:: MATRTOP1 semantic presentation

REAL is non empty non trivial non finite V197() V198() V199() V203() set
NAT is non trivial ordinal non finite cardinal limit_cardinal V197() V198() V199() V200() V201() V202() V203() Element of bool REAL
bool REAL is non trivial non finite set
INT is non empty non trivial non finite V197() V198() V199() V200() V201() V203() set
K868() is strict doubleLoopStr
the carrier of K868() is set
COMPLEX is non empty non trivial non finite V197() V203() set
RAT is non empty non trivial non finite V197() V198() V199() V200() V203() set
[:COMPLEX,COMPLEX:] is Relation-like non trivial non finite complex-valued set
bool [:COMPLEX,COMPLEX:] is non trivial non finite set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is Relation-like non trivial non finite complex-valued set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is non trivial non finite set
[:REAL,REAL:] is Relation-like non trivial non finite complex-valued ext-real-valued real-valued set
bool [:REAL,REAL:] is non trivial non finite set
[:[:REAL,REAL:],REAL:] is Relation-like non trivial non finite complex-valued ext-real-valued real-valued set
bool [:[:REAL,REAL:],REAL:] is non trivial non finite set
[:RAT,RAT:] is Relation-like RAT -valued non trivial non finite complex-valued ext-real-valued real-valued set
bool [:RAT,RAT:] is non trivial non finite set
[:[:RAT,RAT:],RAT:] is Relation-like RAT -valued non trivial non finite complex-valued ext-real-valued real-valued set
bool [:[:RAT,RAT:],RAT:] is non trivial non finite set
[:INT,INT:] is Relation-like RAT -valued INT -valued non trivial non finite complex-valued ext-real-valued real-valued set
bool [:INT,INT:] is non trivial non finite set
[:[:INT,INT:],INT:] is Relation-like RAT -valued INT -valued non trivial non finite complex-valued ext-real-valued real-valued set
bool [:[:INT,INT:],INT:] is non trivial non finite set
[:NAT,NAT:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
[:[:NAT,NAT:],NAT:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:[:NAT,NAT:],NAT:] is set
NAT is non trivial ordinal non finite cardinal limit_cardinal V197() V198() V199() V200() V201() V202() V203() set
bool NAT is non trivial non finite set
bool NAT is non trivial non finite set
K238() is set
1 is non empty ordinal natural V28() real V30() V31() finite cardinal ext-real positive non negative V197() V198() V199() V200() V201() V202() Element of NAT
K284(NAT) is V88() set
2 is non empty ordinal natural V28() real V30() V31() finite cardinal ext-real positive non negative V197() V198() V199() V200() V201() V202() Element of NAT
{} is Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty ordinal natural V28() real finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V197() V198() V199() V200() V201() V202() V203() set
the Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty ordinal natural V28() real finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V197() V198() V199() V200() V201() V202() V203() set is Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty ordinal natural V28() real finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V197() V198() V199() V200() V201() V202() V203() set
0 is Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty ordinal natural V28() real V30() V31() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V197() V198() V199() V200() V201() V202() V203() Element of NAT
K636(0,1,2) is finite V197() V198() V199() V200() V201() V202() set
[:K636(0,1,2),K636(0,1,2):] is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
[:[:K636(0,1,2),K636(0,1,2):],K636(0,1,2):] is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:[:K636(0,1,2),K636(0,1,2):],K636(0,1,2):] is finite V38() set
bool [:K636(0,1,2),K636(0,1,2):] is finite V38() set
K694() is non empty strict multMagma
the carrier of K694() is non empty set
K699() is non empty strict V141() V142() V143() V145() V227() V228() V229() V230() V231() V232() multMagma
K700() is non empty strict V143() V145() V230() V231() V232() M34(K699())
K701() is non empty strict V141() V143() V145() V230() V231() V232() V233() M37(K699(),K700())
K703() is non empty strict V141() V143() V145() multMagma
K704() is non empty strict V141() V143() V145() V233() M34(K703())
{{},1} is non empty finite V38() V197() V198() V199() V200() V201() V202() set
[:NAT,REAL:] is Relation-like non trivial non finite complex-valued ext-real-valued real-valued set
bool [:NAT,REAL:] is non trivial non finite set
[:1,1:] is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:1,1:] is finite V38() set
[:[:1,1:],1:] is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:[:1,1:],1:] is finite V38() set
[:[:1,1:],REAL:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:[:1,1:],REAL:] is set
[:2,2:] is Relation-like RAT -valued INT -valued finite complex-valued ext-real-valued real-valued natural-valued set
[:[:2,2:],REAL:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:[:2,2:],REAL:] is set
TOP-REAL 2 is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL 2) is non empty set
3 is non empty ordinal natural V28() real V30() V31() finite cardinal ext-real positive non negative V197() V198() V199() V200() V201() V202() Element of NAT
addreal is Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total quasi_total V125( REAL ) V126( REAL ) complex-valued ext-real-valued real-valued V251( REAL ) Element of bool [:[:REAL,REAL:],REAL:]
REAL 0 is functional non empty FinSequence-membered FinSequenceSet of REAL
0 -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
TOP-REAL 0 is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
0. (TOP-REAL 0) is Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty ordinal natural V28() real finite finite-yielding V38() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered V64( TOP-REAL 0) ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V197() V198() V199() V200() V201() V202() V203() Element of the carrier of (TOP-REAL 0)
the carrier of (TOP-REAL 0) is non empty set
the ZeroF of (TOP-REAL 0) is Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty ordinal natural V28() real finite finite-yielding V38() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V197() V198() V199() V200() V201() V202() V203() Element of the carrier of (TOP-REAL 0)
{(0. (TOP-REAL 0))} is functional non empty trivial finite V38() 1 -element V197() V198() V199() V200() V201() V202() set
Seg 1 is non empty trivial finite 1 -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= 1 ) } is set
F_Real is non empty non degenerated non trivial right_complementable almost_left_invertible strict V141() V143() V145() V148() V149() V150() right-distributive left-distributive right_unital well-unital V162() left_unital doubleLoopStr
multreal is Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total quasi_total V125( REAL ) V126( REAL ) complex-valued ext-real-valued real-valued V251( REAL ) Element of bool [:[:REAL,REAL:],REAL:]
doubleLoopStr(# REAL,addreal,multreal,1,0 #) is strict doubleLoopStr
the carrier of F_Real is non empty non trivial V197() V198() V199() set
- 1 is V28() real V30() V31() ext-real non positive Element of INT
addcomplex is Relation-like [:COMPLEX,COMPLEX:] -defined COMPLEX -valued Function-like total quasi_total V125( COMPLEX ) V126( COMPLEX ) complex-valued V251( COMPLEX ) Element of bool [:[:COMPLEX,COMPLEX:],COMPLEX:]
<*> REAL is Relation-like non-empty empty-yielding NAT -defined REAL -valued Function-like one-to-one constant functional empty ordinal natural V28() real finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V197() V198() V199() V200() V201() V202() V203() FinSequence of REAL
Sum (<*> REAL) is V28() real ext-real Element of REAL
sqrt 0 is V28() real ext-real non negative Element of REAL
n is set
[:n,REAL:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:n,REAL:] is set
T is Relation-like non-empty n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued positive-yielding nonnegative-yielding Element of bool [:n,REAL:]
A is set
T | A is Relation-like n -defined A -defined n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of bool [:n,REAL:]
Tn is V28() real ext-real set
rng (T | A) is V197() V198() V199() set
rng (T | A) is V197() V198() V199() Element of bool REAL
rng T is V137() V197() V198() V199() Element of bool REAL
n is set
[:n,REAL:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:n,REAL:] is set
T is Relation-like non-empty n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued negative-yielding nonpositive-yielding Element of bool [:n,REAL:]
A is set
T | A is Relation-like n -defined A -defined n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of bool [:n,REAL:]
Tn is V28() real ext-real set
rng (T | A) is V197() V198() V199() set
rng (T | A) is V197() V198() V199() Element of bool REAL
rng T is V137() V197() V198() V199() Element of bool REAL
n is set
[:n,REAL:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:n,REAL:] is set
T is Relation-like n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued nonpositive-yielding Element of bool [:n,REAL:]
A is set
T | A is Relation-like n -defined A -defined n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of bool [:n,REAL:]
Tn is V28() real ext-real set
rng (T | A) is V197() V198() V199() set
rng (T | A) is V197() V198() V199() Element of bool REAL
rng T is V197() V198() V199() Element of bool REAL
n is set
[:n,REAL:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:n,REAL:] is set
T is Relation-like n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued nonnegative-yielding Element of bool [:n,REAL:]
A is set
T | A is Relation-like n -defined A -defined n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of bool [:n,REAL:]
Tn is V28() real ext-real set
rng (T | A) is V197() V198() V199() set
rng (T | A) is V197() V198() V199() Element of bool REAL
rng T is V197() V198() V199() Element of bool REAL
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
sqrt n is Relation-like Function-like complex-valued ext-real-valued real-valued set
dom n is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
dom (sqrt n) is set
A is ordinal natural V28() real finite cardinal ext-real non negative set
Seg A is finite A -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= A ) } is set
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
rng n is finite V197() V198() V199() Element of bool REAL
n is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(n) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
A is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(A) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
(n) + (A) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
the addF of F_Real is Relation-like [: the carrier of F_Real, the carrier of F_Real:] -defined the carrier of F_Real -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:]
[: the carrier of F_Real, the carrier of F_Real:] is Relation-like complex-valued ext-real-valued real-valued set
[:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:] is set
K446( the carrier of F_Real, the carrier of F_Real, the carrier of F_Real, the addF of F_Real,(n),(A)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
n + A is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
sqrt n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
A is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
n ^ A is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
sqrt (n ^ A) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
sqrt A is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(sqrt n) ^ (sqrt A) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
dom (sqrt (n ^ A)) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
dom (n ^ A) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
dom (sqrt A) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
dom A is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
len (sqrt A) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len A is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
dom (sqrt n) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
dom n is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
len (sqrt n) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len n is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len (sqrt (n ^ A)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
L is ordinal natural V28() real finite cardinal ext-real non negative set
(sqrt (n ^ A)) . L is V28() real ext-real set
((sqrt n) ^ (sqrt A)) . L is V28() real ext-real set
(n ^ A) . L is V28() real ext-real set
sqrt ((n ^ A) . L) is V28() real ext-real set
n . L is V28() real ext-real set
(sqrt n) . L is V28() real ext-real set
sqrt (n . L) is V28() real ext-real set
x is ordinal natural V28() real finite cardinal ext-real non negative set
(len n) + x is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
x is ordinal natural V28() real finite cardinal ext-real non negative set
(len n) + x is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
A . x is V28() real ext-real set
(sqrt A) . x is V28() real ext-real set
sqrt (A . x) is V28() real ext-real set
len (n ^ A) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(len (sqrt n)) + (len (sqrt A)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len ((sqrt n) ^ (sqrt A)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
n is V28() real ext-real set
<*n*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued increasing decreasing non-decreasing non-increasing set
[1,n] is set
{1,n} is non empty finite V197() V198() V199() set
{1} is non empty trivial finite V38() 1 -element V197() V198() V199() V200() V201() V202() set
{{1,n},{1}} is non empty finite V38() set
{[1,n]} is Relation-like Function-like constant non empty trivial finite 1 -element set
sqrt <*n*> is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
sqrt n is V28() real ext-real set
<*(sqrt n)*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued increasing decreasing non-decreasing non-increasing set
[1,(sqrt n)] is set
{1,(sqrt n)} is non empty finite V197() V198() V199() set
{{1,(sqrt n)},{1}} is non empty finite V38() set
{[1,(sqrt n)]} is Relation-like Function-like constant non empty trivial finite 1 -element set
<*n*> . 1 is V28() real ext-real set
dom <*n*> is non empty trivial finite 1 -element V197() V198() V199() V200() V201() V202() Element of bool NAT
dom (sqrt <*n*>) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
len <*n*> is non empty ordinal natural V28() real V30() V31() finite cardinal ext-real positive non negative V197() V198() V199() V200() V201() V202() Element of NAT
len (sqrt <*n*>) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(sqrt <*n*>) . 1 is V28() real ext-real set
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
n ^2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
sqrt (n ^2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
abs n is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
absreal is Relation-like REAL -defined REAL -valued Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
n (#) absreal is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
dom (sqrt (n ^2)) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
dom (n ^2) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
dom (abs n) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
dom n is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
Tn is set
n . Tn is V28() real ext-real set
Tm is V28() real ext-real Element of REAL
(n ^2) . Tn is V28() real ext-real set
Tm ^2 is V28() real ext-real Element of REAL
K97(Tm,Tm) is V28() real ext-real non negative set
(sqrt (n ^2)) . Tn is V28() real ext-real set
sqrt ((n ^2) . Tn) is V28() real ext-real set
- Tm is V28() real ext-real Element of REAL
(abs n) . Tn is V28() real ext-real set
abs Tm is V28() real ext-real Element of REAL
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Sum n is V28() real ext-real set
sqrt (Sum n) is V28() real ext-real set
sqrt n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Sum (sqrt n) is V28() real ext-real set
A is ordinal natural V28() real finite cardinal ext-real non negative set
A + 1 is non empty ordinal natural V28() real V30() V31() finite cardinal ext-real positive non negative V197() V198() V199() V200() V201() V202() Element of NAT
Tn is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
len Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Sum Tn is V28() real ext-real set
sqrt (Sum Tn) is V28() real ext-real set
sqrt Tn is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Sum (sqrt Tn) is V28() real ext-real set
rng Tn is finite V197() V198() V199() Element of bool REAL
Tm is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Tm | A is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Seg A is finite A -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= A ) } is set
Tm | (Seg A) is Relation-like NAT -defined Seg A -defined NAT -defined REAL -valued Function-like finite FinSubsequence-like complex-valued ext-real-valued real-valued set
TM is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Tm . (A + 1) is V28() real ext-real set
<*(Tm . (A + 1))*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued increasing decreasing non-decreasing non-increasing set
[1,(Tm . (A + 1))] is set
{1,(Tm . (A + 1))} is non empty finite V197() V198() V199() set
{1} is non empty trivial finite V38() 1 -element V197() V198() V199() V200() V201() V202() set
{{1,(Tm . (A + 1))},{1}} is non empty finite V38() set
{[1,(Tm . (A + 1))]} is Relation-like Function-like constant non empty trivial finite 1 -element set
TM ^ <*(Tm . (A + 1))*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
sqrt Tm is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of bool [:NAT,REAL:]
sqrt TM is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of bool [:NAT,REAL:]
sqrt <*(Tm . (A + 1))*> is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(sqrt TM) ^ (sqrt <*(Tm . (A + 1))*>) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
sqrt (Tm . (A + 1)) is V28() real ext-real set
<*(sqrt (Tm . (A + 1)))*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued increasing decreasing non-decreasing non-increasing set
[1,(sqrt (Tm . (A + 1)))] is set
{1,(sqrt (Tm . (A + 1)))} is non empty finite V197() V198() V199() set
{{1,(sqrt (Tm . (A + 1)))},{1}} is non empty finite V38() set
{[1,(sqrt (Tm . (A + 1)))]} is Relation-like Function-like constant non empty trivial finite 1 -element set
(sqrt TM) ^ <*(sqrt (Tm . (A + 1)))*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Sum (sqrt Tm) is V28() real ext-real set
Sum (sqrt TM) is V28() real ext-real set
(Sum (sqrt TM)) + (sqrt (Tm . (A + 1))) is V28() real ext-real Element of REAL
len TM is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Sum TM is V28() real ext-real Element of REAL
sqrt (Sum TM) is V28() real ext-real Element of REAL
Tn . (A + 1) is V28() real ext-real set
sqrt (Tn . (A + 1)) is V28() real ext-real set
(sqrt (Sum TM)) + (sqrt (Tn . (A + 1))) is V28() real ext-real Element of REAL
(Sum TM) + (Tn . (A + 1)) is V28() real ext-real Element of REAL
dom Tn is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
A is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
len A is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Sum A is V28() real ext-real set
sqrt (Sum A) is V28() real ext-real set
sqrt A is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Sum (sqrt A) is V28() real ext-real set
dom A is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
dom (sqrt A) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
len (sqrt A) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len n is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
A is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
len A is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Sum A is V28() real ext-real set
sqrt (Sum A) is V28() real ext-real set
sqrt A is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Sum (sqrt A) is V28() real ext-real set
n is Relation-like Function-like set
dom n is set
rng n is set
A is set
[:(rng n),(dom n):] is Relation-like set
bool [:(rng n),(dom n):] is set
A is Relation-like rng n -defined dom n -valued Function-like quasi_total Element of bool [:(rng n),(dom n):]
rng A is set
T is set
n | T is Relation-like Function-like set
rng (n | T) is set
dom A is set
Tm is set
A . Tm is set
n . (A . Tm) is set
Tm is set
dom (n | T) is set
TM is set
(n | T) . Tm is set
(n | T) . TM is set
n . Tm is set
n . TM is set
L is set
A . L is set
x is set
A . x is set
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued set
A is set
n - A is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng n is finite V197() set
rng (n - A) is finite set
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
A is set
n - A is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued set
rng (n - A) is finite V197() set
rng n is finite V197() V198() V199() Element of bool REAL
n is Relation-like NAT -defined Function-like finite FinSubsequence-like complex-valued set
Seq n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom n is finite V197() V198() V199() V200() V201() V202() set
Sgm (dom n) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
(Sgm (dom n)) (#) n is Relation-like NAT -defined Function-like finite complex-valued set
n is Relation-like NAT -defined Function-like finite FinSubsequence-like complex-valued ext-real-valued real-valued set
Seq n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued set
dom n is finite V197() V198() V199() V200() V201() V202() set
Sgm (dom n) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
(Sgm (dom n)) (#) n is Relation-like NAT -defined Function-like finite complex-valued ext-real-valued real-valued set
n is set
A is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom A is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
[:(dom A),(dom A):] is Relation-like INT -valued RAT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(dom A),(dom A):] is finite V38() set
A - n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom (A - n) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
[:(dom (A - n)),(dom (A - n)):] is Relation-like INT -valued RAT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(dom (A - n)),(dom (A - n)):] is finite V38() set
T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
T - n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
Tn is Relation-like dom A -defined dom A -valued Function-like one-to-one total quasi_total onto bijective finite complex-valued ext-real-valued real-valued natural-valued Element of bool [:(dom A),(dom A):]
Tn (#) A is Relation-like dom A -defined Function-like finite set
rng Tn is finite V197() V198() V199() V200() V201() V202() Element of bool REAL
Tm is Relation-like Function-like one-to-one set
Tm " is Relation-like Function-like one-to-one set
dom (Tm ") is set
T " n is finite set
Tn .: (T " n) is finite V197() V198() V199() V200() V201() V202() set
A " n is finite set
Tn " (A " n) is finite set
Tn .: (Tn " (A " n)) is finite V197() V198() V199() V200() V201() V202() set
dom Tn is finite set
dom T is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
(dom T) \ (T " n) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
(dom A) \ (A " n) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
card ((dom A) \ (A " n)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
card (dom A) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
card (A " n) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(card (dom A)) - (card (A " n)) is V28() real V30() V31() ext-real Element of INT
len A is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Seg (len A) is finite len A -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= len A ) } is set
Sgm ((dom A) \ (A " n)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
dom (Sgm ((dom A) \ (A " n))) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
Seg (card ((dom A) \ (A " n))) is finite card ((dom A) \ (A " n)) -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= card ((dom A) \ (A " n)) ) } is set
Tm " (A " n) is set
(Tm ") .: (A " n) is finite set
Sgm ((dom T) \ (T " n)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
Tn * (Sgm ((dom T) \ (T " n))) is Relation-like NAT -defined RAT -valued dom A -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued Element of bool [:NAT,(dom A):]
[:NAT,(dom A):] is Relation-like INT -valued RAT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:NAT,(dom A):] is set
rng (Tn * (Sgm ((dom T) \ (T " n)))) is finite V197() V198() V199() V200() V201() V202() Element of bool REAL
rng (Sgm ((dom T) \ (T " n))) is finite V197() V198() V199() V200() V201() V202() Element of bool REAL
Tn .: (rng (Sgm ((dom T) \ (T " n)))) is finite V197() V198() V199() V200() V201() V202() set
Tn .: ((dom T) \ (T " n)) is finite V197() V198() V199() V200() V201() V202() set
Tn .: (dom Tn) is finite V197() V198() V199() V200() V201() V202() set
(Tn .: (dom Tn)) \ (Tn .: (T " n)) is finite V197() V198() V199() V200() V201() V202() Element of bool (Tn .: (dom Tn))
bool (Tn .: (dom Tn)) is finite V38() set
x is Relation-like Function-like one-to-one set
x " is Relation-like Function-like one-to-one set
dom (x ") is set
rng x is set
dom x is set
card ((dom T) \ (T " n)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
card (dom T) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
card (T " n) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(card (dom T)) - (card (T " n)) is V28() real V30() V31() ext-real Element of INT
dom (Sgm ((dom T) \ (T " n))) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
rng (Sgm ((dom A) \ (A " n))) is finite V197() V198() V199() V200() V201() V202() Element of bool REAL
rng (x ") is set
(Tn * (Sgm ((dom T) \ (T " n)))) (#) (x ") is Relation-like NAT -defined Function-like finite set
rng ((Tn * (Sgm ((dom T) \ (T " n)))) (#) (x ")) is finite set
dom (Tn * (Sgm ((dom T) \ (T " n)))) is finite V197() V198() V199() V200() V201() V202() set
dom ((Tn * (Sgm ((dom T) \ (T " n)))) (#) (x ")) is finite V197() V198() V199() V200() V201() V202() set
U is Relation-like dom (A - n) -defined dom (A - n) -valued Function-like total quasi_total finite complex-valued ext-real-valued real-valued natural-valued Element of bool [:(dom (A - n)),(dom (A - n)):]
(x ") (#) x is Relation-like Function-like one-to-one set
id ((dom A) \ (A " n)) is Relation-like (dom A) \ (A " n) -defined (dom A) \ (A " n) -valued INT -valued RAT -valued Function-like one-to-one total quasi_total finite complex-valued ext-real-valued real-valued natural-valued increasing non-decreasing Element of bool [:((dom A) \ (A " n)),((dom A) \ (A " n)):]
[:((dom A) \ (A " n)),((dom A) \ (A " n)):] is Relation-like INT -valued RAT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:((dom A) \ (A " n)),((dom A) \ (A " n)):] is finite V38() set
TMx is Relation-like dom (A - n) -defined dom (A - n) -valued Function-like one-to-one total quasi_total onto bijective finite complex-valued ext-real-valued real-valued natural-valued Element of bool [:(dom (A - n)),(dom (A - n)):]
TMx (#) x is Relation-like dom (A - n) -defined Function-like one-to-one finite set
(id ((dom A) \ (A " n))) * (Tn * (Sgm ((dom T) \ (T " n)))) is Relation-like NAT -defined INT -valued RAT -valued (dom A) \ (A " n) -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued Element of bool [:NAT,((dom A) \ (A " n)):]
[:NAT,((dom A) \ (A " n)):] is Relation-like INT -valued RAT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:NAT,((dom A) \ (A " n)):] is set
TMx (#) (A - n) is Relation-like dom (A - n) -defined Function-like finite set
x (#) A is Relation-like Function-like set
TMx (#) (x (#) A) is Relation-like dom (A - n) -defined Function-like finite set
(Tn * (Sgm ((dom T) \ (T " n)))) (#) A is Relation-like NAT -defined Function-like finite set
(Sgm ((dom T) \ (T " n))) (#) T is Relation-like NAT -defined Function-like finite set
n is set
A is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued set
dom A is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
[:(dom A),(dom A):] is Relation-like INT -valued RAT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(dom A),(dom A):] is finite V38() set
A - n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued set
Sum (A - n) is V28() set
T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued set
T - n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued set
Sum (T - n) is V28() set
rng (T - n) is finite V197() set
rng (A - n) is finite V197() set
TM is Relation-like dom A -defined dom A -valued Function-like one-to-one total quasi_total onto bijective finite complex-valued ext-real-valued real-valued natural-valued Element of bool [:(dom A),(dom A):]
TM (#) A is Relation-like dom A -defined Function-like finite complex-valued set
dom (A - n) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
[:(dom (A - n)),(dom (A - n)):] is Relation-like INT -valued RAT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(dom (A - n)),(dom (A - n)):] is finite V38() set
L is Relation-like dom (A - n) -defined dom (A - n) -valued Function-like one-to-one total quasi_total onto bijective finite complex-valued ext-real-valued real-valued natural-valued Element of bool [:(dom (A - n)),(dom (A - n)):]
L (#) (A - n) is Relation-like dom (A - n) -defined Function-like finite complex-valued set
Tn is Relation-like NAT -defined COMPLEX -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued FinSequence of COMPLEX
addcomplex "**" Tn is V28() Element of COMPLEX
Tm is Relation-like NAT -defined COMPLEX -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued FinSequence of COMPLEX
addcomplex "**" Tm is V28() Element of COMPLEX
n is set
A is Relation-like NAT -defined Function-like finite FinSubsequence-like set
dom A is finite V197() V198() V199() V200() V201() V202() set
[:(dom A),(dom A):] is Relation-like INT -valued RAT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(dom A),(dom A):] is finite V38() set
T is Relation-like NAT -defined Function-like finite FinSubsequence-like set
A | n is Relation-like NAT -defined n -defined NAT -defined Function-like finite FinSubsequence-like set
Seq (A | n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom (A | n) is finite V197() V198() V199() V200() V201() V202() set
Sgm (dom (A | n)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
(Sgm (dom (A | n))) (#) (A | n) is Relation-like NAT -defined Function-like finite set
Tn is ordinal natural V28() real finite cardinal ext-real non negative set
Seg Tn is finite Tn -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= Tn ) } is set
Tm is Relation-like dom A -defined dom A -valued Function-like one-to-one total quasi_total onto bijective finite complex-valued ext-real-valued real-valued natural-valued Element of bool [:(dom A),(dom A):]
Tm (#) A is Relation-like dom A -defined Function-like finite set
Tm " n is finite set
T | (Tm " n) is Relation-like NAT -defined Tm " n -defined NAT -defined Function-like finite FinSubsequence-like set
Seq (T | (Tm " n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom (T | (Tm " n)) is finite V197() V198() V199() V200() V201() V202() set
Sgm (dom (T | (Tm " n))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
(Sgm (dom (T | (Tm " n)))) (#) (T | (Tm " n)) is Relation-like NAT -defined Function-like finite set
dom (Seq (T | (Tm " n))) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
[:(dom (Seq (T | (Tm " n)))),(dom (Seq (T | (Tm " n)))):] is Relation-like INT -valued RAT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(dom (Seq (T | (Tm " n)))),(dom (Seq (T | (Tm " n)))):] is finite V38() set
Sgm (Tm " n) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
dom Tm is finite set
Tm | (Tm " n) is Relation-like dom A -defined Tm " n -defined dom A -defined RAT -valued dom A -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued Element of bool [:(dom A),(dom A):]
dom (Tm | (Tm " n)) is finite set
(dom A) /\ n is finite V197() V198() V199() V200() V201() V202() set
Sgm ((dom A) /\ n) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
rng (Sgm ((dom A) /\ n)) is finite V197() V198() V199() V200() V201() V202() Element of bool REAL
rng Tm is finite V197() V198() V199() V200() V201() V202() Element of bool REAL
Tm " ((dom A) /\ n) is finite set
Tm " is Relation-like dom A -defined dom A -valued Function-like one-to-one total quasi_total onto bijective finite complex-valued ext-real-valued real-valued natural-valued Element of bool [:(dom A),(dom A):]
(Tm ") .: ((dom A) /\ n) is finite V197() V198() V199() V200() V201() V202() set
(Tm | (Tm " n)) * (Sgm (Tm " n)) is Relation-like NAT -defined RAT -valued dom A -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued Element of bool [:NAT,(dom A):]
[:NAT,(dom A):] is Relation-like INT -valued RAT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:NAT,(dom A):] is set
rng (Sgm (Tm " n)) is finite V197() V198() V199() V200() V201() V202() Element of bool REAL
rng (Tm | (Tm " n)) is finite V197() V198() V199() V200() V201() V202() Element of bool REAL
Tm .: (Tm " ((dom A) /\ n)) is finite V197() V198() V199() V200() V201() V202() set
rng ((Tm | (Tm " n)) * (Sgm (Tm " n))) is finite V197() V198() V199() V200() V201() V202() Element of bool REAL
((Tm | (Tm " n)) * (Sgm (Tm " n))) " is Relation-like Function-like set
dom (((Tm | (Tm " n)) * (Sgm (Tm " n))) ") is set
dom (Tm ") is finite set
card ((dom A) /\ n) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
card (Tm " n) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
dom (Sgm (Tm " n)) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
Seg (card ((dom A) /\ n)) is finite card ((dom A) /\ n) -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= card ((dom A) /\ n) ) } is set
dom ((Tm | (Tm " n)) * (Sgm (Tm " n))) is finite V197() V198() V199() V200() V201() V202() set
rng (((Tm | (Tm " n)) * (Sgm (Tm " n))) ") is set
(Sgm ((dom A) /\ n)) (#) (((Tm | (Tm " n)) * (Sgm (Tm " n))) ") is Relation-like NAT -defined Function-like finite set
rng ((Sgm ((dom A) /\ n)) (#) (((Tm | (Tm " n)) * (Sgm (Tm " n))) ")) is finite set
dom T is finite V197() V198() V199() V200() V201() V202() set
dom (Sgm ((dom A) /\ n)) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
dom ((Sgm ((dom A) /\ n)) (#) (((Tm | (Tm " n)) * (Sgm (Tm " n))) ")) is finite V197() V198() V199() V200() V201() V202() set
TMx is Relation-like dom (Seq (T | (Tm " n))) -defined dom (Seq (T | (Tm " n))) -valued Function-like total quasi_total finite complex-valued ext-real-valued real-valued natural-valued Element of bool [:(dom (Seq (T | (Tm " n)))),(dom (Seq (T | (Tm " n)))):]
tmx is Relation-like dom (Seq (T | (Tm " n))) -defined dom (Seq (T | (Tm " n))) -valued Function-like one-to-one total quasi_total onto bijective finite complex-valued ext-real-valued real-valued natural-valued Element of bool [:(dom (Seq (T | (Tm " n)))),(dom (Seq (T | (Tm " n)))):]
((Tm | (Tm " n)) * (Sgm (Tm " n))) * tmx is Relation-like dom (Seq (T | (Tm " n))) -defined RAT -valued dom A -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued Element of bool [:(dom (Seq (T | (Tm " n)))),(dom A):]
[:(dom (Seq (T | (Tm " n)))),(dom A):] is Relation-like INT -valued RAT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(dom (Seq (T | (Tm " n)))),(dom A):] is finite V38() set
(((Tm | (Tm " n)) * (Sgm (Tm " n))) ") (#) ((Tm | (Tm " n)) * (Sgm (Tm " n))) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
(Sgm ((dom A) /\ n)) (#) ((((Tm | (Tm " n)) * (Sgm (Tm " n))) ") (#) ((Tm | (Tm " n)) * (Sgm (Tm " n)))) is Relation-like NAT -defined RAT -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued set
id ((dom A) /\ n) is Relation-like (dom A) /\ n -defined (dom A) /\ n -valued INT -valued RAT -valued Function-like one-to-one total quasi_total finite complex-valued ext-real-valued real-valued natural-valued increasing non-decreasing Element of bool [:((dom A) /\ n),((dom A) /\ n):]
[:((dom A) /\ n),((dom A) /\ n):] is Relation-like INT -valued RAT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:((dom A) /\ n),((dom A) /\ n):] is finite V38() set
(id ((dom A) /\ n)) * (Sgm ((dom A) /\ n)) is Relation-like NAT -defined INT -valued RAT -valued (dom A) /\ n -valued Function-like finite complex-valued ext-real-valued real-valued natural-valued Element of bool [:NAT,((dom A) /\ n):]
[:NAT,((dom A) /\ n):] is Relation-like INT -valued RAT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:NAT,((dom A) /\ n):] is set
A | ((dom A) /\ n) is Relation-like NAT -defined (dom A) /\ n -defined NAT -defined Function-like finite FinSubsequence-like set
tmx (#) (Seq (T | (Tm " n))) is Relation-like dom (Seq (T | (Tm " n))) -defined Function-like finite set
(Tm | (Tm " n)) (#) A is Relation-like dom A -defined Function-like finite set
((Tm | (Tm " n)) * (Sgm (Tm " n))) (#) A is Relation-like NAT -defined Function-like finite set
tmx (#) (((Tm | (Tm " n)) * (Sgm (Tm " n))) (#) A) is Relation-like dom (Seq (T | (Tm " n))) -defined Function-like finite set
((id ((dom A) /\ n)) * (Sgm ((dom A) /\ n))) (#) A is Relation-like NAT -defined Function-like finite set
(id ((dom A) /\ n)) (#) A is Relation-like (dom A) /\ n -defined Function-like finite set
(Sgm ((dom A) /\ n)) (#) ((id ((dom A) /\ n)) (#) A) is Relation-like NAT -defined Function-like finite set
(Sgm ((dom A) /\ n)) (#) (A | n) is Relation-like NAT -defined Function-like finite set
n is set
A is Relation-like NAT -defined Function-like finite FinSubsequence-like complex-valued set
dom A is finite V197() V198() V199() V200() V201() V202() set
[:(dom A),(dom A):] is Relation-like INT -valued RAT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(dom A),(dom A):] is finite V38() set
T is Relation-like NAT -defined Function-like finite FinSubsequence-like complex-valued set
A | n is Relation-like NAT -defined n -defined NAT -defined Function-like finite FinSubsequence-like complex-valued set
Seq (A | n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued set
dom (A | n) is finite V197() V198() V199() V200() V201() V202() set
Sgm (dom (A | n)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
(Sgm (dom (A | n))) (#) (A | n) is Relation-like NAT -defined Function-like finite complex-valued set
Sum (Seq (A | n)) is V28() set
rng (Seq (A | n)) is finite V197() set
Tm is Relation-like dom A -defined dom A -valued Function-like one-to-one total quasi_total onto bijective finite complex-valued ext-real-valued real-valued natural-valued Element of bool [:(dom A),(dom A):]
Tm (#) A is Relation-like dom A -defined Function-like finite complex-valued set
Tm " n is finite set
T | (Tm " n) is Relation-like NAT -defined Tm " n -defined NAT -defined Function-like finite FinSubsequence-like complex-valued set
Seq (T | (Tm " n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued set
dom (T | (Tm " n)) is finite V197() V198() V199() V200() V201() V202() set
Sgm (dom (T | (Tm " n))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
(Sgm (dom (T | (Tm " n)))) (#) (T | (Tm " n)) is Relation-like NAT -defined Function-like finite complex-valued set
Sum (Seq (T | (Tm " n))) is V28() set
dom (Seq (T | (Tm " n))) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
[:(dom (Seq (T | (Tm " n)))),(dom (Seq (T | (Tm " n)))):] is Relation-like INT -valued RAT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(dom (Seq (T | (Tm " n)))),(dom (Seq (T | (Tm " n)))):] is finite V38() set
TM is Relation-like dom (Seq (T | (Tm " n))) -defined dom (Seq (T | (Tm " n))) -valued Function-like one-to-one total quasi_total onto bijective finite complex-valued ext-real-valued real-valued natural-valued Element of bool [:(dom (Seq (T | (Tm " n)))),(dom (Seq (T | (Tm " n)))):]
TM (#) (Seq (T | (Tm " n))) is Relation-like dom (Seq (T | (Tm " n))) -defined Function-like finite complex-valued set
rng (Seq (T | (Tm " n))) is finite V197() set
L is Relation-like NAT -defined COMPLEX -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued FinSequence of COMPLEX
addcomplex "**" L is V28() Element of COMPLEX
Tn is Relation-like NAT -defined COMPLEX -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued FinSequence of COMPLEX
addcomplex "**" Tn is V28() Element of COMPLEX
n is set
A is set
T is Relation-like NAT -defined Function-like finite FinSubsequence-like set
T | A is Relation-like NAT -defined A -defined NAT -defined Function-like finite FinSubsequence-like set
Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Tn Shift T is Relation-like NAT -defined Function-like finite FinSubsequence-like set
(Tn Shift T) | n is Relation-like NAT -defined n -defined NAT -defined Function-like finite FinSubsequence-like set
Tn Shift (T | A) is Relation-like NAT -defined Function-like finite FinSubsequence-like set
dom (Tn Shift (T | A)) is finite V197() V198() V199() V200() V201() V202() set
dom (T | A) is finite V197() V198() V199() V200() V201() V202() set
{ (Tn + b₁) where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : b₁ in dom (T | A) } is set
U is set
TMx is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Tn + TMx is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
dom T is finite V197() V198() V199() V200() V201() V202() set
((Tn Shift T) | n) . U is set
(Tn Shift T) . U is set
T . TMx is set
(T | A) . TMx is set
(Tn Shift (T | A)) . U is set
dom (Tn Shift T) is finite V197() V198() V199() V200() V201() V202() set
{ (Tn + b₁) where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : b₁ in dom T } is set
dom ((Tn Shift T) | n) is finite V197() V198() V199() V200() V201() V202() set
U is set
TMx is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Tn + TMx is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
U is set
TMx is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Tn + TMx is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
n is set
A is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
A | n is Relation-like NAT -defined n -defined NAT -defined Function-like finite FinSubsequence-like set
Seq (A | n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom (A | n) is finite V197() V198() V199() V200() V201() V202() set
Sgm (dom (A | n)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
(Sgm (dom (A | n))) (#) (A | n) is Relation-like NAT -defined Function-like finite set
len A is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
A ^ T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(A ^ T) | n is Relation-like NAT -defined n -defined NAT -defined Function-like finite FinSubsequence-like set
Seq ((A ^ T) | n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom ((A ^ T) | n) is finite V197() V198() V199() V200() V201() V202() set
Sgm (dom ((A ^ T) | n)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
(Sgm (dom ((A ^ T) | n))) (#) ((A ^ T) | n) is Relation-like NAT -defined Function-like finite set
dom (A ^ T) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
n /\ (dom (A ^ T)) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
len T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Seg (len A) is finite len A -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= len A ) } is set
(n /\ (dom (A ^ T))) /\ (Seg (len A)) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
(n /\ (dom (A ^ T))) \ (Seg (len A)) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : b₁ + (len A) in (n /\ (dom (A ^ T))) \ (Seg (len A)) } is set
tmx is set
X is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
X + (len A) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(len A) Shift T is Relation-like NAT -defined Function-like finite FinSubsequence-like set
A \/ ((len A) Shift T) is Relation-like NAT -defined finite set
tmx is V197() V198() V199() V200() V201() V202() Element of bool NAT
T | tmx is Relation-like NAT -defined tmx -defined NAT -defined Function-like finite FinSubsequence-like set
Seq (T | tmx) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom (T | tmx) is finite V197() V198() V199() V200() V201() V202() set
Sgm (dom (T | tmx)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
(Sgm (dom (T | tmx))) (#) (T | tmx) is Relation-like NAT -defined Function-like finite set
(Seq (A | n)) ^ (Seq (T | tmx)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom ((len A) Shift T) is finite V197() V198() V199() V200() V201() V202() set
(n /\ (dom (A ^ T))) /\ (dom ((len A) Shift T)) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
r is set
dom T is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
{ ((len A) + b₁) where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : b₁ in dom T } is set
B is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(len A) + B is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
1 + (len A) is non empty ordinal natural V28() real V30() V31() finite cardinal ext-real positive non negative V197() V198() V199() V200() V201() V202() Element of NAT
B + (len A) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
r is ordinal natural V28() real finite cardinal ext-real non negative set
r + (len A) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
B is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
B + (len A) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
A | ((n /\ (dom (A ^ T))) /\ (Seg (len A))) is Relation-like NAT -defined (n /\ (dom (A ^ T))) /\ (Seg (len A)) -defined NAT -defined Function-like finite FinSubsequence-like set
(len A) Shift (T | tmx) is Relation-like NAT -defined Function-like finite FinSubsequence-like set
(A | ((n /\ (dom (A ^ T))) /\ (Seg (len A)))) \/ ((len A) Shift (T | tmx)) is Relation-like NAT -defined finite set
Seq (A | ((n /\ (dom (A ^ T))) /\ (Seg (len A)))) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom (A | ((n /\ (dom (A ^ T))) /\ (Seg (len A)))) is finite V197() V198() V199() V200() V201() V202() set
Sgm (dom (A | ((n /\ (dom (A ^ T))) /\ (Seg (len A))))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
(Sgm (dom (A | ((n /\ (dom (A ^ T))) /\ (Seg (len A)))))) (#) (A | ((n /\ (dom (A ^ T))) /\ (Seg (len A)))) is Relation-like NAT -defined Function-like finite set
(Seq (A | ((n /\ (dom (A ^ T))) /\ (Seg (len A))))) ^ (Seq (T | tmx)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
r is Relation-like NAT -defined Function-like finite FinSubsequence-like set
Seq r is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom r is finite V197() V198() V199() V200() V201() V202() set
Sgm (dom r) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
(Sgm (dom r)) (#) r is Relation-like NAT -defined Function-like finite set
dom A is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
(dom (A ^ T)) /\ (Seg (len A)) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
n /\ ((dom (A ^ T)) /\ (Seg (len A))) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
A | (n /\ ((dom (A ^ T)) /\ (Seg (len A)))) is Relation-like NAT -defined n /\ ((dom (A ^ T)) /\ (Seg (len A))) -defined NAT -defined Function-like finite FinSubsequence-like set
B is set
dom T is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
Bx is ordinal natural V28() real finite cardinal ext-real non negative set
(len A) + Bx is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
{ ((len A) + b₁) where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : b₁ in dom T } is set
(A ^ T) | (n /\ (dom (A ^ T))) is Relation-like NAT -defined n /\ (dom (A ^ T)) -defined NAT -defined Function-like finite FinSubsequence-like set
id (n /\ (dom (A ^ T))) is Relation-like n /\ (dom (A ^ T)) -defined n /\ (dom (A ^ T)) -valued INT -valued RAT -valued Function-like one-to-one total quasi_total finite complex-valued ext-real-valued real-valued natural-valued increasing non-decreasing Element of bool [:(n /\ (dom (A ^ T))),(n /\ (dom (A ^ T))):]
[:(n /\ (dom (A ^ T))),(n /\ (dom (A ^ T))):] is Relation-like INT -valued RAT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(n /\ (dom (A ^ T))),(n /\ (dom (A ^ T))):] is finite V38() set
(id (n /\ (dom (A ^ T)))) (#) (A ^ T) is Relation-like n /\ (dom (A ^ T)) -defined Function-like finite set
(id (n /\ (dom (A ^ T)))) (#) A is Relation-like n /\ (dom (A ^ T)) -defined Function-like finite set
(id (n /\ (dom (A ^ T)))) (#) ((len A) Shift T) is Relation-like n /\ (dom (A ^ T)) -defined Function-like finite set
((id (n /\ (dom (A ^ T)))) (#) A) \/ ((id (n /\ (dom (A ^ T)))) (#) ((len A) Shift T)) is Relation-like n /\ (dom (A ^ T)) -defined finite set
A | (n /\ (dom (A ^ T))) is Relation-like NAT -defined n /\ (dom (A ^ T)) -defined NAT -defined Function-like finite FinSubsequence-like set
(A | (n /\ (dom (A ^ T)))) \/ ((id (n /\ (dom (A ^ T)))) (#) ((len A) Shift T)) is Relation-like n /\ (dom (A ^ T)) -defined finite set
((len A) Shift T) | (n /\ (dom (A ^ T))) is Relation-like NAT -defined n /\ (dom (A ^ T)) -defined NAT -defined Function-like finite FinSubsequence-like set
(A | (n /\ (dom (A ^ T)))) \/ (((len A) Shift T) | (n /\ (dom (A ^ T)))) is Relation-like NAT -defined finite set
((len A) Shift T) | ((n /\ (dom (A ^ T))) \ (Seg (len A))) is Relation-like NAT -defined (n /\ (dom (A ^ T))) \ (Seg (len A)) -defined NAT -defined Function-like finite FinSubsequence-like set
(A | (n /\ (dom (A ^ T)))) \/ (((len A) Shift T) | ((n /\ (dom (A ^ T))) \ (Seg (len A)))) is Relation-like NAT -defined finite set
(A | ((n /\ (dom (A ^ T))) /\ (Seg (len A)))) \/ (((len A) Shift T) | ((n /\ (dom (A ^ T))) \ (Seg (len A)))) is Relation-like NAT -defined finite set
B is ordinal natural V28() real finite cardinal ext-real non negative set
B + (len A) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
0 + (len A) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
n is set
A is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len A is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
A " n is finite set
T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
T | (A " n) is Relation-like NAT -defined A " n -defined NAT -defined Function-like finite FinSubsequence-like set
Seq (T | (A " n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom (T | (A " n)) is finite V197() V198() V199() V200() V201() V202() set
Sgm (dom (T | (A " n))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
(Sgm (dom (T | (A " n)))) (#) (T | (A " n)) is Relation-like NAT -defined Function-like finite set
Tn is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
A ^ Tn is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(A ^ Tn) " n is finite set
Tn " n is finite set
Tm is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
T ^ Tm is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(T ^ Tm) | ((A ^ Tn) " n) is Relation-like NAT -defined (A ^ Tn) " n -defined NAT -defined Function-like finite FinSubsequence-like set
Seq ((T ^ Tm) | ((A ^ Tn) " n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom ((T ^ Tm) | ((A ^ Tn) " n)) is finite V197() V198() V199() V200() V201() V202() set
Sgm (dom ((T ^ Tm) | ((A ^ Tn) " n))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
(Sgm (dom ((T ^ Tm) | ((A ^ Tn) " n)))) (#) ((T ^ Tm) | ((A ^ Tn) " n)) is Relation-like NAT -defined Function-like finite set
Tm | (Tn " n) is Relation-like NAT -defined Tn " n -defined NAT -defined Function-like finite FinSubsequence-like set
Seq (Tm | (Tn " n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom (Tm | (Tn " n)) is finite V197() V198() V199() V200() V201() V202() set
Sgm (dom (Tm | (Tn " n))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
(Sgm (dom (Tm | (Tn " n)))) (#) (Tm | (Tn " n)) is Relation-like NAT -defined Function-like finite set
(Seq (T | (A " n))) ^ (Seq (Tm | (Tn " n))) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom (T ^ Tm) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
len (T ^ Tm) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Seg (len (T ^ Tm)) is finite len (T ^ Tm) -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= len (T ^ Tm) ) } is set
dom (A ^ Tn) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
len (A ^ Tn) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Seg (len (A ^ Tn)) is finite len (A ^ Tn) -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= len (A ^ Tn) ) } is set
T | ((A ^ Tn) " n) is Relation-like NAT -defined (A ^ Tn) " n -defined NAT -defined Function-like finite FinSubsequence-like set
Seq (T | ((A ^ Tn) " n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom (T | ((A ^ Tn) " n)) is finite V197() V198() V199() V200() V201() V202() set
Sgm (dom (T | ((A ^ Tn) " n))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
(Sgm (dom (T | ((A ^ Tn) " n)))) (#) (T | ((A ^ Tn) " n)) is Relation-like NAT -defined Function-like finite set
((A ^ Tn) " n) /\ (dom (T ^ Tm)) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
U is V197() V198() V199() V200() V201() V202() Element of bool NAT
Tm | U is Relation-like NAT -defined U -defined NAT -defined Function-like finite FinSubsequence-like set
Seq (Tm | U) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom (Tm | U) is finite V197() V198() V199() V200() V201() V202() set
Sgm (dom (Tm | U)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
(Sgm (dom (Tm | U))) (#) (Tm | U) is Relation-like NAT -defined Function-like finite set
(Seq (T | ((A ^ Tn) " n))) ^ (Seq (Tm | U)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom Tm is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
U /\ (dom Tm) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
TMx is set
tmx is ordinal natural V28() real finite cardinal ext-real non negative set
tmx + (len T) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(len T) + 0 is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
dom A is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
(A ^ Tn) . (tmx + (len T)) is set
dom Tn is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
Tn . tmx is set
X is ordinal natural V28() real finite cardinal ext-real non negative set
(len A) + X is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
X is ordinal natural V28() real finite cardinal ext-real non negative set
(len A) + X is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
dom T is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
dom A is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
((A ^ Tn) " n) /\ (dom T) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
TMx is set
A . TMx is set
(A ^ Tn) . TMx is set
(len T) + (len Tm) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(len A) + (len Tn) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
TMx is set
(A ^ Tn) . TMx is set
A . TMx is set
Seg (len Tm) is finite len Tm -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= len Tm ) } is set
dom Tn is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
Seg (len Tn) is finite len Tn -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= len Tn ) } is set
TMx is set
Tn . TMx is set
tmx is ordinal natural V28() real finite cardinal ext-real non negative set
tmx + (len A) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(A ^ Tn) . (tmx + (len A)) is set
Tn . tmx is set
n is set
A is ordinal natural V28() real finite cardinal ext-real non negative set
T is ordinal natural V28() real finite cardinal ext-real non negative set
Tn is non empty set
Tn * is functional non empty FinSequence-membered FinSequenceSet of Tn
Tm is Relation-like NAT -defined Tn * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of A,T,Tn
Tm - n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
Tm " n is finite set
card (Tm " n) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
A -' (card (Tm " n)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
rng (Tm - n) is finite set
rng Tm is finite set
TM is Relation-like NAT -defined Tn * -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of Tn *
len TM is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(len Tm) - (card (Tm " n)) is V28() real V30() V31() ext-real Element of INT
(len Tm) -' (card (Tm " n)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
rng TM is finite set
L is set
x is ordinal natural V28() real finite cardinal ext-real non negative set
TMx is Relation-like NAT -defined Tn -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of Tn
len TMx is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
U is Relation-like NAT -defined Tn -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of Tn
len U is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
x is Relation-like NAT -defined Tn -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of Tn
L is Relation-like NAT -defined Tn * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of Tn *
rng L is finite set
len x is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
U is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len U is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
n is ordinal natural V28() real finite cardinal ext-real non negative set
Seg n is finite n -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= n ) } is set
[:(Seg n),(Seg n):] is Relation-like INT -valued RAT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(Seg n),(Seg n):] is finite V38() set
A is ordinal natural V28() real finite cardinal ext-real non negative set
T is Relation-like Seg n -defined Seg n -valued Function-like total quasi_total finite complex-valued ext-real-valued real-valued natural-valued Element of bool [:(Seg n),(Seg n):]
Tn is non empty set
Tn * is functional non empty FinSequence-membered FinSequenceSet of Tn
Tm is Relation-like NAT -defined Tn * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A,Tn
width Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Seg (width Tm) is finite width Tm -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= width Tm ) } is set
Tm * T is Relation-like NAT -defined Seg n -defined Tn * -valued Tn * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A,Tn
TM is ordinal natural V28() real finite cardinal ext-real non negative set
Col ((Tm * T),TM) is Relation-like NAT -defined Tn -valued Function-like finite len (Tm * T) -element FinSequence-like FinSubsequence-like Element of (len (Tm * T)) -tuples_on Tn
len (Tm * T) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(len (Tm * T)) -tuples_on Tn is functional non empty FinSequence-membered FinSequenceSet of Tn
Col (Tm,TM) is Relation-like NAT -defined Tn -valued Function-like finite len Tm -element FinSequence-like FinSubsequence-like Element of (len Tm) -tuples_on Tn
len Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(len Tm) -tuples_on Tn is functional non empty FinSequence-membered FinSequenceSet of Tn
(Col (Tm,TM)) * T is Relation-like Seg n -defined Tn -valued Function-like finite Element of bool [:(Seg n),Tn:]
[:(Seg n),Tn:] is Relation-like set
bool [:(Seg n),Tn:] is set
dom Tm is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
len (Col (Tm,TM)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
dom (Col (Tm,TM)) is finite len Tm -element V197() V198() V199() V200() V201() V202() Element of bool NAT
dom T is finite set
rng T is finite V197() V198() V199() V200() V201() V202() Element of bool REAL
dom ((Col (Tm,TM)) * T) is finite set
dom (Tm * T) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
L is set
Indices Tm is set
[:(dom Tm),(Seg (width Tm)):] is Relation-like INT -valued RAT -valued finite complex-valued ext-real-valued real-valued natural-valued set
x is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
[x,TM] is set
{x,TM} is non empty finite V38() V197() V198() V199() V200() V201() V202() set
{x} is non empty trivial finite V38() 1 -element V197() V198() V199() V200() V201() V202() set
{{x,TM},{x}} is non empty finite V38() set
T . L is ordinal natural V28() real finite cardinal ext-real non negative set
((Col (Tm,TM)) * T) . L is set
U is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(Col (Tm,TM)) . U is set
Tm * (U,TM) is Element of Tn
(Tm * T) * (x,TM) is Element of Tn
(Col ((Tm * T),TM)) . L is set
len (Col ((Tm * T),TM)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
dom (Col ((Tm * T),TM)) is finite len (Tm * T) -element V197() V198() V199() V200() V201() V202() Element of bool NAT
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is ordinal natural V28() real finite cardinal ext-real non negative set
A -' n is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
T is non empty non degenerated non trivial right_complementable almost_left_invertible V141() V143() V145() V148() V149() V150() right-distributive left-distributive right_unital well-unital V162() left_unital doubleLoopStr
the carrier of T is non empty non trivial set
the carrier of T * is functional non empty FinSequence-membered FinSequenceSet of the carrier of T
Tn is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of T
the_rank_of Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
A -VectSp_over T is non empty right_complementable V148() V149() V150() strict V165(T) V166(T) V167(T) V168(T) finite-dimensional VectSpStr over T
lines Tn is finite Element of bool the carrier of (A -VectSp_over T)
the carrier of (A -VectSp_over T) is non empty set
bool the carrier of (A -VectSp_over T) is set
len Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
the addF of (A -VectSp_over T) is Relation-like [: the carrier of (A -VectSp_over T), the carrier of (A -VectSp_over T):] -defined the carrier of (A -VectSp_over T) -valued Function-like total quasi_total Element of bool [:[: the carrier of (A -VectSp_over T), the carrier of (A -VectSp_over T):], the carrier of (A -VectSp_over T):]
[: the carrier of (A -VectSp_over T), the carrier of (A -VectSp_over T):] is Relation-like set
[:[: the carrier of (A -VectSp_over T), the carrier of (A -VectSp_over T):], the carrier of (A -VectSp_over T):] is Relation-like set
bool [:[: the carrier of (A -VectSp_over T), the carrier of (A -VectSp_over T):], the carrier of (A -VectSp_over T):] is set
the ZeroF of (A -VectSp_over T) is Relation-like Function-like Element of the carrier of (A -VectSp_over T)
the lmult of (A -VectSp_over T) is Relation-like [: the carrier of T, the carrier of (A -VectSp_over T):] -defined the carrier of (A -VectSp_over T) -valued Function-like total quasi_total Element of bool [:[: the carrier of T, the carrier of (A -VectSp_over T):], the carrier of (A -VectSp_over T):]
[: the carrier of T, the carrier of (A -VectSp_over T):] is Relation-like set
[:[: the carrier of T, the carrier of (A -VectSp_over T):], the carrier of (A -VectSp_over T):] is Relation-like set
bool [:[: the carrier of T, the carrier of (A -VectSp_over T):], the carrier of (A -VectSp_over T):] is set
VectSpStr(# the carrier of (A -VectSp_over T), the addF of (A -VectSp_over T), the ZeroF of (A -VectSp_over T), the lmult of (A -VectSp_over T) #) is non empty strict VectSpStr over T
L is Element of bool the carrier of (A -VectSp_over T)
Lin L is non empty right_complementable V148() V149() V150() strict V165(T) V166(T) V167(T) V168(T) finite-dimensional Subspace of A -VectSp_over T
x is finite Element of bool the carrier of (A -VectSp_over T)
card x is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
dim (A -VectSp_over T) is ordinal natural V28() real finite cardinal ext-real non negative set
width Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
A - n is V28() real ext-real Element of REAL
card (lines Tn) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
x \ (lines Tn) is finite Element of bool the carrier of (A -VectSp_over T)
TMx is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng TMx is finite set
tmx is Relation-like NAT -defined the carrier of (A -VectSp_over T) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (A -VectSp_over T)
len tmx is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
card (x \ (lines Tn)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(card x) - (card (lines Tn)) is V28() real V30() V31() ext-real Element of INT
FinS2MX tmx is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len tmx,A, the carrier of T
rng Tn is finite set
X is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of A -' n,A, the carrier of T
rng X is finite set
Tn ^ X is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K96(n,(A -' n)),A, the carrier of T
K96(n,(A -' n)) is ordinal natural V28() real finite cardinal ext-real non negative set
the_rank_of (Tn ^ X) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
lines (Tn ^ X) is finite Element of bool the carrier of (A -VectSp_over T)
(lines Tn) \/ (rng X) is finite set
(lines Tn) \/ x is finite Element of bool the carrier of (A -VectSp_over T)
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is ordinal natural V28() real finite cardinal ext-real non negative set
A -' n is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
T is non empty non degenerated non trivial right_complementable almost_left_invertible V141() V143() V145() V148() V149() V150() right-distributive left-distributive right_unital well-unital V162() left_unital doubleLoopStr
the carrier of T is non empty non trivial set
the carrier of T * is functional non empty FinSequence-membered FinSequenceSet of the carrier of T
Tn is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of T
the_rank_of Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
A - n is V28() real ext-real Element of REAL
1. (T,A) is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of A,A, the carrier of T
Det (1. (T,A)) is Element of the carrier of T
0. T is V64(T) Element of the carrier of T
the ZeroF of T is Element of the carrier of T
Tm is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of A -' n,A, the carrier of T
the_rank_of Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Tn ^ Tm is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K96(n,(A -' n)),A, the carrier of T
K96(n,(A -' n)) is ordinal natural V28() real finite cardinal ext-real non negative set
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is ordinal natural V28() real finite cardinal ext-real non negative set
n -' A is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
T is non empty non degenerated non trivial right_complementable almost_left_invertible V141() V143() V145() V148() V149() V150() right-distributive left-distributive right_unital well-unital V162() left_unital doubleLoopStr
the carrier of T is non empty non trivial set
the carrier of T * is functional non empty FinSequence-membered FinSequenceSet of the carrier of T
Tn is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of T
the_rank_of Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
n - A is V28() real ext-real Element of REAL
1. (T,n) is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n, the carrier of T
len (1. (T,n)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Det (1. (T,n)) is Element of the carrier of T
0. T is V64(T) Element of the carrier of T
the ZeroF of T is Element of the carrier of T
Tm is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n -' A, the carrier of T
the_rank_of Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Tn ^^ Tm is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,K418((width Tn),(width Tm)), the carrier of T
width Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
K418((width Tn),(width Tm)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
n - A is V28() real ext-real Element of REAL
width Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
the Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n -' A, the carrier of T is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n -' A, the carrier of T
Tm is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n -' A, the carrier of T
Tn ^^ Tm is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,K418((width Tn),(width Tm)), the carrier of T
width Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
K418((width Tn),(width Tm)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
the_rank_of (Tn ^^ Tm) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Tn @ is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of T *
width (Tn @) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len (Tn @) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Tm is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of A,n, the carrier of T
the_rank_of Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
TM is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n -' A,n, the carrier of T
Tm ^ TM is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K96(A,(n -' A)),n, the carrier of T
K96(A,(n -' A)) is ordinal natural V28() real finite cardinal ext-real non negative set
the_rank_of (Tm ^ TM) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width TM is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
TM @ is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of T *
len (TM @) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len TM is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width (TM @) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Tm @ is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of T *
(Tm ^ TM) @ is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of T *
L is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n -' A, the carrier of T
Tn ^^ L is Relation-like NAT -defined the carrier of T * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,K418((width Tn),(width L)), the carrier of T
width L is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
K418((width Tn),(width L)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
the_rank_of ((Tm ^ TM) @) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
the carrier of F_Real * is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
n is ordinal natural V28() real finite cardinal ext-real non negative set
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
A is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
len A is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(A) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
((A)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is ordinal natural V28() real finite cardinal ext-real non negative set
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is set
T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
0. (TOP-REAL A) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like V64( TOP-REAL A) complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
the ZeroF of (TOP-REAL A) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
TM is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(TM) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
LineVec2Mx (TM) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of 1, len (TM), the carrier of F_Real
len (TM) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(LineVec2Mx (TM)) * T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
Line (((LineVec2Mx (TM)) * T),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width ((LineVec2Mx (TM)) * T) -element FinSequence-like FinSubsequence-like Element of (width ((LineVec2Mx (TM)) * T)) -tuples_on the carrier of F_Real
width ((LineVec2Mx (TM)) * T) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(width ((LineVec2Mx (TM)) * T)) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
len TM is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width (LineVec2Mx (TM)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
REAL A is functional non empty FinSequence-membered FinSequenceSet of REAL
A -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
U is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
TM is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
x is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(x) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
len x is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
n -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
REAL n is functional non empty FinSequence-membered FinSequenceSet of REAL
L is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
L . x is set
LineVec2Mx (x) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of 1, len (x), the carrier of F_Real
len (x) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(LineVec2Mx (x)) * T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
Line (((LineVec2Mx (x)) * T),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width ((LineVec2Mx (x)) * T) -element FinSequence-like FinSubsequence-like Element of (width ((LineVec2Mx (x)) * T)) -tuples_on the carrier of F_Real
width ((LineVec2Mx (x)) * T) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(width ((LineVec2Mx (x)) * T)) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
TM is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
x is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(x) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
len x is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
L is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
L . x is set
TM is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
L is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
Tn is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
Tm is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
TM is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
Tn . TM is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
(TM) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
LineVec2Mx (TM) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of 1, len (TM), the carrier of F_Real
len (TM) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(LineVec2Mx (TM)) * T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
Line (((LineVec2Mx (TM)) * T),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width ((LineVec2Mx (TM)) * T) -element FinSequence-like FinSubsequence-like Element of (width ((LineVec2Mx (TM)) * T)) -tuples_on the carrier of F_Real
width ((LineVec2Mx (TM)) * T) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(width ((LineVec2Mx (TM)) * T)) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
Tm . TM is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
TM is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
Tn . TM is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
Tm . TM is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
TM is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Tn . TM is set
L is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Tm . L is set
x is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Tn . x is set
(x) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
LineVec2Mx (x) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of 1, len (x), the carrier of F_Real
len (x) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(LineVec2Mx (x)) * T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
Line (((LineVec2Mx (x)) * T),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width ((LineVec2Mx (x)) * T) -element FinSequence-like FinSubsequence-like Element of (width ((LineVec2Mx (x)) * T)) -tuples_on the carrier of F_Real
width ((LineVec2Mx (x)) * T) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(width ((LineVec2Mx (x)) * T)) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
U is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Tm . U is set
(U) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
LineVec2Mx (U) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of 1, len (U), the carrier of F_Real
len (U) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(LineVec2Mx (U)) * T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
Line (((LineVec2Mx (U)) * T),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width ((LineVec2Mx (U)) * T) -element FinSequence-like FinSubsequence-like Element of (width ((LineVec2Mx (U)) * T)) -tuples_on the carrier of F_Real
width ((LineVec2Mx (U)) * T) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(width ((LineVec2Mx (U)) * T)) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is ordinal natural V28() real finite cardinal ext-real non negative set
T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
(n,A,T) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is set
Tn is set
dom (n,A,T) is non empty set
rng (n,A,T) is non empty set
(n,A,T) . Tn is set
Tn is set
dom (n,A,T) is non empty set
(n,A,T) . Tn is set
Tn is set
dom (n,A,T) is non empty set
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is ordinal natural V28() real finite cardinal ext-real non negative set
T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
(n,A,T) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is set
Tn is set
(n,A,T) . Tn is set
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is ordinal natural V28() real finite cardinal ext-real non negative set
T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
(n,A,T) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is set
Tn is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(n,A,T) . Tn is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(Tn) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
len Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
n -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
REAL n is functional non empty FinSequence-membered FinSequenceSet of REAL
dom (n,A,T) is non empty set
rng (n,A,T) is non empty set
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is ordinal natural V28() real finite cardinal ext-real non negative set
T is ordinal natural V28() real finite cardinal ext-real non negative set
Tn is Relation-like NAT -defined Function-like finite T -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(Tn) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Tm is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of T,A, the carrier of F_Real
(T,A,Tm) is Relation-like the carrier of (TOP-REAL T) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL T), the carrier of (TOP-REAL A):]
TOP-REAL T is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL T) is non empty set
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
[: the carrier of (TOP-REAL T), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL T), the carrier of (TOP-REAL A):] is set
(T,A,Tm) . Tn is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
((T,A,Tm) . Tn) . n is V28() real ext-real set
Col (Tm,n) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite len Tm -element FinSequence-like FinSubsequence-like Element of (len Tm) -tuples_on the carrier of F_Real
len Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(len Tm) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
(Tn) "*" (Col (Tm,n)) is V28() real ext-real Element of the carrier of F_Real
mlt ((Tn),(Col (Tm,n))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
the multF of F_Real is Relation-like [: the carrier of F_Real, the carrier of F_Real:] -defined the carrier of F_Real -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:]
[: the carrier of F_Real, the carrier of F_Real:] is Relation-like complex-valued ext-real-valued real-valued set
[:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:] is set
K446( the carrier of F_Real, the carrier of F_Real, the carrier of F_Real, the multF of F_Real,(Tn),(Col (Tm,n))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Sum (mlt ((Tn),(Col (Tm,n)))) is V28() real ext-real Element of the carrier of F_Real
the addF of F_Real is Relation-like [: the carrier of F_Real, the carrier of F_Real:] -defined the carrier of F_Real -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:]
the addF of F_Real "**" (mlt ((Tn),(Col (Tm,n)))) is V28() real ext-real Element of the carrier of F_Real
LineVec2Mx (Tn) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of 1, len (Tn), the carrier of F_Real
len (Tn) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(LineVec2Mx (Tn)) * Tm is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
len Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width (LineVec2Mx (Tn)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width ((LineVec2Mx (Tn)) * Tm) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len (LineVec2Mx (Tn)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len ((LineVec2Mx (Tn)) * Tm) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
[1,n] is set
{1,n} is non empty finite V38() V197() V198() V199() V200() V201() V202() set
{1} is non empty trivial finite V38() 1 -element V197() V198() V199() V200() V201() V202() set
{{1,n},{1}} is non empty finite V38() set
Indices ((LineVec2Mx (Tn)) * Tm) is set
Line (((LineVec2Mx (Tn)) * Tm),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width ((LineVec2Mx (Tn)) * Tm) -element FinSequence-like FinSubsequence-like Element of (width ((LineVec2Mx (Tn)) * Tm)) -tuples_on the carrier of F_Real
(width ((LineVec2Mx (Tn)) * Tm)) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
Seg A is finite A -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= A ) } is set
((LineVec2Mx (Tn)) * Tm) * (1,n) is V28() real ext-real Element of the carrier of F_Real
Line ((LineVec2Mx (Tn)),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width (LineVec2Mx (Tn)) -element FinSequence-like FinSubsequence-like Element of (width (LineVec2Mx (Tn))) -tuples_on the carrier of F_Real
(width (LineVec2Mx (Tn))) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
(Line ((LineVec2Mx (Tn)),1)) "*" (Col (Tm,n)) is V28() real ext-real Element of the carrier of F_Real
mlt ((Line ((LineVec2Mx (Tn)),1)),(Col (Tm,n))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
K446( the carrier of F_Real, the carrier of F_Real, the carrier of F_Real, the multF of F_Real,(Line ((LineVec2Mx (Tn)),1)),(Col (Tm,n))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Sum (mlt ((Line ((LineVec2Mx (Tn)),1)),(Col (Tm,n)))) is V28() real ext-real Element of the carrier of F_Real
the addF of F_Real "**" (mlt ((Line ((LineVec2Mx (Tn)),1)),(Col (Tm,n)))) is V28() real ext-real Element of the carrier of F_Real
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is non empty non degenerated non trivial right_complementable almost_left_invertible V141() V143() V145() V148() V149() V150() right-distributive left-distributive right_unital well-unital V162() left_unital doubleLoopStr
1. (A,n) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n, the carrier of A
the carrier of A is non empty non trivial set
the carrier of A * is functional non empty FinSequence-membered FinSequenceSet of the carrier of A
MX2FinS (1. (A,n)) is Relation-like NAT -defined the carrier of (n -VectSp_over A) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (n -VectSp_over A)
n -VectSp_over A is non empty right_complementable V148() V149() V150() strict V165(A) V166(A) V167(A) V168(A) finite-dimensional VectSpStr over A
the carrier of (n -VectSp_over A) is non empty set
len (MX2FinS (1. (A,n))) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
dim (n -VectSp_over A) is ordinal natural V28() real finite cardinal ext-real non negative set
n is ordinal natural V28() real finite cardinal ext-real non negative set
n -VectSp_over F_Real is non empty right_complementable V148() V149() V150() strict V165( F_Real ) V166( F_Real ) V167( F_Real ) V168( F_Real ) finite-dimensional VectSpStr over F_Real
the carrier of (n -VectSp_over F_Real) is non empty set
1. (F_Real,n) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n, the carrier of F_Real
MX2FinS (1. (F_Real,n)) is Relation-like NAT -defined the carrier of (n -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (n -VectSp_over F_Real)
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
A is ordinal natural V28() real finite cardinal ext-real non negative set
A -VectSp_over F_Real is non empty right_complementable V148() V149() V150() strict V165( F_Real ) V166( F_Real ) V167( F_Real ) V168( F_Real ) finite-dimensional VectSpStr over F_Real
the carrier of (A -VectSp_over F_Real) is non empty set
1. (F_Real,A) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of A,A, the carrier of F_Real
MX2FinS (1. (F_Real,A)) is Relation-like NAT -defined the carrier of (A -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (A -VectSp_over F_Real)
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
(n,A,T) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is set
Tn is Relation-like NAT -defined the carrier of (n -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of n -VectSp_over F_Real
len Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Tm is Relation-like NAT -defined the carrier of (A -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of A -VectSp_over F_Real
len Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
L is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len Tn, len Tm, the carrier of F_Real
Mx2Tran (L,Tn,Tm) is Relation-like the carrier of (n -VectSp_over F_Real) -defined the carrier of (A -VectSp_over F_Real) -valued Function-like non empty total quasi_total V170(n -VectSp_over F_Real,A -VectSp_over F_Real) V213( F_Real ,n -VectSp_over F_Real,A -VectSp_over F_Real) Element of bool [: the carrier of (n -VectSp_over F_Real), the carrier of (A -VectSp_over F_Real):]
[: the carrier of (n -VectSp_over F_Real), the carrier of (A -VectSp_over F_Real):] is Relation-like set
bool [: the carrier of (n -VectSp_over F_Real), the carrier of (A -VectSp_over F_Real):] is set
dom (Mx2Tran (L,Tn,Tm)) is non empty set
REAL n is functional non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
dom (n,A,T) is non empty set
U is set
(n,A,T) . U is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(Mx2Tran (L,Tn,Tm)) . U is set
TMx is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(TMx) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
LineVec2Mx (TMx) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of 1, len (TMx), the carrier of F_Real
len (TMx) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len TMx is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len (LineVec2Mx (TMx)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width (LineVec2Mx (TMx)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
tmx is Relation-like Function-like Element of the carrier of (n -VectSp_over F_Real)
(Mx2Tran (L,Tn,Tm)) . tmx is Relation-like Function-like Element of the carrier of (A -VectSp_over F_Real)
0. (A -VectSp_over F_Real) is Relation-like Function-like V64(A -VectSp_over F_Real) Element of the carrier of (A -VectSp_over F_Real)
the ZeroF of (A -VectSp_over F_Real) is Relation-like Function-like Element of the carrier of (A -VectSp_over F_Real)
0. F_Real is V28() real V64( F_Real ) ext-real Element of the carrier of F_Real
the ZeroF of F_Real is V28() real ext-real Element of the carrier of F_Real
A |-> (0. F_Real) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of A -tuples_on the carrier of F_Real
A -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
0* A is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of REAL A
REAL A is functional non empty FinSequence-membered FinSequenceSet of REAL
A -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
A |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of A -tuples_on REAL
0. (TOP-REAL A) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like V64( TOP-REAL A) complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
the ZeroF of (TOP-REAL A) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
(n,A,T) . TMx is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
tmx is Relation-like Function-like Element of the carrier of (n -VectSp_over F_Real)
(Mx2Tran (L,Tn,Tm)) . tmx is Relation-like Function-like Element of the carrier of (A -VectSp_over F_Real)
((Mx2Tran (L,Tn,Tm)) . tmx) |-- Tm is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
tmx |-- Tn is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
AutMt ((Mx2Tran (L,Tn,Tm)),Tn,Tm) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len Tn, len Tm, the carrier of F_Real
dom (LineVec2Mx (TMx)) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
len T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(LineVec2Mx (TMx)) * T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
Line (((LineVec2Mx (TMx)) * T),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width ((LineVec2Mx (TMx)) * T) -element FinSequence-like FinSubsequence-like Element of (width ((LineVec2Mx (TMx)) * T)) -tuples_on the carrier of F_Real
width ((LineVec2Mx (TMx)) * T) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(width ((LineVec2Mx (TMx)) * T)) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
LineVec2Mx (Line (((LineVec2Mx (TMx)) * T),1)) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of 1, len (Line (((LineVec2Mx (TMx)) * T),1)), the carrier of F_Real
len (Line (((LineVec2Mx (TMx)) * T),1)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Line ((LineVec2Mx (TMx)),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width (LineVec2Mx (TMx)) -element FinSequence-like FinSubsequence-like Element of (width (LineVec2Mx (TMx))) -tuples_on the carrier of F_Real
(width (LineVec2Mx (TMx))) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
LineVec2Mx (Line ((LineVec2Mx (TMx)),1)) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of 1, len (Line ((LineVec2Mx (TMx)),1)), the carrier of F_Real
len (Line ((LineVec2Mx (TMx)),1)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(LineVec2Mx (Line ((LineVec2Mx (TMx)),1))) * T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
LineVec2Mx (((Mx2Tran (L,Tn,Tm)) . tmx) |-- Tm) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of 1, len (((Mx2Tran (L,Tn,Tm)) . tmx) |-- Tm), the carrier of F_Real
len (((Mx2Tran (L,Tn,Tm)) . tmx) |-- Tm) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Line ((LineVec2Mx (Line (((LineVec2Mx (TMx)) * T),1))),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width (LineVec2Mx (Line (((LineVec2Mx (TMx)) * T),1))) -element FinSequence-like FinSubsequence-like Element of (width (LineVec2Mx (Line (((LineVec2Mx (TMx)) * T),1)))) -tuples_on the carrier of F_Real
width (LineVec2Mx (Line (((LineVec2Mx (TMx)) * T),1))) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(width (LineVec2Mx (Line (((LineVec2Mx (TMx)) * T),1)))) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is ordinal natural V28() real finite cardinal ext-real non negative set
Seg A is finite A -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= A ) } is set
[:(Seg A),(Seg A):] is Relation-like INT -valued RAT -valued finite complex-valued ext-real-valued real-valued natural-valued set
bool [:(Seg A),(Seg A):] is finite V38() set
T is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Tn is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of A,n, the carrier of F_Real
(A,n,Tn) is Relation-like the carrier of (TOP-REAL A) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL A), the carrier of (TOP-REAL n):]
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
[: the carrier of (TOP-REAL A), the carrier of (TOP-REAL n):] is Relation-like set
bool [: the carrier of (TOP-REAL A), the carrier of (TOP-REAL n):] is set
(A,n,Tn) . T is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Tm is Relation-like Seg A -defined Seg A -valued Function-like one-to-one total quasi_total onto bijective finite complex-valued ext-real-valued real-valued natural-valued Element of bool [:(Seg A),(Seg A):]
Tn * Tm is Relation-like NAT -defined Seg A -defined the carrier of F_Real * -valued the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of A,n, the carrier of F_Real
(A,n,(Tn * Tm)) is Relation-like the carrier of (TOP-REAL A) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL A), the carrier of (TOP-REAL n):]
Tm (#) T is Relation-like Seg A -defined Function-like finite complex-valued ext-real-valued real-valued set
(A,n,(Tn * Tm)) . (Tm (#) T) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
len T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
rng Tm is finite V197() V198() V199() V200() V201() V202() Element of bool REAL
dom T is finite A -element V197() V198() V199() V200() V201() V202() Element of bool NAT
dom Tm is finite set
dom (Tm (#) T) is finite set
rng (Tm (#) T) is finite V197() V198() V199() Element of bool REAL
rng T is finite V197() V198() V199() Element of bool REAL
TM is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
L is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len L is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
U is ordinal natural V28() real finite cardinal ext-real non negative set
Seg n is finite n -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= n ) } is set
(L) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Col ((Tn * Tm),U) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite len (Tn * Tm) -element FinSequence-like FinSubsequence-like Element of (len (Tn * Tm)) -tuples_on the carrier of F_Real
len (Tn * Tm) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(len (Tn * Tm)) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
mlt ((L),(Col ((Tn * Tm),U))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
the multF of F_Real is Relation-like [: the carrier of F_Real, the carrier of F_Real:] -defined the carrier of F_Real -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:]
[: the carrier of F_Real, the carrier of F_Real:] is Relation-like complex-valued ext-real-valued real-valued set
[:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:] is set
K446( the carrier of F_Real, the carrier of F_Real, the carrier of F_Real, the multF of F_Real,(L),(Col ((Tn * Tm),U))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Col (Tn,U) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite len Tn -element FinSequence-like FinSubsequence-like Element of (len Tn) -tuples_on the carrier of F_Real
(len Tn) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
(Col (Tn,U)) * Tm is Relation-like Seg A -defined the carrier of F_Real -valued Function-like finite complex-valued ext-real-valued real-valued Element of bool [:(Seg A), the carrier of F_Real:]
[:(Seg A), the carrier of F_Real:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg A), the carrier of F_Real:] is set
the multF of F_Real .: (L,((Col (Tn,U)) * Tm)) is set
(T) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
mlt ((T),(Col (Tn,U))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
K446( the carrier of F_Real, the carrier of F_Real, the carrier of F_Real, the multF of F_Real,(T),(Col (Tn,U))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
(mlt ((T),(Col (Tn,U)))) * Tm is Relation-like Seg A -defined the carrier of F_Real -valued Function-like finite complex-valued ext-real-valued real-valued Element of bool [:(Seg A), the carrier of F_Real:]
len (Col (Tn,U)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len (mlt ((T),(Col (Tn,U)))) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
dom (mlt ((T),(Col (Tn,U)))) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
(A,n,(Tn * Tm)) . L is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
((A,n,(Tn * Tm)) . L) . U is V28() real ext-real set
(L) "*" (Col ((Tn * Tm),U)) is V28() real ext-real Element of the carrier of F_Real
Sum (mlt ((L),(Col ((Tn * Tm),U)))) is V28() real ext-real Element of the carrier of F_Real
the addF of F_Real is Relation-like [: the carrier of F_Real, the carrier of F_Real:] -defined the carrier of F_Real -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:]
the addF of F_Real "**" (mlt ((L),(Col ((Tn * Tm),U)))) is V28() real ext-real Element of the carrier of F_Real
(T) "*" (Col (Tn,U)) is V28() real ext-real Element of the carrier of F_Real
Sum (mlt ((T),(Col (Tn,U)))) is V28() real ext-real Element of the carrier of F_Real
the addF of F_Real "**" (mlt ((T),(Col (Tn,U)))) is V28() real ext-real Element of the carrier of F_Real
((A,n,Tn) . T) . U is V28() real ext-real set
len ((A,n,Tn) . T) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len ((A,n,(Tn * Tm)) . L) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
0. (TOP-REAL n) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like V64( TOP-REAL n) complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
the ZeroF of (TOP-REAL n) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is ordinal natural V28() real finite cardinal ext-real non negative set
T is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Tn is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
T + Tn is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Tm is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
(n,A,Tm) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is set
(n,A,Tm) . (T + Tn) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(n,A,Tm) . T is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(n,A,Tm) . Tn is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
((n,A,Tm) . T) + ((n,A,Tm) . Tn) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
0.REAL 0 is Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty ordinal natural V28() real finite finite-yielding V38() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V197() V198() V199() V200() V201() V202() V203() Element of the carrier of (TOP-REAL 0)
0 |-> 0 is Relation-like non-empty empty-yielding NAT -defined REAL -valued Function-like one-to-one constant functional empty ordinal natural V28() real finite finite-yielding V38() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V197() V198() V199() V200() V201() V202() V203() Element of 0 -tuples_on REAL
len Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(Tn) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
LineVec2Mx (Tn) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of 1, len (Tn), the carrier of F_Real
len (Tn) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(T) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
LineVec2Mx (T) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of 1, len (T), the carrier of F_Real
len (T) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len (LineVec2Mx (Tn)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width (LineVec2Mx (Tn)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(LineVec2Mx (Tn)) * Tm is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
width ((LineVec2Mx (Tn)) * Tm) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width (LineVec2Mx (T)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(LineVec2Mx (T)) * Tm is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
width ((LineVec2Mx (T)) * Tm) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len (LineVec2Mx (T)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len ((LineVec2Mx (T)) * Tm) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
[1,1] is set
{1,1} is non empty finite V38() V197() V198() V199() V200() V201() V202() set
{1} is non empty trivial finite V38() 1 -element V197() V198() V199() V200() V201() V202() set
{{1,1},{1}} is non empty finite V38() set
Indices ((LineVec2Mx (T)) * Tm) is set
(((n,A,Tm) . T)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Line (((LineVec2Mx (T)) * Tm),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width ((LineVec2Mx (T)) * Tm) -element FinSequence-like FinSubsequence-like Element of (width ((LineVec2Mx (T)) * Tm)) -tuples_on the carrier of F_Real
(width ((LineVec2Mx (T)) * Tm)) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
(((n,A,Tm) . Tn)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Line (((LineVec2Mx (Tn)) * Tm),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width ((LineVec2Mx (Tn)) * Tm) -element FinSequence-like FinSubsequence-like Element of (width ((LineVec2Mx (Tn)) * Tm)) -tuples_on the carrier of F_Real
(width ((LineVec2Mx (Tn)) * Tm)) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
((T + Tn)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
(T) + (Tn) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
the addF of F_Real is Relation-like [: the carrier of F_Real, the carrier of F_Real:] -defined the carrier of F_Real -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:]
[: the carrier of F_Real, the carrier of F_Real:] is Relation-like complex-valued ext-real-valued real-valued set
[:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:] is set
K446( the carrier of F_Real, the carrier of F_Real, the carrier of F_Real, the addF of F_Real,(T),(Tn)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
LineVec2Mx ((T + Tn)) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of 1, len ((T + Tn)), the carrier of F_Real
len ((T + Tn)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(LineVec2Mx ((T + Tn))) * Tm is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
(LineVec2Mx (T)) + (LineVec2Mx (Tn)) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of 1, len (T), the carrier of F_Real
((LineVec2Mx (T)) + (LineVec2Mx (Tn))) * Tm is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
((LineVec2Mx (T)) * Tm) + ((LineVec2Mx (Tn)) * Tm) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
Line ((((LineVec2Mx (T)) * Tm) + ((LineVec2Mx (Tn)) * Tm)),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width (((LineVec2Mx (T)) * Tm) + ((LineVec2Mx (Tn)) * Tm)) -element FinSequence-like FinSubsequence-like Element of (width (((LineVec2Mx (T)) * Tm) + ((LineVec2Mx (Tn)) * Tm))) -tuples_on the carrier of F_Real
width (((LineVec2Mx (T)) * Tm) + ((LineVec2Mx (Tn)) * Tm)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(width (((LineVec2Mx (T)) * Tm) + ((LineVec2Mx (Tn)) * Tm))) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
(Line (((LineVec2Mx (T)) * Tm),1)) + (Line (((LineVec2Mx (Tn)) * Tm),1)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
K446( the carrier of F_Real, the carrier of F_Real, the carrier of F_Real, the addF of F_Real,(Line (((LineVec2Mx (T)) * Tm),1)),(Line (((LineVec2Mx (Tn)) * Tm),1))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
0. (TOP-REAL A) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like V64( TOP-REAL A) complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
the ZeroF of (TOP-REAL A) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
0* A is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of REAL A
REAL A is functional non empty FinSequence-membered FinSequenceSet of REAL
A -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
A |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of A -tuples_on REAL
0 + 0 is Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty ordinal natural V28() real V30() V31() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V197() V198() V199() V200() V201() V202() V203() Element of NAT
A |-> (0 + 0) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of A -tuples_on REAL
(A |-> 0) + (A |-> 0) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of A -tuples_on REAL
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is ordinal natural V28() real finite cardinal ext-real non negative set
T is V28() real ext-real set
Tn is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
T * Tn is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Tm is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
(n,A,Tm) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is set
(n,A,Tm) . (T * Tn) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(n,A,Tm) . Tn is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
T * ((n,A,Tm) . Tn) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
0.REAL 0 is Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty ordinal natural V28() real finite finite-yielding V38() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V197() V198() V199() V200() V201() V202() V203() Element of the carrier of (TOP-REAL 0)
0 |-> 0 is Relation-like non-empty empty-yielding NAT -defined REAL -valued Function-like one-to-one constant functional empty ordinal natural V28() real finite finite-yielding V38() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V197() V198() V199() V200() V201() V202() V203() Element of 0 -tuples_on REAL
((T * Tn)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
LineVec2Mx ((T * Tn)) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of 1, len ((T * Tn)), the carrier of F_Real
len ((T * Tn)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(Tn) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
LineVec2Mx (Tn) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of 1, len (Tn), the carrier of F_Real
len (Tn) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
x is V28() real ext-real Element of the carrier of F_Real
x * (Tn) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
x multfield is Relation-like the carrier of F_Real -defined the carrier of F_Real -valued Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of bool [: the carrier of F_Real, the carrier of F_Real:]
[: the carrier of F_Real, the carrier of F_Real:] is Relation-like complex-valued ext-real-valued real-valued set
bool [: the carrier of F_Real, the carrier of F_Real:] is set
the multF of F_Real is Relation-like [: the carrier of F_Real, the carrier of F_Real:] -defined the carrier of F_Real -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:]
[:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:] is set
id the carrier of F_Real is Relation-like the carrier of F_Real -defined the carrier of F_Real -valued Function-like one-to-one non empty total quasi_total complex-valued ext-real-valued real-valued increasing non-decreasing Element of bool [: the carrier of F_Real, the carrier of F_Real:]
the multF of F_Real [;] (x,(id the carrier of F_Real)) is Relation-like the carrier of F_Real -defined the carrier of F_Real -valued Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of bool [: the carrier of F_Real, the carrier of F_Real:]
K449( the carrier of F_Real, the carrier of F_Real,(Tn),(x multfield)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
len Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width (LineVec2Mx (Tn)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len (LineVec2Mx (Tn)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(LineVec2Mx (Tn)) * Tm is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
len ((LineVec2Mx (Tn)) * Tm) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(n,A,Tm) . (Tn) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Line (((LineVec2Mx (Tn)) * Tm),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width ((LineVec2Mx (Tn)) * Tm) -element FinSequence-like FinSubsequence-like Element of (width ((LineVec2Mx (Tn)) * Tm)) -tuples_on the carrier of F_Real
width ((LineVec2Mx (Tn)) * Tm) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(width ((LineVec2Mx (Tn)) * Tm)) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
x * (Line (((LineVec2Mx (Tn)) * Tm),1)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width ((LineVec2Mx (Tn)) * Tm) -element FinSequence-like FinSubsequence-like Element of (width ((LineVec2Mx (Tn)) * Tm)) -tuples_on the carrier of F_Real
K449( the carrier of F_Real, the carrier of F_Real,(Line (((LineVec2Mx (Tn)) * Tm),1)),(x multfield)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
x * ((LineVec2Mx (Tn)) * Tm) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
Line ((x * ((LineVec2Mx (Tn)) * Tm)),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width (x * ((LineVec2Mx (Tn)) * Tm)) -element FinSequence-like FinSubsequence-like Element of (width (x * ((LineVec2Mx (Tn)) * Tm))) -tuples_on the carrier of F_Real
width (x * ((LineVec2Mx (Tn)) * Tm)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(width (x * ((LineVec2Mx (Tn)) * Tm))) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
x * (LineVec2Mx (Tn)) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of 1, len (Tn), the carrier of F_Real
(x * (LineVec2Mx (Tn))) * Tm is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
Line (((x * (LineVec2Mx (Tn))) * Tm),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width ((x * (LineVec2Mx (Tn))) * Tm) -element FinSequence-like FinSubsequence-like Element of (width ((x * (LineVec2Mx (Tn))) * Tm)) -tuples_on the carrier of F_Real
width ((x * (LineVec2Mx (Tn))) * Tm) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(width ((x * (LineVec2Mx (Tn))) * Tm)) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
(LineVec2Mx ((T * Tn))) * Tm is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
Line (((LineVec2Mx ((T * Tn))) * Tm),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width ((LineVec2Mx ((T * Tn))) * Tm) -element FinSequence-like FinSubsequence-like Element of (width ((LineVec2Mx ((T * Tn))) * Tm)) -tuples_on the carrier of F_Real
width ((LineVec2Mx ((T * Tn))) * Tm) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(width ((LineVec2Mx ((T * Tn))) * Tm)) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
0. (TOP-REAL A) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like V64( TOP-REAL A) complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
the ZeroF of (TOP-REAL A) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
0* A is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of REAL A
REAL A is functional non empty FinSequence-membered FinSequenceSet of REAL
A -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
A |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of A -tuples_on REAL
T * 0 is V28() real ext-real Element of REAL
A |-> (T * 0) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of A -tuples_on REAL
T * (A |-> 0) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of A -tuples_on REAL
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is ordinal natural V28() real finite cardinal ext-real non negative set
T is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Tn is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
T - Tn is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Tm is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
(n,A,Tm) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is set
(n,A,Tm) . (T - Tn) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(n,A,Tm) . T is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(n,A,Tm) . Tn is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
((n,A,Tm) . T) - ((n,A,Tm) . Tn) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
- Tn is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
T + (- Tn) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * Tn is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
T + ((- 1) * Tn) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(n,A,Tm) . ((- 1) * Tn) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
((n,A,Tm) . T) + ((n,A,Tm) . ((- 1) * Tn)) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(- 1) * ((n,A,Tm) . Tn) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((n,A,Tm) . T) + ((- 1) * ((n,A,Tm) . Tn)) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
- ((n,A,Tm) . Tn) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((n,A,Tm) . T) + (- ((n,A,Tm) . Tn)) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is ordinal natural V28() real finite cardinal ext-real non negative set
T is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Tn is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
(n,A,Tn) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is set
(n,A,Tn) . T is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Tm is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
Tn + Tm is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
(n,A,(Tn + Tm)) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
(n,A,(Tn + Tm)) . T is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(n,A,Tm) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
(n,A,Tm) . T is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
((n,A,Tn) . T) + ((n,A,Tm) . T) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
0.REAL 0 is Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty ordinal natural V28() real finite finite-yielding V38() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V197() V198() V199() V200() V201() V202() V203() Element of the carrier of (TOP-REAL 0)
0 |-> 0 is Relation-like non-empty empty-yielding NAT -defined REAL -valued Function-like one-to-one constant functional empty ordinal natural V28() real finite finite-yielding V38() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V197() V198() V199() V200() V201() V202() V203() Element of 0 -tuples_on REAL
(T) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
LineVec2Mx (T) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of 1, len (T), the carrier of F_Real
len (T) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width (LineVec2Mx (T)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(LineVec2Mx (T)) * Tm is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
width ((LineVec2Mx (T)) * Tm) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(LineVec2Mx (T)) * Tn is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
width ((LineVec2Mx (T)) * Tn) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len (LineVec2Mx (T)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len ((LineVec2Mx (T)) * Tn) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
[1,1] is set
{1,1} is non empty finite V38() V197() V198() V199() V200() V201() V202() set
{1} is non empty trivial finite V38() 1 -element V197() V198() V199() V200() V201() V202() set
{{1,1},{1}} is non empty finite V38() set
Indices ((LineVec2Mx (T)) * Tn) is set
(((n,A,Tn) . T)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Line (((LineVec2Mx (T)) * Tn),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width ((LineVec2Mx (T)) * Tn) -element FinSequence-like FinSubsequence-like Element of (width ((LineVec2Mx (T)) * Tn)) -tuples_on the carrier of F_Real
(width ((LineVec2Mx (T)) * Tn)) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
(((n,A,Tm) . T)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Line (((LineVec2Mx (T)) * Tm),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width ((LineVec2Mx (T)) * Tm) -element FinSequence-like FinSubsequence-like Element of (width ((LineVec2Mx (T)) * Tm)) -tuples_on the carrier of F_Real
(width ((LineVec2Mx (T)) * Tm)) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
(Line (((LineVec2Mx (T)) * Tn),1)) + (Line (((LineVec2Mx (T)) * Tm),1)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
the addF of F_Real is Relation-like [: the carrier of F_Real, the carrier of F_Real:] -defined the carrier of F_Real -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:]
[: the carrier of F_Real, the carrier of F_Real:] is Relation-like complex-valued ext-real-valued real-valued set
[:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:] is set
K446( the carrier of F_Real, the carrier of F_Real, the carrier of F_Real, the addF of F_Real,(Line (((LineVec2Mx (T)) * Tn),1)),(Line (((LineVec2Mx (T)) * Tm),1))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
((LineVec2Mx (T)) * Tn) + ((LineVec2Mx (T)) * Tm) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
Line ((((LineVec2Mx (T)) * Tn) + ((LineVec2Mx (T)) * Tm)),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width (((LineVec2Mx (T)) * Tn) + ((LineVec2Mx (T)) * Tm)) -element FinSequence-like FinSubsequence-like Element of (width (((LineVec2Mx (T)) * Tn) + ((LineVec2Mx (T)) * Tm))) -tuples_on the carrier of F_Real
width (((LineVec2Mx (T)) * Tn) + ((LineVec2Mx (T)) * Tm)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(width (((LineVec2Mx (T)) * Tn) + ((LineVec2Mx (T)) * Tm))) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
(LineVec2Mx (T)) * (Tn + Tm) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
Line (((LineVec2Mx (T)) * (Tn + Tm)),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width ((LineVec2Mx (T)) * (Tn + Tm)) -element FinSequence-like FinSubsequence-like Element of (width ((LineVec2Mx (T)) * (Tn + Tm))) -tuples_on the carrier of F_Real
width ((LineVec2Mx (T)) * (Tn + Tm)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(width ((LineVec2Mx (T)) * (Tn + Tm))) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
0. (TOP-REAL A) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like V64( TOP-REAL A) complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
the ZeroF of (TOP-REAL A) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
0* A is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of REAL A
REAL A is functional non empty FinSequence-membered FinSequenceSet of REAL
A -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
A |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of A -tuples_on REAL
0 + 0 is Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty ordinal natural V28() real V30() V31() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V197() V198() V199() V200() V201() V202() V203() Element of NAT
A |-> (0 + 0) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of A -tuples_on REAL
(A |-> 0) + (A |-> 0) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of A -tuples_on REAL
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is ordinal natural V28() real finite cardinal ext-real non negative set
T is V28() real ext-real set
Tn is V28() real ext-real Element of the carrier of F_Real
Tm is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
TM is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
(n,A,TM) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is set
(n,A,TM) . Tm is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
T * ((n,A,TM) . Tm) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Tn * TM is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
(n,A,(Tn * TM)) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
(n,A,(Tn * TM)) . Tm is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(Tm) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
LineVec2Mx (Tm) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of 1, len (Tm), the carrier of F_Real
len (Tm) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len TM is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width (LineVec2Mx (Tm)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len (LineVec2Mx (Tm)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(LineVec2Mx (Tm)) * TM is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
len ((LineVec2Mx (Tm)) * TM) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Line (((LineVec2Mx (Tm)) * TM),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width ((LineVec2Mx (Tm)) * TM) -element FinSequence-like FinSubsequence-like Element of (width ((LineVec2Mx (Tm)) * TM)) -tuples_on the carrier of F_Real
width ((LineVec2Mx (Tm)) * TM) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(width ((LineVec2Mx (Tm)) * TM)) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
Tn * (Line (((LineVec2Mx (Tm)) * TM),1)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width ((LineVec2Mx (Tm)) * TM) -element FinSequence-like FinSubsequence-like Element of (width ((LineVec2Mx (Tm)) * TM)) -tuples_on the carrier of F_Real
Tn multfield is Relation-like the carrier of F_Real -defined the carrier of F_Real -valued Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of bool [: the carrier of F_Real, the carrier of F_Real:]
[: the carrier of F_Real, the carrier of F_Real:] is Relation-like complex-valued ext-real-valued real-valued set
bool [: the carrier of F_Real, the carrier of F_Real:] is set
the multF of F_Real is Relation-like [: the carrier of F_Real, the carrier of F_Real:] -defined the carrier of F_Real -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:]
[:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:] is set
id the carrier of F_Real is Relation-like the carrier of F_Real -defined the carrier of F_Real -valued Function-like one-to-one non empty total quasi_total complex-valued ext-real-valued real-valued increasing non-decreasing Element of bool [: the carrier of F_Real, the carrier of F_Real:]
the multF of F_Real [;] (Tn,(id the carrier of F_Real)) is Relation-like the carrier of F_Real -defined the carrier of F_Real -valued Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of bool [: the carrier of F_Real, the carrier of F_Real:]
K449( the carrier of F_Real, the carrier of F_Real,(Line (((LineVec2Mx (Tm)) * TM),1)),(Tn multfield)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Tn * ((LineVec2Mx (Tm)) * TM) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
Line ((Tn * ((LineVec2Mx (Tm)) * TM)),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width (Tn * ((LineVec2Mx (Tm)) * TM)) -element FinSequence-like FinSubsequence-like Element of (width (Tn * ((LineVec2Mx (Tm)) * TM))) -tuples_on the carrier of F_Real
width (Tn * ((LineVec2Mx (Tm)) * TM)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(width (Tn * ((LineVec2Mx (Tm)) * TM))) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
(LineVec2Mx (Tm)) * (Tn * TM) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
Line (((LineVec2Mx (Tm)) * (Tn * TM)),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width ((LineVec2Mx (Tm)) * (Tn * TM)) -element FinSequence-like FinSubsequence-like Element of (width ((LineVec2Mx (Tm)) * (Tn * TM))) -tuples_on the carrier of F_Real
width ((LineVec2Mx (Tm)) * (Tn * TM)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(width ((LineVec2Mx (Tm)) * (Tn * TM))) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
0. (TOP-REAL A) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like V64( TOP-REAL A) complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
the ZeroF of (TOP-REAL A) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
0* A is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of REAL A
REAL A is functional non empty FinSequence-membered FinSequenceSet of REAL
A -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
A |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of A -tuples_on REAL
T * (A |-> 0) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of A -tuples_on REAL
T * 0 is V28() real ext-real Element of REAL
A |-> (T * 0) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of A -tuples_on REAL
n is ordinal natural V28() real finite cardinal ext-real non negative set
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
A is ordinal natural V28() real finite cardinal ext-real non negative set
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
Tm is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
(n,A,Tm) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is set
T is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
Tn is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
T + Tn is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
T + Tn is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(n,A,Tm) . (T + Tn) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
(n,A,Tm) . T is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
(n,A,Tm) . Tn is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
((n,A,Tm) . T) + ((n,A,Tm) . Tn) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
((n,A,Tm) . T) + ((n,A,Tm) . Tn) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
n is ordinal natural V28() real finite cardinal ext-real non negative set
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
A is ordinal natural V28() real finite cardinal ext-real non negative set
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
Tm is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
(n,A,Tm) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is set
T is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
Tn is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
T - Tn is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
T - Tn is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(n,A,Tm) . (T - Tn) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
(n,A,Tm) . T is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
(n,A,Tm) . Tn is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
((n,A,Tm) . T) - ((n,A,Tm) . Tn) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
((n,A,Tm) . T) - ((n,A,Tm) . Tn) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
n is ordinal natural V28() real finite cardinal ext-real non negative set
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
0. (TOP-REAL n) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like V64( TOP-REAL n) complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
the ZeroF of (TOP-REAL n) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
A is ordinal natural V28() real finite cardinal ext-real non negative set
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
0. (TOP-REAL A) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like V64( TOP-REAL A) complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
the ZeroF of (TOP-REAL A) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
(n,A,T) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is set
(n,A,T) . (0. (TOP-REAL n)) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
the Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
the Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n) - the Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
the Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n) - the Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(n,A,T) . the Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
((n,A,T) . the Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)) - ((n,A,T) . the Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
((n,A,T) . the Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)) - ((n,A,T) . the Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
n is ordinal natural V28() real finite cardinal ext-real non negative set
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
A is ordinal natural V28() real finite cardinal ext-real non negative set
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
bool the carrier of (TOP-REAL A) is set
T is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
Tn is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of A,n, the carrier of F_Real
(A,n,Tn) is Relation-like the carrier of (TOP-REAL A) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL A), the carrier of (TOP-REAL n):]
[: the carrier of (TOP-REAL A), the carrier of (TOP-REAL n):] is Relation-like set
bool [: the carrier of (TOP-REAL A), the carrier of (TOP-REAL n):] is set
(A,n,Tn) . T is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
x is Element of bool the carrier of (TOP-REAL A)
T + x is Element of bool the carrier of (TOP-REAL A)
(A,n,Tn) .: (T + x) is Element of bool the carrier of (TOP-REAL n)
bool the carrier of (TOP-REAL n) is set
(A,n,Tn) .: x is Element of bool the carrier of (TOP-REAL n)
((A,n,Tn) . T) + ((A,n,Tn) .: x) is Element of bool the carrier of (TOP-REAL n)
dom (A,n,Tn) is non empty set
[#] (TOP-REAL A) is non empty non proper Element of bool the carrier of (TOP-REAL A)
U is set
TMx is set
(A,n,Tn) . TMx is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
{ (T + b₁) where b₁ is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A) : b₁ in x } is set
tmx is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
T + tmx is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
T + tmx is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(A,n,Tn) . tmx is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((A,n,Tn) . T) + ((A,n,Tn) . tmx) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((A,n,Tn) . T) + ((A,n,Tn) . tmx) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
{ (((A,n,Tn) . T) + b₁) where b₁ is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n) : b₁ in (A,n,Tn) .: x } is set
U is set
{ (((A,n,Tn) . T) + b₁) where b₁ is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n) : b₁ in (A,n,Tn) .: x } is set
TMx is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((A,n,Tn) . T) + TMx is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((A,n,Tn) . T) + TMx is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
tmx is set
(A,n,Tn) . tmx is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
X is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
T + X is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
T + X is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
{ (T + b₁) where b₁ is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A) : b₁ in x } is set
(A,n,Tn) . (T + X) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
n is ordinal natural V28() real finite cardinal ext-real non negative set
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
A is ordinal natural V28() real finite cardinal ext-real non negative set
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
bool the carrier of (TOP-REAL A) is set
T is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
Tn is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
(n,A,Tn) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is set
(n,A,Tn) . T is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
x is Element of bool the carrier of (TOP-REAL A)
((n,A,Tn) . T) + x is Element of bool the carrier of (TOP-REAL A)
(n,A,Tn) " (((n,A,Tn) . T) + x) is Element of bool the carrier of (TOP-REAL n)
bool the carrier of (TOP-REAL n) is set
(n,A,Tn) " x is Element of bool the carrier of (TOP-REAL n)
T + ((n,A,Tn) " x) is Element of bool the carrier of (TOP-REAL n)
{ (T + b₁) where b₁ is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n) : b₁ in (n,A,Tn) " x } is set
{ (((n,A,Tn) . T) + b₁) where b₁ is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A) : b₁ in x } is set
dom (n,A,Tn) is non empty set
[#] (TOP-REAL n) is non empty non proper Element of bool the carrier of (TOP-REAL n)
tmx is set
(n,A,Tn) . tmx is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
r is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
((n,A,Tn) . T) + r is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
((n,A,Tn) . T) + r is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
X is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(n,A,Tn) . X is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
((n,A,Tn) . X) - ((n,A,Tn) . T) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
((n,A,Tn) . X) - ((n,A,Tn) . T) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
r + ((n,A,Tn) . T) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
r + ((n,A,Tn) . T) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(r + ((n,A,Tn) . T)) - ((n,A,Tn) . T) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
(r + ((n,A,Tn) . T)) - ((n,A,Tn) . T) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((n,A,Tn) . T) - ((n,A,Tn) . T) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
((n,A,Tn) . T) - ((n,A,Tn) . T) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
r + (((n,A,Tn) . T) - ((n,A,Tn) . T)) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
r + (((n,A,Tn) . T) - ((n,A,Tn) . T)) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
0. (TOP-REAL A) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like V64( TOP-REAL A) complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
the ZeroF of (TOP-REAL A) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
r + (0. (TOP-REAL A)) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
r + (0. (TOP-REAL A)) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
X - T is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
X - T is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(n,A,Tn) . (X - T) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
T + (X - T) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
T + (X - T) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(X - T) + T is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(X - T) + T is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
T - T is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
T - T is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
X - (T - T) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
X - (T - T) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
0. (TOP-REAL n) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like V64( TOP-REAL n) complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
the ZeroF of (TOP-REAL n) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
X - (0. (TOP-REAL n)) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
X - (0. (TOP-REAL n)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
tmx is set
X is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
T + X is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
T + X is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(n,A,Tn) . X is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
(n,A,Tn) . (T + X) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
((n,A,Tn) . T) + ((n,A,Tn) . X) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
((n,A,Tn) . T) + ((n,A,Tn) . X) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(n,A,Tn) . tmx is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
n is ordinal natural V28() real finite cardinal ext-real non negative set
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
A is ordinal natural V28() real finite cardinal ext-real non negative set
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
T is ordinal natural V28() real finite cardinal ext-real non negative set
TOP-REAL T is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL T) is non empty set
Tn is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
width Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
TOP-REAL (width Tn) is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL (width Tn)) is non empty set
(n,A,Tn) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is set
len Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Tm is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of width Tn,T, the carrier of F_Real
((width Tn),T,Tm) is Relation-like the carrier of (TOP-REAL (width Tn)) -defined the carrier of (TOP-REAL T) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL (width Tn)), the carrier of (TOP-REAL T):]
[: the carrier of (TOP-REAL (width Tn)), the carrier of (TOP-REAL T):] is Relation-like set
bool [: the carrier of (TOP-REAL (width Tn)), the carrier of (TOP-REAL T):] is set
((width Tn),T,Tm) * (n,A,Tn) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL T) -valued Function-like Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL T):]
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL T):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL T):] is set
width Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Tn * Tm is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len Tn, width Tm, the carrier of F_Real
((len Tn),(width Tm),(Tn * Tm)) is Relation-like the carrier of (TOP-REAL (len Tn)) -defined the carrier of (TOP-REAL (width Tm)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL (len Tn)), the carrier of (TOP-REAL (width Tm)):]
TOP-REAL (len Tn) is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL (len Tn)) is non empty set
TOP-REAL (width Tm) is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL (width Tm)) is non empty set
[: the carrier of (TOP-REAL (len Tn)), the carrier of (TOP-REAL (width Tm)):] is Relation-like set
bool [: the carrier of (TOP-REAL (len Tn)), the carrier of (TOP-REAL (width Tm)):] is set
T -VectSp_over F_Real is non empty right_complementable V148() V149() V150() strict V165( F_Real ) V166( F_Real ) V167( F_Real ) V168( F_Real ) finite-dimensional VectSpStr over F_Real
the carrier of (T -VectSp_over F_Real) is non empty set
1. (F_Real,T) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of T,T, the carrier of F_Real
MX2FinS (1. (F_Real,T)) is Relation-like NAT -defined the carrier of (T -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (T -VectSp_over F_Real)
A -VectSp_over F_Real is non empty right_complementable V148() V149() V150() strict V165( F_Real ) V166( F_Real ) V167( F_Real ) V168( F_Real ) finite-dimensional VectSpStr over F_Real
the carrier of (A -VectSp_over F_Real) is non empty set
1. (F_Real,A) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of A,A, the carrier of F_Real
MX2FinS (1. (F_Real,A)) is Relation-like NAT -defined the carrier of (A -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (A -VectSp_over F_Real)
n -VectSp_over F_Real is non empty right_complementable V148() V149() V150() strict V165( F_Real ) V166( F_Real ) V167( F_Real ) V168( F_Real ) finite-dimensional VectSpStr over F_Real
the carrier of (n -VectSp_over F_Real) is non empty set
1. (F_Real,n) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n, the carrier of F_Real
MX2FinS (1. (F_Real,n)) is Relation-like NAT -defined the carrier of (n -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (n -VectSp_over F_Real)
x is Relation-like NAT -defined the carrier of (n -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of n -VectSp_over F_Real
len x is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
L is Relation-like NAT -defined the carrier of (A -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of A -VectSp_over F_Real
len L is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
U is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len x, len L, the carrier of F_Real
Mx2Tran (U,x,L) is Relation-like the carrier of (n -VectSp_over F_Real) -defined the carrier of (A -VectSp_over F_Real) -valued Function-like non empty total quasi_total V170(n -VectSp_over F_Real,A -VectSp_over F_Real) V213( F_Real ,n -VectSp_over F_Real,A -VectSp_over F_Real) Element of bool [: the carrier of (n -VectSp_over F_Real), the carrier of (A -VectSp_over F_Real):]
[: the carrier of (n -VectSp_over F_Real), the carrier of (A -VectSp_over F_Real):] is Relation-like set
bool [: the carrier of (n -VectSp_over F_Real), the carrier of (A -VectSp_over F_Real):] is set
TM is Relation-like NAT -defined the carrier of (T -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of T -VectSp_over F_Real
len TM is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
tmx is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len L, len TM, the carrier of F_Real
len tmx is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
TMx is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len x, len TM, the carrier of F_Real
Mx2Tran (TMx,x,TM) is Relation-like the carrier of (n -VectSp_over F_Real) -defined the carrier of (T -VectSp_over F_Real) -valued Function-like non empty total quasi_total V170(n -VectSp_over F_Real,T -VectSp_over F_Real) V213( F_Real ,n -VectSp_over F_Real,T -VectSp_over F_Real) Element of bool [: the carrier of (n -VectSp_over F_Real), the carrier of (T -VectSp_over F_Real):]
[: the carrier of (n -VectSp_over F_Real), the carrier of (T -VectSp_over F_Real):] is Relation-like set
bool [: the carrier of (n -VectSp_over F_Real), the carrier of (T -VectSp_over F_Real):] is set
Mx2Tran (tmx,L,TM) is Relation-like the carrier of (A -VectSp_over F_Real) -defined the carrier of (T -VectSp_over F_Real) -valued Function-like non empty total quasi_total V170(A -VectSp_over F_Real,T -VectSp_over F_Real) V213( F_Real ,A -VectSp_over F_Real,T -VectSp_over F_Real) Element of bool [: the carrier of (A -VectSp_over F_Real), the carrier of (T -VectSp_over F_Real):]
[: the carrier of (A -VectSp_over F_Real), the carrier of (T -VectSp_over F_Real):] is Relation-like set
bool [: the carrier of (A -VectSp_over F_Real), the carrier of (T -VectSp_over F_Real):] is set
(Mx2Tran (tmx,L,TM)) * (Mx2Tran (U,x,L)) is Relation-like the carrier of (n -VectSp_over F_Real) -defined the carrier of (n -VectSp_over F_Real) -defined the carrier of (T -VectSp_over F_Real) -valued the carrier of (T -VectSp_over F_Real) -valued Function-like non empty total quasi_total quasi_total V170(n -VectSp_over F_Real,T -VectSp_over F_Real) V213( F_Real ,n -VectSp_over F_Real,T -VectSp_over F_Real) Element of bool [: the carrier of (n -VectSp_over F_Real), the carrier of (T -VectSp_over F_Real):]
n is ordinal natural V28() real finite cardinal ext-real non negative set
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
1. (F_Real,n) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n, the carrier of F_Real
(n,n,(1. (F_Real,n))) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):] is set
id (TOP-REAL n) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total V170( TOP-REAL n, TOP-REAL n) Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
id the carrier of (TOP-REAL n) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
n -VectSp_over F_Real is non empty right_complementable V148() V149() V150() strict V165( F_Real ) V166( F_Real ) V167( F_Real ) V168( F_Real ) finite-dimensional VectSpStr over F_Real
the carrier of (n -VectSp_over F_Real) is non empty set
MX2FinS (1. (F_Real,n)) is Relation-like NAT -defined the carrier of (n -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (n -VectSp_over F_Real)
T is Relation-like NAT -defined the carrier of (n -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of n -VectSp_over F_Real
len T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Tn is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len T, len T, the carrier of F_Real
Mx2Tran (Tn,T,T) is Relation-like the carrier of (n -VectSp_over F_Real) -defined the carrier of (n -VectSp_over F_Real) -valued Function-like non empty total quasi_total V170(n -VectSp_over F_Real,n -VectSp_over F_Real) V213( F_Real ,n -VectSp_over F_Real,n -VectSp_over F_Real) Element of bool [: the carrier of (n -VectSp_over F_Real), the carrier of (n -VectSp_over F_Real):]
[: the carrier of (n -VectSp_over F_Real), the carrier of (n -VectSp_over F_Real):] is Relation-like set
bool [: the carrier of (n -VectSp_over F_Real), the carrier of (n -VectSp_over F_Real):] is set
[#] (TOP-REAL n) is non empty non proper Element of bool the carrier of (TOP-REAL n)
bool the carrier of (TOP-REAL n) is set
dom (n,n,(1. (F_Real,n))) is non empty set
[#] (n -VectSp_over F_Real) is non empty non proper Element of bool the carrier of (n -VectSp_over F_Real)
bool the carrier of (n -VectSp_over F_Real) is set
id (n -VectSp_over F_Real) is Relation-like the carrier of (n -VectSp_over F_Real) -defined the carrier of (n -VectSp_over F_Real) -valued Function-like non empty total quasi_total V170(n -VectSp_over F_Real,n -VectSp_over F_Real) V213( F_Real ,n -VectSp_over F_Real,n -VectSp_over F_Real) Element of bool [: the carrier of (n -VectSp_over F_Real), the carrier of (n -VectSp_over F_Real):]
id the carrier of (n -VectSp_over F_Real) is Relation-like the carrier of (n -VectSp_over F_Real) -defined the carrier of (n -VectSp_over F_Real) -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of (n -VectSp_over F_Real), the carrier of (n -VectSp_over F_Real):]
AutMt ((id (n -VectSp_over F_Real)),T,T) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len T, len T, the carrier of F_Real
Mx2Tran ((AutMt ((id (n -VectSp_over F_Real)),T,T)),T,T) is Relation-like the carrier of (n -VectSp_over F_Real) -defined the carrier of (n -VectSp_over F_Real) -valued Function-like non empty total quasi_total V170(n -VectSp_over F_Real,n -VectSp_over F_Real) V213( F_Real ,n -VectSp_over F_Real,n -VectSp_over F_Real) Element of bool [: the carrier of (n -VectSp_over F_Real), the carrier of (n -VectSp_over F_Real):]
n is ordinal natural V28() real finite cardinal ext-real non negative set
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
A is ordinal natural V28() real finite cardinal ext-real non negative set
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
(n,A,T) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is set
Tn is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
(n,A,Tn) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
n -VectSp_over F_Real is non empty right_complementable V148() V149() V150() strict V165( F_Real ) V166( F_Real ) V167( F_Real ) V168( F_Real ) finite-dimensional VectSpStr over F_Real
A -VectSp_over F_Real is non empty right_complementable V148() V149() V150() strict V165( F_Real ) V166( F_Real ) V167( F_Real ) V168( F_Real ) finite-dimensional VectSpStr over F_Real
the carrier of (n -VectSp_over F_Real) is non empty set
1. (F_Real,n) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n, the carrier of F_Real
MX2FinS (1. (F_Real,n)) is Relation-like NAT -defined the carrier of (n -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (n -VectSp_over F_Real)
the carrier of (A -VectSp_over F_Real) is non empty set
1. (F_Real,A) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of A,A, the carrier of F_Real
MX2FinS (1. (F_Real,A)) is Relation-like NAT -defined the carrier of (A -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (A -VectSp_over F_Real)
L is Relation-like NAT -defined the carrier of (n -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of n -VectSp_over F_Real
len L is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
x is Relation-like NAT -defined the carrier of (A -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of A -VectSp_over F_Real
len x is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
U is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len L, len x, the carrier of F_Real
Mx2Tran (U,L,x) is Relation-like the carrier of (n -VectSp_over F_Real) -defined the carrier of (A -VectSp_over F_Real) -valued Function-like non empty total quasi_total V170(n -VectSp_over F_Real,A -VectSp_over F_Real) V213( F_Real ,n -VectSp_over F_Real,A -VectSp_over F_Real) Element of bool [: the carrier of (n -VectSp_over F_Real), the carrier of (A -VectSp_over F_Real):]
[: the carrier of (n -VectSp_over F_Real), the carrier of (A -VectSp_over F_Real):] is Relation-like set
bool [: the carrier of (n -VectSp_over F_Real), the carrier of (A -VectSp_over F_Real):] is set
TMx is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len L, len x, the carrier of F_Real
Mx2Tran (TMx,L,x) is Relation-like the carrier of (n -VectSp_over F_Real) -defined the carrier of (A -VectSp_over F_Real) -valued Function-like non empty total quasi_total V170(n -VectSp_over F_Real,A -VectSp_over F_Real) V213( F_Real ,n -VectSp_over F_Real,A -VectSp_over F_Real) Element of bool [: the carrier of (n -VectSp_over F_Real), the carrier of (A -VectSp_over F_Real):]
AutMt ((Mx2Tran (U,L,x)),L,x) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len L, len x, the carrier of F_Real
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is ordinal natural V28() real finite cardinal ext-real non negative set
T is ordinal natural V28() real finite cardinal ext-real non negative set
K96(n,T) is ordinal natural V28() real finite cardinal ext-real non negative set
T |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite T -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of T -tuples_on REAL
T -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
K96(T,n) is ordinal natural V28() real finite cardinal ext-real non negative set
Tn is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Tn ^ (T |-> 0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(T |-> 0) ^ Tn is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Tm is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
(n,A,Tm) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is set
(n,A,Tm) . Tn is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
TM is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of T,A, the carrier of F_Real
Tm ^ TM is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K96(n,T),A, the carrier of F_Real
(K96(n,T),A,(Tm ^ TM)) is Relation-like the carrier of (TOP-REAL K96(n,T)) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL K96(n,T)), the carrier of (TOP-REAL A):]
TOP-REAL K96(n,T) is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL K96(n,T)) is non empty set
[: the carrier of (TOP-REAL K96(n,T)), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL K96(n,T)), the carrier of (TOP-REAL A):] is set
(K96(n,T),A,(Tm ^ TM)) . (Tn ^ (T |-> 0)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
TM ^ Tm is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K96(T,n),A, the carrier of F_Real
(K96(T,n),A,(TM ^ Tm)) is Relation-like the carrier of (TOP-REAL K96(T,n)) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL K96(T,n)), the carrier of (TOP-REAL A):]
TOP-REAL K96(T,n) is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL K96(T,n)) is non empty set
[: the carrier of (TOP-REAL K96(T,n)), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL K96(T,n)), the carrier of (TOP-REAL A):] is set
(K96(T,n),A,(TM ^ Tm)) . ((T |-> 0) ^ Tn) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
len TM is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
L is Relation-like NAT -defined REAL -valued Function-like finite T -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
L ^ Tn is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
width Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len L is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len (L ^ Tn) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
n + T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Tn ^ L is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
len (Tn ^ L) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width TM is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(L) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
X is ordinal natural V28() real finite cardinal ext-real non negative set
Col (TM,X) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite len TM -element FinSequence-like FinSubsequence-like Element of (len TM) -tuples_on the carrier of F_Real
(len TM) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
mlt ((L),(Col (TM,X))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
the multF of F_Real is Relation-like [: the carrier of F_Real, the carrier of F_Real:] -defined the carrier of F_Real -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:]
[: the carrier of F_Real, the carrier of F_Real:] is Relation-like complex-valued ext-real-valued real-valued set
[:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:] is set
K446( the carrier of F_Real, the carrier of F_Real, the carrier of F_Real, the multF of F_Real,(L),(Col (TM,X))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Sum (mlt ((L),(Col (TM,X)))) is V28() real ext-real Element of the carrier of F_Real
the addF of F_Real is Relation-like [: the carrier of F_Real, the carrier of F_Real:] -defined the carrier of F_Real -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:]
the addF of F_Real "**" (mlt ((L),(Col (TM,X)))) is V28() real ext-real Element of the carrier of F_Real
(Tn) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Col (Tm,X) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite len Tm -element FinSequence-like FinSubsequence-like Element of (len Tm) -tuples_on the carrier of F_Real
(len Tm) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
mlt ((Tn),(Col (Tm,X))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
K446( the carrier of F_Real, the carrier of F_Real, the carrier of F_Real, the multF of F_Real,(Tn),(Col (Tm,X))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Sum (mlt ((Tn),(Col (Tm,X)))) is V28() real ext-real Element of the carrier of F_Real
the addF of F_Real "**" (mlt ((Tn),(Col (Tm,X)))) is V28() real ext-real Element of the carrier of F_Real
Seg A is finite A -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= A ) } is set
0. F_Real is V28() real V64( F_Real ) ext-real Element of the carrier of F_Real
the ZeroF of F_Real is V28() real ext-real Element of the carrier of F_Real
(0. F_Real) * (Col (TM,X)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite len TM -element FinSequence-like FinSubsequence-like Element of (len TM) -tuples_on the carrier of F_Real
(0. F_Real) multfield is Relation-like the carrier of F_Real -defined the carrier of F_Real -valued Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of bool [: the carrier of F_Real, the carrier of F_Real:]
bool [: the carrier of F_Real, the carrier of F_Real:] is set
id the carrier of F_Real is Relation-like the carrier of F_Real -defined the carrier of F_Real -valued Function-like one-to-one non empty total quasi_total complex-valued ext-real-valued real-valued increasing non-decreasing Element of bool [: the carrier of F_Real, the carrier of F_Real:]
the multF of F_Real [;] ((0. F_Real),(id the carrier of F_Real)) is Relation-like the carrier of F_Real -defined the carrier of F_Real -valued Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of bool [: the carrier of F_Real, the carrier of F_Real:]
K449( the carrier of F_Real, the carrier of F_Real,(Col (TM,X)),((0. F_Real) multfield)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
T |-> (0. F_Real) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite T -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of T -tuples_on the carrier of F_Real
T -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
Sum (T |-> 0) is V28() real ext-real Element of REAL
len (Col (Tm,X)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len (Col (TM,X)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
((Tn ^ L)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Col ((Tm ^ TM),X) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite len (Tm ^ TM) -element FinSequence-like FinSubsequence-like Element of (len (Tm ^ TM)) -tuples_on the carrier of F_Real
len (Tm ^ TM) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(len (Tm ^ TM)) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
mlt (((Tn ^ L)),(Col ((Tm ^ TM),X))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
K446( the carrier of F_Real, the carrier of F_Real, the carrier of F_Real, the multF of F_Real,((Tn ^ L)),(Col ((Tm ^ TM),X))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
(Tn) ^ (L) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
(Col (Tm,X)) ^ (Col (TM,X)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite K417((len Tm),(len TM)) -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
K417((len Tm),(len TM)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
mlt (((Tn) ^ (L)),((Col (Tm,X)) ^ (Col (TM,X)))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
K446( the carrier of F_Real, the carrier of F_Real, the carrier of F_Real, the multF of F_Real,((Tn) ^ (L)),((Col (Tm,X)) ^ (Col (TM,X)))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
(mlt ((Tn),(Col (Tm,X)))) ^ (mlt ((L),(Col (TM,X)))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Sum (mlt (((Tn ^ L)),(Col ((Tm ^ TM),X)))) is V28() real ext-real Element of the carrier of F_Real
the addF of F_Real "**" (mlt (((Tn ^ L)),(Col ((Tm ^ TM),X)))) is V28() real ext-real Element of the carrier of F_Real
addreal . ((Sum (mlt ((Tn),(Col (Tm,X))))),(Sum (mlt ((L),(Col (TM,X)))))) is set
(Sum (mlt ((Tn),(Col (Tm,X))))) + (Sum (mlt ((L),(Col (TM,X))))) is V28() real ext-real Element of REAL
(Tn) "*" (Col (Tm,X)) is V28() real ext-real Element of the carrier of F_Real
((n,A,Tm) . Tn) . X is V28() real ext-real set
((Tn ^ L)) "*" (Col ((Tm ^ TM),X)) is V28() real ext-real Element of the carrier of F_Real
(K96(n,T),A,(Tm ^ TM)) . (Tn ^ L) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
((K96(n,T),A,(Tm ^ TM)) . (Tn ^ L)) . X is V28() real ext-real set
len ((K96(n,T),A,(Tm ^ TM)) . (Tn ^ L)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len ((n,A,Tm) . Tn) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width TM is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(L) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
tmx is ordinal natural V28() real finite cardinal ext-real non negative set
Col (TM,tmx) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite len TM -element FinSequence-like FinSubsequence-like Element of (len TM) -tuples_on the carrier of F_Real
(len TM) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
mlt ((L),(Col (TM,tmx))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
the multF of F_Real is Relation-like [: the carrier of F_Real, the carrier of F_Real:] -defined the carrier of F_Real -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:]
[: the carrier of F_Real, the carrier of F_Real:] is Relation-like complex-valued ext-real-valued real-valued set
[:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:] is set
K446( the carrier of F_Real, the carrier of F_Real, the carrier of F_Real, the multF of F_Real,(L),(Col (TM,tmx))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Sum (mlt ((L),(Col (TM,tmx)))) is V28() real ext-real Element of the carrier of F_Real
the addF of F_Real is Relation-like [: the carrier of F_Real, the carrier of F_Real:] -defined the carrier of F_Real -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:]
the addF of F_Real "**" (mlt ((L),(Col (TM,tmx)))) is V28() real ext-real Element of the carrier of F_Real
(Tn) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Col (Tm,tmx) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite len Tm -element FinSequence-like FinSubsequence-like Element of (len Tm) -tuples_on the carrier of F_Real
(len Tm) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
mlt ((Tn),(Col (Tm,tmx))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
K446( the carrier of F_Real, the carrier of F_Real, the carrier of F_Real, the multF of F_Real,(Tn),(Col (Tm,tmx))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Sum (mlt ((Tn),(Col (Tm,tmx)))) is V28() real ext-real Element of the carrier of F_Real
the addF of F_Real "**" (mlt ((Tn),(Col (Tm,tmx)))) is V28() real ext-real Element of the carrier of F_Real
Seg A is finite A -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= A ) } is set
0. F_Real is V28() real V64( F_Real ) ext-real Element of the carrier of F_Real
the ZeroF of F_Real is V28() real ext-real Element of the carrier of F_Real
(0. F_Real) * (Col (TM,tmx)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite len TM -element FinSequence-like FinSubsequence-like Element of (len TM) -tuples_on the carrier of F_Real
(0. F_Real) multfield is Relation-like the carrier of F_Real -defined the carrier of F_Real -valued Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of bool [: the carrier of F_Real, the carrier of F_Real:]
bool [: the carrier of F_Real, the carrier of F_Real:] is set
id the carrier of F_Real is Relation-like the carrier of F_Real -defined the carrier of F_Real -valued Function-like one-to-one non empty total quasi_total complex-valued ext-real-valued real-valued increasing non-decreasing Element of bool [: the carrier of F_Real, the carrier of F_Real:]
the multF of F_Real [;] ((0. F_Real),(id the carrier of F_Real)) is Relation-like the carrier of F_Real -defined the carrier of F_Real -valued Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of bool [: the carrier of F_Real, the carrier of F_Real:]
K449( the carrier of F_Real, the carrier of F_Real,(Col (TM,tmx)),((0. F_Real) multfield)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
T |-> (0. F_Real) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite T -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of T -tuples_on the carrier of F_Real
T -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
Sum (T |-> 0) is V28() real ext-real Element of REAL
len (Col (Tm,tmx)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len (Col (TM,tmx)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
((L ^ Tn)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Col ((TM ^ Tm),tmx) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite len (TM ^ Tm) -element FinSequence-like FinSubsequence-like Element of (len (TM ^ Tm)) -tuples_on the carrier of F_Real
len (TM ^ Tm) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(len (TM ^ Tm)) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
mlt (((L ^ Tn)),(Col ((TM ^ Tm),tmx))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
K446( the carrier of F_Real, the carrier of F_Real, the carrier of F_Real, the multF of F_Real,((L ^ Tn)),(Col ((TM ^ Tm),tmx))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
(L) ^ (Tn) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
(Col (TM,tmx)) ^ (Col (Tm,tmx)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite K417((len TM),(len Tm)) -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
K417((len TM),(len Tm)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
mlt (((L) ^ (Tn)),((Col (TM,tmx)) ^ (Col (Tm,tmx)))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
K446( the carrier of F_Real, the carrier of F_Real, the carrier of F_Real, the multF of F_Real,((L) ^ (Tn)),((Col (TM,tmx)) ^ (Col (Tm,tmx)))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
(mlt ((L),(Col (TM,tmx)))) ^ (mlt ((Tn),(Col (Tm,tmx)))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Sum (mlt (((L ^ Tn)),(Col ((TM ^ Tm),tmx)))) is V28() real ext-real Element of the carrier of F_Real
the addF of F_Real "**" (mlt (((L ^ Tn)),(Col ((TM ^ Tm),tmx)))) is V28() real ext-real Element of the carrier of F_Real
addreal . ((Sum (mlt ((L),(Col (TM,tmx))))),(Sum (mlt ((Tn),(Col (Tm,tmx)))))) is set
(Sum (mlt ((Tn),(Col (Tm,tmx))))) + (0. F_Real) is V28() real ext-real Element of REAL
(Tn) "*" (Col (Tm,tmx)) is V28() real ext-real Element of the carrier of F_Real
((n,A,Tm) . Tn) . tmx is V28() real ext-real set
((L ^ Tn)) "*" (Col ((TM ^ Tm),tmx)) is V28() real ext-real Element of the carrier of F_Real
(K96(T,n),A,(TM ^ Tm)) . (L ^ Tn) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
((K96(T,n),A,(TM ^ Tm)) . (L ^ Tn)) . tmx is V28() real ext-real set
len ((K96(T,n),A,(TM ^ Tm)) . (L ^ Tn)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len ((n,A,Tm) . Tn) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
TOP-REAL T is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
0. (TOP-REAL T) is Relation-like NAT -defined Function-like finite T -element FinSequence-like FinSubsequence-like V64( TOP-REAL T) complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL T)
the carrier of (TOP-REAL T) is non empty set
the ZeroF of (TOP-REAL T) is Relation-like NAT -defined Function-like finite T -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL T)
0* T is Relation-like NAT -defined REAL -valued Function-like finite T -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of REAL T
REAL T is functional non empty FinSequence-membered FinSequenceSet of REAL
0. (TOP-REAL A) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like V64( TOP-REAL A) complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
the ZeroF of (TOP-REAL A) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is ordinal natural V28() real finite cardinal ext-real non negative set
T is ordinal natural V28() real finite cardinal ext-real non negative set
K96(n,T) is ordinal natural V28() real finite cardinal ext-real non negative set
Tn is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
len Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
rng Tn is finite V197() V198() V199() Element of bool REAL
n -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of n -tuples_on REAL
L is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
(n,A,L) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is set
(n,A,L) . Tn is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
x is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of T,A, the carrier of F_Real
L ^ x is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K96(n,T),A, the carrier of F_Real
(K96(n,T),A,(L ^ x)) is Relation-like the carrier of (TOP-REAL K96(n,T)) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL K96(n,T)), the carrier of (TOP-REAL A):]
TOP-REAL K96(n,T) is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL K96(n,T)) is non empty set
[: the carrier of (TOP-REAL K96(n,T)), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL K96(n,T)), the carrier of (TOP-REAL A):] is set
(T,A,x) is Relation-like the carrier of (TOP-REAL T) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL T), the carrier of (TOP-REAL A):]
TOP-REAL T is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL T) is non empty set
[: the carrier of (TOP-REAL T), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL T), the carrier of (TOP-REAL A):] is set
U is Relation-like NAT -defined Function-like finite T -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Tn ^ U is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(K96(n,T),A,(L ^ x)) . (Tn ^ U) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(T,A,x) . U is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
((n,A,L) . Tn) + ((T,A,x) . U) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len U is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
rng U is finite V197() V198() V199() Element of bool REAL
T -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
T |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite T -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of T -tuples_on REAL
len (n |-> 0) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
TM is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of n -tuples_on REAL
TMx is Relation-like NAT -defined REAL -valued Function-like finite T -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of T -tuples_on REAL
TM ^ TMx is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len (TM ^ TMx) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
n + T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len (T |-> 0) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Tm is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of n -tuples_on REAL
tmx is Relation-like NAT -defined REAL -valued Function-like finite T -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of T -tuples_on REAL
Tm ^ tmx is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len (Tm ^ tmx) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Tm + TM is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of n -tuples_on REAL
TMx + tmx is Relation-like NAT -defined REAL -valued Function-like finite T -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of T -tuples_on REAL
addreal .: (Tn,TM) is set
addreal .: (Tm,TM) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of n -tuples_on REAL
addreal .: (tmx,TMx) is Relation-like NAT -defined REAL -valued Function-like finite T -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of T -tuples_on REAL
(addreal .: (Tm,TM)) ^ (addreal .: (tmx,TMx)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
addreal .: ((Tm ^ tmx),(TM ^ TMx)) is set
(Tm ^ tmx) + (TM ^ TMx) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(K96(n,T),A,(L ^ x)) . (Tm ^ tmx) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(K96(n,T),A,(L ^ x)) . (TM ^ TMx) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
((K96(n,T),A,(L ^ x)) . (Tm ^ tmx)) + ((K96(n,T),A,(L ^ x)) . (TM ^ TMx)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((n,A,L) . Tn) + ((K96(n,T),A,(L ^ x)) . (TM ^ TMx)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is ordinal natural V28() real finite cardinal ext-real non negative set
T is ordinal natural V28() real finite cardinal ext-real non negative set
A + T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Tn is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Tm is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
width Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(n,A,Tm) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is set
(n,A,Tm) . Tn is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
TM is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,T, the carrier of F_Real
width TM is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
K418((width Tm),(width TM)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Tm ^^ TM is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,K418((width Tm),(width TM)), the carrier of F_Real
(n,K418((width Tm),(width TM)),(Tm ^^ TM)) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL K418((width Tm),(width TM))) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL K418((width Tm),(width TM))):]
TOP-REAL K418((width Tm),(width TM)) is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL K418((width Tm),(width TM))) is non empty set
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL K418((width Tm),(width TM))):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL K418((width Tm),(width TM))):] is set
(n,K418((width Tm),(width TM)),(Tm ^^ TM)) . Tn is Relation-like NAT -defined Function-like finite K418((width Tm),(width TM)) -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(n,T,TM) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL T) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL T):]
TOP-REAL T is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL T) is non empty set
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL T):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL T):] is set
(n,T,TM) . Tn is Relation-like NAT -defined Function-like finite T -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
((n,A,Tm) . Tn) ^ ((n,T,TM) . Tn) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(Tn) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
LineVec2Mx (Tn) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of 1, len (Tn), the carrier of F_Real
len (Tn) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len ((n,A,Tm) . Tn) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len ((n,T,TM) . Tn) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len (((n,A,Tm) . Tn) ^ ((n,T,TM) . Tn)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
tmx is ordinal natural V28() real finite cardinal ext-real non negative set
(((n,A,Tm) . Tn) ^ ((n,T,TM) . Tn)) . tmx is V28() real ext-real set
((n,K418((width Tm),(width TM)),(Tm ^^ TM)) . Tn) . tmx is V28() real ext-real set
dom (((n,A,Tm) . Tn) ^ ((n,T,TM) . Tn)) is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
Col ((Tm ^^ TM),tmx) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite len (Tm ^^ TM) -element FinSequence-like FinSubsequence-like Element of (len (Tm ^^ TM)) -tuples_on the carrier of F_Real
len (Tm ^^ TM) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(len (Tm ^^ TM)) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
(Tn) "*" (Col ((Tm ^^ TM),tmx)) is V28() real ext-real Element of the carrier of F_Real
mlt ((Tn),(Col ((Tm ^^ TM),tmx))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
the multF of F_Real is Relation-like [: the carrier of F_Real, the carrier of F_Real:] -defined the carrier of F_Real -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:]
[: the carrier of F_Real, the carrier of F_Real:] is Relation-like complex-valued ext-real-valued real-valued set
[:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:] is set
K446( the carrier of F_Real, the carrier of F_Real, the carrier of F_Real, the multF of F_Real,(Tn),(Col ((Tm ^^ TM),tmx))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Sum (mlt ((Tn),(Col ((Tm ^^ TM),tmx)))) is V28() real ext-real Element of the carrier of F_Real
the addF of F_Real is Relation-like [: the carrier of F_Real, the carrier of F_Real:] -defined the carrier of F_Real -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:]
the addF of F_Real "**" (mlt ((Tn),(Col ((Tm ^^ TM),tmx)))) is V28() real ext-real Element of the carrier of F_Real
dom ((n,A,Tm) . Tn) is finite A -element V197() V198() V199() V200() V201() V202() Element of bool NAT
((n,A,Tm) . Tn) . tmx is V28() real ext-real set
Col (Tm,tmx) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite len Tm -element FinSequence-like FinSubsequence-like Element of (len Tm) -tuples_on the carrier of F_Real
len Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(len Tm) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
(Tn) "*" (Col (Tm,tmx)) is V28() real ext-real Element of the carrier of F_Real
mlt ((Tn),(Col (Tm,tmx))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
K446( the carrier of F_Real, the carrier of F_Real, the carrier of F_Real, the multF of F_Real,(Tn),(Col (Tm,tmx))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Sum (mlt ((Tn),(Col (Tm,tmx)))) is V28() real ext-real Element of the carrier of F_Real
the addF of F_Real "**" (mlt ((Tn),(Col (Tm,tmx)))) is V28() real ext-real Element of the carrier of F_Real
Seg (width Tm) is finite width Tm -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= width Tm ) } is set
dom ((n,T,TM) . Tn) is finite T -element V197() V198() V199() V200() V201() V202() Element of bool NAT
X is ordinal natural V28() real finite cardinal ext-real non negative set
(len ((n,A,Tm) . Tn)) + X is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
X is ordinal natural V28() real finite cardinal ext-real non negative set
(len ((n,A,Tm) . Tn)) + X is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
((n,T,TM) . Tn) . X is V28() real ext-real set
Col (TM,X) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite len TM -element FinSequence-like FinSubsequence-like Element of (len TM) -tuples_on the carrier of F_Real
len TM is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(len TM) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
(Tn) "*" (Col (TM,X)) is V28() real ext-real Element of the carrier of F_Real
mlt ((Tn),(Col (TM,X))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
K446( the carrier of F_Real, the carrier of F_Real, the carrier of F_Real, the multF of F_Real,(Tn),(Col (TM,X))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Sum (mlt ((Tn),(Col (TM,X)))) is V28() real ext-real Element of the carrier of F_Real
the addF of F_Real "**" (mlt ((Tn),(Col (TM,X)))) is V28() real ext-real Element of the carrier of F_Real
Seg (width TM) is finite width TM -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= width TM ) } is set
dom ((n,A,Tm) . Tn) is finite A -element V197() V198() V199() V200() V201() V202() Element of bool NAT
dom ((n,T,TM) . Tn) is finite T -element V197() V198() V199() V200() V201() V202() Element of bool NAT
len ((n,K418((width Tm),(width TM)),(Tm ^^ TM)) . Tn) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
n is ordinal natural V28() real finite cardinal ext-real non negative set
1. (F_Real,n) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n, the carrier of F_Real
A is ordinal natural V28() real finite cardinal ext-real non negative set
(1. (F_Real,n)) | A is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Real *
Seg A is finite A -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= A ) } is set
(1. (F_Real,n)) | (Seg A) is Relation-like NAT -defined Seg A -defined NAT -defined the carrier of F_Real * -valued Function-like finite FinSubsequence-like set
T is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Tn is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of A,n, the carrier of F_Real
(A,n,Tn) is Relation-like the carrier of (TOP-REAL A) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL A), the carrier of (TOP-REAL n):]
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
[: the carrier of (TOP-REAL A), the carrier of (TOP-REAL n):] is Relation-like set
bool [: the carrier of (TOP-REAL A), the carrier of (TOP-REAL n):] is set
(A,n,Tn) . T is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
((A,n,Tn) . T) | A is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((A,n,Tn) . T) | (Seg A) is Relation-like NAT -defined Seg A -defined NAT -defined Function-like finite FinSubsequence-like complex-valued ext-real-valued real-valued set
n -VectSp_over F_Real is non empty right_complementable V148() V149() V150() strict V165( F_Real ) V166( F_Real ) V167( F_Real ) V168( F_Real ) finite-dimensional VectSpStr over F_Real
len (1. (F_Real,n)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
Tn ^ x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
MX2FinS (1. (F_Real,n)) is Relation-like NAT -defined the carrier of (n -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (n -VectSp_over F_Real)
the carrier of (n -VectSp_over F_Real) is non empty set
U is Relation-like NAT -defined the carrier of (n -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (n -VectSp_over F_Real)
len U is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
A + (len U) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(len U) |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite len U -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of (len U) -tuples_on REAL
(len U) -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
T ^ ((len U) |-> 0) is Relation-like NAT -defined Function-like finite K417(A,(len U)) -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
K417(A,(len U)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
FinS2MX U is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len U,n, the carrier of F_Real
(T ^ ((len U) |-> 0)) | A is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(T ^ ((len U) |-> 0)) | (Seg A) is Relation-like NAT -defined Seg A -defined NAT -defined Function-like finite FinSubsequence-like complex-valued ext-real-valued real-valued set
dom T is finite A -element V197() V198() V199() V200() V201() V202() Element of bool NAT
(T ^ ((len U) |-> 0)) | (dom T) is Relation-like NAT -defined dom T -defined NAT -defined Function-like finite FinSubsequence-like complex-valued ext-real-valued real-valued set
K96(A,(len U)) is ordinal natural V28() real finite cardinal ext-real non negative set
Tn ^ (FinS2MX U) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K96(A,(len U)),n, the carrier of F_Real
(K96(A,(len U)),n,(Tn ^ (FinS2MX U))) is Relation-like the carrier of (TOP-REAL K96(A,(len U))) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL K96(A,(len U))), the carrier of (TOP-REAL n):]
TOP-REAL K96(A,(len U)) is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL K96(A,(len U))) is non empty set
[: the carrier of (TOP-REAL K96(A,(len U))), the carrier of (TOP-REAL n):] is Relation-like set
bool [: the carrier of (TOP-REAL K96(A,(len U))), the carrier of (TOP-REAL n):] is set
(K96(A,(len U)),n,(Tn ^ (FinS2MX U))) . (T ^ ((len U) |-> 0)) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(n,n,(1. (F_Real,n))) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):] is set
(n,n,(1. (F_Real,n))) . (T ^ ((len U) |-> 0)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
id (TOP-REAL n) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total V170( TOP-REAL n, TOP-REAL n) Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
id the carrier of (TOP-REAL n) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
(id (TOP-REAL n)) . (T ^ ((len U) |-> 0)) is set
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is ordinal natural V28() real finite cardinal ext-real non negative set
T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of A,n, the carrier of F_Real
(A,n,T) is Relation-like the carrier of (TOP-REAL A) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL A), the carrier of (TOP-REAL n):]
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
[: the carrier of (TOP-REAL A), the carrier of (TOP-REAL n):] is Relation-like set
bool [: the carrier of (TOP-REAL A), the carrier of (TOP-REAL n):] is set
the_rank_of T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
A -VectSp_over F_Real is non empty right_complementable V148() V149() V150() strict V165( F_Real ) V166( F_Real ) V167( F_Real ) V168( F_Real ) finite-dimensional VectSpStr over F_Real
n -VectSp_over F_Real is non empty right_complementable V148() V149() V150() strict V165( F_Real ) V166( F_Real ) V167( F_Real ) V168( F_Real ) finite-dimensional VectSpStr over F_Real
the carrier of (A -VectSp_over F_Real) is non empty set
1. (F_Real,A) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of A,A, the carrier of F_Real
MX2FinS (1. (F_Real,A)) is Relation-like NAT -defined the carrier of (A -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (A -VectSp_over F_Real)
the carrier of (n -VectSp_over F_Real) is non empty set
1. (F_Real,n) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n, the carrier of F_Real
MX2FinS (1. (F_Real,n)) is Relation-like NAT -defined the carrier of (n -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (n -VectSp_over F_Real)
L is Relation-like NAT -defined the carrier of (A -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of A -VectSp_over F_Real
len L is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
x is Relation-like NAT -defined the carrier of (n -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of n -VectSp_over F_Real
len x is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
U is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len L, len x, the carrier of F_Real
len U is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Mx2Tran (U,L,x) is Relation-like the carrier of (A -VectSp_over F_Real) -defined the carrier of (n -VectSp_over F_Real) -valued Function-like non empty total quasi_total V170(A -VectSp_over F_Real,n -VectSp_over F_Real) V213( F_Real ,A -VectSp_over F_Real,n -VectSp_over F_Real) Element of bool [: the carrier of (A -VectSp_over F_Real), the carrier of (n -VectSp_over F_Real):]
[: the carrier of (A -VectSp_over F_Real), the carrier of (n -VectSp_over F_Real):] is Relation-like set
bool [: the carrier of (A -VectSp_over F_Real), the carrier of (n -VectSp_over F_Real):] is set
ker (Mx2Tran (U,L,x)) is non empty right_complementable V148() V149() V150() strict V165( F_Real ) V166( F_Real ) V167( F_Real ) V168( F_Real ) finite-dimensional Subspace of A -VectSp_over F_Real
(0). (A -VectSp_over F_Real) is non empty right_complementable V148() V149() V150() strict V165( F_Real ) V166( F_Real ) V167( F_Real ) V168( F_Real ) finite-dimensional Subspace of A -VectSp_over F_Real
width U is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
{(0. (TOP-REAL 0))} is functional non empty trivial finite V38() 1 -element V197() V198() V199() V200() V201() V202() Element of bool NAT
rng (A,n,T) is non empty set
card {(0. (TOP-REAL 0))} is non empty ordinal natural V28() real V30() V31() finite cardinal ext-real positive non negative V197() V198() V199() V200() V201() V202() Element of NAT
U @ is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
Space_of_Solutions_of (U @) is non empty right_complementable V148() V149() V150() strict V165( F_Real ) V166( F_Real ) V167( F_Real ) V168( F_Real ) finite-dimensional Subspace of (width (U @)) -VectSp_over F_Real
width (U @) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(width (U @)) -VectSp_over F_Real is non empty right_complementable V148() V149() V150() strict V165( F_Real ) V166( F_Real ) V167( F_Real ) V168( F_Real ) finite-dimensional VectSpStr over F_Real
tmx is non empty right_complementable V148() V149() V150() V165( F_Real ) V166( F_Real ) V167( F_Real ) V168( F_Real ) finite-dimensional Subspace of A -VectSp_over F_Real
[#] tmx is non empty non proper Element of bool the carrier of tmx
the carrier of tmx is non empty set
bool the carrier of tmx is set
0. (A -VectSp_over F_Real) is Relation-like Function-like V64(A -VectSp_over F_Real) Element of the carrier of (A -VectSp_over F_Real)
the ZeroF of (A -VectSp_over F_Real) is Relation-like Function-like Element of the carrier of (A -VectSp_over F_Real)
{(0. (A -VectSp_over F_Real))} is functional non empty trivial finite 1 -element set
X is set
r is Relation-like Function-like Element of the carrier of (A -VectSp_over F_Real)
r |-- L is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
dim tmx is ordinal natural V28() real finite cardinal ext-real non negative set
the_rank_of (U @) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
A - (the_rank_of (U @)) is V28() real ext-real Element of REAL
A - A is V28() real ext-real Element of REAL
[#] (ker (Mx2Tran (U,L,x))) is non empty non proper Element of bool the carrier of (ker (Mx2Tran (U,L,x)))
the carrier of (ker (Mx2Tran (U,L,x))) is non empty set
bool the carrier of (ker (Mx2Tran (U,L,x))) is set
X is set
r is Relation-like Function-like Element of the carrier of (A -VectSp_over F_Real)
r |-- L is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
0. tmx is V64(tmx) Element of the carrier of tmx
the ZeroF of tmx is Element of the carrier of tmx
Tm is set
dom (A,n,T) is non empty set
TM is set
(A,n,T) . Tm is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(A,n,T) . TM is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
[#] (TOP-REAL 0) is non empty non proper Element of bool the carrier of (TOP-REAL 0)
bool the carrier of (TOP-REAL 0) is set
{(0. (TOP-REAL 0))} is functional non empty trivial finite V38() 1 -element V197() V198() V199() V200() V201() V202() Element of bool NAT
len T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
A |-> 1 is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of A -tuples_on REAL
A -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
A |-> 2 is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of A -tuples_on REAL
dom (A,n,T) is non empty set
[#] (TOP-REAL A) is non empty non proper Element of bool the carrier of (TOP-REAL A)
bool the carrier of (TOP-REAL A) is set
Tm is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
(A,n,T) . Tm is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
TM is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
(A,n,T) . TM is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
Seg A is finite A -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= A ) } is set
(Seg A) --> 1 is Relation-like non-empty Seg A -defined REAL -valued INT -valued RAT -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued positive-yielding nonnegative-yielding Element of bool [:(Seg A),REAL:]
[:(Seg A),REAL:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg A),REAL:] is set
{1} is non empty trivial finite V38() 1 -element V197() V198() V199() V200() V201() V202() Element of bool NAT
[:(Seg A),{1}:] is Relation-like INT -valued RAT -valued finite complex-valued ext-real-valued real-valued natural-valued set
(Seg A) --> 2 is Relation-like non-empty Seg A -defined REAL -valued INT -valued RAT -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued natural-valued positive-yielding nonnegative-yielding Element of bool [:(Seg A),REAL:]
{2} is non empty trivial finite V38() 1 -element V197() V198() V199() V200() V201() V202() Element of bool NAT
[:(Seg A),{2}:] is Relation-like INT -valued RAT -valued finite complex-valued ext-real-valued real-valued natural-valued set
width T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
0. F_Real is V28() real V64( F_Real ) ext-real Element of the carrier of F_Real
the ZeroF of F_Real is V28() real ext-real Element of the carrier of F_Real
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n, the carrier of F_Real
(n,n,A) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):] is set
Det A is V28() real ext-real Element of the carrier of F_Real
the_rank_of A is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is ordinal natural V28() real finite cardinal ext-real non negative set
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
(n,A,T) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is set
the_rank_of T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
n -VectSp_over F_Real is non empty right_complementable V148() V149() V150() strict V165( F_Real ) V166( F_Real ) V167( F_Real ) V168( F_Real ) finite-dimensional VectSpStr over F_Real
A -VectSp_over F_Real is non empty right_complementable V148() V149() V150() strict V165( F_Real ) V166( F_Real ) V167( F_Real ) V168( F_Real ) finite-dimensional VectSpStr over F_Real
the carrier of (n -VectSp_over F_Real) is non empty set
1. (F_Real,n) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n, the carrier of F_Real
MX2FinS (1. (F_Real,n)) is Relation-like NAT -defined the carrier of (n -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (n -VectSp_over F_Real)
the carrier of (A -VectSp_over F_Real) is non empty set
1. (F_Real,A) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of A,A, the carrier of F_Real
MX2FinS (1. (F_Real,A)) is Relation-like NAT -defined the carrier of (A -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (A -VectSp_over F_Real)
[#] (A -VectSp_over F_Real) is non empty non proper Element of bool the carrier of (A -VectSp_over F_Real)
bool the carrier of (A -VectSp_over F_Real) is set
REAL A is functional non empty FinSequence-membered FinSequenceSet of REAL
A -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
[#] (TOP-REAL A) is non empty non proper Element of bool the carrier of (TOP-REAL A)
bool the carrier of (TOP-REAL A) is set
L is Relation-like NAT -defined the carrier of (n -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of n -VectSp_over F_Real
len L is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
x is Relation-like NAT -defined the carrier of (A -VectSp_over F_Real) -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of A -VectSp_over F_Real
len x is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
U is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len L, len x, the carrier of F_Real
Mx2Tran (U,L,x) is Relation-like the carrier of (n -VectSp_over F_Real) -defined the carrier of (A -VectSp_over F_Real) -valued Function-like non empty total quasi_total V170(n -VectSp_over F_Real,A -VectSp_over F_Real) V213( F_Real ,n -VectSp_over F_Real,A -VectSp_over F_Real) Element of bool [: the carrier of (n -VectSp_over F_Real), the carrier of (A -VectSp_over F_Real):]
[: the carrier of (n -VectSp_over F_Real), the carrier of (A -VectSp_over F_Real):] is Relation-like set
bool [: the carrier of (n -VectSp_over F_Real), the carrier of (A -VectSp_over F_Real):] is set
dom (Mx2Tran (U,L,x)) is non empty set
[#] (n -VectSp_over F_Real) is non empty non proper Element of bool the carrier of (n -VectSp_over F_Real)
bool the carrier of (n -VectSp_over F_Real) is set
im (Mx2Tran (U,L,x)) is non empty right_complementable V148() V149() V150() strict V165( F_Real ) V166( F_Real ) V167( F_Real ) V168( F_Real ) finite-dimensional Subspace of A -VectSp_over F_Real
[#] (im (Mx2Tran (U,L,x))) is non empty non proper Element of bool the carrier of (im (Mx2Tran (U,L,x)))
the carrier of (im (Mx2Tran (U,L,x))) is non empty set
bool the carrier of (im (Mx2Tran (U,L,x))) is set
(Mx2Tran (U,L,x)) .: ([#] (n -VectSp_over F_Real)) is Element of bool the carrier of (A -VectSp_over F_Real)
rng (Mx2Tran (U,L,x)) is non empty set
(Omega). (A -VectSp_over F_Real) is non empty right_complementable V148() V149() V150() strict V165( F_Real ) V166( F_Real ) V167( F_Real ) V168( F_Real ) finite-dimensional Subspace of A -VectSp_over F_Real
the addF of (A -VectSp_over F_Real) is Relation-like [: the carrier of (A -VectSp_over F_Real), the carrier of (A -VectSp_over F_Real):] -defined the carrier of (A -VectSp_over F_Real) -valued Function-like total quasi_total Element of bool [:[: the carrier of (A -VectSp_over F_Real), the carrier of (A -VectSp_over F_Real):], the carrier of (A -VectSp_over F_Real):]
[: the carrier of (A -VectSp_over F_Real), the carrier of (A -VectSp_over F_Real):] is Relation-like set
[:[: the carrier of (A -VectSp_over F_Real), the carrier of (A -VectSp_over F_Real):], the carrier of (A -VectSp_over F_Real):] is Relation-like set
bool [:[: the carrier of (A -VectSp_over F_Real), the carrier of (A -VectSp_over F_Real):], the carrier of (A -VectSp_over F_Real):] is set
the ZeroF of (A -VectSp_over F_Real) is Relation-like Function-like Element of the carrier of (A -VectSp_over F_Real)
the lmult of (A -VectSp_over F_Real) is Relation-like [: the carrier of F_Real, the carrier of (A -VectSp_over F_Real):] -defined the carrier of (A -VectSp_over F_Real) -valued Function-like total quasi_total Element of bool [:[: the carrier of F_Real, the carrier of (A -VectSp_over F_Real):], the carrier of (A -VectSp_over F_Real):]
[: the carrier of F_Real, the carrier of (A -VectSp_over F_Real):] is Relation-like set
[:[: the carrier of F_Real, the carrier of (A -VectSp_over F_Real):], the carrier of (A -VectSp_over F_Real):] is Relation-like set
bool [:[: the carrier of F_Real, the carrier of (A -VectSp_over F_Real):], the carrier of (A -VectSp_over F_Real):] is set
VectSpStr(# the carrier of (A -VectSp_over F_Real), the addF of (A -VectSp_over F_Real), the ZeroF of (A -VectSp_over F_Real), the lmult of (A -VectSp_over F_Real) #) is non empty strict VectSpStr over F_Real
[#] ((Omega). (A -VectSp_over F_Real)) is non empty non proper Element of bool the carrier of ((Omega). (A -VectSp_over F_Real))
the carrier of ((Omega). (A -VectSp_over F_Real)) is non empty set
bool the carrier of ((Omega). (A -VectSp_over F_Real)) is set
rank (Mx2Tran (U,L,x)) is ordinal natural V28() real finite cardinal ext-real non negative set
dim (im (Mx2Tran (U,L,x))) is ordinal natural V28() real finite cardinal ext-real non negative set
dim ((Omega). (A -VectSp_over F_Real)) is ordinal natural V28() real finite cardinal ext-real non negative set
dim (A -VectSp_over F_Real) is ordinal natural V28() real finite cardinal ext-real non negative set
(Omega). (im (Mx2Tran (U,L,x))) is non empty right_complementable V148() V149() V150() strict V165( F_Real ) V166( F_Real ) V167( F_Real ) V168( F_Real ) finite-dimensional Subspace of im (Mx2Tran (U,L,x))
the addF of (im (Mx2Tran (U,L,x))) is Relation-like [: the carrier of (im (Mx2Tran (U,L,x))), the carrier of (im (Mx2Tran (U,L,x))):] -defined the carrier of (im (Mx2Tran (U,L,x))) -valued Function-like total quasi_total Element of bool [:[: the carrier of (im (Mx2Tran (U,L,x))), the carrier of (im (Mx2Tran (U,L,x))):], the carrier of (im (Mx2Tran (U,L,x))):]
[: the carrier of (im (Mx2Tran (U,L,x))), the carrier of (im (Mx2Tran (U,L,x))):] is Relation-like set
[:[: the carrier of (im (Mx2Tran (U,L,x))), the carrier of (im (Mx2Tran (U,L,x))):], the carrier of (im (Mx2Tran (U,L,x))):] is Relation-like set
bool [:[: the carrier of (im (Mx2Tran (U,L,x))), the carrier of (im (Mx2Tran (U,L,x))):], the carrier of (im (Mx2Tran (U,L,x))):] is set
the ZeroF of (im (Mx2Tran (U,L,x))) is Element of the carrier of (im (Mx2Tran (U,L,x)))
the lmult of (im (Mx2Tran (U,L,x))) is Relation-like [: the carrier of F_Real, the carrier of (im (Mx2Tran (U,L,x))):] -defined the carrier of (im (Mx2Tran (U,L,x))) -valued Function-like total quasi_total Element of bool [:[: the carrier of F_Real, the carrier of (im (Mx2Tran (U,L,x))):], the carrier of (im (Mx2Tran (U,L,x))):]
[: the carrier of F_Real, the carrier of (im (Mx2Tran (U,L,x))):] is Relation-like set
[:[: the carrier of F_Real, the carrier of (im (Mx2Tran (U,L,x))):], the carrier of (im (Mx2Tran (U,L,x))):] is Relation-like set
bool [:[: the carrier of F_Real, the carrier of (im (Mx2Tran (U,L,x))):], the carrier of (im (Mx2Tran (U,L,x))):] is set
VectSpStr(# the carrier of (im (Mx2Tran (U,L,x))), the addF of (im (Mx2Tran (U,L,x))), the ZeroF of (im (Mx2Tran (U,L,x))), the lmult of (im (Mx2Tran (U,L,x))) #) is non empty strict VectSpStr over F_Real
n is ordinal natural V28() real finite cardinal ext-real non negative set
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
A is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n, the carrier of F_Real
(n,n,A) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):] is set
Det A is V28() real ext-real Element of the carrier of F_Real
the_rank_of A is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n, the carrier of F_Real
Det A is V28() real ext-real Element of the carrier of F_Real
(n,n,A) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):] is set
(n,n,A) " is Relation-like Function-like set
A ~ is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n, the carrier of F_Real
T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n, the carrier of F_Real
(n,n,T) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
width T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width A is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len A is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
TM is Relation-like Function-like set
L is Relation-like Function-like set
TM (#) L is Relation-like Function-like set
dom TM is set
id (dom TM) is Relation-like dom TM -defined dom TM -valued Function-like one-to-one total quasi_total Element of bool [:(dom TM),(dom TM):]
[:(dom TM),(dom TM):] is Relation-like set
bool [:(dom TM),(dom TM):] is set
id (TOP-REAL n) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total V170( TOP-REAL n, TOP-REAL n) Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
id the carrier of (TOP-REAL n) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
1. (F_Real,n) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n, the carrier of F_Real
(n,n,(1. (F_Real,n))) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
(n,n,T) * (n,n,A) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
A * T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n, the carrier of F_Real
(n,n,(A * T)) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
dom (n,n,T) is non empty set
[#] (TOP-REAL n) is non empty non proper Element of bool the carrier of (TOP-REAL n)
bool the carrier of (TOP-REAL n) is set
rng (n,n,A) is non empty set
dom (n,n,A) is non empty set
id (dom (n,n,A)) is Relation-like dom (n,n,A) -defined dom (n,n,A) -valued Function-like one-to-one non empty total quasi_total Element of bool [:(dom (n,n,A)),(dom (n,n,A)):]
[:(dom (n,n,A)),(dom (n,n,A)):] is Relation-like set
bool [:(dom (n,n,A)),(dom (n,n,A)):] is set
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is ordinal natural V28() real finite cardinal ext-real non negative set
T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
(n,A,T) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is set
Tn is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(n,A,T) . Tn is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
|.((n,A,T) . Tn).| is V28() real ext-real non negative Element of REAL
sqr ((n,A,T) . Tn) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr ((n,A,T) . Tn)) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((n,A,T) . Tn))) is V28() real ext-real Element of REAL
|.Tn.| is V28() real ext-real non negative Element of REAL
sqr Tn is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr Tn) is V28() real ext-real Element of REAL
sqrt (Sum (sqr Tn)) is V28() real ext-real Element of REAL
(Tn) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
LineVec2Mx (Tn) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of 1, len (Tn), the carrier of F_Real
len (Tn) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(LineVec2Mx (Tn)) * T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of F_Real *
Line (((LineVec2Mx (Tn)) * T),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width ((LineVec2Mx (Tn)) * T) -element FinSequence-like FinSubsequence-like Element of (width ((LineVec2Mx (Tn)) * T)) -tuples_on the carrier of F_Real
width ((LineVec2Mx (Tn)) * T) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(width ((LineVec2Mx (Tn)) * T)) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len x is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
dom x is finite V197() V198() V199() V200() V201() V202() Element of bool NAT
rng x is finite set
U is set
TMx is set
x . TMx is set
tmx is ordinal natural V28() real finite cardinal ext-real non negative set
x . tmx is set
Col (T,tmx) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite len T -element FinSequence-like FinSubsequence-like Element of (len T) -tuples_on the carrier of F_Real
len T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(len T) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
((Col (T,tmx))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
|.((Col (T,tmx))).| is V28() real ext-real non negative Element of REAL
sqr ((Col (T,tmx))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr ((Col (T,tmx)))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((Col (T,tmx))))) is V28() real ext-real Element of REAL
A -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
U is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of A -tuples_on REAL
Sum U is V28() real ext-real Element of REAL
(Sum U) * |.Tn.| is V28() real ext-real Element of REAL
dom U is finite A -element V197() V198() V199() V200() V201() V202() Element of bool NAT
len T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len (Line (((LineVec2Mx (Tn)) * T),1)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
((Line (((LineVec2Mx (Tn)) * T),1))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
sqr ((Line (((LineVec2Mx (Tn)) * T),1))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr ((Line (((LineVec2Mx (Tn)) * T),1)))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((Line (((LineVec2Mx (Tn)) * T),1))))) is V28() real ext-real Element of REAL
TMx is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of A -tuples_on REAL
abs TMx is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
absreal is Relation-like REAL -defined REAL -valued Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
TMx (#) absreal is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
len (abs TMx) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len Tn is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width (LineVec2Mx (Tn)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len (LineVec2Mx (Tn)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len ((LineVec2Mx (Tn)) * T) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
X is ordinal natural V28() real finite cardinal ext-real non negative set
Col (T,X) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite len T -element FinSequence-like FinSubsequence-like Element of (len T) -tuples_on the carrier of F_Real
(len T) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
len (Col (T,X)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
((Col (T,X))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
|(Tn,((Col (T,X))))| is V28() real ext-real Element of REAL
abs |(Tn,((Col (T,X))))| is V28() real ext-real Element of REAL
|.((Col (T,X))).| is V28() real ext-real non negative Element of REAL
sqr ((Col (T,X))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr ((Col (T,X)))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((Col (T,X))))) is V28() real ext-real Element of REAL
|.Tn.| * H₁(X) is V28() real ext-real non negative Element of REAL
Seg A is finite A -element V137() V197() V198() V199() V200() V201() V202() Element of bool NAT
{ b₁ where b₁ is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT : ( 1 <= b₁ & b₁ <= A ) } is set
[1,X] is set
{1,X} is non empty finite V38() V197() V198() V199() V200() V201() V202() set
{1} is non empty trivial finite V38() 1 -element V197() V198() V199() V200() V201() V202() set
{{1,X},{1}} is non empty finite V38() set
Indices ((LineVec2Mx (Tn)) * T) is set
x . X is set
TMx . X is V28() real ext-real set
((LineVec2Mx (Tn)) * T) * (1,X) is V28() real ext-real Element of the carrier of F_Real
Line ((LineVec2Mx (Tn)),1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite width (LineVec2Mx (Tn)) -element FinSequence-like FinSubsequence-like Element of (width (LineVec2Mx (Tn))) -tuples_on the carrier of F_Real
(width (LineVec2Mx (Tn))) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
(Line ((LineVec2Mx (Tn)),1)) "*" (Col (T,X)) is V28() real ext-real Element of the carrier of F_Real
mlt ((Line ((LineVec2Mx (Tn)),1)),(Col (T,X))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
the multF of F_Real is Relation-like [: the carrier of F_Real, the carrier of F_Real:] -defined the carrier of F_Real -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:]
[: the carrier of F_Real, the carrier of F_Real:] is Relation-like complex-valued ext-real-valued real-valued set
[:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:] is set
K446( the carrier of F_Real, the carrier of F_Real, the carrier of F_Real, the multF of F_Real,(Line ((LineVec2Mx (Tn)),1)),(Col (T,X))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Sum (mlt ((Line ((LineVec2Mx (Tn)),1)),(Col (T,X)))) is V28() real ext-real Element of the carrier of F_Real
the addF of F_Real is Relation-like [: the carrier of F_Real, the carrier of F_Real:] -defined the carrier of F_Real -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:[: the carrier of F_Real, the carrier of F_Real:], the carrier of F_Real:]
the addF of F_Real "**" (mlt ((Line ((LineVec2Mx (Tn)),1)),(Col (T,X)))) is V28() real ext-real Element of the carrier of F_Real
mlt ((Tn),(Col (T,X))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
K446( the carrier of F_Real, the carrier of F_Real, the carrier of F_Real, the multF of F_Real,(Tn),(Col (T,X))) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
Sum (mlt ((Tn),(Col (T,X)))) is V28() real ext-real Element of the carrier of F_Real
the addF of F_Real "**" (mlt ((Tn),(Col (T,X)))) is V28() real ext-real Element of the carrier of F_Real
mlt (Tn,((Col (T,X)))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (mlt (Tn,((Col (T,X))))) is V28() real ext-real Element of REAL
tmx is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of A -tuples_on REAL
tmx . X is V28() real ext-real set
|.Tn.| * U is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of A -tuples_on REAL
(|.Tn.| * U) . X is V28() real ext-real set
Sum tmx is V28() real ext-real Element of REAL
Sum (|.Tn.| * U) is V28() real ext-real Element of REAL
sqr TMx is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of A -tuples_on REAL
TMx (#) TMx is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued nonnegative-yielding Element of bool [:NAT,REAL:]
Sum (sqr TMx) is V28() real ext-real Element of REAL
sqrt (Sum (sqr TMx)) is V28() real ext-real Element of REAL
sqrt (sqr TMx) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of bool [:NAT,REAL:]
Sum (sqrt (sqr TMx)) is V28() real ext-real set
|.Tn.| * (Sum U) is V28() real ext-real Element of REAL
X is ordinal natural V28() real finite cardinal ext-real non negative set
U . X is V28() real ext-real set
Col (T,X) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite len T -element FinSequence-like FinSubsequence-like Element of (len T) -tuples_on the carrier of F_Real
((Col (T,X))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
|.((Col (T,X))).| is V28() real ext-real non negative Element of REAL
sqr ((Col (T,X))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr ((Col (T,X)))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((Col (T,X))))) is V28() real ext-real Element of REAL
TMx is ordinal natural V28() real finite cardinal ext-real non negative set
U . TMx is V28() real ext-real set
Col (T,TMx) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite len T -element FinSequence-like FinSubsequence-like Element of (len T) -tuples_on the carrier of F_Real
len T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(len T) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
((Col (T,TMx))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
|.((Col (T,TMx))).| is V28() real ext-real non negative Element of REAL
sqr ((Col (T,TMx))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr ((Col (T,TMx)))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((Col (T,TMx))))) is V28() real ext-real Element of REAL
0. (TOP-REAL A) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like V64( TOP-REAL A) complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
the ZeroF of (TOP-REAL A) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
|.(0. (TOP-REAL A)).| is V28() real ext-real non negative Element of REAL
sqr (0. (TOP-REAL A)) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr (0. (TOP-REAL A))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr (0. (TOP-REAL A)))) is V28() real ext-real Element of REAL
TMx is ordinal natural V28() real finite cardinal ext-real non negative set
U . TMx is V28() real ext-real set
Col (T,TMx) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite len T -element FinSequence-like FinSubsequence-like Element of (len T) -tuples_on the carrier of F_Real
((Col (T,TMx))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
|.((Col (T,TMx))).| is V28() real ext-real non negative Element of REAL
sqr ((Col (T,TMx))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr ((Col (T,TMx)))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((Col (T,TMx))))) is V28() real ext-real Element of REAL
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is ordinal natural V28() real finite cardinal ext-real non negative set
T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of A,n, the carrier of F_Real
(A,n,T) is Relation-like the carrier of (TOP-REAL A) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL A), the carrier of (TOP-REAL n):]
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
[: the carrier of (TOP-REAL A), the carrier of (TOP-REAL n):] is Relation-like set
bool [: the carrier of (TOP-REAL A), the carrier of (TOP-REAL n):] is set
the Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(A,n,T) . the Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
|.((A,n,T) . the Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set ).| is V28() real ext-real non negative Element of REAL
sqr ((A,n,T) . the Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set ) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr ((A,n,T) . the Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set )) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((A,n,T) . the Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set ))) is V28() real ext-real Element of REAL
|. the Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set .| is V28() real ext-real non negative Element of REAL
sqr the Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr the Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set ) is V28() real ext-real Element of REAL
sqrt (Sum (sqr the Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set )) is V28() real ext-real Element of REAL
Tm is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum Tm is V28() real ext-real Element of REAL
(Sum Tm) * |. the Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set .| is V28() real ext-real Element of REAL
dom Tm is finite n -element V197() V198() V199() V200() V201() V202() Element of bool NAT
TM is ordinal natural V28() real finite cardinal ext-real non negative set
Tm . TM is V28() real ext-real set
Col (T,TM) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite len T -element FinSequence-like FinSubsequence-like Element of (len T) -tuples_on the carrier of F_Real
len T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(len T) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
((Col (T,TM))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
|.((Col (T,TM))).| is V28() real ext-real non negative Element of REAL
sqr ((Col (T,TM))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr ((Col (T,TM)))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((Col (T,TM))))) is V28() real ext-real Element of REAL
TM is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(A,n,T) . TM is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
|.((A,n,T) . TM).| is V28() real ext-real non negative Element of REAL
sqr ((A,n,T) . TM) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr ((A,n,T) . TM)) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((A,n,T) . TM))) is V28() real ext-real Element of REAL
|.TM.| is V28() real ext-real non negative Element of REAL
sqr TM is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr TM) is V28() real ext-real Element of REAL
sqrt (Sum (sqr TM)) is V28() real ext-real Element of REAL
(Sum Tm) * |.TM.| is V28() real ext-real Element of REAL
L is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum L is V28() real ext-real Element of REAL
(Sum L) * |.TM.| is V28() real ext-real Element of REAL
dom L is finite n -element V197() V198() V199() V200() V201() V202() Element of bool NAT
len L is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
x is ordinal natural V28() real finite cardinal ext-real non negative set
Tm . x is V28() real ext-real set
Col (T,x) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite len T -element FinSequence-like FinSubsequence-like Element of (len T) -tuples_on the carrier of F_Real
len T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(len T) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
((Col (T,x))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
|.((Col (T,x))).| is V28() real ext-real non negative Element of REAL
sqr ((Col (T,x))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr ((Col (T,x)))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((Col (T,x))))) is V28() real ext-real Element of REAL
L . x is V28() real ext-real set
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is ordinal natural V28() real finite cardinal ext-real non negative set
T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of A,n, the carrier of F_Real
(A,n,T) is Relation-like the carrier of (TOP-REAL A) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL A), the carrier of (TOP-REAL n):]
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
[: the carrier of (TOP-REAL A), the carrier of (TOP-REAL n):] is Relation-like set
bool [: the carrier of (TOP-REAL A), the carrier of (TOP-REAL n):] is set
Tn is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
dom Tn is finite n -element V197() V198() V199() V200() V201() V202() Element of bool NAT
Sum Tn is V28() real ext-real Element of REAL
1 + (Sum Tn) is V28() real ext-real Element of REAL
Tm is V28() real ext-real Element of REAL
TM is ordinal natural V28() real finite cardinal ext-real non negative set
Tn . TM is V28() real ext-real set
Col (T,TM) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite len T -element FinSequence-like FinSubsequence-like Element of (len T) -tuples_on the carrier of F_Real
len T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(len T) -tuples_on the carrier of F_Real is functional non empty FinSequence-membered FinSequenceSet of the carrier of F_Real
((Col (T,TM))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
|.((Col (T,TM))).| is V28() real ext-real non negative Element of REAL
sqr ((Col (T,TM))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr ((Col (T,TM)))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((Col (T,TM))))) is V28() real ext-real Element of REAL
TM is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(A,n,T) . TM is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
|.((A,n,T) . TM).| is V28() real ext-real non negative Element of REAL
sqr ((A,n,T) . TM) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr ((A,n,T) . TM)) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((A,n,T) . TM))) is V28() real ext-real Element of REAL
|.TM.| is V28() real ext-real non negative Element of REAL
sqr TM is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr TM) is V28() real ext-real Element of REAL
sqrt (Sum (sqr TM)) is V28() real ext-real Element of REAL
Tm * |.TM.| is V28() real ext-real Element of REAL
(Sum Tn) * |.TM.| is V28() real ext-real Element of REAL
n is ordinal natural V28() real finite cardinal ext-real non negative set
A is ordinal natural V28() real finite cardinal ext-real non negative set
T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of A,n, the carrier of F_Real
the_rank_of T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(A,n,T) is Relation-like the carrier of (TOP-REAL A) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL A), the carrier of (TOP-REAL n):]
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL A) is non empty set
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL n) is non empty set
[: the carrier of (TOP-REAL A), the carrier of (TOP-REAL n):] is Relation-like set
bool [: the carrier of (TOP-REAL A), the carrier of (TOP-REAL n):] is set
n -' A is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Tn is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n -' A,n, the carrier of F_Real
T ^ Tn is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K96(A,(n -' A)),n, the carrier of F_Real
K96(A,(n -' A)) is ordinal natural V28() real finite cardinal ext-real non negative set
the_rank_of (T ^ Tn) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width T is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
n - A is V28() real ext-real Element of REAL
id (TOP-REAL n) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total V170( TOP-REAL n, TOP-REAL n) Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):] is set
id the carrier of (TOP-REAL n) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
dom (id (TOP-REAL n)) is non empty set
[#] (TOP-REAL n) is non empty non proper Element of bool the carrier of (TOP-REAL n)
bool the carrier of (TOP-REAL n) is set
(n -' A) |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -' A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of (n -' A) -tuples_on REAL
(n -' A) -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
sqr ((n -' A) |-> 0) is Relation-like NAT -defined REAL -valued Function-like finite n -' A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of (n -' A) -tuples_on REAL
0 ^2 is set
K97(0,0) is Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty ordinal natural V28() real finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V197() V198() V199() V200() V201() V202() V203() set
(n -' A) |-> (0 ^2) is Relation-like NAT -defined Function-like finite n -' A -element FinSequence-like FinSubsequence-like set
0* 0 is Relation-like non-empty empty-yielding NAT -defined REAL -valued Function-like one-to-one constant functional empty ordinal natural V28() real finite finite-yielding V38() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V197() V198() V199() V200() V201() V202() V203() Element of REAL 0
0 |-> 0 is Relation-like non-empty empty-yielding NAT -defined REAL -valued Function-like one-to-one constant functional empty ordinal natural V28() real finite finite-yielding V38() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V197() V198() V199() V200() V201() V202() V203() Element of 0 -tuples_on REAL
(n -' A) |-> (0* 0) is Relation-like NAT -defined REAL 0 -valued Function-like finite n -' A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of (n -' A) -tuples_on (REAL 0)
(n -' A) -tuples_on (REAL 0) is functional non empty FinSequence-membered FinSequenceSet of REAL 0
Sum (sqr ((n -' A) |-> 0)) is V28() real ext-real Element of REAL
(n -' A) * 0 is Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty ordinal natural V28() real V30() V31() finite finite-yielding V38() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V197() V198() V199() V200() V201() V202() V203() Element of NAT
Tm is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n, the carrier of F_Real
Tm ~ is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n, the carrier of F_Real
(n,n,(Tm ~)) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
x is V28() real ext-real Element of REAL
U is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
|.U.| is V28() real ext-real non negative Element of REAL
sqr U is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr U) is V28() real ext-real Element of REAL
sqrt (Sum (sqr U)) is V28() real ext-real Element of REAL
(A,n,T) . U is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
|.((A,n,T) . U).| is V28() real ext-real non negative Element of REAL
sqr ((A,n,T) . U) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr ((A,n,T) . U)) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((A,n,T) . U))) is V28() real ext-real Element of REAL
x * |.((A,n,T) . U).| is V28() real ext-real Element of REAL
U ^ ((n -' A) |-> 0) is Relation-like NAT -defined Function-like finite K417(A,(n -' A)) -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
K417(A,(n -' A)) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(n,n,Tm) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
(n,n,Tm) . (U ^ ((n -' A) |-> 0)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
Det Tm is V28() real ext-real Element of the carrier of F_Real
width Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
width (Tm ~) is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
len Tm is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
(n,n,(Tm ~)) * (n,n,Tm) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
TOP-REAL (width Tm) is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL (width Tm)) is non empty set
X is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of width Tm,n, the carrier of F_Real
((width Tm),n,X) is Relation-like the carrier of (TOP-REAL (width Tm)) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL (width Tm)), the carrier of (TOP-REAL n):]
[: the carrier of (TOP-REAL (width Tm)), the carrier of (TOP-REAL n):] is Relation-like set
bool [: the carrier of (TOP-REAL (width Tm)), the carrier of (TOP-REAL n):] is set
((width Tm),n,X) * (n,n,Tm) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
width X is ordinal natural V28() real V30() V31() finite cardinal ext-real non negative V197() V198() V199() V200() V201() V202() Element of NAT
Tm * X is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len Tm, width X, the carrier of F_Real
((len Tm),(width X),(Tm * X)) is Relation-like the carrier of (TOP-REAL (len Tm)) -defined the carrier of (TOP-REAL (width X)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL (len Tm)), the carrier of (TOP-REAL (width X)):]
TOP-REAL (len Tm) is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL (len Tm)) is non empty set
TOP-REAL (width X) is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
the carrier of (TOP-REAL (width X)) is non empty set
[: the carrier of (TOP-REAL (len Tm)), the carrier of (TOP-REAL (width X)):] is Relation-like set
bool [: the carrier of (TOP-REAL (len Tm)), the carrier of (TOP-REAL (width X)):] is set
1. (F_Real,n) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n, the carrier of F_Real
(n,n,(1. (F_Real,n))) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
(U) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
((U)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(((n -' A) |-> 0)) is Relation-like NAT -defined the carrier of F_Real -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of the carrier of F_Real
((((n -' A) |-> 0))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
sqr (U ^ ((n -' A) |-> 0)) is Relation-like NAT -defined REAL -valued Function-like finite K417(A,(n -' A)) -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(sqr U) ^ (sqr ((n -' A) |-> 0)) is Relation-like NAT -defined REAL -valued Function-like finite K417(A,(n -' A)) -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr (U ^ ((n -' A) |-> 0))) is V28() real ext-real Element of REAL
(Sum (sqr U)) + (Sum (sqr ((n -' A) |-> 0))) is V28() real ext-real Element of REAL
|.(U ^ ((n -' A) |-> 0)).| is V28() real ext-real non negative Element of REAL
sqrt (Sum (sqr (U ^ ((n -' A) |-> 0)))) is V28() real ext-real Element of REAL
(id (TOP-REAL n)) . (U ^ ((n -' A) |-> 0)) is set
(n,n,(Tm ~)) . ((n,n,Tm) . (U ^ ((n -' A) |-> 0))) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
0* A is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of REAL A
REAL A is functional non empty FinSequence-membered FinSequenceSet of REAL
A -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
A |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of A -tuples_on REAL
|.(0* A).| is V28() real ext-real non negative Element of REAL
sqr (0* A) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr (0* A)) is V28() real ext-real Element of REAL
sqrt (Sum (sqr (0* A))) is V28() real ext-real Element of REAL
Tn is non empty ordinal natural V28() real V30() V31() finite cardinal ext-real positive non negative V197() V198() V199() V200() V201() V202() Element of NAT
Tm is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
|.Tm.| is V28() real ext-real non negative Element of REAL
sqr Tm is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr Tm) is V28() real ext-real Element of REAL
sqrt (Sum (sqr Tm)) is V28() real ext-real Element of REAL
(A,n,T) . Tm is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
|.((A,n,T) . Tm).| is V28() real ext-real non negative Element of REAL
sqr ((A,n,T) . Tm) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr ((A,n,T) . Tm)) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((A,n,T) . Tm))) is V28() real ext-real Element of REAL
Tn * |.((A,n,T) . Tm).| is V28() real ext-real non negative Element of REAL
n is ordinal natural V28() real finite cardinal ext-real non negative set
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
A is ordinal natural V28() real finite cardinal ext-real non negative set
TOP-REAL A is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
T is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,A, the carrier of F_Real
(n,A,T) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL A) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):]
the carrier of (TOP-REAL n) is non empty set
the carrier of (TOP-REAL A) is non empty set
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL A):] is set
L is V28() real ext-real Element of REAL
x is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(n,A,T) . x is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
U is a_neighborhood of (n,A,T) . x
Euclid A is non empty V217() V218() strict Reflexive discerning V278() triangle MetrStruct
REAL A is functional non empty FinSequence-membered FinSequenceSet of REAL
A -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
Pitag_dist A is Relation-like [:(REAL A),(REAL A):] -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:[:(REAL A),(REAL A):],REAL:]
[:(REAL A),(REAL A):] is Relation-like set
[:[:(REAL A),(REAL A):],REAL:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:[:(REAL A),(REAL A):],REAL:] is set
MetrStruct(# (REAL A),(Pitag_dist A) #) is strict MetrStruct
the carrier of (Euclid A) is non empty set
TMx is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
Euclid n is non empty V217() V218() strict Reflexive discerning V278() triangle MetrStruct
REAL n is functional non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
Pitag_dist n is Relation-like [:(REAL n),(REAL n):] -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:[:(REAL n),(REAL n):],REAL:]
[:(REAL n),(REAL n):] is Relation-like set
[:[:(REAL n),(REAL n):],REAL:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:[:(REAL n),(REAL n):],REAL:] is set
MetrStruct(# (REAL n),(Pitag_dist n) #) is strict MetrStruct
the carrier of (Euclid n) is non empty set
tmx is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (Euclid A)
Int U is Element of bool the carrier of (TOP-REAL A)
bool the carrier of (TOP-REAL A) is set
r is V28() real ext-real set
Ball (tmx,r) is Element of bool the carrier of (Euclid A)
bool the carrier of (Euclid A) is set
bool the carrier of (TOP-REAL n) is set
X is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (Euclid n)
r / L is V28() real ext-real Element of REAL
Ball (X,(r / L)) is Element of bool the carrier of (Euclid n)
bool the carrier of (Euclid n) is set
B is Element of bool the carrier of (TOP-REAL n)
Int B is Element of bool the carrier of (TOP-REAL n)
Bx is a_neighborhood of x
K782( the carrier of (TOP-REAL n), the carrier of (TOP-REAL A),(n,A,T),Bx) is Element of bool the carrier of (TOP-REAL A)
y is set
(n,A,T) .: Bx is Element of bool the carrier of (TOP-REAL A)
dom (n,A,T) is non empty set
p is set
(n,A,T) . p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued set
(r / L) * L is V28() real ext-real Element of REAL
p is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(n,A,T) . p is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
TMp is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
tmp is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (Euclid A)
dist (tmx,tmp) is V28() real ext-real Element of REAL
((n,A,T) . x) - ((n,A,T) . p) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
((n,A,T) . x) - ((n,A,T) . p) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
|.(((n,A,T) . x) - ((n,A,T) . p)).| is V28() real ext-real non negative Element of REAL
sqr (((n,A,T) . x) - ((n,A,T) . p)) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr (((n,A,T) . x) - ((n,A,T) . p))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr (((n,A,T) . x) - ((n,A,T) . p)))) is V28() real ext-real Element of REAL
x - p is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
x - p is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(n,A,T) . (x - p) is Relation-like NAT -defined Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (TOP-REAL A)
|.((n,A,T) . (x - p)).| is V28() real ext-real non negative Element of REAL
sqr ((n,A,T) . (x - p)) is Relation-like NAT -defined REAL -valued Function-like finite A -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr ((n,A,T) . (x - p))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((n,A,T) . (x - p)))) is V28() real ext-real Element of REAL
|.(x - p).| is V28() real ext-real non negative Element of REAL
sqr (x - p) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr (x - p)) is V28() real ext-real Element of REAL
sqrt (Sum (sqr (x - p))) is V28() real ext-real Element of REAL
L * |.(x - p).| is V28() real ext-real Element of REAL
P is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued Element of the carrier of (Euclid n)
dist (X,P) is V28() real ext-real Element of REAL
(dist (X,P)) * L is V28() real ext-real Element of REAL
A is non empty non degenerated non trivial right_complementable almost_left_invertible V141() V143() V145() V148() V149() V150() right-distributive left-distributive right_unital well-unital V162() left_unital doubleLoopStr
the carrier of A is non empty non trivial set
the carrier of A * is functional non empty FinSequence-membered FinSequenceSet of the carrier of A
n is ordinal natural V28() real finite cardinal ext-real non negative set
1. (A,n) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n, the carrier of A
n is ordinal natural V28() real finite cardinal ext-real non negative set
TOP-REAL n is non empty TopSpace-like right_complementable V148() V149() V150() V151() V152() V153() V154() V217() V218() V287() L22()
A is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular invertible Matrix of n,n, the carrier of F_Real
(n,n,A) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
the carrier of (TOP-REAL n) is non empty set
[: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):] is set
A ~ is Relation-like NAT -defined the carrier of F_Real * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of n,n, the carrier of F_Real
(n,n,(A ~)) is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]
Det A is V28() real ext-real Element of the carrier of F_Real
(n,n,A) " is Relation-like Function-like set
rng (n,n,A) is non empty set
[#] (TOP-REAL n) is non empty non proper Element of bool the carrier of (TOP-REAL n)
bool the carrier of (TOP-REAL n) is set
dom (n,n,A) is non empty set
(n,n,A) /" is Relation-like the carrier of (TOP-REAL n) -defined the carrier of (TOP-REAL n) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of (TOP-REAL n):]