4( Seg k) V5({k}) Function-like V30( Seg k,{k}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg k),{k}))
{k} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg k),{k}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg k),{k})) is finite V44() set
Product (k |-> k) is complex real ext-real set
((0,0) * (m,k)) * (k,k) is complex real ext-real Element of REAL
(m,0) is complex real ext-real set
0 |-> m is V1() V4( NAT ) V5( RAT ) Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative integer finite finite-yielding V44() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered complex-valued ext-real-valued real-valued natural-valued V61() V62() V63() V64() V65() V66() V67() set
(Seg 0) --> m is V1() V4( Seg 0) V5({m}) Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative V30( Seg 0,{m}) integer finite finite-yielding V44() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-valued ext-real-valued real-valued natural-valued V61() V62() V63() V64() V65() V66() V67() Element of K19(K20((Seg 0),{m}))
K20((Seg 0),{m}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg 0),{m})) is finite V44() set
Product (0 |-> m) is complex real ext-real set
1 * (m,0) is complex real ext-real Element of REAL
(k,0) is complex real ext-real set
0 |-> k is V1() V4( NAT ) V5( RAT ) Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative integer finite finite-yielding V44() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered complex-valued ext-real-valued real-valued natural-valued V61() V62() V63() V64() V65() V66() V67() set
(Seg 0) --> k is V1() V4( Seg 0) V5({k}) Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative V30( Seg 0,{k}) integer finite finite-yielding V44() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-valued ext-real-valued real-valued natural-valued V61() V62() V63() V64() V65() V66() V67() Element of K19(K20((Seg 0),{k}))
K20((Seg 0),{k}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg 0),{k})) is finite V44() set
Product (0 |-> k) is complex real ext-real set
(1 * (m,0)) * (k,0) is complex real ext-real Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is complex real ext-real set
(k,m) is complex real ext-real set
m |-> k is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
(Seg m) --> k is V1() V4( Seg m) V5({k}) Function-like V30( Seg m,{k}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg m),{k}))
{k} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg m),{k}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg m),{k})) is finite V44() set
Product (m |-> k) is complex real ext-real set
n is complex real ext-real set
(k,n,m) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(k,n,m) . 1 is complex real ext-real set
1 - 1 is complex real ext-real integer Element of REAL
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m - t is complex real ext-real integer Element of REAL
len (k,n,m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
dom (k,n,m) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
Seg (m + 1) is non empty finite m + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m + 1 ) } is set
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(0,m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(k,t) is complex real ext-real set
t |-> k is V1() V4( NAT ) Function-like finite t -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg t is finite t -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= t ) } is set
(Seg t) --> k is V1() V4( Seg t) V5({k}) Function-like V30( Seg t,{k}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg t),{k}))
K20((Seg t),{k}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg t),{k})) is finite V44() set
Product (t |-> k) is complex real ext-real set
(0,m) * (k,t) is complex real ext-real Element of REAL
(n,t) is complex real ext-real set
t |-> n is V1() V4( NAT ) Function-like finite t -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg t is finite t -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= t ) } is set
(Seg t) --> n is V1() V4( Seg t) V5({n}) Function-like V30( Seg t,{n}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg t),{n}))
{n} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg t),{n}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg t),{n})) is finite V44() set
Product (t |-> n) is complex real ext-real set
((0,m) * (k,t)) * (n,t) is complex real ext-real Element of REAL
1 * (k,t) is complex real ext-real Element of REAL
(1 * (k,t)) * (n,t) is complex real ext-real Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is complex real ext-real set
n is complex real ext-real set
(k,n,m) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(k,n,m) . (m + 1) is complex real ext-real set
(n,m) is complex real ext-real set
m |-> n is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
(Seg m) --> n is V1() V4( Seg m) V5({n}) Function-like V30( Seg m,{n}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg m),{n}))
{n} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg m),{n}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg m),{n})) is finite V44() set
Product (m |-> n) is complex real ext-real set
(m + 1) - 1 is complex real ext-real integer Element of REAL
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m - t is complex real ext-real integer Element of REAL
len (k,n,m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
dom (k,n,m) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
Seg (m + 1) is non empty finite m + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m + 1 ) } is set
(m,m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(k,t) is complex real ext-real set
t |-> k is V1() V4( NAT ) Function-like finite t -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg t is finite t -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= t ) } is set
(Seg t) --> k is V1() V4( Seg t) V5({k}) Function-like V30( Seg t,{k}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg t),{k}))
{k} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg t),{k}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg t),{k})) is finite V44() set
Product (t |-> k) is complex real ext-real set
(m,m) * (k,t) is complex real ext-real Element of REAL
(n,t) is complex real ext-real set
t |-> n is V1() V4( NAT ) Function-like finite t -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg t is finite t -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= t ) } is set
(Seg t) --> n is V1() V4( Seg t) V5({n}) Function-like V30( Seg t,{n}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg t),{n}))
K20((Seg t),{n}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg t),{n})) is finite V44() set
Product (t |-> n) is complex real ext-real set
((m,m) * (k,t)) * (n,t) is complex real ext-real Element of REAL
1 * (k,t) is complex real ext-real Element of REAL
(1 * (k,t)) * (n,t) is complex real ext-real Element of REAL
1 * (n,t) is complex real ext-real Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is complex real ext-real set
n is complex real ext-real set
k + n is complex real ext-real set
((k + n),m) is complex real ext-real set
m |-> (k + n) is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
(Seg m) --> (k + n) is V1() V4( Seg m) V5({(k + n)}) Function-like V30( Seg m,{(k + n)}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg m),{(k + n)}))
{(k + n)} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg m),{(k + n)}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg m),{(k + n)})) is finite V44() set
Product (m |-> (k + n)) is complex real ext-real set
(k,n,m) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (k,n,m) is complex real ext-real Element of REAL
K205() is V1() V4(K20(REAL,REAL)) V5( REAL ) Function-like V30(K20(REAL,REAL), REAL ) complex-valued ext-real-valued real-valued Element of K19(K20(K20(REAL,REAL),REAL))
K258(REAL,(k,n,m),K205()) is complex real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
((k + n),k) is complex real ext-real set
k |-> (k + n) is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
(Seg k) --> (k + n) is V1() V4( Seg k) V5({(k + n)}) Function-like V30( Seg k,{(k + n)}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg k),{(k + n)}))
K20((Seg k),{(k + n)}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg k),{(k + n)})) is finite V44() set
Product (k |-> (k + n)) is complex real ext-real set
(k,n,k) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (k,n,k) is complex real ext-real Element of REAL
K258(REAL,(k,n,k),K205()) is complex real ext-real Element of REAL
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((k + n),(k + 1)) is complex real ext-real set
(k + 1) |-> (k + n) is V1() V4( NAT ) Function-like finite k + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg (k + 1) is non empty finite k + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k + 1 ) } is set
(Seg (k + 1)) --> (k + n) is V1() V4( Seg (k + 1)) V5({(k + n)}) Function-like V30( Seg (k + 1),{(k + n)}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg (k + 1)),{(k + n)}))
K20((Seg (k + 1)),{(k + n)}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg (k + 1)),{(k + n)})) is finite V44() set
Product ((k + 1) |-> (k + n)) is complex real ext-real set
(k,n,(k + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (k,n,(k + 1)) is complex real ext-real Element of REAL
K258(REAL,(k,n,(k + 1)),K205()) is complex real ext-real Element of REAL
t is complex real ext-real Element of REAL
t is complex real ext-real Element of REAL
(t,t,k) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
t * (t,t,k) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K337(t) is V1() V4( REAL ) V5( REAL ) Function-like V30( REAL , REAL ) complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
id REAL is V1() V4( REAL ) V5( REAL ) non empty total complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
K207() [;] (t,(id REAL)) is set
K337(t) * (t,t,k) is V1() finite FinSequence-like complex-valued ext-real-valued real-valued set
<*0*> is V1() V4( NAT ) V5( REAL ) Function-like one-to-one non empty V12() finite 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued V55() decreasing non-decreasing non-increasing FinSequence of REAL
[1,0] is set
{1,0} is finite V44() V61() V62() V63() V64() V65() V66() set
{{1,0},{1}} is finite V44() set
{[1,0]} is non empty V12() finite 1 -element set
(t * (t,t,k)) ^ <*0*> is V1() V4( NAT ) V5( REAL ) Function-like non empty finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
t * (t,t,k) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K337(t) is V1() V4( REAL ) V5( REAL ) Function-like V30( REAL , REAL ) complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
K207() [;] (t,(id REAL)) is set
K337(t) * (t,t,k) is V1() finite FinSequence-like complex-valued ext-real-valued real-valued set
<*0*> ^ (t * (t,t,k)) is V1() V4( NAT ) V5( REAL ) Function-like non empty finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
t + t is complex real ext-real Element of REAL
((t + t),(k + 1)) is complex real ext-real Element of REAL
(k + 1) |-> (t + t) is V1() V4( NAT ) Function-like finite k + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(Seg (k + 1)) --> (t + t) is V1() V4( Seg (k + 1)) V5({(t + t)}) Function-like V30( Seg (k + 1),{(t + t)}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg (k + 1)),{(t + t)}))
{(t + t)} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg (k + 1)),{(t + t)}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg (k + 1)),{(t + t)})) is finite V44() set
Product ((k + 1) |-> (t + t)) is complex real ext-real set
Sum (t,t,k) is complex real ext-real Element of REAL
K258(REAL,(t,t,k),K205()) is complex real ext-real Element of REAL
(t + t) * (Sum (t,t,k)) is complex real ext-real Element of REAL
t * (Sum (t,t,k)) is complex real ext-real Element of REAL
t * (Sum (t,t,k)) is complex real ext-real Element of REAL
(t * (Sum (t,t,k))) + (t * (Sum (t,t,k))) is complex real ext-real Element of REAL
Sum (t * (t,t,k)) is complex real ext-real Element of REAL
K258(REAL,(t * (t,t,k)),K205()) is complex real ext-real Element of REAL
(Sum (t * (t,t,k))) + (t * (Sum (t,t,k))) is complex real ext-real Element of REAL
Sum (t * (t,t,k)) is complex real ext-real Element of REAL
K258(REAL,(t * (t,t,k)),K205()) is complex real ext-real Element of REAL
(Sum (t * (t,t,k))) + (Sum (t * (t,t,k))) is complex real ext-real Element of REAL
len (<*0*> ^ (t * (t,t,k))) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
<*0*> is V1() V4( NAT ) V5( NAT ) Function-like one-to-one non empty V12() finite 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued V55() decreasing non-decreasing non-increasing FinSequence of NAT
len <*0*> is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
len (t * (t,t,k)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(len <*0*>) + (len (t * (t,t,k))) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
1 + (len (t * (t,t,k))) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
len (t,t,k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
1 + (len (t,t,k)) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(k + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((k + 1) + 1) -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
REAL * is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = (k + 1) + 1 } is set
k is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
len (t * (t,t,k)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(len (t * (t,t,k))) + (len <*0*>) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(len (t * (t,t,k))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(len (t,t,k)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k1 is V1() V4( NAT ) V5( REAL ) Function-like finite (k + 1) + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of ((k + 1) + 1) -tuples_on REAL
Sum k1 is complex real ext-real Element of REAL
K258(REAL,k1,K205()) is complex real ext-real Element of REAL
0 + (Sum (t * (t,t,k))) is complex real ext-real Element of REAL
m1 is V1() V4( NAT ) V5( REAL ) Function-like finite (k + 1) + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of ((k + 1) + 1) -tuples_on REAL
Sum m1 is complex real ext-real Element of REAL
K258(REAL,m1,K205()) is complex real ext-real Element of REAL
(Sum (t * (t,t,k))) + 0 is complex real ext-real Element of REAL
k + (<*0*> ^ (t * (t,t,k))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K205() .: (k,(<*0*> ^ (t * (t,t,k)))) is set
Sum (k + (<*0*> ^ (t * (t,t,k)))) is complex real ext-real Element of REAL
K258(REAL,(k + (<*0*> ^ (t * (t,t,k)))),K205()) is complex real ext-real Element of REAL
m1 + k1 is V1() V4( NAT ) V5( REAL ) Function-like finite (k + 1) + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of ((k + 1) + 1) -tuples_on REAL
K205() .: (m1,k1) is set
len k1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
len (m1 + k1) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
len m1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(t,t,(k + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
dom (t,t,(k + 1)) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
s is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m1 + k1) . s is complex real ext-real set
(t,t,(k + 1)) . s is complex real ext-real set
k1 /. s is complex real ext-real Element of REAL
m1 /. s is complex real ext-real Element of REAL
(t,t,k) /. s is complex real ext-real Element of REAL
len (t,t,(k + 1)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
Seg ((k + 1) + 1) is non empty finite (k + 1) + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= (k + 1) + 1 ) } is set
dom m1 is finite (k + 1) + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
dom k1 is finite (k + 1) + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
Seg (len (t,t,k)) is finite len (t,t,k) -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= len (t,t,k) ) } is set
dom (t,t,k) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
dom (t * (t,t,k)) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
(t,t,k) . 1 is complex real ext-real set
(t,t,k) . s is complex real ext-real set
(t,k) is complex real ext-real Element of REAL
k |-> t is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(Seg k) --> t is V1() V4( Seg k) V5({t}) Function-like V30( Seg k,{t}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg k),{t}))
{t} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg k),{t}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg k),{t})) is finite V44() set
Product (k |-> t) is complex real ext-real set
(t * (t,t,k)) ^ <*0*> is V1() V4( NAT ) Function-like non empty finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
((t * (t,t,k)) ^ <*0*>) . 1 is complex real ext-real set
(t * (t,t,k)) . 1 is complex real ext-real set
t * (t,k) is complex real ext-real Element of REAL
(t,(k + 1)) is complex real ext-real Element of REAL
(k + 1) |-> t is V1() V4( NAT ) Function-like finite k + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(Seg (k + 1)) --> t is V1() V4( Seg (k + 1)) V5({t}) Function-like V30( Seg (k + 1),{t}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg (k + 1)),{t}))
K20((Seg (k + 1)),{t}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg (k + 1)),{t})) is finite V44() set
Product ((k + 1) |-> t) is complex real ext-real set
k1 . s is complex real ext-real set
m1 . s is complex real ext-real set
<*0*> ^ (t * (t,t,k)) is V1() V4( NAT ) Function-like non empty finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(<*0*> ^ (t * (t,t,k))) . 1 is complex real ext-real set
(m1 /. s) + 0 is complex real ext-real Element of REAL
s - 1 is complex real ext-real integer Element of REAL
j is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(t,t,k) /. j is complex real ext-real Element of REAL
j + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
dom (m1 + k1) is finite (k + 1) + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( not b₁ <= 1 & not (k + 1) + 1 <= b₁ ) } is set
m2 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(t * (t,t,k)) ^ <*0*> is V1() V4( NAT ) Function-like non empty finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
((t * (t,t,k)) ^ <*0*>) . s is complex real ext-real set
m2 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
j - 1 is complex real ext-real integer Element of REAL
l2 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(k + 1) - 1 is complex real ext-real integer Element of REAL
m2 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k - m2 is complex real ext-real integer Element of REAL
l1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
Seg (len (t,t,k)) is finite len (t,t,k) -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= len (t,t,k) ) } is set
dom (t,t,k) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
(t,t,k) . j is complex real ext-real set
l1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
l1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(t,t,k) . s is complex real ext-real set
dom (t * (t,t,k)) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
(t * (t,t,k)) . s is complex real ext-real set
t * ((t,t,k) /. s) is complex real ext-real Element of REAL
m1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k - m1 is complex real ext-real integer Element of REAL
l1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
l1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(k + 1) - (m2 + 1) is complex real ext-real integer Element of REAL
dom (t * (t,t,k)) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
<*0*> ^ (t * (t,t,k)) is V1() V4( NAT ) Function-like non empty finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(<*0*> ^ (t * (t,t,k))) . s is complex real ext-real set
(len <*0*>) + j is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(<*0*> ^ (t * (t,t,k))) . ((len <*0*>) + j) is complex real ext-real set
(t * (t,t,k)) . j is complex real ext-real set
t * ((t,t,k) /. j) is complex real ext-real Element of REAL
(t * ((t,t,k) /. s)) + (t * ((t,t,k) /. j)) is complex real ext-real Element of REAL
(t,l1) is complex real ext-real Element of REAL
l1 |-> t is V1() V4( NAT ) Function-like finite l1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg l1 is finite l1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= l1 ) } is set
(Seg l1) --> t is V1() V4( Seg l1) V5({t}) Function-like V30( Seg l1,{t}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg l1),{t}))
{t} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg l1),{t}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg l1),{t})) is finite V44() set
Product (l1 |-> t) is complex real ext-real set
(m1,k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(t,l1) * (m1,k) is complex real ext-real Element of REAL
(t,m1) is complex real ext-real Element of REAL
m1 |-> t is V1() V4( NAT ) Function-like finite m1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg m1 is finite m1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m1 ) } is set
(Seg m1) --> t is V1() V4( Seg m1) V5({t}) Function-like V30( Seg m1,{t}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg m1),{t}))
{t} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg m1),{t}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg m1),{t})) is finite V44() set
Product (m1 |-> t) is complex real ext-real set
((t,l1) * (m1,k)) * (t,m1) is complex real ext-real Element of REAL
t * (((t,l1) * (m1,k)) * (t,m1)) is complex real ext-real Element of REAL
(t * (((t,l1) * (m1,k)) * (t,m1))) + (t * ((t,t,k) /. j)) is complex real ext-real Element of REAL
t * (t,l1) is complex real ext-real Element of REAL
(m1,k) * (t,m1) is complex real ext-real Element of REAL
(t * (t,l1)) * ((m1,k) * (t,m1)) is complex real ext-real Element of REAL
((t * (t,l1)) * ((m1,k) * (t,m1))) + (t * ((t,t,k) /. j)) is complex real ext-real Element of REAL
(t,(l1 + 1)) is complex real ext-real Element of REAL
(l1 + 1) |-> t is V1() V4( NAT ) Function-like finite l1 + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg (l1 + 1) is non empty finite l1 + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= l1 + 1 ) } is set
(Seg (l1 + 1)) --> t is V1() V4( Seg (l1 + 1)) V5({t}) Function-like V30( Seg (l1 + 1),{t}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg (l1 + 1)),{t}))
K20((Seg (l1 + 1)),{t}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg (l1 + 1)),{t})) is finite V44() set
Product ((l1 + 1) |-> t) is complex real ext-real set
(t,(l1 + 1)) * ((m1,k) * (t,m1)) is complex real ext-real Element of REAL
((t,(l1 + 1)) * ((m1,k) * (t,m1))) + (t * ((t,t,k) /. j)) is complex real ext-real Element of REAL
(t,m2) is complex real ext-real Element of REAL
m2 |-> t is V1() V4( NAT ) Function-like finite m2 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg m2 is finite m2 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m2 ) } is set
(Seg m2) --> t is V1() V4( Seg m2) V5({t}) Function-like V30( Seg m2,{t}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg m2),{t}))
K20((Seg m2),{t}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg m2),{t})) is finite V44() set
Product (m2 |-> t) is complex real ext-real set
(m2,k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
l2 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(t,l2) is complex real ext-real Element of REAL
l2 |-> t is V1() V4( NAT ) Function-like finite l2 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg l2 is finite l2 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= l2 ) } is set
(Seg l2) --> t is V1() V4( Seg l2) V5({t}) Function-like V30( Seg l2,{t}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg l2),{t}))
K20((Seg l2),{t}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg l2),{t})) is finite V44() set
Product (l2 |-> t) is complex real ext-real set
(m2,k) * (t,l2) is complex real ext-real Element of REAL
(t,m2) * ((m2,k) * (t,l2)) is complex real ext-real Element of REAL
t * ((t,m2) * ((m2,k) * (t,l2))) is complex real ext-real Element of REAL
((t,(l1 + 1)) * ((m1,k) * (t,m1))) + (t * ((t,m2) * ((m2,k) * (t,l2)))) is complex real ext-real Element of REAL
t * (t,m2) is complex real ext-real Element of REAL
(t * (t,m2)) * ((m2,k) * (t,l2)) is complex real ext-real Element of REAL
((t,(l1 + 1)) * ((m1,k) * (t,m1))) + ((t * (t,m2)) * ((m2,k) * (t,l2))) is complex real ext-real Element of REAL
((m2 + 1),k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(t,(m2 + 1)) is complex real ext-real Element of REAL
(m2 + 1) |-> t is V1() V4( NAT ) Function-like finite m2 + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg (m2 + 1) is non empty finite m2 + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m2 + 1 ) } is set
(Seg (m2 + 1)) --> t is V1() V4( Seg (m2 + 1)) V5({t}) Function-like V30( Seg (m2 + 1),{t}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg (m2 + 1)),{t}))
K20((Seg (m2 + 1)),{t}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg (m2 + 1)),{t})) is finite V44() set
Product ((m2 + 1) |-> t) is complex real ext-real set
((m2 + 1),k) * (t,(m2 + 1)) is complex real ext-real Element of REAL
(t,(l1 + 1)) * (((m2 + 1),k) * (t,(m2 + 1))) is complex real ext-real Element of REAL
(t,(m2 + 1)) * ((m2,k) * (t,l2)) is complex real ext-real Element of REAL
((t,(l1 + 1)) * (((m2 + 1),k) * (t,(m2 + 1)))) + ((t,(m2 + 1)) * ((m2,k) * (t,l2))) is complex real ext-real Element of REAL
((m2 + 1),k) + (m2,k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(((m2 + 1),k) + (m2,k)) * (t,(l1 + 1)) is complex real ext-real Element of REAL
((((m2 + 1),k) + (m2,k)) * (t,(l1 + 1))) * (t,(m2 + 1)) is complex real ext-real Element of REAL
((m2 + 1),(k + 1)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((m2 + 1),(k + 1)) * (t,(l1 + 1)) is complex real ext-real Element of REAL
(((m2 + 1),(k + 1)) * (t,(l1 + 1))) * (t,(m2 + 1)) is complex real ext-real Element of REAL
{((k + 1) + 1)} is non empty V12() finite V44() 1 -element V61() V62() V63() V64() V65() V66() set
((k + 1) + 1) - 1 is complex real ext-real integer Element of REAL
Seg (len (t,t,k)) is finite len (t,t,k) -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= len (t,t,k) ) } is set
dom (t,t,k) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
(t,t,k) . (k + 1) is complex real ext-real set
(t,k) is complex real ext-real Element of REAL
k |-> t is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(Seg k) --> t is V1() V4( Seg k) V5({t}) Function-like V30( Seg k,{t}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg k),{t}))
{t} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg k),{t}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg k),{t})) is finite V44() set
Product (k |-> t) is complex real ext-real set
(t,t,k) . j is complex real ext-real set
dom (t * (t,t,k)) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
<*0*> ^ (t * (t,t,k)) is V1() V4( NAT ) Function-like non empty finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
1 + k is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(1 + k) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(<*0*> ^ (t * (t,t,k))) . ((1 + k) + 1) is complex real ext-real set
(len <*0*>) + j is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(<*0*> ^ (t * (t,t,k))) . ((len <*0*>) + j) is complex real ext-real set
(t * (t,t,k)) . j is complex real ext-real set
t * (t,k) is complex real ext-real Element of REAL
(t,(k + 1)) is complex real ext-real Element of REAL
(k + 1) |-> t is V1() V4( NAT ) Function-like finite k + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(Seg (k + 1)) --> t is V1() V4( Seg (k + 1)) V5({t}) Function-like V30( Seg (k + 1),{t}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg (k + 1)),{t}))
K20((Seg (k + 1)),{t}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg (k + 1)),{t})) is finite V44() set
Product ((k + 1) |-> t) is complex real ext-real set
k1 . s is complex real ext-real set
(t * (t,t,k)) ^ <*0*> is V1() V4( NAT ) Function-like non empty finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
((t * (t,t,k)) ^ <*0*>) . ((len (t * (t,t,k))) + 1) is complex real ext-real set
m1 . s is complex real ext-real set
0 + (k1 /. s) is complex real ext-real Element of REAL
{1} \/ { b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( not b₁ <= 1 & not (k + 1) + 1 <= b₁ ) } is set
({1} \/ { b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( not b₁ <= 1 & not (k + 1) + 1 <= b₁ ) } ) \/ {((k + 1) + 1)} is set
len (t,t,(k + 1)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((k + n),0) is complex real ext-real set
0 |-> (k + n) is V1() V4( NAT ) V5( RAT ) Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative integer finite finite-yielding V44() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered complex-valued ext-real-valued real-valued natural-valued V61() V62() V63() V64() V65() V66() V67() set
(Seg 0) --> (k + n) is V1() V4( Seg 0) V5({(k + n)}) Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative V30( Seg 0,{(k + n)}) integer finite finite-yielding V44() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-valued ext-real-valued real-valued natural-valued V61() V62() V63() V64() V65() V66() V67() Element of K19(K20((Seg 0),{(k + n)}))
K20((Seg 0),{(k + n)}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg 0),{(k + n)})) is finite V44() set
Product (0 |-> (k + n)) is complex real ext-real set
<*1*> is V1() V4( NAT ) V5( REAL ) Function-like one-to-one non empty V12() finite 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued V55() decreasing non-decreasing non-increasing FinSequence of REAL
Sum <*1*> is complex real ext-real Element of REAL
K258(REAL,<*1*>,K205()) is complex real ext-real Element of REAL
(k,n,0) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (k,n,0) is complex real ext-real Element of REAL
K258(REAL,(k,n,0),K205()) is complex real ext-real Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
Seg (k + 1) is non empty finite k + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k + 1 ) } is set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n - 1 is complex real ext-real integer Element of REAL
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(t,k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(k,k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
n is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
dom n is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
rng n is finite set
t is set
t is set
n . t is set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k - 1 is complex real ext-real integer Element of REAL
n . k is set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(k,k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is complex real ext-real Element of REAL
t is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
dom t is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t - 1 is complex real ext-real integer Element of REAL
t . t is complex real ext-real set
(k,m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
dom k is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
n is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
dom n is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k . t is complex real ext-real set
n . t is complex real ext-real set
Seg (m + 1) is non empty finite m + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m + 1 ) } is set
t - 1 is complex real ext-real integer Element of REAL
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(t,m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1,1,m) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
dom (m) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m) . k is complex real ext-real set
(1,1,m) . k is complex real ext-real set
len (m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
Seg (len (m)) is finite len (m) -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= len (m) ) } is set
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
Seg (m + 1) is non empty finite m + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m + 1 ) } is set
k - 1 is complex real ext-real integer Element of REAL
(m + 1) - 1 is complex real ext-real integer Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m - n is complex real ext-real integer Element of REAL
len (1,1,m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
Seg (len (1,1,m)) is finite len (1,1,m) -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= len (1,1,m) ) } is set
dom (1,1,m) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
(n,m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(1,t) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
t |-> 1 is V1() V4( NAT ) Function-like finite t -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg t is finite t -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= t ) } is set
(Seg t) --> 1 is V1() V4( Seg t) V5( RAT ) V5( INT ) V5({1}) Function-like V30( Seg t,{1}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg t),{1}))
K20((Seg t),{1}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg t),{1})) is finite V44() set
Product (t |-> 1) is complex real ext-real set
(n,m) * (1,t) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(1,n) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
n |-> 1 is V1() V4( NAT ) Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg n is finite n -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= n ) } is set
(Seg n) --> 1 is V1() V4( Seg n) V5( RAT ) V5( INT ) V5({1}) Function-like V30( Seg n,{1}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg n),{1}))
K20((Seg n),{1}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg n),{1})) is finite V44() set
Product (n |-> 1) is complex real ext-real set
((n,m) * (1,t)) * (1,n) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(n,m) * 1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((n,m) * 1) * (1,n) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
len (m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
len (1,1,m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(2,m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
m |-> 2 is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
(Seg m) --> 2 is V1() V4( Seg m) V5( RAT ) V5( INT ) V5({2}) Function-like V30( Seg m,{2}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),{2}))
{2} is non empty V12() finite V44() 1 -element V61() V62() V63() V64() V65() V66() set
K20((Seg m),{2}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),{2})) is finite V44() set
Product (m |-> 2) is complex real ext-real set
(m) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (m) is complex real ext-real Element of REAL
K205() is V1() V4(K20(REAL,REAL)) V5( REAL ) Function-like V30(K20(REAL,REAL), REAL ) complex-valued ext-real-valued real-valued Element of K19(K20(K20(REAL,REAL),REAL))
K258(REAL,(m),K205()) is complex real ext-real Element of REAL
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((1 + 1),m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
m |-> (1 + 1) is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(Seg m) --> (1 + 1) is V1() V4( Seg m) V5( RAT ) V5( INT ) V5({(1 + 1)}) Function-like V30( Seg m,{(1 + 1)}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),{(1 + 1)}))
{(1 + 1)} is non empty V12() finite V44() 1 -element V61() V62() V63() V64() V65() V66() set
K20((Seg m),{(1 + 1)}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),{(1 + 1)})) is finite V44() set
Product (m |-> (1 + 1)) is complex real ext-real set
(1,1,m) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (1,1,m) is complex real ext-real Element of REAL
K258(REAL,(1,1,m),K205()) is complex real ext-real Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k * m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n * m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(n + 1) * m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(n + 1) * m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
1 * m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(n * m) + (1 * m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
n + m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
0 * m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n * m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal Element of REAL
idseq m is V1() V4( NAT ) V5( RAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
id (Seg m) is V1() V4( Seg m) V5( RAT ) V5( INT ) V5( Seg m) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),(Seg m)))
K20((Seg m),(Seg m)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),(Seg m))) is finite V44() set
Product (idseq m) is complex real ext-real set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
idseq m is V1() V4( NAT ) V5( RAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
id (Seg m) is V1() V4( Seg m) V5( RAT ) V5( INT ) V5( Seg m) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),(Seg m)))
K20((Seg m),(Seg m)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),(Seg m))) is finite V44() set
Product (idseq m) is complex real ext-real set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((n + 1)) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
idseq (n + 1) is V1() V4( NAT ) V5( RAT ) Function-like finite n + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg (n + 1) is non empty finite n + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= n + 1 ) } is set
id (Seg (n + 1)) is V1() V4( Seg (n + 1)) V5( RAT ) V5( INT ) V5( Seg (n + 1)) non empty total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg (n + 1)),(Seg (n + 1))))
K20((Seg (n + 1)),(Seg (n + 1))) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg (n + 1)),(Seg (n + 1)))) is finite V44() set
Product (idseq (n + 1)) is complex real ext-real set
(n) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
idseq n is V1() V4( NAT ) V5( RAT ) Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg n is finite n -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= n ) } is set
id (Seg n) is V1() V4( Seg n) V5( RAT ) V5( INT ) V5( Seg n) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg n),(Seg n)))
K20((Seg n),(Seg n)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg n),(Seg n))) is finite V44() set
Product (idseq n) is complex real ext-real set
(n + 1) * (n) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m + 1) / m is complex real ext-real non negative Element of REAL
m / m is complex real ext-real non negative set
1 / m is complex real ext-real non negative Element of REAL
(m / m) + (1 / m) is complex real ext-real non negative Element of REAL
1 + (1 / m) is non empty complex real ext-real positive non negative Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m / (m + 1) is complex real ext-real non negative Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
idseq m is V1() V4( NAT ) V5( RAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
id (Seg m) is V1() V4( Seg m) V5( RAT ) V5( INT ) V5( Seg m) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),(Seg m)))
K20((Seg m),(Seg m)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),(Seg m))) is finite V44() set
Product (idseq m) is complex real ext-real set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(k) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
idseq k is V1() V4( NAT ) V5( RAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
id (Seg k) is V1() V4( Seg k) V5( RAT ) V5( INT ) V5( Seg k) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg k),(Seg k)))
K20((Seg k),(Seg k)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg k),(Seg k))) is finite V44() set
Product (idseq k) is complex real ext-real set
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((k + 1)) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
idseq (k + 1) is V1() V4( NAT ) V5( RAT ) Function-like finite k + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg (k + 1) is non empty finite k + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k + 1 ) } is set
id (Seg (k + 1)) is V1() V4( Seg (k + 1)) V5( RAT ) V5( INT ) V5( Seg (k + 1)) non empty total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg (k + 1)),(Seg (k + 1))))
K20((Seg (k + 1)),(Seg (k + 1))) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg (k + 1)),(Seg (k + 1)))) is finite V44() set
Product (idseq (k + 1)) is complex real ext-real set
(k) * (k + 1) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(k + 1) * k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(0) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m * n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m * t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(k + 1) * n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m * t) * n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k * t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(k * t) / (k + 1) is complex real ext-real non negative Element of REAL
k / (k + 1) is complex real ext-real non negative Element of REAL
t * (k / (k + 1)) is complex real ext-real non negative Element of REAL
t - n is complex real ext-real integer set
(m * t) - (m * n) is complex real ext-real integer set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m * t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m + k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
((m + k)) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
idseq (m + k) is V1() V4( NAT ) V5( RAT ) Function-like finite m + k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg (m + k) is finite m + k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m + k ) } is set
id (Seg (m + k)) is V1() V4( Seg (m + k)) V5( RAT ) V5( INT ) V5( Seg (m + k)) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg (m + k)),(Seg (m + k))))
K20((Seg (m + k)),(Seg (m + k))) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg (m + k)),(Seg (m + k)))) is finite V44() set
Product (idseq (m + k)) is complex real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t + (n + 1) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer finite cardinal set
((t + (n + 1))) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
idseq (t + (n + 1)) is V1() V4( NAT ) V5( RAT ) Function-like finite t + (n + 1) -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg (t + (n + 1)) is non empty finite t + (n + 1) -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= t + (n + 1) ) } is set
id (Seg (t + (n + 1))) is V1() V4( Seg (t + (n + 1))) V5( RAT ) V5( INT ) V5( Seg (t + (n + 1))) non empty total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg (t + (n + 1))),(Seg (t + (n + 1)))))
K20((Seg (t + (n + 1))),(Seg (t + (n + 1)))) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg (t + (n + 1))),(Seg (t + (n + 1))))) is finite V44() set
Product (idseq (t + (n + 1))) is complex real ext-real set
t + n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
((t + n)) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
idseq (t + n) is V1() V4( NAT ) V5( RAT ) Function-like finite t + n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg (t + n) is finite t + n -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= t + n ) } is set
id (Seg (t + n)) is V1() V4( Seg (t + n)) V5( RAT ) V5( INT ) V5( Seg (t + n)) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg (t + n)),(Seg (t + n))))
K20((Seg (t + n)),(Seg (t + n))) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg (t + n)),(Seg (t + n)))) is finite V44() set
Product (idseq (t + n)) is complex real ext-real set
(t + n) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((t + n)) * ((t + n) + 1) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n + 0 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
((n + 0)) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
idseq (n + 0) is V1() V4( NAT ) V5( RAT ) Function-like finite n + 0 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg (n + 0) is finite n + 0 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= n + 0 ) } is set
id (Seg (n + 0)) is V1() V4( Seg (n + 0)) V5( RAT ) V5( INT ) V5( Seg (n + 0)) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg (n + 0)),(Seg (n + 0))))
K20((Seg (n + 0)),(Seg (n + 0))) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg (n + 0)),(Seg (n + 0)))) is finite V44() set
Product (idseq (n + 0)) is complex real ext-real set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(k) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
idseq k is V1() V4( NAT ) V5( RAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
id (Seg k) is V1() V4( Seg k) V5( RAT ) V5( INT ) V5( Seg k) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg k),(Seg k)))
K20((Seg k),(Seg k)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg k),(Seg k))) is finite V44() set
Product (idseq k) is complex real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m + n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(k) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
idseq k is V1() V4( NAT ) V5( RAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
id (Seg k) is V1() V4( Seg k) V5( RAT ) V5( INT ) V5( Seg k) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg k),(Seg k)))
K20((Seg k),(Seg k)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg k),(Seg k))) is finite V44() set
Product (idseq k) is complex real ext-real set
(k) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m lcm k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k lcm n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m lcm (k lcm n) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m lcm k) lcm n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m lcm k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m lcm n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m lcm 1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m lcm k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m * k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m gcd k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k gcd n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m gcd (k gcd n) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m gcd k) gcd n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m gcd k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k gcd n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m gcd 1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m gcd 0 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m gcd k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m gcd k) lcm k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m lcm k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m gcd (m lcm k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m lcm k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m gcd (m lcm k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k gcd m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(k gcd m) lcm m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m gcd n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k gcd n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n gcd m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
n gcd k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m gcd k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
0 * n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m lcm k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m * k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
0 * n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m gcd k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m gcd n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m gcd k) lcm (m gcd n) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k lcm n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m gcd (k lcm n) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n gcd k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m lcm (n gcd k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m lcm n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m lcm n) gcd k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m gcd k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m lcm k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k mod m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k div m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m * (k div m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k - (m * (k div m)) is complex real ext-real integer Element of REAL
n is complex real ext-real integer set
k - n is complex real ext-real integer set
t is complex real ext-real integer set
n + t is complex real ext-real integer set
(n + t) - n is complex real ext-real integer set
m is complex real ext-real integer set
k is complex real ext-real integer set
k mod m is complex real ext-real integer set
m is complex real ext-real integer set
k is complex real ext-real integer set
k mod m is complex real ext-real integer set
m is complex real ext-real integer set
k is complex real ext-real integer set
k div m is complex real ext-real integer set
(k div m) * m is complex real ext-real integer set
k mod m is complex real ext-real integer set
((k div m) * m) + (k mod m) is complex real ext-real integer set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m gcd k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
1 * m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
0 * k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(1 * m) + (0 * k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
0 * m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
1 * k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(0 * m) + (1 * k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t is complex real ext-real integer set
t * m is complex real ext-real integer set
t is complex real ext-real integer set
t * k is complex real ext-real integer set
(t * m) + (t * k) is complex real ext-real integer set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t is complex real ext-real integer set
t * m is complex real ext-real integer set
t is complex real ext-real integer set
t * k is complex real ext-real integer set
(t * m) + (t * k) is complex real ext-real integer set
t is complex real ext-real integer set
t * m is complex real ext-real integer set
t is complex real ext-real integer set
t * k is complex real ext-real integer set
(t * m) + (t * k) is complex real ext-real integer set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is complex real ext-real integer set
k * m is complex real ext-real integer set
k is complex real ext-real integer set
k * k is complex real ext-real integer set
(k * m) + (k * k) is complex real ext-real integer set
k1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n * k1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(n * k1) + m1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
s is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
c₁₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
n * c₁₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k - (n * c₁₁) is complex real ext-real integer Element of REAL
t * c₁₁ is complex real ext-real integer Element of REAL
k - (t * c₁₁) is complex real ext-real integer Element of REAL
(k - (t * c₁₁)) * m is complex real ext-real integer Element of REAL
t * c₁₁ is complex real ext-real integer Element of REAL
k - (t * c₁₁) is complex real ext-real integer Element of REAL
(k - (t * c₁₁)) * k is complex real ext-real integer Element of REAL
((k - (t * c₁₁)) * m) + ((k - (t * c₁₁)) * k) is complex real ext-real integer Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k * k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k * m1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is complex real ext-real integer set
k1 is complex real ext-real integer set
t * m1 is complex real ext-real integer set
t * k is complex real ext-real integer set
(t * m1) + (t * k) is complex real ext-real integer set
k1 * ((t * m1) + (t * k)) is complex real ext-real integer set
c₁₁ is complex real ext-real integer set
k1 * c₁₁ is complex real ext-real integer set
0 * m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
1 * k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(0 * m) + (1 * k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
1 * m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
0 * k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(1 * m) + (0 * k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is complex real ext-real integer set
k * m is complex real ext-real integer set
k is complex real ext-real integer set
k * k is complex real ext-real integer set
(k * m) + (k * k) is complex real ext-real integer set
m is V61() V62() V63() V64() V65() V66() Element of K19(NAT)
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m is V61() V62() V63() V64() V65() V66() Element of K19(NAT)
k is V61() V62() V63() V64() V65() V66() Element of K19(NAT)
n is set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
n is set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
() is V61() V62() V63() V64() V65() V66() Element of K19(NAT)
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is V61() V62() V63() V64() V65() V66() Element of K19(NAT)
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is V61() V62() V63() V64() V65() V66() Element of K19(NAT)
n is V61() V62() V63() V64() V65() V66() Element of K19(NAT)
t is set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
t is set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m) is V61() V62() V63() V64() V65() V66() Element of K19(NAT)
k is set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m) is V61() V62() V63() V64() V65() V66() Element of K19(NAT)
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(k) is V61() V62() V63() V64() V65() V66() Element of K19(NAT)
n is set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m) is V61() V62() V63() V64() V65() V66() Element of K19(NAT)
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
k is set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m) is V61() V62() V63() V64() V65() V66() Element of K19(NAT)
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m) is V61() V62() V63() V64() V65() V66() Element of K19(NAT)
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer prime finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer prime finite cardinal set
(n) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
idseq n is V1() V4( NAT ) V5( RAT ) Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued set
Seg n is finite n -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= n ) } is set
id (Seg n) is V1() V4( Seg n) V5( RAT ) V5( INT ) V5( Seg n) total finite complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg n),(Seg n)))
K20((Seg n),(Seg n)) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg n),(Seg n))) is finite V44() set
Product (idseq n) is complex real ext-real set
2 + 0 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(n) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer prime finite cardinal set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer prime finite cardinal set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer prime finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer prime finite cardinal set
(2) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
m is set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
k is set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(k) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{m} is non empty V12() finite V44() 1 -element V61() V62() V63() V64() V65() V66() set
(m) \/ {m} is finite V61() V62() V63() V64() V65() V66() set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer prime finite cardinal set
(m) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{m} is non empty V12() finite V44() 1 -element V61() V62() V63() V64() V65() V66() set
(m) \/ {m} is finite V61() V62() V63() V64() V65() V66() set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(k) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
n is set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(k) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( not m <= b₁ & b₁ is prime ) } is set
k is set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(n) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
card (n) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of omega
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer prime finite cardinal set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(t) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
card (t) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of omega
{n} is non empty V12() finite V44() 1 -element V61() V62() V63() V64() V65() V66() set
(n) \/ {n} is finite V61() V62() V63() V64() V65() V66() set
t is set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( not 2 <= b₁ & b₁ is prime ) } is set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(k) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
card (k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of omega
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer prime V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(k) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
card (k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of omega
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer prime V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(n) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
card (n) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of omega
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
{k} is non empty V12() finite V44() 1 -element V61() V62() V63() V64() V65() V66() set
(k) \/ {k} is finite V61() V62() V63() V64() V65() V66() set
card ((k) \/ {k}) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of omega
{n} is non empty V12() finite V44() 1 -element V61() V62() V63() V64() V65() V66() set
(n) \/ {n} is finite V61() V62() V63() V64() V65() V66() set
card ((n) \/ {n}) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of omega
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( not m <= b₁ & b₁ is prime ) } is set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
card () is non empty epsilon-transitive epsilon-connected ordinal cardinal set
card (Seg k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of omega
card k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of omega
m is finite set
card m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of omega
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((k + 1)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer prime V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(((k + 1))) is finite V61() V62() V63() V64() V65() V66() Element of K19(NAT)
card (((k + 1))) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of omega
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k * n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t * k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t * k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t * k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t * k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t mod t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k * k1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t div t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
t * (t div t) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(t * (t div t)) + (t mod t) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(t * (t div t)) * k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(t mod t) * k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((t * (t div t)) * k) + ((t mod t) * k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(t div t) * k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
t * ((t div t) * k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k * k1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t * k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t * k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k * k1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k * m1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
c₁₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t * c₁₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
1 * m1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
t * k1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(t * k1) * k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m1 * k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k * (m1 * k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is complex set
(m,2) is complex set
2 |-> m is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-valued set
(Seg 2) --> m is V1() V4( Seg 2) V5({m}) Function-like V30( Seg 2,{m}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg 2),{m}))
{m} is non empty V12() finite 1 -element V61() set
K20((Seg 2),{m}) is finite complex-valued set
K19(K20((Seg 2),{m})) is finite V44() set
Product (2 |-> m) is complex set
m * m is complex set
m ^2 is set
(m,1) is complex set
1 |-> m is V1() V4( NAT ) Function-like non empty V12() finite 1 -element FinSequence-like FinSubsequence-like complex-valued set
(Seg 1) --> m is V1() V4( Seg 1) V5({m}) Function-like V30( Seg 1,{m}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg 1),{m}))
K20((Seg 1),{m}) is finite complex-valued set
K19(K20((Seg 1),{m})) is finite V44() set
Product (1 |-> m) is complex set
(m,1) * m is complex set
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m,(1 + 1)) is complex set
(1 + 1) |-> m is V1() V4( NAT ) Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like complex-valued set
Seg (1 + 1) is non empty finite 1 + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= 1 + 1 ) } is set
(Seg (1 + 1)) --> m is V1() V4( Seg (1 + 1)) V5({m}) Function-like V30( Seg (1 + 1),{m}) finite FinSequence-like FinSubsequence-like complex-valued Element of K19(K20((Seg (1 + 1)),{m}))
K20((Seg (1 + 1)),{m}) is finite complex-valued set
K19(K20((Seg (1 + 1)),{m})) is finite V44() set
Product ((1 + 1) |-> m) is complex set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m div k is complex real ext-real integer set
m div k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n mod t is complex real ext-real integer set
n mod t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is complex real ext-real set
(k,m) is complex real ext-real set
m |-> k is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
(Seg m) --> k is V1() V4( Seg m) V5({k}) Function-like V30( Seg m,{k}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg m),{k}))
{k} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg m),{k}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg m),{k})) is finite V44() set
Product (m |-> k) is complex real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
t is complex real ext-real set
(t,(n + 1)) is complex real ext-real set
(n + 1) |-> t is V1() V4( NAT ) Function-like finite n + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg (n + 1) is non empty finite n + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= n + 1 ) } is set
(Seg (n + 1)) --> t is V1() V4( Seg (n + 1)) V5({t}) Function-like V30( Seg (n + 1),{t}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg (n + 1)),{t}))
{t} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg (n + 1)),{t}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg (n + 1)),{t})) is finite V44() set
Product ((n + 1) |-> t) is complex real ext-real set
(t,n) is complex real ext-real set
n |-> t is V1() V4( NAT ) Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg n is finite n -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= n ) } is set
(Seg n) --> t is V1() V4( Seg n) V5({t}) Function-like V30( Seg n,{t}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of K19(K20((Seg n),{t}))
K20((Seg n),{t}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg n),{t})) is finite V44() set
Product (n |-> t) is complex real ext-real set
t * (t,n) is complex real ext-real set
n is complex real ext-real set
(n,0) is complex real ext-real set
0 |-> n is V1() V4( NAT ) V5( RAT ) Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative integer finite finite-yielding V44() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered complex-valued ext-real-valued real-valued natural-valued V61() V62() V63() V64() V65() V66() V67() set
(Seg 0) --> n is V1() V4( Seg 0) V5({n}) Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative V30( Seg 0,{n}) integer finite finite-yielding V44() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-valued ext-real-valued real-valued natural-valued V61() V62() V63() V64() V65() V66() V67() Element of K19(K20((Seg 0),{n}))
{n} is non empty V12() finite 1 -element V61() V62() V63() set
K20((Seg 0),{n}) is finite complex-valued ext-real-valued real-valued set
K19(K20((Seg 0),{n})) is finite V44() set
Product (0 |-> n) is complex real ext-real set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(0,m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
m |-> 0 is V1() empty-yielding V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
(Seg m) --> 0 is V1() V4( Seg m) V5( RAT ) V5( INT ) V5({0}) Function-like V30( Seg m,{0}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),{0}))
{0} is non empty V12() finite V44() 1 -element V61() V62() V63() V64() V65() V66() set
K20((Seg m),{0}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),{0})) is finite V44() set
Product (m |-> 0) is complex real ext-real set
1 + 0 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m,k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k |-> m is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
(Seg k) --> m is V1() V4( Seg k) V5( RAT ) V5( INT ) V5({m}) Function-like V30( Seg k,{m}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg k),{m}))
{m} is non empty V12() finite V44() 1 -element V61() V62() V63() V64() V65() V66() set
K20((Seg k),{m}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg k),{m})) is finite V44() set
Product (k |-> m) is complex real ext-real set
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(2,0) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
0 |-> 2 is V1() V4( NAT ) V5( RAT ) Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative integer finite finite-yielding V44() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered complex-valued ext-real-valued real-valued natural-valued V61() V62() V63() V64() V65() V66() V67() set
(Seg 0) --> 2 is V1() V4( Seg 0) V5( RAT ) V5( INT ) V5({2}) Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative V30( Seg 0,{2}) integer finite finite-yielding V44() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-valued ext-real-valued real-valued natural-valued V61() V62() V63() V64() V65() V66() V67() Element of K19(K20((Seg 0),{2}))
{2} is non empty V12() finite V44() 1 -element V61() V62() V63() V64() V65() V66() set
K20((Seg 0),{2}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg 0),{2})) is finite V44() set
Product (0 |-> 2) is complex real ext-real set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(2,m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
m |-> 2 is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
(Seg m) --> 2 is V1() V4( Seg m) V5( RAT ) V5( INT ) V5({2}) Function-like V30( Seg m,{2}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),{2}))
K20((Seg m),{2}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),{2})) is finite V44() set
Product (m |-> 2) is complex real ext-real set
(m + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(2,(m + 1)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
(m + 1) |-> 2 is V1() V4( NAT ) Function-like finite m + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg (m + 1) is non empty finite m + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m + 1 ) } is set
(Seg (m + 1)) --> 2 is V1() V4( Seg (m + 1)) V5( RAT ) V5( INT ) V5({2}) Function-like V30( Seg (m + 1),{2}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg (m + 1)),{2}))
K20((Seg (m + 1)),{2}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg (m + 1)),{2})) is finite V44() set
Product ((m + 1) |-> 2) is complex real ext-real set
(2,m) - m is complex real ext-real integer Element of REAL
2 * 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
2 * ((2,m) - m) is complex real ext-real integer Element of REAL
(2,(m + 1)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(2,(m + 1)) - ((m + 1) + 1) is complex real ext-real integer Element of REAL
2 * (2,m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
2 * m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(2 * m) - m is complex real ext-real integer Element of REAL
((2 * m) - m) + 2 is complex real ext-real integer Element of REAL
(2 * (2,m)) - (((2 * m) - m) + 2) is complex real ext-real integer Element of REAL
m - 2 is complex real ext-real integer Element of REAL
(2 * ((2,m) - m)) + (m - 2) is complex real ext-real integer Element of REAL
2 + (m - 2) is complex real ext-real integer Element of REAL
0 + ((m + 1) + 1) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(2,m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
m |-> 2 is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
(Seg m) --> 2 is V1() V4( Seg m) V5( RAT ) V5( INT ) V5({2}) Function-like V30( Seg m,{2}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),{2}))
K20((Seg m),{2}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),{2})) is finite V44() set
Product (m |-> 2) is complex real ext-real set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(2,m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
m |-> 2 is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
(Seg m) --> 2 is V1() V4( Seg m) V5( RAT ) V5( INT ) V5({2}) Function-like V30( Seg m,{2}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),{2}))
K20((Seg m),{2}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),{2})) is finite V44() set
Product (m |-> 2) is complex real ext-real set
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
F₄() is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
F₃() is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
F₁(0) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
F₂(0) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
F₃() gcd F₄() is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
K19(K20(NAT,NAT)) is V12() non finite set
m is V1() V4( NAT ) V5( NAT ) Function-like V30( NAT , NAT ) complex-valued ext-real-valued real-valued natural-valued Element of K19(K20(NAT,NAT))
m . 0 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m . (0 + 1) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
IFEQ ((m . 0),0,0,F₂(0)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m . 1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m . k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
F₁(k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m . t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
F₂(t) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
IFEQ ((m . t),0,0,F₂(t)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k + 2 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m . (k + 2) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m . k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m . (k + 1) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
H₂(k) mod H₂(k + 1) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
F₂(k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
IFEQ ((m . k),0,0,F₂(k)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k + (1 + 1) is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m . (k + (1 + 1)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(k + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m . ((k + 1) + 1) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
F₂((k + 1)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
IFEQ ((m . (k + 1)),0,0,F₂((k + 1))) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
F₁(k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
F₁(k) mod F₂(k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(k + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m . ((k + 1) + 1) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
F₂((k + 1)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
IFEQ ((m . (k + 1)),0,0,F₂((k + 1))) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m . k) mod (m . (k + 1)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m . k) mod (m . (k + 1)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m . k) mod (m . (k + 1)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m . k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m . (k + 1) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
F₁(k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
F₂(k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
IFEQ ((m . k),0,0,F₂(k)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m,k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k |-> m is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
(Seg k) --> m is V1() V4( Seg k) V5( INT ) V5({m}) Function-like V30( Seg k,{m}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg k),{m}))
{m} is non empty V12() finite V44() 1 -element V61() V62() V63() V64() V65() V66() set
K20((Seg k),{m}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg k),{m})) is finite V44() set
Product (k |-> m) is complex real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m,n) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n |-> m is V1() V4( NAT ) Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg n is finite n -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= n ) } is set
(Seg n) --> m is V1() V4( Seg n) V5( INT ) V5({m}) Function-like V30( Seg n,{m}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg n),{m}))
K20((Seg n),{m}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg n),{m})) is finite V44() set
Product (n |-> m) is complex real ext-real set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m,(n + 1)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(n + 1) |-> m is V1() V4( NAT ) Function-like finite n + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg (n + 1) is non empty finite n + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= n + 1 ) } is set
(Seg (n + 1)) --> m is V1() V4( Seg (n + 1)) V5( INT ) V5({m}) Function-like V30( Seg (n + 1),{m}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg (n + 1)),{m}))
K20((Seg (n + 1)),{m}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg (n + 1)),{m})) is finite V44() set
Product ((n + 1) |-> m) is complex real ext-real set
(m,n) * m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m,0) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
0 |-> m is V1() V4( NAT ) V5( RAT ) Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative integer finite finite-yielding V44() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered complex-valued ext-real-valued real-valued natural-valued V61() V62() V63() V64() V65() V66() V67() set
(Seg 0) --> m is V1() V4( Seg 0) V5( INT ) V5({m}) Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative V30( Seg 0,{m}) integer finite finite-yielding V44() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-valued ext-real-valued real-valued natural-valued V61() V62() V63() V64() V65() V66() V67() Element of K19(K20((Seg 0),{m}))
K20((Seg 0),{m}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg 0),{m})) is finite V44() set
Product (0 |-> m) is complex real ext-real set
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(2,m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
m |-> 2 is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
(Seg m) --> 2 is V1() V4( Seg m) V5( RAT ) V5( INT ) V5({2}) Function-like V30( Seg m,{2}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),{2}))
K20((Seg m),{2}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),{2})) is finite V44() set
Product (m |-> 2) is complex real ext-real set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
2 * k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(2 * k) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(2,m) * ((2 * k) + 1) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(2,n) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
n |-> 2 is V1() V4( NAT ) Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg n is finite n -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= n ) } is set
(Seg n) --> 2 is V1() V4( Seg n) V5( RAT ) V5( INT ) V5({2}) Function-like V30( Seg n,{2}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg n),{2}))
K20((Seg n),{2}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg n),{2})) is finite V44() set
Product (n |-> 2) is complex real ext-real set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
2 * t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(2 * t) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(2,n) * ((2 * t) + 1) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n + t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(2,(k + 1)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(k + 1) |-> 2 is V1() V4( NAT ) Function-like finite k + 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg (k + 1) is non empty finite k + 1 -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k + 1 ) } is set
(Seg (k + 1)) --> 2 is V1() V4( Seg (k + 1)) V5( RAT ) V5( INT ) V5({2}) Function-like V30( Seg (k + 1),{2}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg (k + 1)),{2}))
K20((Seg (k + 1)),{2}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg (k + 1)),{2})) is finite V44() set
Product ((k + 1) |-> 2) is complex real ext-real set
(2,n) * (2,(k + 1)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(2,(k + 1)) * ((2 * k) + 1) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(2,n) * ((2,(k + 1)) * ((2 * k) + 1)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(2,k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
k |-> 2 is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
(Seg k) --> 2 is V1() V4( Seg k) V5( RAT ) V5( INT ) V5({2}) Function-like V30( Seg k,{2}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg k),{2}))
K20((Seg k),{2}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg k),{2})) is finite V44() set
Product (k |-> 2) is complex real ext-real set
(2,1) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
1 |-> 2 is V1() V4( NAT ) Function-like one-to-one non empty V12() finite 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued V55() decreasing non-decreasing non-increasing set
(Seg 1) --> 2 is V1() V4( Seg 1) V5( RAT ) V5( INT ) V5({2}) Function-like V30( Seg 1,{2}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg 1),{2}))
K20((Seg 1),{2}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg 1),{2})) is finite V44() set
Product (1 |-> 2) is complex real ext-real set
(2,k) * (2,1) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
((2,k) * (2,1)) * ((2 * k) + 1) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
2 * (2,k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(2 * (2,k)) * ((2 * k) + 1) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(2,k) * ((2 * k) + 1) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
2 * ((2,k) * ((2 * k) + 1)) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(2,m) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
m |-> 2 is V1() V4( NAT ) Function-like finite m -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg m is finite m -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= m ) } is set
(Seg m) --> 2 is V1() V4( Seg m) V5( RAT ) V5( INT ) V5({2}) Function-like V30( Seg m,{2}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg m),{2}))
K20((Seg m),{2}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg m),{2})) is finite V44() set
Product (m |-> 2) is complex real ext-real set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
2 * k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(2 * k) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(2,m) * ((2 * k) + 1) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(2,n) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal Element of REAL
n |-> 2 is V1() V4( NAT ) Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg n is finite n -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= n ) } is set
(Seg n) --> 2 is V1() V4( Seg n) V5( RAT ) V5( INT ) V5({2}) Function-like V30( Seg n,{2}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg n),{2}))
K20((Seg n),{2}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg n),{2})) is finite V44() set
Product (n |-> 2) is complex real ext-real set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
2 * t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(2 * t) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(2,n) * ((2 * t) + 1) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m,k) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k |-> m is V1() V4( NAT ) Function-like finite k -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg k is finite k -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
(Seg k) --> m is V1() V4( Seg k) V5( INT ) V5({m}) Function-like V30( Seg k,{m}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg k),{m}))
{m} is non empty V12() finite V44() 1 -element V61() V62() V63() V64() V65() V66() set
K20((Seg k),{m}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg k),{m})) is finite V44() set
Product (k |-> m) is complex real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
(m,n) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
n |-> m is V1() V4( NAT ) Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg n is finite n -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= n ) } is set
(Seg n) --> m is V1() V4( Seg n) V5( INT ) V5({m}) Function-like V30( Seg n,{m}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg n),{m}))
K20((Seg n),{m}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg n),{m})) is finite V44() set
Product (n |-> m) is complex real ext-real set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
k + t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT
(m,t) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set
t |-> m is V1() V4( NAT ) Function-like finite t -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Seg t is finite t -element V61() V62() V63() V64() V65() V66() Element of K19(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer V35() finite cardinal V61() V62() V63() V64() V65() V66() Element of NAT : ( 1 <= b₁ & b₁ <= t ) } is set
(Seg t) --> m is V1() V4( Seg t) V5( INT ) V5({m}) Function-like V30( Seg t,{m}) finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20((Seg t),{m}))
K20((Seg t),{m}) is V5( RAT ) V5( INT ) finite complex-valued ext-real-valued real-valued natural-valued set
K19(K20((Seg t),{m})) is finite V44() set
Product (t |-> m) is complex real ext-real set
(m,k) * (m,t) is epsilon-transitive epsilon-connected ordinal natural complex real ext-real non negative integer finite cardinal set