REAL is non empty non trivial non finite V126() V127() V128() V132() set
NAT is non empty non trivial ordinal non finite cardinal limit_cardinal V126() V127() V128() V129() V130() V131() V132() Element of bool REAL
bool REAL is non empty non trivial non finite set
RAT is non empty non trivial non finite V126() V127() V128() V129() V132() set
COMPLEX is non empty non trivial non finite V126() V132() set
INT is non empty non trivial non finite V126() V127() V128() V129() V130() V132() set
[:COMPLEX,COMPLEX:] is non empty non trivial Relation-like non finite complex-yielding set
bool [:COMPLEX,COMPLEX:] is non empty non trivial non finite set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is non empty non trivial Relation-like non finite complex-yielding set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is non empty non trivial non finite set
[:REAL,REAL:] is non empty non trivial Relation-like non finite complex-yielding ext-real-valued real-valued set
bool [:REAL,REAL:] is non empty non trivial non finite set
[:[:REAL,REAL:],REAL:] is non empty non trivial Relation-like non finite complex-yielding ext-real-valued real-valued set
bool [:[:REAL,REAL:],REAL:] is non empty non trivial non finite set
[:RAT,RAT:] is non empty non trivial Relation-like RAT -valued non finite complex-yielding ext-real-valued real-valued set
bool [:RAT,RAT:] is non empty non trivial non finite set
[:[:RAT,RAT:],RAT:] is non empty non trivial Relation-like RAT -valued non finite complex-yielding ext-real-valued real-valued set
bool [:[:RAT,RAT:],RAT:] is non empty non trivial non finite set
[:INT,INT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-yielding ext-real-valued real-valued set
bool [:INT,INT:] is non empty non trivial non finite set
[:[:INT,INT:],INT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-yielding ext-real-valued real-valued set
bool [:[:INT,INT:],INT:] is non empty non trivial non finite set
[:NAT,NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-yielding ext-real-valued real-valued natural-valued set
[:[:NAT,NAT:],NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:NAT,NAT:],NAT:] is non empty non trivial non finite set
omega is non empty non trivial ordinal non finite cardinal limit_cardinal V126() V127() V128() V129() V130() V131() V132() set
bool omega is non empty non trivial non finite set
bool NAT is non empty non trivial non finite set
K346() is non empty strict multMagma
the carrier of K346() is non empty set
<REAL,+> is non empty strict V97() V98() V99() V101() left-invertible right-invertible invertible left-cancelable right-cancelable V153() multMagma
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:[:REAL,REAL:],REAL:]
multMagma(# REAL,addreal #) is strict multMagma
K352() is non empty strict V99() V101() left-cancelable right-cancelable V153() SubStr of <REAL,+>
<NAT,+> is non empty strict V97() V99() V101() left-cancelable right-cancelable V153() uniquely-decomposable SubStr of K352()
<REAL,*> is non empty strict V97() V99() V101() multMagma
multreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:[:REAL,REAL:],REAL:]
multMagma(# REAL,multreal #) is strict multMagma
<NAT,*> is non empty strict V97() V99() V101() uniquely-decomposable SubStr of <REAL,*>
{} is empty trivial ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() set
the empty trivial ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() set is empty trivial ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() set
2 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
[:NAT,REAL:] is non empty non trivial Relation-like non finite complex-yielding ext-real-valued real-valued set
bool [:NAT,REAL:] is non empty non trivial non finite set
1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
[:1,1:] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:1,1:] is non empty finite V39() set
[:[:1,1:],1:] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:1,1:],1:] is non empty finite V39() set
[:[:1,1:],REAL:] is non empty non trivial Relation-like non finite complex-yielding ext-real-valued real-valued set
bool [:[:1,1:],REAL:] is non empty non trivial non finite set
[:2,2:] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
[:[:2,2:],REAL:] is non empty non trivial Relation-like non finite complex-yielding ext-real-valued real-valued set
bool [:[:2,2:],REAL:] is non empty non trivial non finite set
TOP-REAL 2 is non empty right_complementable constituted-Functions constituted-FinSeqs Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V197() V227() L20()
the carrier of (TOP-REAL 2) is non empty set
{{},1} is non empty finite V39() V126() V127() V128() V129() V130() V131() set
K235() is strict doubleLoopStr
the carrier of K235() is set
the carrier of K235() * is non empty functional FinSequence-membered FinSequenceSet of the carrier of K235()
REAL * is non empty functional FinSequence-membered FinSequenceSet of REAL
K379(NAT) is V168() set
ExtREAL is non empty V127() set
0 is empty trivial ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional V33() V34() finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() Element of NAT
3 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
Seg 1 is non empty trivial finite 1 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
{1} is non empty trivial finite V39() 1 -element V126() V127() V128() V129() V130() V131() set
Seg 2 is non empty finite 2 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
{1,2} is non empty finite V39() V126() V127() V128() V129() V130() V131() set
sqrt 1 is V11() V12() ext-real Element of REAL
- 1 is V11() V12() ext-real non positive Element of REAL
B is Relation-like Function-like set
n is Relation-like Function-like set
B (#) n is Relation-like Function-like set
dom (B (#) n) is set
dom B is set
dom n is set
B " (dom n) is set
(dom B) /\ (B " (dom n)) is set
B0 is set
B . B0 is set
B0 is set
B . B0 is set
n is Relation-like set
rng n is set
dom n is set
B is set
n " B is set
(rng n) /\ B is set
n " (rng n) is set
n is set
B is non empty set
[:n,B:] is Relation-like set
bool [:n,B:] is non empty set
B0 is Relation-like n -defined B -valued Function-like total quasi_total Element of bool [:n,B:]
card n is ordinal cardinal set
card B is non empty ordinal cardinal set
<*1*> is non empty trivial Relation-like NAT -defined NAT -valued Function-like one-to-one constant finite 1 -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing FinSequence of NAT
n is set
<*n*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like set
<*1*> (#) <*n*> is Relation-like NAT -defined Function-like finite set
dom <*n*> is non empty trivial finite 1 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
rng <*1*> is non empty trivial finite 1 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
{1} is non empty trivial finite V39() 1 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
dom (<*1*> (#) <*n*>) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
dom <*1*> is non empty trivial finite 1 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(<*1*> (#) <*n*>) . 1 is set
<*1*> . 1 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
<*n*> . (<*1*> . 1) is set
<*n*> . 1 is set
REAL 0 is non empty functional FinSequence-membered FinSequenceSet of REAL
0 -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = 0 } is set
<*> REAL is empty trivial proper ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined REAL -valued Function-like one-to-one constant functional finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() FinSequence of REAL
n is empty trivial ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined REAL -valued Function-like one-to-one constant functional finite finite-yielding V39() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() Element of REAL 0
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B - B0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:[:REAL,REAL:],REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total quasi_total complex-yielding ext-real-valued real-valued increasing non-decreasing Element of bool [:REAL,REAL:]
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
K660(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (B,B0) is set
- B0 is Relation-like Function-like complex-yielding set
B0 (#) compreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
K38(1) is V11() V12() ext-real non positive set
K38(1) * B0 is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
B0 (#) (K38(1) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
B + (- B0) is Relation-like Function-like set
B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(B - B0) + B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
addreal .: ((B - B0),B) is set
((B - B0) + B) + B0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
addreal .: (((B - B0) + B),B0) is set
B + B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
addreal .: (B,B) is set
D0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
I is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
D0 - I is Relation-like NAT -defined REAL -valued Function-like complex-yielding ext-real-valued real-valued Element of bool [:NAT,REAL:]
diffreal .: (D0,I) is set
- I is Relation-like Function-like complex-yielding set
I (#) compreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
K38(1) * I is Relation-like Function-like set
I (#) (K38(1) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
D0 + (- I) is Relation-like Function-like set
x0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
(D0 - I) + x0 is Relation-like NAT -defined REAL -valued Function-like complex-yielding ext-real-valued real-valued Element of bool [:NAT,REAL:]
((D0 - I) + x0) + I is Relation-like NAT -defined REAL -valued Function-like complex-yielding ext-real-valued real-valued Element of bool [:NAT,REAL:]
- I is Relation-like NAT -defined REAL -valued Function-like complex-yielding ext-real-valued real-valued Element of bool [:NAT,REAL:]
D0 + (- I) is Relation-like NAT -defined REAL -valued Function-like complex-yielding ext-real-valued real-valued Element of bool [:NAT,REAL:]
(D0 + (- I)) + I is Relation-like NAT -defined REAL -valued Function-like complex-yielding ext-real-valued real-valued Element of bool [:NAT,REAL:]
((D0 + (- I)) + I) + x0 is Relation-like NAT -defined REAL -valued Function-like complex-yielding ext-real-valued real-valued Element of bool [:NAT,REAL:]
I + (- I) is Relation-like NAT -defined REAL -valued Function-like complex-yielding ext-real-valued real-valued Element of bool [:NAT,REAL:]
D0 + (I + (- I)) is Relation-like NAT -defined REAL -valued Function-like complex-yielding ext-real-valued real-valued Element of bool [:NAT,REAL:]
(D0 + (I + (- I))) + x0 is Relation-like NAT -defined REAL -valued Function-like complex-yielding ext-real-valued real-valued Element of bool [:NAT,REAL:]
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(Seg n) --> 0 is Relation-like Seg n -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),{0}:]
{0} is non empty trivial functional finite V39() 1 -element V126() V127() V128() V129() V130() V131() set
[:(Seg n),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),{0}:] is non empty finite V39() set
D0 + (n |-> 0) is Relation-like NAT -defined REAL -valued Function-like complex-yielding ext-real-valued real-valued Element of bool [:NAT,REAL:]
addreal .: (D0,(n |-> 0)) is set
(D0 + (n |-> 0)) + x0 is Relation-like NAT -defined REAL -valued Function-like complex-yielding ext-real-valued real-valued Element of bool [:NAT,REAL:]
D0 + x0 is Relation-like NAT -defined REAL -valued Function-like complex-yielding ext-real-valued real-valued Element of bool [:NAT,REAL:]
addreal .: (D0,x0) is set
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
<:n,B:> is Relation-like Function-like set
dom <:n,B:> is set
dom n is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
dom B is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
(dom n) /\ (dom B) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
n is set
B is Relation-like NAT -defined n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of n
B0 is Relation-like NAT -defined n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of n
<:B,B0:> is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
[:n,n:] is Relation-like set
rng B is finite Element of bool n
bool n is non empty set
rng B0 is finite Element of bool n
[:(rng B),(rng B0):] is Relation-like finite set
rng <:B,B0:> is finite set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
n + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B is ordinal natural V11() V12() ext-real non negative finite cardinal set
B0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
n + B0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B is ordinal natural V11() V12() ext-real non negative finite cardinal set
B + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n + 1) + B is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
len n is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B is ordinal natural V11() V12() ext-real non negative finite cardinal set
B + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
dom n is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
n . (B + 1) is V11() V12() ext-real Element of REAL
n . B is V11() V12() ext-real Element of REAL
B is ext-real set
B0 is ext-real set
D0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
D0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
n . B is V11() V12() ext-real Element of REAL
I is ordinal natural V11() V12() ext-real non negative finite cardinal set
D0 + I is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(D0 + 1) + I is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
n . ((D0 + 1) + I) is V11() V12() ext-real Element of REAL
I + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
D0 + (I + 1) is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(D0 + 1) + (I + 1) is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
n . ((D0 + 1) + (I + 1)) is V11() V12() ext-real Element of REAL
(D0 + I) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(D0 + I) + 0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
1 + (D0 + I) is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
((D0 + 1) + I) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
n . (((D0 + 1) + I) + 1) is V11() V12() ext-real Element of REAL
D0 + 0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(D0 + 1) + 0 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
n . ((D0 + 1) + 0) is V11() V12() ext-real Element of REAL
B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
I is ordinal natural V11() V12() ext-real non negative finite cardinal set
(D0 + 1) + I is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(len n) - 0 is V11() V12() ext-real non negative Element of REAL
B - 1 is V11() V12() ext-real Element of REAL
D0 + I is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
n . B0 is V11() V12() ext-real Element of REAL
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
len n is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
B is ordinal natural V11() V12() ext-real non negative finite cardinal set
n . B0 is V11() V12() ext-real Element of REAL
n . B is V11() V12() ext-real Element of REAL
B + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B is ordinal natural V11() V12() ext-real non negative finite cardinal set
(B + 1) + B is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
n . ((B + 1) + B) is V11() V12() ext-real Element of REAL
B + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B + 1) + (B + 1) is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
n . ((B + 1) + (B + 1)) is V11() V12() ext-real Element of REAL
((B + 1) + B) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
n . (((B + 1) + B) + 1) is V11() V12() ext-real Element of REAL
(B + 1) + 0 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
n . ((B + 1) + 0) is V11() V12() ext-real Element of REAL
B0 -' (B + 1) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B + 1) + (B0 -' (B + 1)) is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
n . ((B + 1) + (B0 -' (B + 1))) is V11() V12() ext-real Element of REAL
B0 - (B + 1) is V11() V12() ext-real Element of REAL
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
len n is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B is ordinal natural V11() V12() ext-real non negative finite cardinal set
B0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
n . B is V11() V12() ext-real Element of REAL
n . B0 is V11() V12() ext-real Element of REAL
n is Relation-like NAT -defined RAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued set
len n is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
n . 1 is ordinal natural V11() V12() ext-real non negative V34() finite cardinal Element of REAL
B is ordinal natural V11() V12() ext-real non negative finite cardinal set
n . B is ordinal natural V11() V12() ext-real non negative V34() finite cardinal Element of REAL
B0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
n . B0 is ordinal natural V11() V12() ext-real non negative V34() finite cardinal Element of REAL
B0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
n . (B0 + 1) is ordinal natural V11() V12() ext-real non negative V34() finite cardinal Element of REAL
0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
n . 0 is ordinal natural V11() V12() ext-real non negative V34() finite cardinal Element of REAL
n is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of n is non empty set
B is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of n
the carrier of B is non empty set
the Mult of B is non empty Relation-like [:REAL, the carrier of B:] -defined the carrier of B -valued Function-like total quasi_total Element of bool [:[:REAL, the carrier of B:], the carrier of B:]
[:REAL, the carrier of B:] is non empty non trivial Relation-like non finite set
[:[:REAL, the carrier of B:], the carrier of B:] is non empty non trivial Relation-like non finite set
bool [:[:REAL, the carrier of B:], the carrier of B:] is non empty non trivial non finite set
[:REAL, the carrier of n:] is non empty non trivial Relation-like non finite set
the Mult of n is non empty Relation-like [:REAL, the carrier of n:] -defined the carrier of n -valued Function-like total quasi_total Element of bool [:[:REAL, the carrier of n:], the carrier of n:]
[:[:REAL, the carrier of n:], the carrier of n:] is non empty non trivial Relation-like non finite set
bool [:[:REAL, the carrier of n:], the carrier of n:] is non empty non trivial non finite set
the Mult of n | [:REAL, the carrier of n:] is Relation-like [:REAL, the carrier of n:] -defined [:REAL, the carrier of n:] -defined the carrier of n -valued Function-like Element of bool [:[:REAL, the carrier of n:], the carrier of n:]
0. B is zero Element of the carrier of B
the ZeroF of B is Element of the carrier of B
0. n is zero Element of the carrier of n
the ZeroF of n is Element of the carrier of n
the addF of B is non empty Relation-like [: the carrier of B, the carrier of B:] -defined the carrier of B -valued Function-like total quasi_total Element of bool [:[: the carrier of B, the carrier of B:], the carrier of B:]
[: the carrier of B, the carrier of B:] is non empty Relation-like set
[:[: the carrier of B, the carrier of B:], the carrier of B:] is non empty Relation-like set
bool [:[: the carrier of B, the carrier of B:], the carrier of B:] is non empty set
the addF of n is non empty Relation-like [: the carrier of n, the carrier of n:] -defined the carrier of n -valued Function-like total quasi_total Element of bool [:[: the carrier of n, the carrier of n:], the carrier of n:]
[: the carrier of n, the carrier of n:] is non empty Relation-like set
[:[: the carrier of n, the carrier of n:], the carrier of n:] is non empty Relation-like set
bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is non empty set
the addF of n || the carrier of n is set
the addF of n | [: the carrier of n, the carrier of n:] is Relation-like [: the carrier of n, the carrier of n:] -defined [: the carrier of n, the carrier of n:] -defined the carrier of n -valued Function-like Element of bool [:[: the carrier of n, the carrier of n:], the carrier of n:]
n is set
B is Relation-like NAT -defined n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of n
dom B is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
[:(dom B),(dom B):] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(dom B),(dom B):] is non empty finite V39() set
B0 is Relation-like dom B -defined dom B -valued Function-like one-to-one total quasi_total onto bijective finite complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(dom B),(dom B):]
B * B0 is Relation-like dom B -defined n -valued Function-like finite Element of bool [:(dom B),n:]
[:(dom B),n:] is Relation-like set
bool [:(dom B),n:] is non empty set
B is Relation-like Function-like set
dom B is set
B0 " (dom B) is finite V126() V127() V128() V129() V130() V131() Element of bool (dom B)
bool (dom B) is non empty finite V39() set
rng B0 is finite V126() V127() V128() V129() V130() V131() Element of bool (dom B)
B0 " (rng B0) is finite V126() V127() V128() V129() V130() V131() Element of bool (dom B)
dom B0 is finite V126() V127() V128() V129() V130() V131() Element of bool (dom B)
B0 (#) B is Relation-like dom B -defined Function-like finite set
dom (B0 (#) B) is finite V126() V127() V128() V129() V130() V131() Element of bool (dom B)
len B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len B) is finite len B -element V126() V127() V128() V129() V130() V131() Element of bool NAT
rng (B * B0) is finite Element of bool n
bool n is non empty set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
B is ordinal natural V11() V12() ext-real non negative finite cardinal set
B0 is non empty set
B is Relation-like NAT -defined B0 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of B0
len B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Swap (B,n,B) is Relation-like NAT -defined B0 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of B0
(Swap (B,n,B)) . n is set
B . B is set
(Swap (B,n,B)) . B is set
B . n is set
B /. B is Element of B0
Replace (B,n,(B /. B)) is Relation-like NAT -defined B0 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of B0
len (Replace (B,n,(B /. B))) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
len (Swap (B,n,B)) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(Swap (B,n,B)) /. B is Element of B0
B /. n is Element of B0
Replace ((Replace (B,n,(B /. B))),B,(B /. n)) is Relation-like NAT -defined B0 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of B0
(Replace ((Replace (B,n,(B /. B))),B,(B /. n))) /. B is Element of B0
Swap (B,B,n) is Relation-like NAT -defined B0 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of B0
Replace (B,B,(B /. n)) is Relation-like NAT -defined B0 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of B0
len (Replace (B,B,(B /. n))) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(Swap (B,n,B)) /. n is Element of B0
Replace ((Replace (B,B,(B /. n))),n,(B /. B)) is Relation-like NAT -defined B0 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of B0
(Replace ((Replace (B,B,(B /. n))),n,(B /. B))) /. n is Element of B0
[:{},{}:] is empty trivial ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined RAT -valued INT -valued Function-like one-to-one constant functional finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() set
bool [:{},{}:] is non empty finite V39() set
rng {} is empty trivial proper ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() with_non-empty_elements Element of bool RAT
bool RAT is non empty non trivial non finite set
dom {} is empty trivial proper ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() Element of bool NAT
n is empty trivial non proper ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding {} -defined {} -valued Function-like one-to-one constant functional total quasi_total finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() Element of bool [:{},{}:]
{1} is non empty trivial finite V39() 1 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
[:{1},{1}:] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:{1},{1}:] is non empty finite V39() set
rng <*1*> is non empty trivial finite 1 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
dom <*1*> is non empty trivial finite 1 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
B is non empty Relation-like {1} -defined {1} -valued Function-like total quasi_total finite complex-yielding ext-real-valued real-valued natural-valued Element of bool [:{1},{1}:]
n is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
sort_a n is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued V259() FinSequence of REAL
dom (sort_a n) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
dom n is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
B is Relation-like Function-like set
dom B is set
rng B is set
B (#) n is Relation-like REAL -valued Function-like complex-yielding ext-real-valued real-valued set
B is Relation-like Function-like set
dom B is set
rng B is set
B (#) (sort_a n) is Relation-like REAL -valued Function-like complex-yielding ext-real-valued real-valued set
n is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued FinSequence of NAT
dom n is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
[:(dom n),(dom n):] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(dom n),(dom n):] is non empty finite V39() set
rng n is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
B is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
sort_a B is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued V259() FinSequence of REAL
dom (sort_a B) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
dom B is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
B0 is Relation-like Function-like set
dom B0 is set
rng B0 is set
B0 (#) B is Relation-like REAL -valued Function-like complex-yielding ext-real-valued real-valued set
rng (sort_a B) is finite V126() V127() V128() Element of bool REAL
rng B is finite V126() V127() V128() Element of bool REAL
B is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued FinSequence of NAT
rng B is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
dom B is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
len B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len B) is finite len B -element V126() V127() V128() V129() V130() V131() Element of bool NAT
D0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
D0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B . (D0 + 1) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
B . D0 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
D0 is Relation-like dom n -defined dom n -valued Function-like total quasi_total finite complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(dom n),(dom n):]
I is Relation-like dom n -defined dom n -valued Function-like one-to-one total quasi_total onto bijective finite complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(dom n),(dom n):]
n * I is Relation-like dom n -defined NAT -valued RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(dom n),NAT:]
[:(dom n),NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:(dom n),NAT:] is non empty set
dom I is finite V126() V127() V128() V129() V130() V131() Element of bool (dom n)
bool (dom n) is non empty finite V39() set
B is empty trivial non proper ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding {} -defined {} -valued Function-like one-to-one constant functional total quasi_total finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() Element of bool [:{},{}:]
n * B is empty trivial non proper ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {} -defined NAT -valued RAT -valued Function-like one-to-one constant functional finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() Element of bool [:{},NAT:]
[:{},NAT:] is empty trivial ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined RAT -valued INT -valued Function-like one-to-one constant functional finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() set
bool [:{},NAT:] is non empty finite V39() set
B0 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued FinSequence of NAT
n is set
B is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
B0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
|(B,B0)| is V11() V12() ext-real Element of REAL
mlt (B,B0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,B0) is set
Sum (mlt (B,B0)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,B0)),addreal) is V11() V12() ext-real Element of REAL
n is set
B is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
B0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
|(B,B0)| is V11() V12() ext-real Element of REAL
mlt (B,B0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,B0) is set
Sum (mlt (B,B0)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,B0)),addreal) is V11() V12() ext-real Element of REAL
B is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
B0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
|(B,B0)| is V11() V12() ext-real Element of REAL
mlt (B,B0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,B0) is set
Sum (mlt (B,B0)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,B0)),addreal) is V11() V12() ext-real Element of REAL
n is set
B is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
|.B.| is V11() V12() ext-real non negative Element of REAL
sqr B is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
B (#) sqrreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
mlt (B,B) is Relation-like Function-like set
multreal .: (B,B) is set
Sum (sqr B) is V11() V12() ext-real Element of REAL
K608(REAL,(sqr B),addreal) is V11() V12() ext-real Element of REAL
sqrt (Sum (sqr B)) is V11() V12() ext-real Element of REAL
n is () set
B is () set
n \/ B is set
B0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
|.B0.| is V11() V12() ext-real non negative Element of REAL
sqr B0 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
B0 (#) sqrreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
mlt (B0,B0) is Relation-like Function-like set
multreal .: (B0,B0) is set
Sum (sqr B0) is V11() V12() ext-real Element of REAL
K608(REAL,(sqr B0),addreal) is V11() V12() ext-real Element of REAL
sqrt (Sum (sqr B0)) is V11() V12() ext-real Element of REAL
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
|.n.| is V11() V12() ext-real non negative Element of REAL
sqr n is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
n (#) sqrreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
mlt (n,n) is Relation-like Function-like set
multreal .: (n,n) is set
Sum (sqr n) is V11() V12() ext-real Element of REAL
K608(REAL,(sqr n),addreal) is V11() V12() ext-real Element of REAL
sqrt (Sum (sqr n)) is V11() V12() ext-real Element of REAL
{n} is non empty trivial functional finite V39() 1 -element set
B is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
|.B.| is V11() V12() ext-real non negative Element of REAL
sqr B is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
B (#) sqrreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
mlt (B,B) is Relation-like Function-like set
multreal .: (B,B) is set
Sum (sqr B) is V11() V12() ext-real Element of REAL
K608(REAL,(sqr B),addreal) is V11() V12() ext-real Element of REAL
sqrt (Sum (sqr B)) is V11() V12() ext-real Element of REAL
n is set
B is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
|.B.| is V11() V12() ext-real non negative Element of REAL
sqr B is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
B (#) sqrreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
mlt (B,B) is Relation-like Function-like set
multreal .: (B,B) is set
Sum (sqr B) is V11() V12() ext-real Element of REAL
K608(REAL,(sqr B),addreal) is V11() V12() ext-real Element of REAL
sqrt (Sum (sqr B)) is V11() V12() ext-real Element of REAL
{B} is non empty trivial functional finite V39() 1 -element set
n \/ {B} is non empty set
n is set
n is set
bool [:NAT,NAT:] is non empty non trivial non finite set
{<*1*>} is non empty trivial functional finite V39() 1 -element Element of bool (bool [:NAT,NAT:])
bool (bool [:NAT,NAT:]) is non empty non trivial non finite set
B is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
B0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
|(B,B0)| is V11() V12() ext-real Element of REAL
mlt (B,B0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,B0) is set
Sum (mlt (B,B0)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,B0)),addreal) is V11() V12() ext-real Element of REAL
B is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
|.B.| is V11() V12() ext-real non negative Element of REAL
sqr B is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
B (#) sqrreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
mlt (B,B) is Relation-like Function-like set
multreal .: (B,B) is set
Sum (sqr B) is V11() V12() ext-real Element of REAL
K608(REAL,(sqr B),addreal) is V11() V12() ext-real Element of REAL
sqrt (Sum (sqr B)) is V11() V12() ext-real Element of REAL
1 ^2 is V11() V12() ext-real Element of REAL
K37(1,1) is ordinal natural V11() V12() ext-real non negative finite cardinal set
<*(1 ^2)*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant finite 1 -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued increasing decreasing non-decreasing non-increasing FinSequence of REAL
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
{} (REAL n) is empty trivial proper ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() () () () Element of bool (REAL n)
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
B is functional FinSequence-membered Element of bool (REAL n)
B is functional FinSequence-membered Element of bool (REAL n)
bool (REAL 0) is non empty set
n is functional FinSequence-membered Element of bool (REAL 0)
the Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of n
B0 is empty trivial ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined REAL -valued Function-like one-to-one constant functional finite finite-yielding V39() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() () () () Element of REAL 0
len B0 is empty trivial ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional V33() V34() finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() () () () Element of NAT
0* (len B0) is Relation-like NAT -defined REAL -valued Function-like finite len B0 -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL (len B0)
REAL (len B0) is non empty functional FinSequence-membered FinSequenceSet of REAL
(len B0) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = len B0 } is set
(len B0) |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite len B0 -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of (len B0) -tuples_on REAL
Seg (len B0) is empty trivial proper ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional finite finite-yielding V39() cardinal len B0 -element {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() () () () Element of bool NAT
(Seg (len B0)) --> 0 is empty trivial non proper ordinal T-Sequence-like natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding Seg (len B0) -defined RAT -valued INT -valued {0} -valued Function-like one-to-one constant functional total quasi_total finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() () () () Element of bool [:(Seg (len B0)),{0}:]
{0} is non empty trivial functional finite V39() 1 -element V126() V127() V128() V129() V130() V131() set
[:(Seg (len B0)),{0}:] is empty trivial ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined RAT -valued INT -valued Function-like one-to-one constant functional finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() () () () set
bool [:(Seg (len B0)),{0}:] is non empty finite V39() set
|((0* (len B0)),(0* (len B0)))| is V11() V12() ext-real Element of REAL
mlt ((0* (len B0)),(0* (len B0))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: ((0* (len B0)),(0* (len B0))) is set
Sum (mlt ((0* (len B0)),(0* (len B0)))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt ((0* (len B0)),(0* (len B0)))),addreal) is V11() V12() ext-real Element of REAL
|.(0* (len B0)).| is V11() V12() ext-real non negative Element of REAL
sqr (0* (len B0)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(0* (len B0)) (#) sqrreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
mlt ((0* (len B0)),(0* (len B0))) is Relation-like Function-like set
Sum (sqr (0* (len B0))) is V11() V12() ext-real Element of REAL
K608(REAL,(sqr (0* (len B0))),addreal) is V11() V12() ext-real Element of REAL
sqrt (Sum (sqr (0* (len B0)))) is V11() V12() ext-real Element of REAL
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
0* n is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(Seg n) --> 0 is Relation-like Seg n -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),{0}:]
{0} is non empty trivial functional finite V39() 1 -element V126() V127() V128() V129() V130() V131() set
[:(Seg n),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),{0}:] is non empty finite V39() set
B is functional FinSequence-membered Element of bool (REAL n)
B0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|.B0.| is V11() V12() ext-real non negative Element of REAL
sqr B0 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
B0 (#) sqrreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
mlt (B0,B0) is Relation-like Function-like set
multreal .: (B0,B0) is set
Sum (sqr B0) is V11() V12() ext-real Element of REAL
K608(REAL,(sqr B0),addreal) is V11() V12() ext-real Element of REAL
sqrt (Sum (sqr B0)) is V11() V12() ext-real Element of REAL
1 / |.B0.| is V11() V12() ext-real non negative Element of REAL
(1 / |.B0.|) * B0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(1 / |.B0.|) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total quasi_total complex-yielding ext-real-valued real-valued increasing non-decreasing Element of bool [:REAL,REAL:]
multreal [;] ((1 / |.B0.|),(id REAL)) is set
B0 (#) ((1 / |.B0.|) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
{B} is non empty trivial functional finite V39() 1 -element FinSequence-membered Element of bool (REAL n)
B \/ {B} is non empty functional FinSequence-membered Element of bool (REAL n)
D0 is functional FinSequence-membered Element of bool (REAL n)
len B0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
I is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
x0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
|(I,x0)| is V11() V12() ext-real Element of REAL
mlt (I,x0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (I,x0) is set
Sum (mlt (I,x0)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (I,x0)),addreal) is V11() V12() ext-real Element of REAL
p is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
len p is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
z0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
len z0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
|(I,B0)| is V11() V12() ext-real Element of REAL
mlt (I,B0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (I,B0) is set
Sum (mlt (I,B0)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (I,B0)),addreal) is V11() V12() ext-real Element of REAL
(1 / |.B0.|) * |(I,B0)| is V11() V12() ext-real Element of REAL
|(x0,B0)| is V11() V12() ext-real Element of REAL
mlt (x0,B0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (x0,B0) is set
Sum (mlt (x0,B0)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (x0,B0)),addreal) is V11() V12() ext-real Element of REAL
(1 / |.B0.|) * |(x0,B0)| is V11() V12() ext-real Element of REAL
|(p,((1 / |.B0.|) * B0))| is V11() V12() ext-real Element of REAL
mlt (p,((1 / |.B0.|) * B0)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (p,((1 / |.B0.|) * B0)) is set
Sum (mlt (p,((1 / |.B0.|) * B0))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (p,((1 / |.B0.|) * B0))),addreal) is V11() V12() ext-real Element of REAL
|.B.| is V11() V12() ext-real non negative Element of REAL
sqr B is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
B (#) sqrreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
mlt (B,B) is Relation-like Function-like set
multreal .: (B,B) is set
Sum (sqr B) is V11() V12() ext-real Element of REAL
K608(REAL,(sqr B),addreal) is V11() V12() ext-real Element of REAL
sqrt (Sum (sqr B)) is V11() V12() ext-real Element of REAL
abs (1 / |.B0.|) is V11() V12() ext-real Element of REAL
(abs (1 / |.B0.|)) * |.B0.| is V11() V12() ext-real Element of REAL
(1 / |.B0.|) * |.B0.| is V11() V12() ext-real non negative Element of REAL
I is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
|.I.| is V11() V12() ext-real non negative Element of REAL
sqr I is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
I (#) sqrreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
mlt (I,I) is Relation-like Function-like set
multreal .: (I,I) is set
Sum (sqr I) is V11() V12() ext-real Element of REAL
K608(REAL,(sqr I),addreal) is V11() V12() ext-real Element of REAL
sqrt (Sum (sqr I)) is V11() V12() ext-real Element of REAL
len B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
|(B,B0)| is V11() V12() ext-real Element of REAL
mlt (B,B0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,B0) is set
Sum (mlt (B,B0)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,B0)),addreal) is V11() V12() ext-real Element of REAL
(1 / |.B0.|) * |(B,B0)| is V11() V12() ext-real Element of REAL
|(B,((1 / |.B0.|) * B0))| is V11() V12() ext-real Element of REAL
mlt (B,((1 / |.B0.|) * B0)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,((1 / |.B0.|) * B0)) is set
Sum (mlt (B,((1 / |.B0.|) * B0))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,((1 / |.B0.|) * B0))),addreal) is V11() V12() ext-real Element of REAL
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
[#] (REAL n) is non empty non proper functional FinSequence-membered Element of bool (REAL n)
bool (REAL n) is non empty set
B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B is V11() V12() ext-real Element of REAL
B * B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total quasi_total complex-yielding ext-real-valued real-valued increasing non-decreasing Element of bool [:REAL,REAL:]
multreal [;] (B,(id REAL)) is set
B (#) (B multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
D0 is V11() V12() ext-real Element of REAL
D0 * B0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
D0 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (D0,(id REAL)) is set
B0 (#) (D0 multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
(B * B) + (D0 * B0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
addreal .: ((B * B),(D0 * B0)) is set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
0* n is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(Seg n) --> 0 is Relation-like Seg n -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),{0}:]
{0} is non empty trivial functional finite V39() 1 -element V126() V127() V128() V129() V130() V131() set
[:(Seg n),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),{0}:] is non empty finite V39() set
{(0* n)} is non empty trivial functional finite V39() 1 -element FinSequence-membered Element of bool (REAL n)
bool (REAL n) is non empty set
B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B is V11() V12() ext-real Element of REAL
B * B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total quasi_total complex-yielding ext-real-valued real-valued increasing non-decreasing Element of bool [:REAL,REAL:]
multreal [;] (B,(id REAL)) is set
B (#) (B multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
D0 is V11() V12() ext-real Element of REAL
D0 * B0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
D0 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (D0,(id REAL)) is set
B0 (#) (D0 multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
(B * B) + (D0 * B0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
addreal .: ((B * B),(D0 * B0)) is set
I is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
0* I is Relation-like NAT -defined REAL -valued Function-like finite I -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL I
REAL I is non empty functional FinSequence-membered FinSequenceSet of REAL
I -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = I } is set
I |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite I -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of I -tuples_on REAL
Seg I is finite I -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(Seg I) --> 0 is Relation-like Seg I -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg I),{0}:]
[:(Seg I),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg I),{0}:] is non empty finite V39() set
D0 * (0* I) is Relation-like NAT -defined REAL -valued Function-like finite I -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL I
(0* I) (#) (D0 multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
(0* I) + (D0 * (0* I)) is Relation-like NAT -defined REAL -valued Function-like finite I -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL I
addreal .: ((0* I),(D0 * (0* I))) is set
(0* I) + (0* I) is Relation-like NAT -defined REAL -valued Function-like finite I -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL I
addreal .: ((0* I),(0* I)) is set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
0* n is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(Seg n) --> 0 is Relation-like Seg n -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),{0}:]
{0} is non empty trivial functional finite V39() 1 -element V126() V127() V128() V129() V130() V131() set
[:(Seg n),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),{0}:] is non empty finite V39() set
{(0* n)} is non empty trivial functional finite V39() 1 -element FinSequence-membered Element of bool (REAL n)
B is functional FinSequence-membered Element of bool (REAL n)
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
B is functional FinSequence-membered Element of bool (REAL n)
{ b1 where b1 is functional FinSequence-membered Element of bool (REAL n) : ( b1 is (n) & B c= b1 ) } is set
meet { b1 where b1 is functional FinSequence-membered Element of bool (REAL n) : ( b1 is (n) & B c= b1 ) } is set
[#] (REAL n) is non empty non proper non proper functional FinSequence-membered (n) Element of bool (REAL n)
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
B is functional FinSequence-membered Element of bool (REAL n)
(n,B) is functional FinSequence-membered Element of bool (REAL n)
{ b1 where b1 is functional FinSequence-membered Element of bool (REAL n) : ( b1 is (n) & B c= b1 ) } is set
meet { b1 where b1 is functional FinSequence-membered Element of bool (REAL n) : ( b1 is (n) & B c= b1 ) } is set
[#] (REAL n) is non empty non proper non proper functional FinSequence-membered (n) Element of bool (REAL n)
B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
D0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
I is V11() V12() ext-real Element of REAL
I * B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
I multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total quasi_total complex-yielding ext-real-valued real-valued increasing non-decreasing Element of bool [:REAL,REAL:]
multreal [;] (I,(id REAL)) is set
B (#) (I multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
x0 is V11() V12() ext-real Element of REAL
x0 * D0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
x0 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (x0,(id REAL)) is set
D0 (#) (x0 multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
(I * B) + (x0 * D0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
addreal .: ((I * B),(x0 * D0)) is set
z0 is set
p is functional FinSequence-membered Element of bool (REAL n)
B0 is non empty set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
B is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
len B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B /. 1 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
<*(B /. 1)*> is non empty trivial Relation-like NAT -defined REAL n -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL n
0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B0 is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
B0 . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B is ordinal natural V11() V12() ext-real non negative finite cardinal set
B + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B0 . (B + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B0 /. B is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
B /. (B + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(B0 /. B) + (B /. (B + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B is ordinal natural V11() V12() ext-real non negative finite cardinal set
B + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B + 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B + 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
D0 is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
len D0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
D0 . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
D0 is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
len D0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
D0 . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
D0 /. (B + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
B /. ((B + 1) + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(D0 /. (B + 1)) + (B /. ((B + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
<*((D0 /. (B + 1)) + (B /. ((B + 1) + 1)))*> is non empty trivial Relation-like NAT -defined REAL n -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL n
D0 ^ <*((D0 /. (B + 1)) + (B /. ((B + 1) + 1)))*> is non empty Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like Element of (REAL n) *
(REAL n) * is non empty functional FinSequence-membered FinSequenceSet of REAL n
Seg (len D0) is finite len D0 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
dom D0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
I is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
len I is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
len <*((D0 /. (B + 1)) + (B /. ((B + 1) + 1)))*> is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(len D0) + (len <*((D0 /. (B + 1)) + (B /. ((B + 1) + 1)))*>) is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
x0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
x0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
I . (x0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
I /. x0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
B /. (x0 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(I /. x0) + (B /. (x0 + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
D0 . (x0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
I . x0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
D0 . x0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
D0 /. x0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
I . x0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
D0 . x0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
D0 /. x0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
I . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(B + 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B + 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B + 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
D0 is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
len D0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
D0 . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
I is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
len I is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
I . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(len B) -' 1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(len B) - 1 is V11() V12() ext-real Element of REAL
((len B) -' 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
len B0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
B0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B . (B0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B /. B0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
B /. (B0 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(B /. B0) + (B /. (B0 + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B0 is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
len B0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B0 . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
len B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
D0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
B0 . D0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B . D0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
D0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B0 . (D0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B . (D0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B /. D0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
B /. (D0 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(B /. D0) + (B /. (D0 + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B0 /. D0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(B0 /. D0) + (B /. (D0 + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B0 . 0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B . 0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
B is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
len B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
(n,B) . (len B) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
0* n is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(Seg n) --> 0 is Relation-like Seg n -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),{0}:] is non empty finite V39() set
len (n,B) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
dom (n,B) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
rng (n,B) is functional finite FinSequence-membered Element of bool (REAL n)
bool (REAL n) is non empty set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
B is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
dom B is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
[:(dom B),(dom B):] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(dom B),(dom B):] is non empty finite V39() set
B0 is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
(n,B0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(n,B) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B is Relation-like dom B -defined dom B -valued Function-like one-to-one total quasi_total onto bijective finite complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(dom B),(dom B):]
((REAL n),B,B) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
B * B is Relation-like dom B -defined REAL n -valued Function-like finite Element of bool [:(dom B),(REAL n):]
[:(dom B),(REAL n):] is Relation-like set
bool [:(dom B),(REAL n):] is non empty set
len B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len B) is finite len B -element V126() V127() V128() V129() V130() V131() Element of bool NAT
dom B is finite V126() V127() V128() V129() V130() V131() Element of bool (dom B)
bool (dom B) is non empty finite V39() set
rng B is finite V126() V127() V128() V129() V130() V131() Element of bool (dom B)
dom B0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
len B0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len B0) is finite len B0 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(n,B) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
len (n,B) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
I is ordinal natural V11() V12() ext-real non negative finite cardinal set
I + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . (I + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) /. I is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
B /. (I + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,B) /. I) + (B /. (I + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(len B) -' 1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(len B) - 1 is V11() V12() ext-real Element of REAL
((len B) -' 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
I is ordinal natural V11() V12() ext-real non negative finite cardinal set
B . I is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
I is ordinal natural V11() V12() ext-real non negative finite cardinal set
I + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . (I + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(I + 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . ((I + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(I + 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . ((I + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
x0 is Relation-like dom B -defined dom B -valued Function-like one-to-one total quasi_total onto bijective finite complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(dom B),(dom B):]
((REAL n),B,x0) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
B * x0 is Relation-like dom B -defined REAL n -valued Function-like finite Element of bool [:(dom B),(REAL n):]
(n,((REAL n),B,x0)) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
(n,((REAL n),B,x0)) . ((I + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom x0 is finite V126() V127() V128() V129() V130() V131() Element of bool (dom B)
rng x0 is finite V126() V127() V128() V129() V130() V131() Element of bool (dom B)
dom ((REAL n),B,x0) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
len ((REAL n),B,x0) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len ((REAL n),B,x0)) is finite len ((REAL n),B,x0) -element V126() V127() V128() V129() V130() V131() Element of bool NAT
z0 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued FinSequence of NAT
len z0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
p is set
x0 . p is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
p0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Swap (z0,p0,((I + 1) + 1)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued FinSequence of NAT
q is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued FinSequence of NAT
rng q is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
len q is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
dom q is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
Seg (len z0) is finite len z0 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
u4 is Relation-like dom B -defined dom B -valued Function-like total quasi_total finite complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(dom B),(dom B):]
u0 is Relation-like dom B -defined dom B -valued Function-like one-to-one total quasi_total onto bijective finite complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(dom B),(dom B):]
u0 . p0 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
z0 . ((I + 1) + 1) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
dom u0 is finite V126() V127() V128() V129() V130() V131() Element of bool (dom B)
rng u0 is finite V126() V127() V128() V129() V130() V131() Element of bool (dom B)
((REAL n),B,u0) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
B * u0 is Relation-like dom B -defined REAL n -valued Function-like finite Element of bool [:(dom B),(REAL n):]
dom ((REAL n),B,u0) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
len ((REAL n),B,u0) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len ((REAL n),B,u0)) is finite len ((REAL n),B,u0) -element V126() V127() V128() V129() V130() V131() Element of bool NAT
B . ((I + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((REAL n),B,x0) . p0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,((REAL n),B,u0)) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
len (n,((REAL n),B,u0)) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
q . ((I + 1) + 1) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
B3 is ordinal natural V11() V12() ext-real non negative finite cardinal set
u0 . B3 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
q /. B3 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
z0 /. B3 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
x0 . B3 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
B /. ((I + 1) + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
len (n,((REAL n),B,x0)) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B3 is ordinal natural V11() V12() ext-real non negative finite cardinal set
(n,((REAL n),B,x0)) . B3 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,((REAL n),B,u0)) . B3 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B3 -' 1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
1 + (B3 -' 1) is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B3 - 1 is V11() V12() ext-real Element of REAL
(B3 - 1) + 1 is V11() V12() ext-real Element of REAL
aq is ordinal natural V11() V12() ext-real non negative finite cardinal set
1 + aq is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,((REAL n),B,x0)) . (1 + aq) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,((REAL n),B,u0)) . (1 + aq) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
aq + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
1 + (aq + 1) is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,((REAL n),B,x0)) . (1 + (aq + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,((REAL n),B,u0)) . (1 + (aq + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(aq + 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
z0 /. ((aq + 1) + 1) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
z0 . ((aq + 1) + 1) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
q /. ((aq + 1) + 1) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
q . ((aq + 1) + 1) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
((REAL n),B,x0) . ((aq + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
x0 . ((aq + 1) + 1) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
B . (x0 . ((aq + 1) + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
u0 . ((aq + 1) + 1) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
B . (u0 . ((aq + 1) + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((REAL n),B,u0) . ((aq + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((REAL n),B,u0) /. ((aq + 1) + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(n,((REAL n),B,u0)) /. (1 + aq) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(n,((REAL n),B,x0)) /. (1 + aq) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(n,((REAL n),B,u0)) /. (aq + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((REAL n),B,x0) /. ((aq + 1) + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,((REAL n),B,u0)) /. (aq + 1)) + (((REAL n),B,x0) /. ((aq + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
((n,((REAL n),B,u0)) /. (aq + 1)) + (((REAL n),B,u0) /. ((aq + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
q /. 1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
q . 1 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
z0 /. 1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
z0 . 1 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
((REAL n),B,x0) . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
x0 . 1 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
B . (x0 . 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
u0 . 1 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
B . (u0 . 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((REAL n),B,u0) . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
1 + 0 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,((REAL n),B,x0)) . (1 + 0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,((REAL n),B,u0)) . (1 + 0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((REAL n),B,x0) /. ((I + 1) + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((REAL n),B,x0) /. p0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
B3 is ordinal natural V11() V12() ext-real non negative finite cardinal set
(n,((REAL n),B,x0)) . B3 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,((REAL n),B,u0)) /. B3 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,((REAL n),B,u0)) /. B3) - (((REAL n),B,x0) /. ((I + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(((n,((REAL n),B,u0)) /. B3) - (((REAL n),B,x0) /. ((I + 1) + 1))) + (((REAL n),B,x0) /. p0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
aq is ordinal natural V11() V12() ext-real non negative finite cardinal set
p0 + aq is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,((REAL n),B,x0)) . (p0 + aq) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,((REAL n),B,u0)) /. (p0 + aq) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,((REAL n),B,u0)) /. (p0 + aq)) - (((REAL n),B,x0) /. ((I + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(((n,((REAL n),B,u0)) /. (p0 + aq)) - (((REAL n),B,x0) /. ((I + 1) + 1))) + (((REAL n),B,x0) /. p0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
aq + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
p0 + (aq + 1) is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,((REAL n),B,x0)) . (p0 + (aq + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,((REAL n),B,u0)) /. (p0 + (aq + 1)) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,((REAL n),B,u0)) /. (p0 + (aq + 1))) - (((REAL n),B,x0) /. ((I + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(((n,((REAL n),B,u0)) /. (p0 + (aq + 1))) - (((REAL n),B,x0) /. ((I + 1) + 1))) + (((REAL n),B,x0) /. p0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(p0 + aq) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
((REAL n),B,x0) /. ((p0 + aq) + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((REAL n),B,u0) /. ((p0 + aq) + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((REAL n),B,u0) . ((p0 + aq) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
u0 . ((p0 + aq) + 1) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
B . (u0 . ((p0 + aq) + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
q /. ((p0 + aq) + 1) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B . (q /. ((p0 + aq) + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
z0 /. ((p0 + aq) + 1) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B . (z0 /. ((p0 + aq) + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
z0 . ((p0 + aq) + 1) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
B . (z0 . ((p0 + aq) + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((REAL n),B,x0) . ((p0 + aq) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,((REAL n),B,u0)) . (p0 + (aq + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((n,((REAL n),B,u0)) /. (p0 + aq)) + (((REAL n),B,u0) /. ((p0 + aq) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
((n,((REAL n),B,u0)) /. (p0 + aq)) + (((REAL n),B,x0) /. ((p0 + aq) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u2 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
bq is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u2 + bq is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
addreal .: (u2,bq) is set
x3 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(u2 + bq) - x3 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:[:REAL,REAL:],REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total quasi_total complex-yielding ext-real-valued real-valued increasing non-decreasing Element of bool [:REAL,REAL:]
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
K660(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: ((u2 + bq),x3) is set
- x3 is Relation-like Function-like complex-yielding set
x3 (#) compreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
K38(1) is V11() V12() ext-real non positive set
K38(1) * x3 is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
x3 (#) (K38(1) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
(u2 + bq) + (- x3) is Relation-like Function-like set
j is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
((u2 + bq) - x3) + j is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
addreal .: (((u2 + bq) - x3),j) is set
u2 - x3 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
diffreal .: (u2,x3) is set
u2 + (- x3) is Relation-like Function-like set
(u2 - x3) + bq is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
addreal .: ((u2 - x3),bq) is set
((u2 - x3) + bq) + j is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
addreal .: (((u2 - x3) + bq),j) is set
(u2 - x3) + j is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
addreal .: ((u2 - x3),j) is set
((u2 - x3) + j) + bq is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
addreal .: (((u2 - x3) + j),bq) is set
(n,((REAL n),B,x0)) /. (p0 + aq) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,((REAL n),B,x0)) /. (p0 + aq)) + (((REAL n),B,x0) /. ((p0 + aq) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
((((n,((REAL n),B,u0)) /. (p0 + aq)) - (((REAL n),B,x0) /. ((I + 1) + 1))) + (((REAL n),B,x0) /. p0)) + (((REAL n),B,x0) /. ((p0 + aq) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
p0 + 0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,((REAL n),B,u0)) /. (p0 + 0) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(n,((REAL n),B,u0)) . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((REAL n),B,u0) . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
x0 . ((I + 1) + 1) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
B . (x0 . ((I + 1) + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((REAL n),B,x0) . ((I + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((n,((REAL n),B,u0)) /. (p0 + 0)) - (((REAL n),B,x0) /. ((I + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(((n,((REAL n),B,u0)) /. (p0 + 0)) - (((REAL n),B,x0) /. ((I + 1) + 1))) + (((REAL n),B,x0) /. p0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
0* n is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(Seg n) --> 0 is Relation-like Seg n -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),{0}:] is non empty finite V39() set
(0* n) + (((REAL n),B,x0) /. p0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(n,((REAL n),B,x0)) . (p0 + 0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((REAL n),B,x0) . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((REAL n),B,u0) /. p0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((REAL n),B,u0) . p0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
x0 . ((I + 1) + 1) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
B . (x0 . ((I + 1) + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((REAL n),B,x0) . ((I + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
p0 -' 1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
p0 - 1 is V11() V12() ext-real Element of REAL
p0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(p0 + 1) - 1 is V11() V12() ext-real Element of REAL
(n,((REAL n),B,x0)) /. (p0 -' 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(n,((REAL n),B,x0)) . (p0 -' 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
p0 + 0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,((REAL n),B,u0)) . (p0 + 0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,((REAL n),B,u0)) /. (p0 -' 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(p0 -' 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
((REAL n),B,u0) /. ((p0 -' 1) + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,((REAL n),B,u0)) /. (p0 -' 1)) + (((REAL n),B,u0) /. ((p0 -' 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
((n,((REAL n),B,u0)) /. (p0 -' 1)) + (((REAL n),B,x0) /. ((I + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(n,((REAL n),B,u0)) /. (p0 + 0) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,((REAL n),B,u0)) /. (p0 + 0)) - (((REAL n),B,x0) /. ((I + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(((n,((REAL n),B,u0)) /. (p0 -' 1)) + (((REAL n),B,x0) /. ((I + 1) + 1))) - (((REAL n),B,x0) /. ((I + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(n,((REAL n),B,u0)) . (p0 -' 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,((REAL n),B,x0)) . (p0 + 0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((REAL n),B,x0) /. ((p0 -' 1) + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,((REAL n),B,x0)) /. (p0 -' 1)) + (((REAL n),B,x0) /. ((p0 -' 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
((n,((REAL n),B,u0)) /. (p0 -' 1)) + (((REAL n),B,x0) /. p0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(((n,((REAL n),B,u0)) /. (p0 + 0)) - (((REAL n),B,x0) /. ((I + 1) + 1))) + (((REAL n),B,x0) /. p0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
p0 + 0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,((REAL n),B,x0)) . (p0 + 0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,((REAL n),B,u0)) /. (p0 + 0) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,((REAL n),B,u0)) /. (p0 + 0)) - (((REAL n),B,x0) /. ((I + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(((n,((REAL n),B,u0)) /. (p0 + 0)) - (((REAL n),B,x0) /. ((I + 1) + 1))) + (((REAL n),B,x0) /. p0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
p0 + 0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,((REAL n),B,x0)) . (p0 + 0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,((REAL n),B,u0)) /. (p0 + 0) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,((REAL n),B,u0)) /. (p0 + 0)) - (((REAL n),B,x0) /. ((I + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(((n,((REAL n),B,u0)) /. (p0 + 0)) - (((REAL n),B,x0) /. ((I + 1) + 1))) + (((REAL n),B,x0) /. p0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B3 -' p0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B3 - p0 is V11() V12() ext-real Element of REAL
p0 + (B3 -' p0) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
((REAL n),B,u0) /. ((I + 1) + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((REAL n),B,u0) . ((I + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B3 is ordinal natural V11() V12() ext-real non negative finite cardinal set
(n,((REAL n),B,x0)) . B3 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,((REAL n),B,u0)) . B3 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
aq is ordinal natural V11() V12() ext-real non negative finite cardinal set
((I + 1) + 1) + aq is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,((REAL n),B,x0)) . (((I + 1) + 1) + aq) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,((REAL n),B,u0)) . (((I + 1) + 1) + aq) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
aq + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
((I + 1) + 1) + (aq + 1) is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,((REAL n),B,x0)) . (((I + 1) + 1) + (aq + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,((REAL n),B,u0)) . (((I + 1) + 1) + (aq + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(((I + 1) + 1) + aq) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
((REAL n),B,u0) /. ((((I + 1) + 1) + aq) + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((REAL n),B,u0) . ((((I + 1) + 1) + aq) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
u0 . ((((I + 1) + 1) + aq) + 1) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
B . (u0 . ((((I + 1) + 1) + aq) + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
q /. ((((I + 1) + 1) + aq) + 1) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B . (q /. ((((I + 1) + 1) + aq) + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
z0 /. ((((I + 1) + 1) + aq) + 1) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B . (z0 /. ((((I + 1) + 1) + aq) + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
z0 . ((((I + 1) + 1) + aq) + 1) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
B . (z0 . ((((I + 1) + 1) + aq) + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((REAL n),B,x0) . ((((I + 1) + 1) + aq) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,((REAL n),B,u0)) /. (((I + 1) + 1) + aq) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(n,((REAL n),B,x0)) /. (((I + 1) + 1) + aq) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((REAL n),B,x0) /. ((((I + 1) + 1) + aq) + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,((REAL n),B,x0)) /. (((I + 1) + 1) + aq)) + (((REAL n),B,x0) /. ((((I + 1) + 1) + aq) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
((n,((REAL n),B,u0)) /. (((I + 1) + 1) + aq)) + (((REAL n),B,x0) /. ((((I + 1) + 1) + aq) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
((n,((REAL n),B,u0)) /. (((I + 1) + 1) + aq)) + (((REAL n),B,u0) /. ((((I + 1) + 1) + aq) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(n,((REAL n),B,x0)) . (I + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,((REAL n),B,u0)) /. (I + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,((REAL n),B,u0)) /. (I + 1)) - (((REAL n),B,x0) /. ((I + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(((n,((REAL n),B,u0)) /. (I + 1)) - (((REAL n),B,x0) /. ((I + 1) + 1))) + (((REAL n),B,x0) /. p0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(n,((REAL n),B,x0)) /. (I + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,((REAL n),B,x0)) /. (I + 1)) + (((REAL n),B,x0) /. ((I + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
((((n,((REAL n),B,u0)) /. (I + 1)) - (((REAL n),B,x0) /. ((I + 1) + 1))) + (((REAL n),B,x0) /. p0)) + (((REAL n),B,x0) /. ((I + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
((n,((REAL n),B,u0)) /. (I + 1)) + (((REAL n),B,x0) /. p0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
((n,((REAL n),B,u0)) /. (I + 1)) + (((REAL n),B,u0) /. ((I + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
((I + 1) + 1) + 0 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,((REAL n),B,x0)) . (((I + 1) + 1) + 0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,((REAL n),B,u0)) . (((I + 1) + 1) + 0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B3 -' ((I + 1) + 1) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
((I + 1) + 1) + (B3 -' ((I + 1) + 1)) is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B3 - ((I + 1) + 1) is V11() V12() ext-real Element of REAL
(B3 - ((I + 1) + 1)) + ((I + 1) + 1) is V11() V12() ext-real Element of REAL
(n,B) /. (I + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(n,((REAL n),B,u0)) /. (I + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(n,((REAL n),B,u0)) . (I + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((n,B) /. (I + 1)) + (B /. ((I + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
((n,((REAL n),B,u0)) /. (I + 1)) + (B /. ((I + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
((n,((REAL n),B,u0)) /. (I + 1)) + (((REAL n),B,u0) /. ((I + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(n,((REAL n),B,u0)) . ((I + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B3 is ordinal natural V11() V12() ext-real non negative finite cardinal set
x0 . B3 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
len (n,((REAL n),B,x0)) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,((REAL n),B,x0)) /. (I + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(n,((REAL n),B,x0)) . (I + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B . ((I + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((REAL n),B,x0) . p0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) /. (I + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
B /. ((I + 1) + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,B) /. (I + 1)) + (B /. ((I + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
((n,((REAL n),B,x0)) /. (I + 1)) + (B /. ((I + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
((REAL n),B,x0) /. ((I + 1) + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,((REAL n),B,x0)) /. (I + 1)) + (((REAL n),B,x0) /. ((I + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
x0 is Relation-like dom B -defined dom B -valued Function-like one-to-one total quasi_total onto bijective finite complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(dom B),(dom B):]
((REAL n),B,x0) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
B * x0 is Relation-like dom B -defined REAL n -valued Function-like finite Element of bool [:(dom B),(REAL n):]
(n,((REAL n),B,x0)) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
(n,((REAL n),B,x0)) . ((I + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) . (0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
I is Relation-like dom B -defined dom B -valued Function-like one-to-one total quasi_total onto bijective finite complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(dom B),(dom B):]
((REAL n),B,I) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
B * I is Relation-like dom B -defined REAL n -valued Function-like finite Element of bool [:(dom B),(REAL n):]
(n,((REAL n),B,I)) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
(n,((REAL n),B,I)) . (0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng I is finite V126() V127() V128() V129() V130() V131() Element of bool (dom B)
dom I is finite V126() V127() V128() V129() V130() V131() Element of bool (dom B)
I . 1 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
x0 is set
I . x0 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
z0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,((REAL n),B,I)) . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((REAL n),B,I) . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . (0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
I is Relation-like dom B -defined dom B -valued Function-like one-to-one total quasi_total onto bijective finite complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(dom B),(dom B):]
((REAL n),B,I) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
B * I is Relation-like dom B -defined REAL n -valued Function-like finite Element of bool [:(dom B),(REAL n):]
(n,((REAL n),B,I)) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
(n,((REAL n),B,I)) . (0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) . (len B) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,((REAL n),B,B)) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
(n,((REAL n),B,B)) . (len B) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B0) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
(n,B0) . (len B0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
rng B is finite V126() V127() V128() V129() V130() V131() Element of bool (dom B)
bool (dom B) is non empty finite V39() set
dom ((REAL n),B,B) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
dom B is finite V126() V127() V128() V129() V130() V131() Element of bool (dom B)
Seg (len B) is finite len B -element V126() V127() V128() V129() V130() V131() Element of bool NAT
dom B0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
len B0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
0* n is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(Seg n) --> 0 is Relation-like Seg n -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),{0}:] is non empty finite V39() set
len B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
0* n is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(Seg n) --> 0 is Relation-like Seg n -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),{0}:] is non empty finite V39() set
B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B |-> (0* n) is Relation-like NAT -defined REAL n -valued Function-like finite B -element FinSequence-like FinSubsequence-like Element of B -tuples_on (REAL n)
B -tuples_on (REAL n) is non empty functional FinSequence-membered FinSequenceSet of REAL n
(REAL n) * is non empty functional FinSequence-membered FinSequenceSet of REAL n
{ b1 where b1 is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like Element of (REAL n) * : len b1 = B } is set
Seg B is finite B -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(Seg B) --> (0* n) is Relation-like Seg B -defined {(0* n)} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like Element of bool [:(Seg B),{(0* n)}:]
{(0* n)} is non empty trivial functional finite V39() 1 -element set
[:(Seg B),{(0* n)}:] is Relation-like finite set
bool [:(Seg B),{(0* n)}:] is non empty finite V39() set
(n,(B |-> (0* n))) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
dom (B |-> (0* n)) is finite B -element V126() V127() V128() V129() V130() V131() Element of bool NAT
B is ordinal natural V11() V12() ext-real non negative finite cardinal set
(B |-> (0* n)) . B is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (B |-> (0* n)) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,(B |-> (0* n))) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
len (n,(B |-> (0* n))) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B |-> (0* n)) . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,(B |-> (0* n))) . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
D0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
D0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,(B |-> (0* n))) . (D0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(D0 + 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,(B |-> (0* n))) . ((D0 + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(D0 + 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len (B |-> (0* n))) is finite len (B |-> (0* n)) -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(B |-> (0* n)) . ((D0 + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,(B |-> (0* n))) /. (D0 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(n,(B |-> (0* n))) . ((D0 + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(B |-> (0* n)) /. ((D0 + 1) + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,(B |-> (0* n))) /. (D0 + 1)) + ((B |-> (0* n)) /. ((D0 + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(0* n) + (0* n) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
addreal .: ((0* n),(0* n)) is set
0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len (B |-> (0* n))) is finite len (B |-> (0* n)) -element V126() V127() V128() V129() V130() V131() Element of bool NAT
0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,(B |-> (0* n))) . (0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(len (n,(B |-> (0* n)))) -' 1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
((len (n,(B |-> (0* n)))) -' 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,(B |-> (0* n))) . (((len (n,(B |-> (0* n)))) -' 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(len (n,(B |-> (0* n)))) - 1 is V11() V12() ext-real Element of REAL
len (B |-> (0* n)) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
len (B |-> (0* n)) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
0* n is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(Seg n) --> 0 is Relation-like Seg n -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),{0}:] is non empty finite V39() set
B is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
dom B is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
(n,B) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B0 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued FinSequence of NAT
rng B0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
B * B0 is Relation-like NAT -defined REAL n -valued Function-like finite Element of bool [:NAT,(REAL n):]
[:NAT,(REAL n):] is non empty non trivial Relation-like non finite set
bool [:NAT,(REAL n):] is non empty non trivial non finite set
B is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
(n,B) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B0 (#) B is Relation-like NAT -defined REAL n -valued Function-like finite set
dom (B0 (#) B) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
dom B0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
dom (B * B0) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
dom B is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
len B0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len B0) is finite len B0 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
len B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
D0 is set
B0 . D0 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
I is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B0 . 1 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
len B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len B) is finite len B -element V126() V127() V128() V129() V130() V131() Element of bool NAT
x0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
len B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len B) is finite len B -element V126() V127() V128() V129() V130() V131() Element of bool NAT
0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len B) is finite len B -element V126() V127() V128() V129() V130() V131() Element of bool NAT
B0 . (len B0) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
B0 . 1 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
D0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
D0 -' 1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
D0 - 1 is V11() V12() ext-real Element of REAL
(len B) -' 1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(len B) - 1 is V11() V12() ext-real Element of REAL
((len B) -' 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
len (n,B) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
x0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
x0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . (x0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) /. x0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
B /. (x0 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,B) /. x0) + (B /. (x0 + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(n,B) . (len B) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
len (n,B) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
z0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
z0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . (z0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) /. z0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
B /. (z0 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,B) /. z0) + (B /. (z0 + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(n,B) . (len B) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
z0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
z0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . (z0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(z0 + 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . ((z0 + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(z0 + 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . ((z0 + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B /. ((z0 + 1) + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
B . ((z0 + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
p is set
B0 . p is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
p0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) /. (z0 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,B) /. (z0 + 1)) + (B /. ((z0 + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
z0 is set
B0 . z0 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
p is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . (0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
1 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(1 + 1) - 1 is V11() V12() ext-real Element of REAL
(D0 -' 1) -' 1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
((D0 -' 1) -' 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(D0 -' 1) - 1 is V11() V12() ext-real Element of REAL
((D0 -' 1) - 1) + 1 is V11() V12() ext-real Element of REAL
B . D0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((D0 -' 1) -' 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . (((D0 -' 1) -' 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B /. D0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(n,B) /. 1 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(D0 -' 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) /. (D0 -' 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(n,B) . (D0 -' 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) . D0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(0* n) + ((n,B) /. 1) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B0 . (0 + 1) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
(n,B) . (B0 . (0 + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) . (0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B0 . (0 + 1) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
(n,B) . (B0 . (0 + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) . (0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B0 . (0 + 1) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
(n,B) . (B0 . (0 + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) . (0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B0 . (0 + 1) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
(n,B) . (B0 . (0 + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) . (0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
z0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
z0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B0 . (z0 + 1) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
(n,B) . (B0 . (z0 + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) . (z0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(z0 + 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B0 . ((z0 + 1) + 1) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
(n,B) . (B0 . ((z0 + 1) + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) . ((z0 + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(z0 + 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B0 . ((z0 + 1) + 1) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
(n,B) . (B0 . ((z0 + 1) + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) . ((z0 + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
Seg (len (n,B)) is finite len (n,B) -element V126() V127() V128() V129() V130() V131() Element of bool NAT
B0 . z0 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
p is ordinal natural V11() V12() ext-real non negative finite cardinal set
p + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . (p + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(p + 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . ((p + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(p + 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . ((p + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
p0 is set
B0 . p0 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
q is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B0 . q is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
B /. ((p + 1) + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
B . ((p + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) /. (p + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,B) /. (p + 1)) + (B /. ((p + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(B0 . ((z0 + 1) + 1)) -' 1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
((B0 . ((z0 + 1) + 1)) -' 1) -' 1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(((B0 . ((z0 + 1) + 1)) -' 1) -' 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . ((((B0 . ((z0 + 1) + 1)) -' 1) -' 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B0 . z0 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
1 + (B0 . (z0 + 1)) is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B0 . (z0 + 1)) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
((B0 . (z0 + 1)) + 1) - 1 is V11() V12() ext-real Element of REAL
(B0 . ((z0 + 1) + 1)) - 1 is V11() V12() ext-real Element of REAL
1 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(1 + 1) - 1 is V11() V12() ext-real Element of REAL
((B0 . ((z0 + 1) + 1)) - 1) - 1 is V11() V12() ext-real Element of REAL
B /. (B0 . ((z0 + 1) + 1)) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
B . (B0 . ((z0 + 1) + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B . ((z0 + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(B0 . ((z0 + 1) + 1)) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
((B0 . ((z0 + 1) + 1)) + 1) - 1 is V11() V12() ext-real Element of REAL
(n,B) /. ((B0 . ((z0 + 1) + 1)) -' 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(n,B) . ((B0 . ((z0 + 1) + 1)) -' 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) /. (z0 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
B /. ((z0 + 1) + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,B) /. (z0 + 1)) + (B /. ((z0 + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
((n,B) /. ((B0 . ((z0 + 1) + 1)) -' 1)) + (B /. ((z0 + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
((n,B) /. ((B0 . ((z0 + 1) + 1)) -' 1)) + (B /. (B0 . ((z0 + 1) + 1))) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
((B0 . ((z0 + 1) + 1)) -' 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . (((B0 . ((z0 + 1) + 1)) -' 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
1 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B0 . (1 + 1) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
(B0 . (1 + 1)) -' 1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B0 . (1 + 1)) - 1 is V11() V12() ext-real Element of REAL
((B0 . ((z0 + 1) + 1)) -' 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B /. 1 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(n,B) /. (z0 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
B /. ((z0 + 1) + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,B) /. (z0 + 1)) + (B /. ((z0 + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B /. (1 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(B /. 1) + (B /. (1 + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B . (1 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(B0 . 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
((B0 . 1) + 1) - 1 is V11() V12() ext-real Element of REAL
(B0 . (1 + 1)) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
((B0 . (1 + 1)) + 1) - 1 is V11() V12() ext-real Element of REAL
(1 + 1) - 1 is V11() V12() ext-real Element of REAL
((B0 . (1 + 1)) -' 1) -' 1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
((B0 . (1 + 1)) -' 1) - 1 is V11() V12() ext-real Element of REAL
(((B0 . (1 + 1)) -' 1) -' 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B /. (B0 . ((z0 + 1) + 1)) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
B . (B0 . (1 + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) /. ((B0 . ((z0 + 1) + 1)) -' 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(n,B) . ((B0 . (1 + 1)) -' 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) . (((B0 . ((z0 + 1) + 1)) -' 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((n,B) /. ((B0 . ((z0 + 1) + 1)) -' 1)) + (B /. (B0 . ((z0 + 1) + 1))) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(n,B) . (len (n,B)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
z0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
z0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . (z0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(z0 + 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . ((z0 + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(z0 + 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . ((z0 + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
p is set
B0 . p is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
p0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) /. (z0 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
B /. ((z0 + 1) + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,B) /. (z0 + 1)) + (B /. ((z0 + 1) + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B . ((z0 + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(len B0) -' 1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(len B0) - 1 is V11() V12() ext-real Element of REAL
((len B0) -' 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B0 . (((len B0) -' 1) + 1) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
(n,B) . (B0 . (((len B0) -' 1) + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) . (((len B0) -' 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) . (0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B . (B0 . 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
Seg (len B) is finite len B -element V126() V127() V128() V129() V130() V131() Element of bool NAT
D0 is set
B . D0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(len B) |-> (0* n) is Relation-like NAT -defined REAL n -valued Function-like finite len B -element FinSequence-like FinSubsequence-like Element of (len B) -tuples_on (REAL n)
(len B) -tuples_on (REAL n) is non empty functional FinSequence-membered FinSequenceSet of REAL n
(REAL n) * is non empty functional FinSequence-membered FinSequenceSet of REAL n
{ b1 where b1 is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like Element of (REAL n) * : len b1 = len B } is set
(Seg (len B)) --> (0* n) is Relation-like Seg (len B) -defined {(0* n)} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like Element of bool [:(Seg (len B)),{(0* n)}:]
{(0* n)} is non empty trivial functional finite V39() 1 -element set
[:(Seg (len B)),{(0* n)}:] is Relation-like finite set
bool [:(Seg (len B)),{(0* n)}:] is non empty finite V39() set
((len B) |-> (0* n)) . D0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom ((len B) |-> (0* n)) is finite len B -element V126() V127() V128() V129() V130() V131() Element of bool NAT
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
0* n is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(Seg n) --> 0 is Relation-like Seg n -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),{0}:] is non empty finite V39() set
B is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
dom B is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
(n,B) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B0 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued FinSequence of NAT
rng B0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
B * B0 is Relation-like NAT -defined REAL n -valued Function-like finite Element of bool [:NAT,(REAL n):]
[:NAT,(REAL n):] is non empty non trivial Relation-like non finite set
bool [:NAT,(REAL n):] is non empty non trivial non finite set
B is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
(n,B) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
dom B0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
[:(dom B0),(dom B0):] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(dom B0),(dom B0):] is non empty finite V39() set
I is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued FinSequence of NAT
D0 is Relation-like dom B0 -defined dom B0 -valued Function-like one-to-one total quasi_total onto bijective finite complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(dom B0),(dom B0):]
B0 * D0 is Relation-like dom B0 -defined NAT -valued RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(dom B0),NAT:]
[:(dom B0),NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:(dom B0),NAT:] is non empty set
dom I is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
rng I is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
dom (B * B0) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
dom B is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
[:(dom B),(dom B):] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(dom B),(dom B):] is non empty finite V39() set
B * I is Relation-like NAT -defined REAL n -valued Function-like finite Element of bool [:NAT,(REAL n):]
z0 is Relation-like Function-like set
dom z0 is set
len B0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len B0) is finite len B0 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
rng z0 is set
rng B is functional finite FinSequence-membered Element of bool (REAL n)
bool (REAL n) is non empty set
p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng p is finite set
p0 is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
x0 is Relation-like dom B -defined dom B -valued Function-like one-to-one total quasi_total onto bijective finite complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(dom B),(dom B):]
((REAL n),B,x0) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
B * x0 is Relation-like dom B -defined REAL n -valued Function-like finite Element of bool [:(dom B),(REAL n):]
[:(dom B),(REAL n):] is Relation-like set
bool [:(dom B),(REAL n):] is non empty set
(n,p0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
B is ordinal natural V11() V12() ext-real non negative finite cardinal set
Base_FinSeq (n,B) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
len (Base_FinSeq (n,B)) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
B is ordinal natural V11() V12() ext-real non negative finite cardinal set
(n,B) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
B0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
(n,B0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(n,B) . B is V11() V12() ext-real Element of REAL
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
B is ordinal natural V11() V12() ext-real non negative finite cardinal set
(n,B) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
sqr (n,B) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
(n,B) (#) sqrreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
mlt ((n,B),(n,B)) is Relation-like Function-like set
multreal .: ((n,B),(n,B)) is set
sqrreal * (n,B) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued Element of bool [:NAT,REAL:]
dom (sqrreal * (n,B)) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
dom sqrreal is non empty V126() V127() V128() Element of bool REAL
(n,B) " (dom sqrreal) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
rng (n,B) is finite V126() V127() V128() Element of bool REAL
dom (n,B) is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
B0 is set
((n,B) (#) sqrreal) . B0 is V11() V12() ext-real Element of REAL
(n,B) . B0 is V11() V12() ext-real Element of REAL
sqrreal . ((n,B) . B0) is V11() V12() ext-real Element of REAL
len (n,B) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len (n,B)) is finite len (n,B) -element V126() V127() V128() V129() V130() V131() Element of bool NAT
B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
sqrreal . 1 is V11() V12() ext-real Element of REAL
1 ^2 is V11() V12() ext-real Element of REAL
K37(1,1) is ordinal natural V11() V12() ext-real non negative finite cardinal set
sqrreal . 0 is V11() V12() ext-real Element of REAL
0 ^2 is V11() V12() ext-real Element of REAL
K37(0,0) is empty trivial ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() () () () set
(n,B) " REAL is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
B is ordinal natural V11() V12() ext-real non negative finite cardinal set
(B,n) is Relation-like NAT -defined REAL -valued Function-like finite B -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL B
REAL B is non empty functional FinSequence-membered FinSequenceSet of REAL
B -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = B } is set
Sum (B,n) is V11() V12() ext-real Element of REAL
K608(REAL,(B,n),addreal) is V11() V12() ext-real Element of REAL
B is set
D0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
D0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
D0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:NAT,REAL:]
len (B,n) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
D0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
D0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B . (D0 + 1) is V11() V12() ext-real Element of REAL
B . D0 is V11() V12() ext-real Element of REAL
(B,n) . (D0 + 1) is V11() V12() ext-real Element of REAL
addreal . ((B . D0),((B,n) . (D0 + 1))) is V11() V12() ext-real Element of REAL
[(B . D0),((B,n) . (D0 + 1))] is non empty set
{(B . D0),((B,n) . (D0 + 1))} is non empty finite V126() V127() V128() set
{(B . D0)} is non empty trivial finite 1 -element V126() V127() V128() set
{{(B . D0),((B,n) . (D0 + 1))},{(B . D0)}} is non empty finite V39() set
addreal . [(B . D0),((B,n) . (D0 + 1))] is V11() V12() ext-real set
addreal . (0,0) is V11() V12() ext-real Element of REAL
[0,0] is non empty set
{0,0} is non empty functional finite V39() V126() V127() V128() V129() V130() V131() set
{{0,0},{0}} is non empty finite V39() set
addreal . [0,0] is V11() V12() ext-real set
0 + 0 is empty trivial ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional V33() V34() finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() () () () Element of NAT
addreal . (1,0) is V11() V12() ext-real Element of REAL
[1,0] is non empty set
{1,0} is non empty finite V39() V126() V127() V128() V129() V130() V131() set
{{1,0},{1}} is non empty finite V39() set
addreal . [1,0] is V11() V12() ext-real set
1 + 0 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
addreal . (0,1) is V11() V12() ext-real Element of REAL
[0,1] is non empty set
{0,1} is non empty finite V39() V126() V127() V128() V129() V130() V131() set
{{0,1},{0}} is non empty finite V39() set
addreal . [0,1] is V11() V12() ext-real set
0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B . 1 is V11() V12() ext-real Element of REAL
(B,n) . 1 is V11() V12() ext-real Element of REAL
B . (len (B,n)) is V11() V12() ext-real Element of REAL
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
B is ordinal natural V11() V12() ext-real non negative finite cardinal set
(B,n) is Relation-like NAT -defined REAL -valued Function-like finite B -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL B
REAL B is non empty functional FinSequence-membered FinSequenceSet of REAL
B -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = B } is set
|.(B,n).| is V11() V12() ext-real non negative Element of REAL
sqr (B,n) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(B,n) (#) sqrreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
mlt ((B,n),(B,n)) is Relation-like Function-like set
multreal .: ((B,n),(B,n)) is set
Sum (sqr (B,n)) is V11() V12() ext-real Element of REAL
K608(REAL,(sqr (B,n)),addreal) is V11() V12() ext-real Element of REAL
sqrt (Sum (sqr (B,n))) is V11() V12() ext-real Element of REAL
Sum (B,n) is V11() V12() ext-real Element of REAL
K608(REAL,(B,n),addreal) is V11() V12() ext-real Element of REAL
sqrt (Sum (B,n)) is V11() V12() ext-real Element of REAL
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
B is ordinal natural V11() V12() ext-real non negative finite cardinal set
(B,n) is Relation-like NAT -defined REAL -valued Function-like finite B -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL B
REAL B is non empty functional FinSequence-membered FinSequenceSet of REAL
B -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = B } is set
B0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
(B,B0) is Relation-like NAT -defined REAL -valued Function-like finite B -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL B
|((B,n),(B,B0))| is V11() V12() ext-real Element of REAL
mlt ((B,n),(B,B0)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: ((B,n),(B,B0)) is set
Sum (mlt ((B,n),(B,B0))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt ((B,n),(B,B0))),addreal) is V11() V12() ext-real Element of REAL
0* B is Relation-like NAT -defined REAL -valued Function-like finite B -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL B
B |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite B -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of B -tuples_on REAL
Seg B is finite B -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(Seg B) --> 0 is Relation-like Seg B -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg B),{0}:]
[:(Seg B),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg B),{0}:] is non empty finite V39() set
dom (0* B) is finite B -element V126() V127() V128() V129() V130() V131() Element of bool NAT
len (B |-> 0) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len (B |-> 0)) is finite len (B |-> 0) -element V126() V127() V128() V129() V130() V131() Element of bool NAT
dom (B,B0) is finite B -element V126() V127() V128() V129() V130() V131() Element of bool NAT
len (B,B0) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len (B,B0)) is finite len (B,B0) -element V126() V127() V128() V129() V130() V131() Element of bool NAT
dom (B,n) is finite B -element V126() V127() V128() V129() V130() V131() Element of bool NAT
len (B,n) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len (B,n)) is finite len (B,n) -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(REAL,(B,n),(B,B0)) is Relation-like NAT -defined [:REAL,REAL:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:REAL,REAL:]
dom (REAL,(B,n),(B,B0)) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
(dom (B,n)) /\ (dom (B,B0)) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
dom multreal is non empty Relation-like REAL -defined REAL -valued complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal * (REAL,(B,n),(B,B0)) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued Element of bool [:NAT,REAL:]
dom (multreal * (REAL,(B,n),(B,B0))) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
(REAL,(B,n),(B,B0)) " [:REAL,REAL:] is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
I is set
(multreal * (REAL,(B,n),(B,B0))) . I is V11() V12() ext-real Element of REAL
(0* B) . I is V11() V12() ext-real Element of REAL
(REAL,(B,n),(B,B0)) . I is set
multreal . ((REAL,(B,n),(B,B0)) . I) is V11() V12() ext-real Element of REAL
x0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B,n) . x0 is V11() V12() ext-real Element of REAL
(B,B0) . x0 is V11() V12() ext-real Element of REAL
[((B,n) . x0),((B,B0) . x0)] is non empty Element of [:REAL,REAL:]
{((B,n) . x0),((B,B0) . x0)} is non empty finite V126() V127() V128() set
{((B,n) . x0)} is non empty trivial finite 1 -element V126() V127() V128() set
{{((B,n) . x0),((B,B0) . x0)},{((B,n) . x0)}} is non empty finite V39() set
multreal . [((B,n) . x0),((B,B0) . x0)] is V11() V12() ext-real Element of REAL
multreal . (((B,n) . x0),((B,B0) . x0)) is V11() V12() ext-real Element of REAL
[((B,n) . x0),((B,B0) . x0)] is non empty set
multreal . [((B,n) . x0),((B,B0) . x0)] is V11() V12() ext-real set
1 * 0 is empty trivial ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional V33() V34() finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() () () () Element of NAT
multreal . (((B,n) . x0),((B,B0) . x0)) is V11() V12() ext-real Element of REAL
[((B,n) . x0),((B,B0) . x0)] is non empty set
multreal . [((B,n) . x0),((B,B0) . x0)] is V11() V12() ext-real set
z0 is V11() V12() ext-real Element of REAL
0 * z0 is V11() V12() ext-real Element of REAL
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
B is ordinal natural V11() V12() ext-real non negative finite cardinal set
(n,B) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B0,(n,B))| is V11() V12() ext-real Element of REAL
mlt (B0,(n,B)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B0,(n,B)) is set
Sum (mlt (B0,(n,B))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B0,(n,B))),addreal) is V11() V12() ext-real Element of REAL
B0 . B is V11() V12() ext-real Element of REAL
len B0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
len (n,B) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
len (mlt (B0,(n,B))) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B0 /. B is V11() V12() ext-real Element of REAL
(B0 /. B) * (n,B) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(B0 /. B) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total quasi_total complex-yielding ext-real-valued real-valued increasing non-decreasing Element of bool [:REAL,REAL:]
multreal [;] ((B0 /. B),(id REAL)) is set
(n,B) (#) ((B0 /. B) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
D0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
(mlt (B0,(n,B))) . D0 is V11() V12() ext-real Element of REAL
((B0 /. B) * (n,B)) . D0 is V11() V12() ext-real Element of REAL
B0 /. D0 is V11() V12() ext-real Element of REAL
(n,B) . D0 is V11() V12() ext-real Element of REAL
(B0 /. D0) * ((n,B) . D0) is V11() V12() ext-real Element of REAL
I is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . I is V11() V12() ext-real Element of REAL
(n,B) . D0 is V11() V12() ext-real Element of REAL
(B0 /. B) * ((n,B) . D0) is V11() V12() ext-real Element of REAL
B0 /. D0 is V11() V12() ext-real Element of REAL
(B0 /. D0) * ((n,B) . D0) is V11() V12() ext-real Element of REAL
B0 /. D0 is V11() V12() ext-real Element of REAL
(n,B) . D0 is V11() V12() ext-real Element of REAL
(B0 /. D0) * ((n,B) . D0) is V11() V12() ext-real Element of REAL
B0 /. D0 is V11() V12() ext-real Element of REAL
(n,B) . D0 is V11() V12() ext-real Element of REAL
(B0 /. D0) * ((n,B) . D0) is V11() V12() ext-real Element of REAL
B0 . D0 is V11() V12() ext-real Element of REAL
(B0 . D0) * ((n,B) . D0) is V11() V12() ext-real Element of REAL
len ((B0 /. B) * (n,B)) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Sum (n,B) is V11() V12() ext-real Element of REAL
K608(REAL,(n,B),addreal) is V11() V12() ext-real Element of REAL
(B0 /. B) * (Sum (n,B)) is V11() V12() ext-real Element of REAL
(B0 /. B) * 1 is V11() V12() ext-real Element of REAL
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
B is ordinal natural V11() V12() ext-real non negative finite cardinal set
B0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
D0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B0,D0) is Relation-like NAT -defined REAL -valued Function-like finite B0 -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL B0
REAL B0 is non empty functional FinSequence-membered FinSequenceSet of REAL
B0 -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = B0 } is set
|(B,(B0,D0))| is V11() V12() ext-real Element of REAL
mlt (B,(B0,D0)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,(B0,D0)) is set
Sum (mlt (B,(B0,D0))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,(B0,D0))),addreal) is V11() V12() ext-real Element of REAL
|(B,(B0,D0))| * (B0,D0) is Relation-like NAT -defined REAL -valued Function-like finite B0 -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL B0
|(B,(B0,D0))| multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total quasi_total complex-yielding ext-real-valued real-valued increasing non-decreasing Element of bool [:REAL,REAL:]
multreal [;] (|(B,(B0,D0))|,(id REAL)) is set
(B0,D0) (#) (|(B,(B0,D0))| multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
I is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
x0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
(n,x0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,(n,x0))| is V11() V12() ext-real Element of REAL
mlt (B,(n,x0)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,(n,x0)) is set
Sum (mlt (B,(n,x0))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,(n,x0))),addreal) is V11() V12() ext-real Element of REAL
|(B,(n,x0))| * (n,x0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,(n,x0))| multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (|(B,(n,x0))|,(id REAL)) is set
(n,x0) (#) (|(B,(n,x0))| multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
B0 is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
dom B0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
B is ordinal natural V11() V12() ext-real non negative finite cardinal set
B0 . B is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,(n,B))| is V11() V12() ext-real Element of REAL
mlt (B,(n,B)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,(n,B)) is set
Sum (mlt (B,(n,B))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,(n,B))),addreal) is V11() V12() ext-real Element of REAL
|(B,(n,B))| * (n,B) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,(n,B))| multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total quasi_total complex-yielding ext-real-valued real-valued increasing non-decreasing Element of bool [:REAL,REAL:]
multreal [;] (|(B,(n,B))|,(id REAL)) is set
(n,B) (#) (|(B,(n,B))| multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
len B0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len B0) is finite len B0 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
B0 is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
len B0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
len B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
I is ordinal natural V11() V12() ext-real non negative finite cardinal set
B0 . I is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B . I is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
x0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B0 . x0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
D0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(D0,x0) is Relation-like NAT -defined REAL -valued Function-like finite D0 -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL D0
REAL D0 is non empty functional FinSequence-membered FinSequenceSet of REAL
D0 -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = D0 } is set
|(B,(D0,x0))| is V11() V12() ext-real Element of REAL
mlt (B,(D0,x0)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,(D0,x0)) is set
Sum (mlt (B,(D0,x0))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,(D0,x0))),addreal) is V11() V12() ext-real Element of REAL
|(B,(D0,x0))| * (D0,x0) is Relation-like NAT -defined REAL -valued Function-like finite D0 -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL D0
|(B,(D0,x0))| multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total quasi_total complex-yielding ext-real-valued real-valued increasing non-decreasing Element of bool [:REAL,REAL:]
multreal [;] (|(B,(D0,x0))|,(id REAL)) is set
(D0,x0) (#) (|(B,(D0,x0))| multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(n,B) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
(n,(n,B)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
len (n,B) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,(n,B)) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
len (n,(n,B)) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,(n,B)) . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
I is ordinal natural V11() V12() ext-real non negative finite cardinal set
(n,(n,B)) /. I is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
I + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,(n,B)) /. (I + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
z0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
((n,(n,B)) /. (I + 1)) . z0 is set
B . z0 is V11() V12() ext-real Element of REAL
(n,(n,B)) . (I + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) /. (I + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(n,B) . (I + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B,(I + 1)) is Relation-like NAT -defined REAL -valued Function-like finite B -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL B
REAL B is non empty functional FinSequence-membered FinSequenceSet of REAL
B -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = B } is set
|(B,(B,(I + 1)))| is V11() V12() ext-real Element of REAL
mlt (B,(B,(I + 1))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,(B,(I + 1))) is set
Sum (mlt (B,(B,(I + 1)))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,(B,(I + 1)))),addreal) is V11() V12() ext-real Element of REAL
|(B,(B,(I + 1)))| * (B,(I + 1)) is Relation-like NAT -defined REAL -valued Function-like finite B -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL B
|(B,(B,(I + 1)))| multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total quasi_total complex-yielding ext-real-valued real-valued increasing non-decreasing Element of bool [:REAL,REAL:]
multreal [;] (|(B,(B,(I + 1)))|,(id REAL)) is set
(B,(I + 1)) (#) (|(B,(B,(I + 1)))| multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
p is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
((n,(n,B)) /. I) + ((n,B) /. (I + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
p . z0 is V11() V12() ext-real Element of REAL
u4 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u4 . z0 is V11() V12() ext-real Element of REAL
q is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
q . z0 is V11() V12() ext-real Element of REAL
(u4 . z0) + (q . z0) is V11() V12() ext-real Element of REAL
((n,B) /. (I + 1)) . z0 is set
x0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
x0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B,(x0 + 1)) is Relation-like NAT -defined REAL -valued Function-like finite B -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL B
p0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B,(x0 + 1)) . p0 is V11() V12() ext-real Element of REAL
|(B,(B,(I + 1)))| * ((B,(x0 + 1)) . p0) is V11() V12() ext-real Element of REAL
|(B,(B,(I + 1)))| * 0 is V11() V12() ext-real Element of REAL
((n,(n,B)) /. I) . z0 is set
((n,B) /. (I + 1)) . z0 is set
x0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
x0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B,(x0 + 1)) is Relation-like NAT -defined REAL -valued Function-like finite B -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL B
p0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B,(x0 + 1)) . p0 is V11() V12() ext-real Element of REAL
|(B,(B,(I + 1)))| * ((B,(x0 + 1)) . p0) is V11() V12() ext-real Element of REAL
|(B,(B,(I + 1)))| * 1 is V11() V12() ext-real Element of REAL
B . (I + 1) is V11() V12() ext-real Element of REAL
((n,B) /. (I + 1)) . z0 is set
x0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
x0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B,(x0 + 1)) is Relation-like NAT -defined REAL -valued Function-like finite B -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL B
p0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B,(x0 + 1)) . p0 is V11() V12() ext-real Element of REAL
|(B,(B,(I + 1)))| * ((B,(x0 + 1)) . p0) is V11() V12() ext-real Element of REAL
|(B,(B,(I + 1)))| * 0 is V11() V12() ext-real Element of REAL
(n,(n,B)) /. 1 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,(n,B)) /. 1) . z0 is set
B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B,1) is Relation-like NAT -defined REAL -valued Function-like finite B -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL B
REAL B is non empty functional FinSequence-membered FinSequenceSet of REAL
B -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = B } is set
|(B,(B,1))| is V11() V12() ext-real Element of REAL
mlt (B,(B,1)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,(B,1)) is set
Sum (mlt (B,(B,1))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,(B,1))),addreal) is V11() V12() ext-real Element of REAL
|(B,(B,1))| * (B,1) is Relation-like NAT -defined REAL -valued Function-like finite B -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL B
|(B,(B,1))| multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total quasi_total complex-yielding ext-real-valued real-valued increasing non-decreasing Element of bool [:REAL,REAL:]
multreal [;] (|(B,(B,1))|,(id REAL)) is set
(B,1) (#) (|(B,(B,1))| multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
(|(B,(B,1))| * (B,1)) . z0 is V11() V12() ext-real Element of REAL
p0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B,1) . p0 is V11() V12() ext-real Element of REAL
|(B,(B,1))| * ((B,1) . p0) is V11() V12() ext-real Element of REAL
|(B,(B,1))| * 0 is V11() V12() ext-real Element of REAL
((n,(n,B)) /. 1) . 1 is set
(|(B,(B,1))| * (B,1)) . 1 is V11() V12() ext-real Element of REAL
(B,1) . 1 is V11() V12() ext-real Element of REAL
|(B,(B,1))| * ((B,1) . 1) is V11() V12() ext-real Element of REAL
|(B,(B,1))| * 1 is V11() V12() ext-real Element of REAL
B . 1 is V11() V12() ext-real Element of REAL
(n,(n,B)) /. (0 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,(n,B)) /. (0 + 1)) . z0 is set
z0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
((n,(n,B)) /. (I + 1)) . z0 is set
B . z0 is V11() V12() ext-real Element of REAL
(n,(n,B)) /. (len (n,B)) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
len B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
I is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
len I is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,(n,B)) /. 0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
x0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
((n,(n,B)) /. 0) . x0 is set
B . x0 is V11() V12() ext-real Element of REAL
x0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
((n,(n,B)) /. (len (n,B))) . x0 is set
B . x0 is V11() V12() ext-real Element of REAL
(n,(n,B)) . (len (n,B)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (n,B) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
0* n is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(Seg n) --> 0 is Relation-like Seg n -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),{0}:] is non empty finite V39() set
len (n,B) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,(n,B)) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
(n,(n,B)) . (len (n,B)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
0* n is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(Seg n) --> 0 is Relation-like Seg n -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),{0}:] is non empty finite V39() set
len (n,B) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,(n,B)) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
(n,(n,B)) . (len (n,B)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
0* n is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(Seg n) --> 0 is Relation-like Seg n -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),{0}:] is non empty finite V39() set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
{ (n,b1) where b1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
B is set
B0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n is non empty ordinal natural V11() V12() ext-real positive non negative finite cardinal set
(n) is functional FinSequence-membered Element of bool (REAL n)
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
{ (n,b1) where b1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,1) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(0) is functional FinSequence-membered Element of bool (REAL 0)
{ (0,b1) where b1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT : ( 1 <= b1 & b1 <= 0 ) } is set
n is set
B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(0,B) is empty trivial ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined REAL -valued Function-like one-to-one constant functional finite finite-yielding V39() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() () () () Element of REAL 0
n is non empty ordinal natural V11() V12() ext-real positive non negative finite cardinal set
(n) is functional FinSequence-membered Element of bool (REAL n)
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
{ (n,b1) where b1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
(n) is functional FinSequence-membered Element of bool (REAL n)
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
{ (n,b1) where b1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n : ex b2 being ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT st
( 1 <= b2 & b2 <= n & b1 = (n,b2) ) } is set
B0 is set
B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
D0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,D0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B0 is set
B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
B is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
|(B0,B)| is V11() V12() ext-real Element of REAL
mlt (B0,B) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B0,B) is set
Sum (mlt (B0,B)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B0,B)),addreal) is V11() V12() ext-real Element of REAL
D0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
I is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,I) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
x0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
z0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,z0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
|.B0.| is V11() V12() ext-real non negative Element of REAL
sqr B0 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
B0 (#) sqrreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
mlt (B0,B0) is Relation-like Function-like set
multreal .: (B0,B0) is set
Sum (sqr B0) is V11() V12() ext-real Element of REAL
K608(REAL,(sqr B0),addreal) is V11() V12() ext-real Element of REAL
sqrt (Sum (sqr B0)) is V11() V12() ext-real Element of REAL
B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
D0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,D0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B0 is functional FinSequence-membered () () () Element of bool (REAL n)
B is set
D0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
0* n is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(Seg n) --> 0 is Relation-like Seg n -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),{0}:] is non empty finite V39() set
I is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
D0 . I is V11() V12() ext-real Element of REAL
(n,I) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(D0,(n,I))| is V11() V12() ext-real Element of REAL
mlt (D0,(n,I)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (D0,(n,I)) is set
Sum (mlt (D0,(n,I))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (D0,(n,I))),addreal) is V11() V12() ext-real Element of REAL
|.(0* n).| is V11() V12() ext-real non negative Element of REAL
sqr (0* n) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(0* n) (#) sqrreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
mlt ((0* n),(0* n)) is Relation-like Function-like set
multreal .: ((0* n),(0* n)) is set
Sum (sqr (0* n)) is V11() V12() ext-real Element of REAL
K608(REAL,(sqr (0* n)),addreal) is V11() V12() ext-real Element of REAL
sqrt (Sum (sqr (0* n))) is V11() V12() ext-real Element of REAL
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
(n) is functional FinSequence-membered () () () (n) (n) Element of bool (REAL n)
{ (n,b1) where b1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
n is non empty ordinal natural V11() V12() ext-real positive non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
B is functional FinSequence-membered () () () (n) (n) Element of bool (REAL n)
(n) is non empty functional FinSequence-membered () () () (n) (n) Element of bool (REAL n)
{ (n,b1) where b1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
n is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
REAL-US n is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V194() V195() L17()
the carrier of (REAL-US n) is non empty set
B is Element of the carrier of (REAL-US n)
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
B0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
REAL-US n is non empty right_complementable constituted-Functions constituted-FinSeqs Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V194() V195() L17()
the carrier of (REAL-US n) is non empty set
B is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of (REAL-US n)
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
B0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
REAL-US n is non empty right_complementable constituted-Functions constituted-FinSeqs Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V194() V195() L17()
the carrier of (REAL-US n) is non empty set
B is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
B is Relation-like Function-like complex-yielding ext-real-valued real-valued set
B0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
D0 is Relation-like Function-like complex-yielding ext-real-valued real-valued set
B + B0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
the addF of (REAL-US n) is non empty Relation-like [: the carrier of (REAL-US n), the carrier of (REAL-US n):] -defined the carrier of (REAL-US n) -valued Function-like total quasi_total Element of bool [:[: the carrier of (REAL-US n), the carrier of (REAL-US n):], the carrier of (REAL-US n):]
[: the carrier of (REAL-US n), the carrier of (REAL-US n):] is non empty Relation-like set
[:[: the carrier of (REAL-US n), the carrier of (REAL-US n):], the carrier of (REAL-US n):] is non empty Relation-like set
bool [:[: the carrier of (REAL-US n), the carrier of (REAL-US n):], the carrier of (REAL-US n):] is non empty set
the addF of (REAL-US n) . (B,B0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
[B,B0] is non empty set
{B,B0} is non empty functional finite V39() set
{B} is non empty trivial functional finite V39() 1 -element set
{{B,B0},{B}} is non empty finite V39() set
the addF of (REAL-US n) . [B,B0] is set
B + D0 is Relation-like Function-like set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
Euclid_add n is non empty Relation-like [:(REAL n),(REAL n):] -defined REAL n -valued Function-like total quasi_total V208( REAL n) V209( REAL n) Element of bool [:[:(REAL n),(REAL n):],(REAL n):]
[:(REAL n),(REAL n):] is non empty Relation-like set
[:[:(REAL n),(REAL n):],(REAL n):] is non empty Relation-like set
bool [:[:(REAL n),(REAL n):],(REAL n):] is non empty set
I is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
x0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(Euclid_add n) . (I,x0) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
[I,x0] is non empty set
{I,x0} is non empty functional finite V39() set
{I} is non empty trivial functional finite V39() 1 -element set
{{I,x0},{I}} is non empty finite V39() set
(Euclid_add n) . [I,x0] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B + B0 is Relation-like Function-like set
addreal .: (B,B0) is set
n is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
REAL-US n is non empty right_complementable constituted-Functions constituted-FinSeqs Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V194() V195() L17()
the carrier of (REAL-US n) is non empty set
B is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
B0 is Relation-like Function-like complex-yielding ext-real-valued real-valued set
B is V11() V12() ext-real Element of REAL
D0 is V11() V12() ext-real Element of REAL
B * B is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
the Mult of (REAL-US n) is non empty Relation-like [:REAL, the carrier of (REAL-US n):] -defined the carrier of (REAL-US n) -valued Function-like total quasi_total Element of bool [:[:REAL, the carrier of (REAL-US n):], the carrier of (REAL-US n):]
[:REAL, the carrier of (REAL-US n):] is non empty non trivial Relation-like non finite set
[:[:REAL, the carrier of (REAL-US n):], the carrier of (REAL-US n):] is non empty non trivial Relation-like non finite set
bool [:[:REAL, the carrier of (REAL-US n):], the carrier of (REAL-US n):] is non empty non trivial non finite set
the Mult of (REAL-US n) . (B,B) is set
[B,B] is non empty set
{B,B} is non empty finite set
{B} is non empty trivial finite 1 -element V126() V127() V128() set
{{B,B},{B}} is non empty finite V39() set
the Mult of (REAL-US n) . [B,B] is set
D0 * B0 is Relation-like Function-like set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
Euclid_mult n is non empty Relation-like [:REAL,(REAL n):] -defined REAL n -valued Function-like total quasi_total Element of bool [:[:REAL,(REAL n):],(REAL n):]
[:REAL,(REAL n):] is non empty non trivial Relation-like non finite set
[:[:REAL,(REAL n):],(REAL n):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(REAL n):],(REAL n):] is non empty non trivial non finite set
I is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(Euclid_mult n) . (D0,I) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
[D0,I] is non empty set
{D0,I} is non empty finite set
{D0} is non empty trivial finite 1 -element V126() V127() V128() set
{{D0,I},{D0}} is non empty finite V39() set
(Euclid_mult n) . [D0,I] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B * B is Relation-like Function-like set
B multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total quasi_total complex-yielding ext-real-valued real-valued increasing non-decreasing Element of bool [:REAL,REAL:]
multreal [;] (B,(id REAL)) is set
B (#) (B multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
n is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
REAL-US n is non empty right_complementable constituted-Functions constituted-FinSeqs Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V194() V195() L17()
the carrier of (REAL-US n) is non empty set
B is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
B0 is Relation-like Function-like complex-yielding ext-real-valued real-valued set
- B is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
- B0 is Relation-like Function-like complex-yielding set
K38(1) is V11() V12() ext-real non positive set
K38(1) * B0 is Relation-like Function-like set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
REAL-NS n is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V189() V190() V191() V192() L16()
the carrier of (REAL-NS n) is non empty set
B is Element of the carrier of (REAL-NS n)
- B is Element of the carrier of (REAL-NS n)
D0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
- D0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
D0 (#) compreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
K38(1) * D0 is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
D0 (#) (K38(1) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
- B is Relation-like Function-like complex-yielding set
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
B (#) compreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
K38(1) * B is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
B (#) (K38(1) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
n is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
REAL-US n is non empty right_complementable constituted-Functions constituted-FinSeqs Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V194() V195() L17()
the carrier of (REAL-US n) is non empty set
B is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
B is Relation-like Function-like complex-yielding ext-real-valued real-valued set
B0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
D0 is Relation-like Function-like complex-yielding ext-real-valued real-valued set
B - B0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
- B0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
- B0 is Relation-like Function-like complex-yielding set
B0 (#) compreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
K38(1) * B0 is Relation-like Function-like set
B0 (#) (K38(1) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
B + (- B0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
the addF of (REAL-US n) is non empty Relation-like [: the carrier of (REAL-US n), the carrier of (REAL-US n):] -defined the carrier of (REAL-US n) -valued Function-like total quasi_total Element of bool [:[: the carrier of (REAL-US n), the carrier of (REAL-US n):], the carrier of (REAL-US n):]
[: the carrier of (REAL-US n), the carrier of (REAL-US n):] is non empty Relation-like set
[:[: the carrier of (REAL-US n), the carrier of (REAL-US n):], the carrier of (REAL-US n):] is non empty Relation-like set
bool [:[: the carrier of (REAL-US n), the carrier of (REAL-US n):], the carrier of (REAL-US n):] is non empty set
the addF of (REAL-US n) . (B,(- B0)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
[B,(- B0)] is non empty set
{B,(- B0)} is non empty functional finite V39() set
{B} is non empty trivial functional finite V39() 1 -element set
{{B,(- B0)},{B}} is non empty finite V39() set
the addF of (REAL-US n) . [B,(- B0)] is set
B + (- B0) is Relation-like Function-like set
addreal .: (B,(- B0)) is set
B - D0 is Relation-like Function-like set
- D0 is Relation-like Function-like complex-yielding set
K38(1) * D0 is Relation-like Function-like set
B + (- D0) is Relation-like Function-like set
B - B0 is Relation-like Function-like set
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:[:REAL,REAL:],REAL:]
K660(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (B,B0) is set
B + (- B0) is Relation-like Function-like set
n is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
REAL-US n is non empty right_complementable constituted-Functions constituted-FinSeqs Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V194() V195() L17()
the carrier of (REAL-US n) is non empty set
bool the carrier of (REAL-US n) is non empty set
B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Euclid_scalar n is non empty Relation-like [:(REAL n),(REAL n):] -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:[:(REAL n),(REAL n):],REAL:]
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
[:(REAL n),(REAL n):] is non empty Relation-like set
[:[:(REAL n),(REAL n):],REAL:] is non empty non trivial Relation-like non finite complex-yielding ext-real-valued real-valued set
bool [:[:(REAL n),(REAL n):],REAL:] is non empty non trivial non finite set
B0 is Relation-like NAT -defined the carrier of (REAL-US n) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (REAL-US n)
rng B0 is finite Element of bool the carrier of (REAL-US n)
B0 . B is set
B0 /. B is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
B is Element of bool the carrier of (REAL-US n)
D0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
I is Relation-like the carrier of (REAL-US n) -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Linear_Combination of B
Carrier I is Element of bool the carrier of (REAL-US n)
I (#) B0 is Relation-like NAT -defined the carrier of (REAL-US n) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (REAL-US n)
dom (I (#) B0) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
Sum (I (#) B0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
(Euclid_scalar n) . (D0,(Sum (I (#) B0))) is set
[D0,(Sum (I (#) B0))] is non empty set
{D0,(Sum (I (#) B0))} is non empty functional finite V39() set
{D0} is non empty trivial functional finite V39() 1 -element set
{{D0,(Sum (I (#) B0))},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,(Sum (I (#) B0))] is V11() V12() ext-real set
I . (B0 /. B) is V11() V12() ext-real Element of REAL
(I . (B0 /. B)) * D0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
the Mult of (REAL-US n) is non empty Relation-like [:REAL, the carrier of (REAL-US n):] -defined the carrier of (REAL-US n) -valued Function-like total quasi_total Element of bool [:[:REAL, the carrier of (REAL-US n):], the carrier of (REAL-US n):]
[:REAL, the carrier of (REAL-US n):] is non empty non trivial Relation-like non finite set
[:[:REAL, the carrier of (REAL-US n):], the carrier of (REAL-US n):] is non empty non trivial Relation-like non finite set
bool [:[:REAL, the carrier of (REAL-US n):], the carrier of (REAL-US n):] is non empty non trivial non finite set
the Mult of (REAL-US n) . ((I . (B0 /. B)),D0) is set
[(I . (B0 /. B)),D0] is non empty set
{(I . (B0 /. B)),D0} is non empty finite set
{(I . (B0 /. B))} is non empty trivial finite 1 -element V126() V127() V128() set
{{(I . (B0 /. B)),D0},{(I . (B0 /. B))}} is non empty finite V39() set
the Mult of (REAL-US n) . [(I . (B0 /. B)),D0] is set
(I . (B0 /. B)) * D0 is Relation-like Function-like set
(I . (B0 /. B)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] ((I . (B0 /. B)),(id REAL)) is set
D0 (#) ((I . (B0 /. B)) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
(Euclid_scalar n) . (D0,((I . (B0 /. B)) * D0)) is set
[D0,((I . (B0 /. B)) * D0)] is non empty set
{D0,((I . (B0 /. B)) * D0)} is non empty functional finite V39() set
{{D0,((I . (B0 /. B)) * D0)},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,((I . (B0 /. B)) * D0)] is V11() V12() ext-real set
len (I (#) B0) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
len B0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len B0) is finite len B0 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
dom B0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
Seg (len (I (#) B0)) is finite len (I (#) B0) -element V126() V127() V128() V129() V130() V131() Element of bool NAT
[:NAT, the carrier of (REAL-US n):] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of (REAL-US n):] is non empty non trivial non finite set
x0 is Relation-like NAT -defined the carrier of (REAL-US n) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (REAL-US n)
Sum x0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
len x0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
0. (REAL-US n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like zero complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
the ZeroF of (REAL-US n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
p is non empty Relation-like NAT -defined the carrier of (REAL-US n) -valued Function-like total quasi_total Element of bool [:NAT, the carrier of (REAL-US n):]
p . (len x0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
p . 0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
0* n is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(Seg n) --> 0 is Relation-like Seg n -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),{0}:] is non empty finite V39() set
(Euclid_scalar n) . (D0,(p . 0)) is set
[D0,(p . 0)] is non empty set
{D0,(p . 0)} is non empty functional finite V39() set
{{D0,(p . 0)},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,(p . 0)] is V11() V12() ext-real set
z0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(z0,(0* n))| is V11() V12() ext-real Element of REAL
mlt (z0,(0* n)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,(0* n)) is set
Sum (mlt (z0,(0* n))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,(0* n))),addreal) is V11() V12() ext-real Element of REAL
p0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
p . p0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
(Euclid_scalar n) . (D0,(p . p0)) is set
[D0,(p . p0)] is non empty set
{D0,(p . p0)} is non empty functional finite V39() set
{{D0,(p . p0)},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,(p . p0)] is V11() V12() ext-real set
p0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
p . (p0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
(Euclid_scalar n) . (D0,(p . (p0 + 1))) is set
[D0,(p . (p0 + 1))] is non empty set
{D0,(p . (p0 + 1))} is non empty functional finite V39() set
{{D0,(p . (p0 + 1))},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,(p . (p0 + 1))] is V11() V12() ext-real set
Seg (len x0) is finite len x0 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
dom x0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
x0 . (p0 + 1) is set
rng x0 is finite Element of bool the carrier of (REAL-US n)
q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
(p . p0) + q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
the addF of (REAL-US n) is non empty Relation-like [: the carrier of (REAL-US n), the carrier of (REAL-US n):] -defined the carrier of (REAL-US n) -valued Function-like total quasi_total Element of bool [:[: the carrier of (REAL-US n), the carrier of (REAL-US n):], the carrier of (REAL-US n):]
[: the carrier of (REAL-US n), the carrier of (REAL-US n):] is non empty Relation-like set
[:[: the carrier of (REAL-US n), the carrier of (REAL-US n):], the carrier of (REAL-US n):] is non empty Relation-like set
bool [:[: the carrier of (REAL-US n), the carrier of (REAL-US n):], the carrier of (REAL-US n):] is non empty set
the addF of (REAL-US n) . ((p . p0),q) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
[(p . p0),q] is non empty set
{(p . p0),q} is non empty functional finite V39() set
{(p . p0)} is non empty trivial functional finite V39() 1 -element set
{{(p . p0),q},{(p . p0)}} is non empty finite V39() set
the addF of (REAL-US n) . [(p . p0),q] is set
(p . p0) + q is Relation-like Function-like set
addreal .: ((p . p0),q) is set
B0 /. (p0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
B0 . (p0 + 1) is set
u0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u4 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u0 + u4 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
addreal .: (u0,u4) is set
|(z0,(u0 + u4))| is V11() V12() ext-real Element of REAL
mlt (z0,(u0 + u4)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,(u0 + u4)) is set
Sum (mlt (z0,(u0 + u4))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,(u0 + u4))),addreal) is V11() V12() ext-real Element of REAL
|(z0,u0)| is V11() V12() ext-real Element of REAL
mlt (z0,u0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,u0) is set
Sum (mlt (z0,u0)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,u0)),addreal) is V11() V12() ext-real Element of REAL
|(z0,u4)| is V11() V12() ext-real Element of REAL
mlt (z0,u4) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,u4) is set
Sum (mlt (z0,u4)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,u4)),addreal) is V11() V12() ext-real Element of REAL
|(z0,u0)| + |(z0,u4)| is V11() V12() ext-real Element of REAL
I . (B0 /. (p0 + 1)) is V11() V12() ext-real Element of REAL
(I . (B0 /. (p0 + 1))) * (B0 /. (p0 + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
the Mult of (REAL-US n) . ((I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))) is set
[(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))] is non empty set
{(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))} is non empty finite set
{(I . (B0 /. (p0 + 1)))} is non empty trivial finite 1 -element V126() V127() V128() set
{{(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))},{(I . (B0 /. (p0 + 1)))}} is non empty finite V39() set
the Mult of (REAL-US n) . [(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))] is set
(I . (B0 /. (p0 + 1))) * (B0 /. (p0 + 1)) is Relation-like Function-like set
(I . (B0 /. (p0 + 1))) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] ((I . (B0 /. (p0 + 1))),(id REAL)) is set
(B0 /. (p0 + 1)) (#) ((I . (B0 /. (p0 + 1))) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
B3 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(z0,B3)| is V11() V12() ext-real Element of REAL
mlt (z0,B3) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,B3) is set
Sum (mlt (z0,B3)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,B3)),addreal) is V11() V12() ext-real Element of REAL
(I . (B0 /. (p0 + 1))) * |(z0,B3)| is V11() V12() ext-real Element of REAL
(I . (B0 /. (p0 + 1))) * 0 is V11() V12() ext-real Element of REAL
p0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
p . p0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
(Euclid_scalar n) . (D0,(p . p0)) is set
[D0,(p . p0)] is non empty set
{D0,(p . p0)} is non empty functional finite V39() set
{{D0,(p . p0)},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,(p . p0)] is V11() V12() ext-real set
q is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
p . q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
(Euclid_scalar n) . (D0,(p . q)) is set
[D0,(p . q)] is non empty set
{D0,(p . q)} is non empty functional finite V39() set
{{D0,(p . q)},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,(p . q)] is V11() V12() ext-real set
p0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
p . p0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
(Euclid_scalar n) . (D0,(p . p0)) is set
[D0,(p . p0)] is non empty set
{D0,(p . p0)} is non empty functional finite V39() set
{{D0,(p . p0)},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,(p . p0)] is V11() V12() ext-real set
p0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
p . (p0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
(Euclid_scalar n) . (D0,(p . (p0 + 1))) is set
[D0,(p . (p0 + 1))] is non empty set
{D0,(p . (p0 + 1))} is non empty functional finite V39() set
{{D0,(p . (p0 + 1))},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,(p . (p0 + 1))] is V11() V12() ext-real set
Seg (len x0) is finite len x0 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
B0 /. (p0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
B0 . (p0 + 1) is set
dom x0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
x0 . (p0 + 1) is set
rng x0 is finite Element of bool the carrier of (REAL-US n)
q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
(p . p0) + q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
the addF of (REAL-US n) is non empty Relation-like [: the carrier of (REAL-US n), the carrier of (REAL-US n):] -defined the carrier of (REAL-US n) -valued Function-like total quasi_total Element of bool [:[: the carrier of (REAL-US n), the carrier of (REAL-US n):], the carrier of (REAL-US n):]
[: the carrier of (REAL-US n), the carrier of (REAL-US n):] is non empty Relation-like set
[:[: the carrier of (REAL-US n), the carrier of (REAL-US n):], the carrier of (REAL-US n):] is non empty Relation-like set
bool [:[: the carrier of (REAL-US n), the carrier of (REAL-US n):], the carrier of (REAL-US n):] is non empty set
the addF of (REAL-US n) . ((p . p0),q) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
[(p . p0),q] is non empty set
{(p . p0),q} is non empty functional finite V39() set
{(p . p0)} is non empty trivial functional finite V39() 1 -element set
{{(p . p0),q},{(p . p0)}} is non empty finite V39() set
the addF of (REAL-US n) . [(p . p0),q] is set
(p . p0) + q is Relation-like Function-like set
addreal .: ((p . p0),q) is set
I . (B0 /. (p0 + 1)) is V11() V12() ext-real Element of REAL
(I . (B0 /. (p0 + 1))) * (B0 /. (p0 + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
the Mult of (REAL-US n) . ((I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))) is set
[(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))] is non empty set
{(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))} is non empty finite set
{(I . (B0 /. (p0 + 1)))} is non empty trivial finite 1 -element V126() V127() V128() set
{{(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))},{(I . (B0 /. (p0 + 1)))}} is non empty finite V39() set
the Mult of (REAL-US n) . [(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))] is set
(I . (B0 /. (p0 + 1))) * (B0 /. (p0 + 1)) is Relation-like Function-like set
(I . (B0 /. (p0 + 1))) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] ((I . (B0 /. (p0 + 1))),(id REAL)) is set
(B0 /. (p0 + 1)) (#) ((I . (B0 /. (p0 + 1))) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
B3 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(z0,B3)| is V11() V12() ext-real Element of REAL
mlt (z0,B3) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,B3) is set
Sum (mlt (z0,B3)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,B3)),addreal) is V11() V12() ext-real Element of REAL
u4 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(z0,u4)| is V11() V12() ext-real Element of REAL
mlt (z0,u4) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,u4) is set
Sum (mlt (z0,u4)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,u4)),addreal) is V11() V12() ext-real Element of REAL
(I . (B0 /. (p0 + 1))) * |(z0,u4)| is V11() V12() ext-real Element of REAL
(I . (B0 /. (p0 + 1))) * 0 is V11() V12() ext-real Element of REAL
u0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u0 + B3 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
addreal .: (u0,B3) is set
|(z0,(u0 + B3))| is V11() V12() ext-real Element of REAL
mlt (z0,(u0 + B3)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,(u0 + B3)) is set
Sum (mlt (z0,(u0 + B3))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,(u0 + B3))),addreal) is V11() V12() ext-real Element of REAL
|(z0,u0)| is V11() V12() ext-real Element of REAL
mlt (z0,u0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,u0) is set
Sum (mlt (z0,u0)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,u0)),addreal) is V11() V12() ext-real Element of REAL
|(z0,u0)| + |(z0,B3)| is V11() V12() ext-real Element of REAL
x0 . (p0 + 1) is set
rng x0 is finite Element of bool the carrier of (REAL-US n)
q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
B0 /. (p0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
I . (B0 /. (p0 + 1)) is V11() V12() ext-real Element of REAL
(I . (B0 /. (p0 + 1))) * (B0 /. (p0 + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
the Mult of (REAL-US n) . ((I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))) is set
[(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))] is non empty set
{(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))} is non empty finite set
{(I . (B0 /. (p0 + 1)))} is non empty trivial finite 1 -element V126() V127() V128() set
{{(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))},{(I . (B0 /. (p0 + 1)))}} is non empty finite V39() set
the Mult of (REAL-US n) . [(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))] is set
(I . (B0 /. (p0 + 1))) * (B0 /. (p0 + 1)) is Relation-like Function-like set
(I . (B0 /. (p0 + 1))) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] ((I . (B0 /. (p0 + 1))),(id REAL)) is set
(B0 /. (p0 + 1)) (#) ((I . (B0 /. (p0 + 1))) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
u4 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(z0,u4)| is V11() V12() ext-real Element of REAL
mlt (z0,u4) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,u4) is set
Sum (mlt (z0,u4)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,u4)),addreal) is V11() V12() ext-real Element of REAL
(I . (B0 /. B)) * z0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
z0 (#) ((I . (B0 /. B)) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
|(z0,((I . (B0 /. B)) * z0))| is V11() V12() ext-real Element of REAL
mlt (z0,((I . (B0 /. B)) * z0)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,((I . (B0 /. B)) * z0)) is set
Sum (mlt (z0,((I . (B0 /. B)) * z0))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,((I . (B0 /. B)) * z0))),addreal) is V11() V12() ext-real Element of REAL
(p . p0) + q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
the addF of (REAL-US n) is non empty Relation-like [: the carrier of (REAL-US n), the carrier of (REAL-US n):] -defined the carrier of (REAL-US n) -valued Function-like total quasi_total Element of bool [:[: the carrier of (REAL-US n), the carrier of (REAL-US n):], the carrier of (REAL-US n):]
[: the carrier of (REAL-US n), the carrier of (REAL-US n):] is non empty Relation-like set
[:[: the carrier of (REAL-US n), the carrier of (REAL-US n):], the carrier of (REAL-US n):] is non empty Relation-like set
bool [:[: the carrier of (REAL-US n), the carrier of (REAL-US n):], the carrier of (REAL-US n):] is non empty set
the addF of (REAL-US n) . ((p . p0),q) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
[(p . p0),q] is non empty set
{(p . p0),q} is non empty functional finite V39() set
{(p . p0)} is non empty trivial functional finite V39() 1 -element set
{{(p . p0),q},{(p . p0)}} is non empty finite V39() set
the addF of (REAL-US n) . [(p . p0),q] is set
(p . p0) + q is Relation-like Function-like set
addreal .: ((p . p0),q) is set
u0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(z0,u0)| is V11() V12() ext-real Element of REAL
mlt (z0,u0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,u0) is set
Sum (mlt (z0,u0)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,u0)),addreal) is V11() V12() ext-real Element of REAL
u0 + u4 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
addreal .: (u0,u4) is set
|(z0,(u0 + u4))| is V11() V12() ext-real Element of REAL
mlt (z0,(u0 + u4)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,(u0 + u4)) is set
Sum (mlt (z0,(u0 + u4))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,(u0 + u4))),addreal) is V11() V12() ext-real Element of REAL
|(z0,u0)| + |(z0,u4)| is V11() V12() ext-real Element of REAL
p0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
p . p0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
(Euclid_scalar n) . (D0,(p . p0)) is set
[D0,(p . p0)] is non empty set
{D0,(p . p0)} is non empty functional finite V39() set
{{D0,(p . p0)},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,(p . p0)] is V11() V12() ext-real set
q is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
p . q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
(Euclid_scalar n) . (D0,(p . q)) is set
[D0,(p . q)] is non empty set
{D0,(p . q)} is non empty functional finite V39() set
{{D0,(p . q)},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,(p . q)] is V11() V12() ext-real set
n is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
REAL-US n is non empty right_complementable constituted-Functions constituted-FinSeqs Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V194() V195() L17()
the carrier of (REAL-US n) is non empty set
B is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
(n,B) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B0 is Relation-like NAT -defined the carrier of (REAL-US n) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (REAL-US n)
Sum B0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
len B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
len (n,B) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) . (len B) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(len B) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
0. (REAL-US n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like zero complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
the ZeroF of (REAL-US n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
I is set
(n,B) /. I is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
IFEQ (I,0,(0. (REAL-US n)),((n,B) /. I)) is set
IFIN (I,((len B) + 1),(IFEQ (I,0,(0. (REAL-US n)),((n,B) /. I))),(0. (REAL-US n))) is set
x0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) /. x0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
IFEQ (I,0,(0. (REAL-US n)),((n,B) /. x0)) is set
x0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
x0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
[:NAT, the carrier of (REAL-US n):] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of (REAL-US n):] is non empty non trivial non finite set
I is non empty Relation-like NAT -defined the carrier of (REAL-US n) -valued Function-like total quasi_total Element of bool [:NAT, the carrier of (REAL-US n):]
len B0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
x0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
x0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B0 . (x0 + 1) is set
I . (x0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
I . x0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
z0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
(I . x0) + z0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
the addF of (REAL-US n) is non empty Relation-like [: the carrier of (REAL-US n), the carrier of (REAL-US n):] -defined the carrier of (REAL-US n) -valued Function-like total quasi_total Element of bool [:[: the carrier of (REAL-US n), the carrier of (REAL-US n):], the carrier of (REAL-US n):]
[: the carrier of (REAL-US n), the carrier of (REAL-US n):] is non empty Relation-like set
[:[: the carrier of (REAL-US n), the carrier of (REAL-US n):], the carrier of (REAL-US n):] is non empty Relation-like set
bool [:[: the carrier of (REAL-US n), the carrier of (REAL-US n):], the carrier of (REAL-US n):] is non empty set
the addF of (REAL-US n) . ((I . x0),z0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
[(I . x0),z0] is non empty set
{(I . x0),z0} is non empty functional finite V39() set
{(I . x0)} is non empty trivial functional finite V39() 1 -element set
{{(I . x0),z0},{(I . x0)}} is non empty finite V39() set
the addF of (REAL-US n) . [(I . x0),z0] is set
(I . x0) + z0 is Relation-like Function-like set
addreal .: ((I . x0),z0) is set
(n,B) /. x0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
IFEQ (x0,0,(0. (REAL-US n)),((n,B) /. x0)) is set
IFIN (x0,((len B) + 1),(IFEQ (x0,0,(0. (REAL-US n)),((n,B) /. x0))),(0. (REAL-US n))) is set
(n,B) /. (x0 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
IFEQ ((x0 + 1),0,(0. (REAL-US n)),((n,B) /. (x0 + 1))) is set
IFIN ((x0 + 1),((len B) + 1),(IFEQ ((x0 + 1),0,(0. (REAL-US n)),((n,B) /. (x0 + 1)))),(0. (REAL-US n))) is set
(n,B) /. 1 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(n,B) /. x0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
IFEQ (x0,0,(0. (REAL-US n)),((n,B) /. x0)) is set
IFIN (x0,((len B) + 1),(IFEQ (x0,0,(0. (REAL-US n)),((n,B) /. x0))),(0. (REAL-US n))) is set
0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) /. (x0 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
IFEQ ((x0 + 1),0,(0. (REAL-US n)),((n,B) /. (x0 + 1))) is set
IFIN ((x0 + 1),((len B) + 1),(IFEQ ((x0 + 1),0,(0. (REAL-US n)),((n,B) /. (x0 + 1)))),(0. (REAL-US n))) is set
(n,B) . (x0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B /. (x0 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,B) /. x0) + (B /. (x0 + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
I . 0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
(n,B) /. 0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
IFEQ (0,0,(0. (REAL-US n)),((n,B) /. 0)) is set
IFIN (0,((len B) + 1),(IFEQ (0,0,(0. (REAL-US n)),((n,B) /. 0))),(0. (REAL-US n))) is set
I . (len B0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
(n,B) /. (len B) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
IFEQ ((len B),0,(0. (REAL-US n)),((n,B) /. (len B))) is set
IFIN ((len B),((len B) + 1),(IFEQ ((len B),0,(0. (REAL-US n)),((n,B) /. (len B)))),(0. (REAL-US n))) is set
len B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
0. (REAL-US n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like zero complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
the ZeroF of (REAL-US n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
NAT --> (0. (REAL-US n)) is non empty T-Sequence-like Relation-like NAT -defined the carrier of (REAL-US n) -valued Function-like total quasi_total Element of bool [:NAT, the carrier of (REAL-US n):]
[:NAT, the carrier of (REAL-US n):] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of (REAL-US n):] is non empty non trivial non finite set
len B0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
I is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
x0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
I + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B0 . (I + 1) is set
(NAT --> (0. (REAL-US n))) . (I + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
(NAT --> (0. (REAL-US n))) . I is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
((NAT --> (0. (REAL-US n))) . I) + x0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
the addF of (REAL-US n) is non empty Relation-like [: the carrier of (REAL-US n), the carrier of (REAL-US n):] -defined the carrier of (REAL-US n) -valued Function-like total quasi_total Element of bool [:[: the carrier of (REAL-US n), the carrier of (REAL-US n):], the carrier of (REAL-US n):]
[: the carrier of (REAL-US n), the carrier of (REAL-US n):] is non empty Relation-like set
[:[: the carrier of (REAL-US n), the carrier of (REAL-US n):], the carrier of (REAL-US n):] is non empty Relation-like set
bool [:[: the carrier of (REAL-US n), the carrier of (REAL-US n):], the carrier of (REAL-US n):] is non empty set
the addF of (REAL-US n) . (((NAT --> (0. (REAL-US n))) . I),x0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
[((NAT --> (0. (REAL-US n))) . I),x0] is non empty set
{((NAT --> (0. (REAL-US n))) . I),x0} is non empty functional finite V39() set
{((NAT --> (0. (REAL-US n))) . I)} is non empty trivial functional finite V39() 1 -element set
{{((NAT --> (0. (REAL-US n))) . I),x0},{((NAT --> (0. (REAL-US n))) . I)}} is non empty finite V39() set
the addF of (REAL-US n) . [((NAT --> (0. (REAL-US n))) . I),x0] is set
((NAT --> (0. (REAL-US n))) . I) + x0 is Relation-like Function-like set
addreal .: (((NAT --> (0. (REAL-US n))) . I),x0) is set
(NAT --> (0. (REAL-US n))) . (len B0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
0* n is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(Seg n) --> 0 is Relation-like Seg n -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),{0}:] is non empty finite V39() set
(NAT --> (0. (REAL-US n))) . 0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
len B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
[:NAT, the carrier of (REAL-US n):] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of (REAL-US n):] is non empty non trivial non finite set
len B0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
0. (REAL-US n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like zero complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
the ZeroF of (REAL-US n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
len B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
[:NAT, the carrier of (REAL-US n):] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of (REAL-US n):] is non empty non trivial non finite set
len B0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
0. (REAL-US n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like zero complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
the ZeroF of (REAL-US n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
D0 is non empty Relation-like NAT -defined the carrier of (REAL-US n) -valued Function-like total quasi_total Element of bool [:NAT, the carrier of (REAL-US n):]
D0 . (len B0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
D0 . 0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
I is non empty Relation-like NAT -defined the carrier of (REAL-US n) -valued Function-like total quasi_total Element of bool [:NAT, the carrier of (REAL-US n):]
I . (len B0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
I . 0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
n is set
RealVectSpace n is non empty right_complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs (n,REAL) is non empty functional FUNCTION_DOMAIN of n, REAL
RealFuncZero n is Relation-like n -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of Funcs (n,REAL)
n --> 0 is Relation-like n -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:n,NAT:]
[:n,NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:n,NAT:] is non empty set
RealFuncAdd n is non empty Relation-like [:(Funcs (n,REAL)),(Funcs (n,REAL)):] -defined Funcs (n,REAL) -valued Function-like total quasi_total Element of bool [:[:(Funcs (n,REAL)),(Funcs (n,REAL)):],(Funcs (n,REAL)):]
[:(Funcs (n,REAL)),(Funcs (n,REAL)):] is non empty Relation-like set
[:[:(Funcs (n,REAL)),(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty Relation-like set
bool [:[:(Funcs (n,REAL)),(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty set
RealFuncExtMult n is non empty Relation-like [:REAL,(Funcs (n,REAL)):] -defined Funcs (n,REAL) -valued Function-like total quasi_total Element of bool [:[:REAL,(Funcs (n,REAL)):],(Funcs (n,REAL)):]
[:REAL,(Funcs (n,REAL)):] is non empty non trivial Relation-like non finite set
[:[:REAL,(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty non trivial non finite set
RLSStruct(# (Funcs (n,REAL)),(RealFuncZero n),(RealFuncAdd n),(RealFuncExtMult n) #) is strict RLSStruct
the carrier of (RealVectSpace n) is non empty set
B is Element of the carrier of (RealVectSpace n)
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
RealVectSpace (Seg n) is non empty right_complementable constituted-Functions strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ((Seg n),REAL) is non empty functional FUNCTION_DOMAIN of Seg n, REAL
RealFuncZero (Seg n) is Relation-like Seg n -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of Funcs ((Seg n),REAL)
(Seg n) --> 0 is Relation-like Seg n -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),NAT:]
[:(Seg n),NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),NAT:] is non empty set
RealFuncAdd (Seg n) is non empty Relation-like [:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] is non empty Relation-like set
[:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty Relation-like set
bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty set
RealFuncExtMult (Seg n) is non empty Relation-like [:REAL,(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:REAL,(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
[:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial non finite set
RLSStruct(# (Funcs ((Seg n),REAL)),(RealFuncZero (Seg n)),(RealFuncAdd (Seg n)),(RealFuncExtMult (Seg n)) #) is strict RLSStruct
the carrier of (RealVectSpace (Seg n)) is non empty set
B is Relation-like Function-like Element of the carrier of (RealVectSpace (Seg n))
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
n is set
RealVectSpace n is non empty right_complementable constituted-Functions strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs (n,REAL) is non empty functional FUNCTION_DOMAIN of n, REAL
RealFuncZero n is Relation-like n -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of Funcs (n,REAL)
n --> 0 is Relation-like n -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:n,NAT:]
[:n,NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:n,NAT:] is non empty set
RealFuncAdd n is non empty Relation-like [:(Funcs (n,REAL)),(Funcs (n,REAL)):] -defined Funcs (n,REAL) -valued Function-like total quasi_total Element of bool [:[:(Funcs (n,REAL)),(Funcs (n,REAL)):],(Funcs (n,REAL)):]
[:(Funcs (n,REAL)),(Funcs (n,REAL)):] is non empty Relation-like set
[:[:(Funcs (n,REAL)),(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty Relation-like set
bool [:[:(Funcs (n,REAL)),(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty set
RealFuncExtMult n is non empty Relation-like [:REAL,(Funcs (n,REAL)):] -defined Funcs (n,REAL) -valued Function-like total quasi_total Element of bool [:[:REAL,(Funcs (n,REAL)):],(Funcs (n,REAL)):]
[:REAL,(Funcs (n,REAL)):] is non empty non trivial Relation-like non finite set
[:[:REAL,(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty non trivial non finite set
RLSStruct(# (Funcs (n,REAL)),(RealFuncZero n),(RealFuncAdd n),(RealFuncExtMult n) #) is strict RLSStruct
the carrier of (RealVectSpace n) is non empty set
B is Relation-like Function-like Element of the carrier of (RealVectSpace n)
[:n,REAL:] is Relation-like complex-yielding ext-real-valued real-valued set
bool [:n,REAL:] is non empty set
n is set
RealVectSpace n is non empty right_complementable constituted-Functions strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs (n,REAL) is non empty functional FUNCTION_DOMAIN of n, REAL
RealFuncZero n is Relation-like n -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of Funcs (n,REAL)
n --> 0 is Relation-like n -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:n,NAT:]
[:n,NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:n,NAT:] is non empty set
RealFuncAdd n is non empty Relation-like [:(Funcs (n,REAL)),(Funcs (n,REAL)):] -defined Funcs (n,REAL) -valued Function-like total quasi_total Element of bool [:[:(Funcs (n,REAL)),(Funcs (n,REAL)):],(Funcs (n,REAL)):]
[:(Funcs (n,REAL)),(Funcs (n,REAL)):] is non empty Relation-like set
[:[:(Funcs (n,REAL)),(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty Relation-like set
bool [:[:(Funcs (n,REAL)),(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty set
RealFuncExtMult n is non empty Relation-like [:REAL,(Funcs (n,REAL)):] -defined Funcs (n,REAL) -valued Function-like total quasi_total Element of bool [:[:REAL,(Funcs (n,REAL)):],(Funcs (n,REAL)):]
[:REAL,(Funcs (n,REAL)):] is non empty non trivial Relation-like non finite set
[:[:REAL,(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty non trivial non finite set
RLSStruct(# (Funcs (n,REAL)),(RealFuncZero n),(RealFuncAdd n),(RealFuncExtMult n) #) is strict RLSStruct
the carrier of (RealVectSpace n) is non empty set
B is Relation-like Function-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace n)
B is Relation-like Function-like complex-yielding ext-real-valued real-valued set
B0 is Relation-like Function-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace n)
D0 is Relation-like Function-like complex-yielding ext-real-valued real-valued set
B + B0 is Relation-like Function-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace n)
the addF of (RealVectSpace n) is non empty Relation-like [: the carrier of (RealVectSpace n), the carrier of (RealVectSpace n):] -defined the carrier of (RealVectSpace n) -valued Function-like total quasi_total Element of bool [:[: the carrier of (RealVectSpace n), the carrier of (RealVectSpace n):], the carrier of (RealVectSpace n):]
[: the carrier of (RealVectSpace n), the carrier of (RealVectSpace n):] is non empty Relation-like set
[:[: the carrier of (RealVectSpace n), the carrier of (RealVectSpace n):], the carrier of (RealVectSpace n):] is non empty Relation-like set
bool [:[: the carrier of (RealVectSpace n), the carrier of (RealVectSpace n):], the carrier of (RealVectSpace n):] is non empty set
the addF of (RealVectSpace n) . (B,B0) is Relation-like Function-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace n)
[B,B0] is non empty set
{B,B0} is non empty functional finite set
{B} is non empty trivial functional finite 1 -element set
{{B,B0},{B}} is non empty finite V39() set
the addF of (RealVectSpace n) . [B,B0] is set
B + D0 is Relation-like Function-like set
dom B0 is set
dom (B + B0) is set
I is set
(B + B0) . I is V11() V12() ext-real Element of REAL
B . I is V11() V12() ext-real Element of REAL
D0 . I is V11() V12() ext-real Element of REAL
(B . I) + (D0 . I) is V11() V12() ext-real Element of REAL
dom B is set
dom B is set
dom D0 is set
(dom B) /\ (dom D0) is set
B + B0 is Relation-like Function-like set
n is set
RealVectSpace n is non empty right_complementable constituted-Functions strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs (n,REAL) is non empty functional FUNCTION_DOMAIN of n, REAL
RealFuncZero n is Relation-like n -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of Funcs (n,REAL)
n --> 0 is Relation-like n -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:n,NAT:]
[:n,NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:n,NAT:] is non empty set
RealFuncAdd n is non empty Relation-like [:(Funcs (n,REAL)),(Funcs (n,REAL)):] -defined Funcs (n,REAL) -valued Function-like total quasi_total Element of bool [:[:(Funcs (n,REAL)),(Funcs (n,REAL)):],(Funcs (n,REAL)):]
[:(Funcs (n,REAL)),(Funcs (n,REAL)):] is non empty Relation-like set
[:[:(Funcs (n,REAL)),(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty Relation-like set
bool [:[:(Funcs (n,REAL)),(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty set
RealFuncExtMult n is non empty Relation-like [:REAL,(Funcs (n,REAL)):] -defined Funcs (n,REAL) -valued Function-like total quasi_total Element of bool [:[:REAL,(Funcs (n,REAL)):],(Funcs (n,REAL)):]
[:REAL,(Funcs (n,REAL)):] is non empty non trivial Relation-like non finite set
[:[:REAL,(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty non trivial non finite set
RLSStruct(# (Funcs (n,REAL)),(RealFuncZero n),(RealFuncAdd n),(RealFuncExtMult n) #) is strict RLSStruct
the carrier of (RealVectSpace n) is non empty set
B is Relation-like Function-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace n)
B0 is Relation-like Function-like complex-yielding ext-real-valued real-valued set
B is V11() V12() ext-real Element of REAL
D0 is V11() V12() ext-real Element of REAL
B * B is Relation-like Function-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace n)
the Mult of (RealVectSpace n) is non empty Relation-like [:REAL, the carrier of (RealVectSpace n):] -defined the carrier of (RealVectSpace n) -valued Function-like total quasi_total Element of bool [:[:REAL, the carrier of (RealVectSpace n):], the carrier of (RealVectSpace n):]
[:REAL, the carrier of (RealVectSpace n):] is non empty non trivial Relation-like non finite set
[:[:REAL, the carrier of (RealVectSpace n):], the carrier of (RealVectSpace n):] is non empty non trivial Relation-like non finite set
bool [:[:REAL, the carrier of (RealVectSpace n):], the carrier of (RealVectSpace n):] is non empty non trivial non finite set
the Mult of (RealVectSpace n) . (B,B) is set
[B,B] is non empty set
{B,B} is non empty finite set
{B} is non empty trivial finite 1 -element V126() V127() V128() set
{{B,B},{B}} is non empty finite V39() set
the Mult of (RealVectSpace n) . [B,B] is set
D0 * B0 is Relation-like Function-like set
dom B is set
dom (B * B) is set
I is set
(B * B) . I is V11() V12() ext-real Element of REAL
B0 . I is V11() V12() ext-real Element of REAL
D0 * (B0 . I) is V11() V12() ext-real Element of REAL
B * B is Relation-like Function-like set
n is set
RealVectSpace n is non empty right_complementable constituted-Functions strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs (n,REAL) is non empty functional FUNCTION_DOMAIN of n, REAL
RealFuncZero n is Relation-like n -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of Funcs (n,REAL)
n --> 0 is Relation-like n -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:n,NAT:]
[:n,NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:n,NAT:] is non empty set
RealFuncAdd n is non empty Relation-like [:(Funcs (n,REAL)),(Funcs (n,REAL)):] -defined Funcs (n,REAL) -valued Function-like total quasi_total Element of bool [:[:(Funcs (n,REAL)),(Funcs (n,REAL)):],(Funcs (n,REAL)):]
[:(Funcs (n,REAL)),(Funcs (n,REAL)):] is non empty Relation-like set
[:[:(Funcs (n,REAL)),(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty Relation-like set
bool [:[:(Funcs (n,REAL)),(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty set
RealFuncExtMult n is non empty Relation-like [:REAL,(Funcs (n,REAL)):] -defined Funcs (n,REAL) -valued Function-like total quasi_total Element of bool [:[:REAL,(Funcs (n,REAL)):],(Funcs (n,REAL)):]
[:REAL,(Funcs (n,REAL)):] is non empty non trivial Relation-like non finite set
[:[:REAL,(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty non trivial non finite set
RLSStruct(# (Funcs (n,REAL)),(RealFuncZero n),(RealFuncAdd n),(RealFuncExtMult n) #) is strict RLSStruct
the carrier of (RealVectSpace n) is non empty set
B is Relation-like Function-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace n)
B0 is Relation-like Function-like complex-yielding ext-real-valued real-valued set
- B is Relation-like Function-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace n)
- B0 is Relation-like Function-like complex-yielding set
K38(1) * B0 is Relation-like Function-like set
B is set
dom B0 is set
(- B) . B is V11() V12() ext-real Element of REAL
(- 1) * B is Relation-like Function-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace n)
the Mult of (RealVectSpace n) is non empty Relation-like [:REAL, the carrier of (RealVectSpace n):] -defined the carrier of (RealVectSpace n) -valued Function-like total quasi_total Element of bool [:[:REAL, the carrier of (RealVectSpace n):], the carrier of (RealVectSpace n):]
[:REAL, the carrier of (RealVectSpace n):] is non empty non trivial Relation-like non finite set
[:[:REAL, the carrier of (RealVectSpace n):], the carrier of (RealVectSpace n):] is non empty non trivial Relation-like non finite set
bool [:[:REAL, the carrier of (RealVectSpace n):], the carrier of (RealVectSpace n):] is non empty non trivial non finite set
the Mult of (RealVectSpace n) . ((- 1),B) is set
[(- 1),B] is non empty set
{(- 1),B} is non empty finite set
{(- 1)} is non empty trivial finite 1 -element V126() V127() V128() set
{{(- 1),B},{(- 1)}} is non empty finite V39() set
the Mult of (RealVectSpace n) . [(- 1),B] is set
(- 1) * B is Relation-like Function-like set
((- 1) * B) . B is V11() V12() ext-real Element of REAL
B0 . B is V11() V12() ext-real Element of REAL
(- 1) * (B0 . B) is V11() V12() ext-real Element of REAL
- (B0 . B) is V11() V12() ext-real Element of REAL
dom (- B) is set
- B is Relation-like Function-like complex-yielding set
K38(1) * B is Relation-like Function-like set
n is set
RealVectSpace n is non empty right_complementable constituted-Functions strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs (n,REAL) is non empty functional FUNCTION_DOMAIN of n, REAL
RealFuncZero n is Relation-like n -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of Funcs (n,REAL)
n --> 0 is Relation-like n -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:n,NAT:]
[:n,NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:n,NAT:] is non empty set
RealFuncAdd n is non empty Relation-like [:(Funcs (n,REAL)),(Funcs (n,REAL)):] -defined Funcs (n,REAL) -valued Function-like total quasi_total Element of bool [:[:(Funcs (n,REAL)),(Funcs (n,REAL)):],(Funcs (n,REAL)):]
[:(Funcs (n,REAL)),(Funcs (n,REAL)):] is non empty Relation-like set
[:[:(Funcs (n,REAL)),(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty Relation-like set
bool [:[:(Funcs (n,REAL)),(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty set
RealFuncExtMult n is non empty Relation-like [:REAL,(Funcs (n,REAL)):] -defined Funcs (n,REAL) -valued Function-like total quasi_total Element of bool [:[:REAL,(Funcs (n,REAL)):],(Funcs (n,REAL)):]
[:REAL,(Funcs (n,REAL)):] is non empty non trivial Relation-like non finite set
[:[:REAL,(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(Funcs (n,REAL)):],(Funcs (n,REAL)):] is non empty non trivial non finite set
RLSStruct(# (Funcs (n,REAL)),(RealFuncZero n),(RealFuncAdd n),(RealFuncExtMult n) #) is strict RLSStruct
the carrier of (RealVectSpace n) is non empty set
B is Relation-like Function-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace n)
B is Relation-like Function-like complex-yielding ext-real-valued real-valued set
B0 is Relation-like Function-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace n)
D0 is Relation-like Function-like complex-yielding ext-real-valued real-valued set
B - B0 is Relation-like Function-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace n)
- B0 is Relation-like Function-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace n)
- B0 is Relation-like Function-like complex-yielding set
K38(1) * B0 is Relation-like Function-like set
B + (- B0) is Relation-like Function-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace n)
the addF of (RealVectSpace n) is non empty Relation-like [: the carrier of (RealVectSpace n), the carrier of (RealVectSpace n):] -defined the carrier of (RealVectSpace n) -valued Function-like total quasi_total Element of bool [:[: the carrier of (RealVectSpace n), the carrier of (RealVectSpace n):], the carrier of (RealVectSpace n):]
[: the carrier of (RealVectSpace n), the carrier of (RealVectSpace n):] is non empty Relation-like set
[:[: the carrier of (RealVectSpace n), the carrier of (RealVectSpace n):], the carrier of (RealVectSpace n):] is non empty Relation-like set
bool [:[: the carrier of (RealVectSpace n), the carrier of (RealVectSpace n):], the carrier of (RealVectSpace n):] is non empty set
the addF of (RealVectSpace n) . (B,(- B0)) is Relation-like Function-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace n)
[B,(- B0)] is non empty set
{B,(- B0)} is non empty functional finite set
{B} is non empty trivial functional finite 1 -element set
{{B,(- B0)},{B}} is non empty finite V39() set
the addF of (RealVectSpace n) . [B,(- B0)] is set
B + (- B0) is Relation-like Function-like set
B - D0 is Relation-like Function-like set
- D0 is Relation-like Function-like complex-yielding set
K38(1) * D0 is Relation-like Function-like set
B + (- D0) is Relation-like Function-like set
B - B0 is Relation-like Function-like set
B + (- B0) is Relation-like Function-like set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
RealVectSpace (Seg n) is non empty right_complementable constituted-Functions constituted-FinSeqs strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ((Seg n),REAL) is non empty functional FUNCTION_DOMAIN of Seg n, REAL
RealFuncZero (Seg n) is Relation-like Seg n -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of Funcs ((Seg n),REAL)
(Seg n) --> 0 is Relation-like Seg n -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),NAT:]
[:(Seg n),NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),NAT:] is non empty set
RealFuncAdd (Seg n) is non empty Relation-like [:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] is non empty Relation-like set
[:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty Relation-like set
bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty set
RealFuncExtMult (Seg n) is non empty Relation-like [:REAL,(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:REAL,(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
[:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial non finite set
RLSStruct(# (Funcs ((Seg n),REAL)),(RealFuncZero (Seg n)),(RealFuncAdd (Seg n)),(RealFuncExtMult (Seg n)) #) is strict RLSStruct
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
B is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of RealVectSpace (Seg n)
the carrier of B is non empty set
B0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B is V11() V12() ext-real Element of REAL
B * B0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (B,(id REAL)) is set
B0 (#) (B multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
the carrier of (RealVectSpace (Seg n)) is non empty set
D0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
B * D0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
the Mult of (RealVectSpace (Seg n)) is non empty Relation-like [:REAL, the carrier of (RealVectSpace (Seg n)):] -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like total quasi_total Element of bool [:[:REAL, the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):]
[:REAL, the carrier of (RealVectSpace (Seg n)):] is non empty non trivial Relation-like non finite set
[:[:REAL, the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL, the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty non trivial non finite set
the Mult of (RealVectSpace (Seg n)) . (B,D0) is set
[B,D0] is non empty set
{B,D0} is non empty finite set
{B} is non empty trivial finite 1 -element V126() V127() V128() set
{{B,D0},{B}} is non empty finite V39() set
the Mult of (RealVectSpace (Seg n)) . [B,D0] is set
B * D0 is Relation-like Function-like set
D0 (#) (B multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
RealVectSpace (Seg n) is non empty right_complementable constituted-Functions constituted-FinSeqs strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ((Seg n),REAL) is non empty functional FUNCTION_DOMAIN of Seg n, REAL
RealFuncZero (Seg n) is Relation-like Seg n -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of Funcs ((Seg n),REAL)
(Seg n) --> 0 is Relation-like Seg n -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),NAT:]
[:(Seg n),NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),NAT:] is non empty set
RealFuncAdd (Seg n) is non empty Relation-like [:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] is non empty Relation-like set
[:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty Relation-like set
bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty set
RealFuncExtMult (Seg n) is non empty Relation-like [:REAL,(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:REAL,(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
[:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial non finite set
RLSStruct(# (Funcs ((Seg n),REAL)),(RealFuncZero (Seg n)),(RealFuncAdd (Seg n)),(RealFuncExtMult (Seg n)) #) is strict RLSStruct
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
B is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of RealVectSpace (Seg n)
the carrier of B is non empty set
B0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B0 + B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
addreal .: (B0,B) is set
the carrier of (RealVectSpace (Seg n)) is non empty set
D0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
I is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
D0 + I is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
the addF of (RealVectSpace (Seg n)) is non empty Relation-like [: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):] -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like total quasi_total Element of bool [:[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):]
[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):] is non empty Relation-like set
[:[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty Relation-like set
bool [:[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty set
the addF of (RealVectSpace (Seg n)) . (D0,I) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
[D0,I] is non empty set
{D0,I} is non empty functional finite V39() set
{D0} is non empty trivial functional finite V39() 1 -element set
{{D0,I},{D0}} is non empty finite V39() set
the addF of (RealVectSpace (Seg n)) . [D0,I] is set
D0 + I is Relation-like Function-like set
addreal .: (D0,I) is set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
RealVectSpace (Seg n) is non empty right_complementable constituted-Functions constituted-FinSeqs strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ((Seg n),REAL) is non empty functional FUNCTION_DOMAIN of Seg n, REAL
RealFuncZero (Seg n) is Relation-like Seg n -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of Funcs ((Seg n),REAL)
(Seg n) --> 0 is Relation-like Seg n -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),NAT:]
[:(Seg n),NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),NAT:] is non empty set
RealFuncAdd (Seg n) is non empty Relation-like [:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] is non empty Relation-like set
[:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty Relation-like set
bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty set
RealFuncExtMult (Seg n) is non empty Relation-like [:REAL,(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:REAL,(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
[:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial non finite set
RLSStruct(# (Funcs ((Seg n),REAL)),(RealFuncZero (Seg n)),(RealFuncAdd (Seg n)),(RealFuncExtMult (Seg n)) #) is strict RLSStruct
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
B is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of RealVectSpace (Seg n)
the carrier of B is non empty set
B0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
D0 is V11() V12() ext-real Element of REAL
D0 * B0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
D0 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (D0,(id REAL)) is set
B0 (#) (D0 multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
I is V11() V12() ext-real Element of REAL
I * B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
I multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (I,(id REAL)) is set
B (#) (I multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
(D0 * B0) + (I * B) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
addreal .: ((D0 * B0),(I * B)) is set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
RealVectSpace (Seg n) is non empty right_complementable constituted-Functions constituted-FinSeqs strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ((Seg n),REAL) is non empty functional FUNCTION_DOMAIN of Seg n, REAL
RealFuncZero (Seg n) is Relation-like Seg n -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of Funcs ((Seg n),REAL)
(Seg n) --> 0 is Relation-like Seg n -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),NAT:]
[:(Seg n),NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),NAT:] is non empty set
RealFuncAdd (Seg n) is non empty Relation-like [:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] is non empty Relation-like set
[:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty Relation-like set
bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty set
RealFuncExtMult (Seg n) is non empty Relation-like [:REAL,(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:REAL,(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
[:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial non finite set
RLSStruct(# (Funcs ((Seg n),REAL)),(RealFuncZero (Seg n)),(RealFuncAdd (Seg n)),(RealFuncExtMult (Seg n)) #) is strict RLSStruct
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
B is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of RealVectSpace (Seg n)
the carrier of B is non empty set
B0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
D0 is V11() V12() ext-real Element of REAL
D0 * B0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
D0 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (D0,(id REAL)) is set
B0 (#) (D0 multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
(D0 * B0) + B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
addreal .: ((D0 * B0),B) is set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
Euclid_scalar n is non empty Relation-like [:(REAL n),(REAL n):] -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:[:(REAL n),(REAL n):],REAL:]
[:(REAL n),(REAL n):] is non empty Relation-like set
[:[:(REAL n),(REAL n):],REAL:] is non empty non trivial Relation-like non finite complex-yielding ext-real-valued real-valued set
bool [:[:(REAL n),(REAL n):],REAL:] is non empty non trivial non finite set
B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(Euclid_scalar n) . (B,B0) is V11() V12() ext-real Element of REAL
[B,B0] is non empty set
{B,B0} is non empty functional finite V39() set
{B} is non empty trivial functional finite V39() 1 -element set
{{B,B0},{B}} is non empty finite V39() set
(Euclid_scalar n) . [B,B0] is V11() V12() ext-real set
|(B,B0)| is V11() V12() ext-real Element of REAL
mlt (B,B0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,B0) is set
Sum (mlt (B,B0)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,B0)),addreal) is V11() V12() ext-real Element of REAL
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
RealVectSpace (Seg n) is non empty right_complementable constituted-Functions constituted-FinSeqs strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ((Seg n),REAL) is non empty functional FUNCTION_DOMAIN of Seg n, REAL
RealFuncZero (Seg n) is Relation-like Seg n -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of Funcs ((Seg n),REAL)
(Seg n) --> 0 is Relation-like Seg n -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),NAT:]
[:(Seg n),NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),NAT:] is non empty set
RealFuncAdd (Seg n) is non empty Relation-like [:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] is non empty Relation-like set
[:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty Relation-like set
bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty set
RealFuncExtMult (Seg n) is non empty Relation-like [:REAL,(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:REAL,(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
[:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial non finite set
RLSStruct(# (Funcs ((Seg n),REAL)),(RealFuncZero (Seg n)),(RealFuncAdd (Seg n)),(RealFuncExtMult (Seg n)) #) is strict RLSStruct
the carrier of (RealVectSpace (Seg n)) is non empty set
bool the carrier of (RealVectSpace (Seg n)) is non empty set
Euclid_scalar n is non empty Relation-like [:(REAL n),(REAL n):] -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:[:(REAL n),(REAL n):],REAL:]
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
[:(REAL n),(REAL n):] is non empty Relation-like set
[:[:(REAL n),(REAL n):],REAL:] is non empty non trivial Relation-like non finite complex-yielding ext-real-valued real-valued set
bool [:[:(REAL n),(REAL n):],REAL:] is non empty non trivial non finite set
B is ordinal natural V11() V12() ext-real non negative finite cardinal set
B0 is Relation-like NAT -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (RealVectSpace (Seg n))
rng B0 is finite Element of bool the carrier of (RealVectSpace (Seg n))
B0 . B is set
B0 /. B is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
B is Element of bool the carrier of (RealVectSpace (Seg n))
D0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
I is Relation-like the carrier of (RealVectSpace (Seg n)) -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Linear_Combination of B
Carrier I is Element of bool the carrier of (RealVectSpace (Seg n))
I (#) B0 is Relation-like NAT -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (RealVectSpace (Seg n))
dom (I (#) B0) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
Sum (I (#) B0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
(Euclid_scalar n) . (D0,(Sum (I (#) B0))) is set
[D0,(Sum (I (#) B0))] is non empty set
{D0,(Sum (I (#) B0))} is non empty functional finite V39() set
{D0} is non empty trivial functional finite V39() 1 -element set
{{D0,(Sum (I (#) B0))},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,(Sum (I (#) B0))] is V11() V12() ext-real set
I . (B0 /. B) is V11() V12() ext-real Element of REAL
(I . (B0 /. B)) * D0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
the Mult of (RealVectSpace (Seg n)) is non empty Relation-like [:REAL, the carrier of (RealVectSpace (Seg n)):] -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like total quasi_total Element of bool [:[:REAL, the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):]
[:REAL, the carrier of (RealVectSpace (Seg n)):] is non empty non trivial Relation-like non finite set
[:[:REAL, the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL, the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty non trivial non finite set
the Mult of (RealVectSpace (Seg n)) . ((I . (B0 /. B)),D0) is set
[(I . (B0 /. B)),D0] is non empty set
{(I . (B0 /. B)),D0} is non empty finite set
{(I . (B0 /. B))} is non empty trivial finite 1 -element V126() V127() V128() set
{{(I . (B0 /. B)),D0},{(I . (B0 /. B))}} is non empty finite V39() set
the Mult of (RealVectSpace (Seg n)) . [(I . (B0 /. B)),D0] is set
(I . (B0 /. B)) * D0 is Relation-like Function-like set
(I . (B0 /. B)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] ((I . (B0 /. B)),(id REAL)) is set
D0 (#) ((I . (B0 /. B)) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
(Euclid_scalar n) . (D0,((I . (B0 /. B)) * D0)) is set
[D0,((I . (B0 /. B)) * D0)] is non empty set
{D0,((I . (B0 /. B)) * D0)} is non empty functional finite V39() set
{{D0,((I . (B0 /. B)) * D0)},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,((I . (B0 /. B)) * D0)] is V11() V12() ext-real set
len (I (#) B0) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
len B0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len B0) is finite len B0 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
dom B0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
[:NAT, the carrier of (RealVectSpace (Seg n)):] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of (RealVectSpace (Seg n)):] is non empty non trivial non finite set
x0 is Relation-like NAT -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (RealVectSpace (Seg n))
Sum x0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
len x0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
0. (RealVectSpace (Seg n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like zero complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
the ZeroF of (RealVectSpace (Seg n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
p is non empty Relation-like NAT -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like total quasi_total Element of bool [:NAT, the carrier of (RealVectSpace (Seg n)):]
p . (len x0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
p . 0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
(Euclid_scalar n) . (D0,(p . 0)) is set
[D0,(p . 0)] is non empty set
{D0,(p . 0)} is non empty functional finite V39() set
{{D0,(p . 0)},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,(p . 0)] is V11() V12() ext-real set
z0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
0* n is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
(Seg n) --> 0 is Relation-like Seg n -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),{0}:] is non empty finite V39() set
|(z0,(0* n))| is V11() V12() ext-real Element of REAL
mlt (z0,(0* n)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,(0* n)) is set
Sum (mlt (z0,(0* n))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,(0* n))),addreal) is V11() V12() ext-real Element of REAL
Seg (len (I (#) B0)) is finite len (I (#) B0) -element V126() V127() V128() V129() V130() V131() Element of bool NAT
p0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
p . p0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
(Euclid_scalar n) . (D0,(p . p0)) is set
[D0,(p . p0)] is non empty set
{D0,(p . p0)} is non empty functional finite V39() set
{{D0,(p . p0)},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,(p . p0)] is V11() V12() ext-real set
p0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
p . (p0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
(Euclid_scalar n) . (D0,(p . (p0 + 1))) is set
[D0,(p . (p0 + 1))] is non empty set
{D0,(p . (p0 + 1))} is non empty functional finite V39() set
{{D0,(p . (p0 + 1))},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,(p . (p0 + 1))] is V11() V12() ext-real set
Seg (len x0) is finite len x0 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
dom x0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
x0 . (p0 + 1) is set
rng x0 is finite Element of bool the carrier of (RealVectSpace (Seg n))
q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
B0 /. (p0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
B0 . (p0 + 1) is set
u0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(z0,u0)| is V11() V12() ext-real Element of REAL
mlt (z0,u0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,u0) is set
Sum (mlt (z0,u0)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,u0)),addreal) is V11() V12() ext-real Element of REAL
u4 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u0 + u4 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
addreal .: (u0,u4) is set
|(z0,(u0 + u4))| is V11() V12() ext-real Element of REAL
mlt (z0,(u0 + u4)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,(u0 + u4)) is set
Sum (mlt (z0,(u0 + u4))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,(u0 + u4))),addreal) is V11() V12() ext-real Element of REAL
|(z0,u4)| is V11() V12() ext-real Element of REAL
mlt (z0,u4) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,u4) is set
Sum (mlt (z0,u4)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,u4)),addreal) is V11() V12() ext-real Element of REAL
|(z0,u0)| + |(z0,u4)| is V11() V12() ext-real Element of REAL
I . (B0 /. (p0 + 1)) is V11() V12() ext-real Element of REAL
(I . (B0 /. (p0 + 1))) * (B0 /. (p0 + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
the Mult of (RealVectSpace (Seg n)) . ((I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))) is set
[(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))] is non empty set
{(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))} is non empty finite set
{(I . (B0 /. (p0 + 1)))} is non empty trivial finite 1 -element V126() V127() V128() set
{{(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))},{(I . (B0 /. (p0 + 1)))}} is non empty finite V39() set
the Mult of (RealVectSpace (Seg n)) . [(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))] is set
(I . (B0 /. (p0 + 1))) * (B0 /. (p0 + 1)) is Relation-like Function-like set
(I . (B0 /. (p0 + 1))) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] ((I . (B0 /. (p0 + 1))),(id REAL)) is set
(B0 /. (p0 + 1)) (#) ((I . (B0 /. (p0 + 1))) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
B3 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(z0,B3)| is V11() V12() ext-real Element of REAL
mlt (z0,B3) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,B3) is set
Sum (mlt (z0,B3)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,B3)),addreal) is V11() V12() ext-real Element of REAL
(I . (B0 /. (p0 + 1))) * |(z0,B3)| is V11() V12() ext-real Element of REAL
(I . (B0 /. (p0 + 1))) * 0 is V11() V12() ext-real Element of REAL
(p . p0) + q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
the addF of (RealVectSpace (Seg n)) is non empty Relation-like [: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):] -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like total quasi_total Element of bool [:[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):]
[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):] is non empty Relation-like set
[:[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty Relation-like set
bool [:[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty set
the addF of (RealVectSpace (Seg n)) . ((p . p0),q) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
[(p . p0),q] is non empty set
{(p . p0),q} is non empty functional finite V39() set
{(p . p0)} is non empty trivial functional finite V39() 1 -element set
{{(p . p0),q},{(p . p0)}} is non empty finite V39() set
the addF of (RealVectSpace (Seg n)) . [(p . p0),q] is set
(p . p0) + q is Relation-like Function-like set
addreal .: ((p . p0),q) is set
(Euclid_scalar n) . (D0,((p . p0) + q)) is set
[D0,((p . p0) + q)] is non empty set
{D0,((p . p0) + q)} is non empty functional finite V39() set
{{D0,((p . p0) + q)},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,((p . p0) + q)] is V11() V12() ext-real set
p0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
p . p0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
(Euclid_scalar n) . (D0,(p . p0)) is set
[D0,(p . p0)] is non empty set
{D0,(p . p0)} is non empty functional finite V39() set
{{D0,(p . p0)},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,(p . p0)] is V11() V12() ext-real set
q is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
p . q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
(Euclid_scalar n) . (D0,(p . q)) is set
[D0,(p . q)] is non empty set
{D0,(p . q)} is non empty functional finite V39() set
{{D0,(p . q)},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,(p . q)] is V11() V12() ext-real set
p0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
p . p0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
(Euclid_scalar n) . (D0,(p . p0)) is set
[D0,(p . p0)] is non empty set
{D0,(p . p0)} is non empty functional finite V39() set
{{D0,(p . p0)},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,(p . p0)] is V11() V12() ext-real set
p0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
p . (p0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
(Euclid_scalar n) . (D0,(p . (p0 + 1))) is set
[D0,(p . (p0 + 1))] is non empty set
{D0,(p . (p0 + 1))} is non empty functional finite V39() set
{{D0,(p . (p0 + 1))},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,(p . (p0 + 1))] is V11() V12() ext-real set
Seg (len x0) is finite len x0 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
B0 /. (p0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
B0 . (p0 + 1) is set
dom x0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
x0 . (p0 + 1) is set
rng x0 is finite Element of bool the carrier of (RealVectSpace (Seg n))
q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
B3 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u4 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B3 + u4 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
addreal .: (B3,u4) is set
|(z0,(B3 + u4))| is V11() V12() ext-real Element of REAL
mlt (z0,(B3 + u4)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,(B3 + u4)) is set
Sum (mlt (z0,(B3 + u4))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,(B3 + u4))),addreal) is V11() V12() ext-real Element of REAL
|(z0,B3)| is V11() V12() ext-real Element of REAL
mlt (z0,B3) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,B3) is set
Sum (mlt (z0,B3)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,B3)),addreal) is V11() V12() ext-real Element of REAL
|(z0,u4)| is V11() V12() ext-real Element of REAL
mlt (z0,u4) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,u4) is set
Sum (mlt (z0,u4)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,u4)),addreal) is V11() V12() ext-real Element of REAL
|(z0,B3)| + |(z0,u4)| is V11() V12() ext-real Element of REAL
I . (B0 /. (p0 + 1)) is V11() V12() ext-real Element of REAL
(I . (B0 /. (p0 + 1))) * (B0 /. (p0 + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
the Mult of (RealVectSpace (Seg n)) . ((I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))) is set
[(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))] is non empty set
{(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))} is non empty finite set
{(I . (B0 /. (p0 + 1)))} is non empty trivial finite 1 -element V126() V127() V128() set
{{(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))},{(I . (B0 /. (p0 + 1)))}} is non empty finite V39() set
the Mult of (RealVectSpace (Seg n)) . [(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))] is set
(I . (B0 /. (p0 + 1))) * (B0 /. (p0 + 1)) is Relation-like Function-like set
(I . (B0 /. (p0 + 1))) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] ((I . (B0 /. (p0 + 1))),(id REAL)) is set
(B0 /. (p0 + 1)) (#) ((I . (B0 /. (p0 + 1))) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
u0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(z0,u0)| is V11() V12() ext-real Element of REAL
mlt (z0,u0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,u0) is set
Sum (mlt (z0,u0)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,u0)),addreal) is V11() V12() ext-real Element of REAL
(I . (B0 /. (p0 + 1))) * |(z0,u0)| is V11() V12() ext-real Element of REAL
(I . (B0 /. (p0 + 1))) * 0 is V11() V12() ext-real Element of REAL
(p . p0) + q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
the addF of (RealVectSpace (Seg n)) is non empty Relation-like [: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):] -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like total quasi_total Element of bool [:[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):]
[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):] is non empty Relation-like set
[:[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty Relation-like set
bool [:[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty set
the addF of (RealVectSpace (Seg n)) . ((p . p0),q) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
[(p . p0),q] is non empty set
{(p . p0),q} is non empty functional finite V39() set
{(p . p0)} is non empty trivial functional finite V39() 1 -element set
{{(p . p0),q},{(p . p0)}} is non empty finite V39() set
the addF of (RealVectSpace (Seg n)) . [(p . p0),q] is set
(p . p0) + q is Relation-like Function-like set
addreal .: ((p . p0),q) is set
(Euclid_scalar n) . (D0,((p . p0) + q)) is set
[D0,((p . p0) + q)] is non empty set
{D0,((p . p0) + q)} is non empty functional finite V39() set
{{D0,((p . p0) + q)},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,((p . p0) + q)] is V11() V12() ext-real set
x0 . (p0 + 1) is set
rng x0 is finite Element of bool the carrier of (RealVectSpace (Seg n))
q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
B0 /. (p0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
I . (B0 /. (p0 + 1)) is V11() V12() ext-real Element of REAL
(I . (B0 /. (p0 + 1))) * (B0 /. (p0 + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
the Mult of (RealVectSpace (Seg n)) . ((I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))) is set
[(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))] is non empty set
{(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))} is non empty finite set
{(I . (B0 /. (p0 + 1)))} is non empty trivial finite 1 -element V126() V127() V128() set
{{(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))},{(I . (B0 /. (p0 + 1)))}} is non empty finite V39() set
the Mult of (RealVectSpace (Seg n)) . [(I . (B0 /. (p0 + 1))),(B0 /. (p0 + 1))] is set
(I . (B0 /. (p0 + 1))) * (B0 /. (p0 + 1)) is Relation-like Function-like set
(I . (B0 /. (p0 + 1))) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] ((I . (B0 /. (p0 + 1))),(id REAL)) is set
(B0 /. (p0 + 1)) (#) ((I . (B0 /. (p0 + 1))) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
u4 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(z0,u4)| is V11() V12() ext-real Element of REAL
mlt (z0,u4) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,u4) is set
Sum (mlt (z0,u4)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,u4)),addreal) is V11() V12() ext-real Element of REAL
(I . (B0 /. B)) * z0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
z0 (#) ((I . (B0 /. B)) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
|(z0,((I . (B0 /. B)) * z0))| is V11() V12() ext-real Element of REAL
mlt (z0,((I . (B0 /. B)) * z0)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,((I . (B0 /. B)) * z0)) is set
Sum (mlt (z0,((I . (B0 /. B)) * z0))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,((I . (B0 /. B)) * z0))),addreal) is V11() V12() ext-real Element of REAL
u0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(z0,u0)| is V11() V12() ext-real Element of REAL
mlt (z0,u0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,u0) is set
Sum (mlt (z0,u0)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,u0)),addreal) is V11() V12() ext-real Element of REAL
u0 + u4 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
addreal .: (u0,u4) is set
|(z0,(u0 + u4))| is V11() V12() ext-real Element of REAL
mlt (z0,(u0 + u4)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (z0,(u0 + u4)) is set
Sum (mlt (z0,(u0 + u4))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (z0,(u0 + u4))),addreal) is V11() V12() ext-real Element of REAL
|(z0,u0)| + |(z0,u4)| is V11() V12() ext-real Element of REAL
(p . p0) + q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
the addF of (RealVectSpace (Seg n)) is non empty Relation-like [: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):] -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like total quasi_total Element of bool [:[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):]
[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):] is non empty Relation-like set
[:[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty Relation-like set
bool [:[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty set
the addF of (RealVectSpace (Seg n)) . ((p . p0),q) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
[(p . p0),q] is non empty set
{(p . p0),q} is non empty functional finite V39() set
{(p . p0)} is non empty trivial functional finite V39() 1 -element set
{{(p . p0),q},{(p . p0)}} is non empty finite V39() set
the addF of (RealVectSpace (Seg n)) . [(p . p0),q] is set
(p . p0) + q is Relation-like Function-like set
addreal .: ((p . p0),q) is set
(Euclid_scalar n) . (D0,((p . p0) + q)) is set
[D0,((p . p0) + q)] is non empty set
{D0,((p . p0) + q)} is non empty functional finite V39() set
{{D0,((p . p0) + q)},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,((p . p0) + q)] is V11() V12() ext-real set
p0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
p . p0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
(Euclid_scalar n) . (D0,(p . p0)) is set
[D0,(p . p0)] is non empty set
{D0,(p . p0)} is non empty functional finite V39() set
{{D0,(p . p0)},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,(p . p0)] is V11() V12() ext-real set
q is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
p . q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
(Euclid_scalar n) . (D0,(p . q)) is set
[D0,(p . q)] is non empty set
{D0,(p . q)} is non empty functional finite V39() set
{{D0,(p . q)},{D0}} is non empty finite V39() set
(Euclid_scalar n) . [D0,(p . q)] is V11() V12() ext-real set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
RealVectSpace (Seg n) is non empty right_complementable constituted-Functions constituted-FinSeqs strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ((Seg n),REAL) is non empty functional FUNCTION_DOMAIN of Seg n, REAL
RealFuncZero (Seg n) is Relation-like Seg n -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of Funcs ((Seg n),REAL)
(Seg n) --> 0 is Relation-like Seg n -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),NAT:]
[:(Seg n),NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),NAT:] is non empty set
RealFuncAdd (Seg n) is non empty Relation-like [:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] is non empty Relation-like set
[:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty Relation-like set
bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty set
RealFuncExtMult (Seg n) is non empty Relation-like [:REAL,(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:REAL,(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
[:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial non finite set
RLSStruct(# (Funcs ((Seg n),REAL)),(RealFuncZero (Seg n)),(RealFuncAdd (Seg n)),(RealFuncExtMult (Seg n)) #) is strict RLSStruct
the carrier of (RealVectSpace (Seg n)) is non empty set
bool the carrier of (RealVectSpace (Seg n)) is non empty set
B is Element of bool the carrier of (RealVectSpace (Seg n))
B0 is Relation-like the carrier of (RealVectSpace (Seg n)) -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Linear_Combination of B
Sum B0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
0. (RealVectSpace (Seg n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like zero complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
the ZeroF of (RealVectSpace (Seg n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
Carrier B0 is Element of bool the carrier of (RealVectSpace (Seg n))
the Element of Carrier B0 is Element of Carrier B0
D0 is Relation-like NAT -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (RealVectSpace (Seg n))
rng D0 is finite Element of bool the carrier of (RealVectSpace (Seg n))
B0 (#) D0 is Relation-like NAT -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (RealVectSpace (Seg n))
Sum (B0 (#) D0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
{ b1 where b1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n)) : not B0 . b1 = 0 } is set
I is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
B0 . I is V11() V12() ext-real Element of REAL
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
Euclid_scalar n is non empty Relation-like [:(REAL n),(REAL n):] -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:[:(REAL n),(REAL n):],REAL:]
[:(REAL n),(REAL n):] is non empty Relation-like set
[:[:(REAL n),(REAL n):],REAL:] is non empty non trivial Relation-like non finite complex-yielding ext-real-valued real-valued set
bool [:[:(REAL n),(REAL n):],REAL:] is non empty non trivial non finite set
(Euclid_scalar n) . (I,(Sum (B0 (#) D0))) is set
[I,(Sum (B0 (#) D0))] is non empty set
{I,(Sum (B0 (#) D0))} is non empty functional finite V39() set
{I} is non empty trivial functional finite V39() 1 -element set
{{I,(Sum (B0 (#) D0))},{I}} is non empty finite V39() set
(Euclid_scalar n) . [I,(Sum (B0 (#) D0))] is V11() V12() ext-real set
x0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
0* n is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
(Seg n) --> 0 is Relation-like Seg n -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),{0}:] is non empty finite V39() set
|(x0,(0* n))| is V11() V12() ext-real Element of REAL
mlt (x0,(0* n)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (x0,(0* n)) is set
Sum (mlt (x0,(0* n))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (x0,(0* n))),addreal) is V11() V12() ext-real Element of REAL
dom D0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
z0 is set
D0 . z0 is set
D0 /. z0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
p is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
D0 /. p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
len D0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len D0) is finite len D0 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
len (B0 (#) D0) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
dom (B0 (#) D0) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
B0 . (D0 /. p) is V11() V12() ext-real Element of REAL
(B0 . (D0 /. p)) * I is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
the Mult of (RealVectSpace (Seg n)) is non empty Relation-like [:REAL, the carrier of (RealVectSpace (Seg n)):] -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like total quasi_total Element of bool [:[:REAL, the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):]
[:REAL, the carrier of (RealVectSpace (Seg n)):] is non empty non trivial Relation-like non finite set
[:[:REAL, the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL, the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty non trivial non finite set
the Mult of (RealVectSpace (Seg n)) . ((B0 . (D0 /. p)),I) is set
[(B0 . (D0 /. p)),I] is non empty set
{(B0 . (D0 /. p)),I} is non empty finite set
{(B0 . (D0 /. p))} is non empty trivial finite 1 -element V126() V127() V128() set
{{(B0 . (D0 /. p)),I},{(B0 . (D0 /. p))}} is non empty finite V39() set
the Mult of (RealVectSpace (Seg n)) . [(B0 . (D0 /. p)),I] is set
(B0 . (D0 /. p)) * I is Relation-like Function-like set
(B0 . (D0 /. p)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] ((B0 . (D0 /. p)),(id REAL)) is set
I (#) ((B0 . (D0 /. p)) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
(Euclid_scalar n) . (I,((B0 . (D0 /. p)) * I)) is set
[I,((B0 . (D0 /. p)) * I)] is non empty set
{I,((B0 . (D0 /. p)) * I)} is non empty functional finite V39() set
{{I,((B0 . (D0 /. p)) * I)},{I}} is non empty finite V39() set
(Euclid_scalar n) . [I,((B0 . (D0 /. p)) * I)] is V11() V12() ext-real set
(B0 . (D0 /. p)) * x0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
x0 (#) ((B0 . (D0 /. p)) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
|(x0,((B0 . (D0 /. p)) * x0))| is V11() V12() ext-real Element of REAL
mlt (x0,((B0 . (D0 /. p)) * x0)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (x0,((B0 . (D0 /. p)) * x0)) is set
Sum (mlt (x0,((B0 . (D0 /. p)) * x0))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (x0,((B0 . (D0 /. p)) * x0))),addreal) is V11() V12() ext-real Element of REAL
|(x0,x0)| is V11() V12() ext-real Element of REAL
mlt (x0,x0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (x0,x0) is set
Sum (mlt (x0,x0)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (x0,x0)),addreal) is V11() V12() ext-real Element of REAL
(B0 . (D0 /. p)) * |(x0,x0)| is V11() V12() ext-real Element of REAL
|.x0.| is V11() V12() ext-real non negative Element of REAL
sqr x0 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
x0 (#) sqrreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
mlt (x0,x0) is Relation-like Function-like set
Sum (sqr x0) is V11() V12() ext-real Element of REAL
K608(REAL,(sqr x0),addreal) is V11() V12() ext-real Element of REAL
sqrt (Sum (sqr x0)) is V11() V12() ext-real Element of REAL
|.x0.| ^2 is V11() V12() ext-real Element of REAL
K37(|.x0.|,|.x0.|) is V11() V12() ext-real non negative set
(B0 . (D0 /. p)) * (|.x0.| ^2) is V11() V12() ext-real Element of REAL
1 ^2 is V11() V12() ext-real Element of REAL
K37(1,1) is ordinal natural V11() V12() ext-real non negative finite cardinal set
(B0 . (D0 /. p)) * (1 ^2) is V11() V12() ext-real Element of REAL
p0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
B0 . p0 is V11() V12() ext-real Element of REAL
n is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
REAL-US n is non empty right_complementable constituted-Functions constituted-FinSeqs Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V194() V195() L17()
the carrier of (REAL-US n) is non empty set
bool the carrier of (REAL-US n) is non empty set
B is Element of bool the carrier of (REAL-US n)
B0 is Relation-like the carrier of (REAL-US n) -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Linear_Combination of B
Sum B0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
0. (REAL-US n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like zero complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
the ZeroF of (REAL-US n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
Carrier B0 is Element of bool the carrier of (REAL-US n)
the Element of Carrier B0 is Element of Carrier B0
D0 is Relation-like NAT -defined the carrier of (REAL-US n) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (REAL-US n)
rng D0 is finite Element of bool the carrier of (REAL-US n)
B0 (#) D0 is Relation-like NAT -defined the carrier of (REAL-US n) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (REAL-US n)
Sum (B0 (#) D0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
{ b1 where b1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n) : not B0 . b1 = 0 } is set
I is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
B0 . I is V11() V12() ext-real Element of REAL
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
0* n is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(Seg n) --> 0 is Relation-like Seg n -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),{0}:] is non empty finite V39() set
Euclid_scalar n is non empty Relation-like [:(REAL n),(REAL n):] -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:[:(REAL n),(REAL n):],REAL:]
[:(REAL n),(REAL n):] is non empty Relation-like set
[:[:(REAL n),(REAL n):],REAL:] is non empty non trivial Relation-like non finite complex-yielding ext-real-valued real-valued set
bool [:[:(REAL n),(REAL n):],REAL:] is non empty non trivial non finite set
(Euclid_scalar n) . (I,(Sum (B0 (#) D0))) is set
[I,(Sum (B0 (#) D0))] is non empty set
{I,(Sum (B0 (#) D0))} is non empty functional finite V39() set
{I} is non empty trivial functional finite V39() 1 -element set
{{I,(Sum (B0 (#) D0))},{I}} is non empty finite V39() set
(Euclid_scalar n) . [I,(Sum (B0 (#) D0))] is V11() V12() ext-real set
x0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(x0,(0* n))| is V11() V12() ext-real Element of REAL
mlt (x0,(0* n)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (x0,(0* n)) is set
Sum (mlt (x0,(0* n))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (x0,(0* n))),addreal) is V11() V12() ext-real Element of REAL
dom D0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
z0 is set
D0 . z0 is set
D0 /. z0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
p is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
D0 /. p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
len D0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len D0) is finite len D0 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
len (B0 (#) D0) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
dom (B0 (#) D0) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
B0 . (D0 /. p) is V11() V12() ext-real Element of REAL
(B0 . (D0 /. p)) * I is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
the Mult of (REAL-US n) is non empty Relation-like [:REAL, the carrier of (REAL-US n):] -defined the carrier of (REAL-US n) -valued Function-like total quasi_total Element of bool [:[:REAL, the carrier of (REAL-US n):], the carrier of (REAL-US n):]
[:REAL, the carrier of (REAL-US n):] is non empty non trivial Relation-like non finite set
[:[:REAL, the carrier of (REAL-US n):], the carrier of (REAL-US n):] is non empty non trivial Relation-like non finite set
bool [:[:REAL, the carrier of (REAL-US n):], the carrier of (REAL-US n):] is non empty non trivial non finite set
the Mult of (REAL-US n) . ((B0 . (D0 /. p)),I) is set
[(B0 . (D0 /. p)),I] is non empty set
{(B0 . (D0 /. p)),I} is non empty finite set
{(B0 . (D0 /. p))} is non empty trivial finite 1 -element V126() V127() V128() set
{{(B0 . (D0 /. p)),I},{(B0 . (D0 /. p))}} is non empty finite V39() set
the Mult of (REAL-US n) . [(B0 . (D0 /. p)),I] is set
(B0 . (D0 /. p)) * I is Relation-like Function-like set
(B0 . (D0 /. p)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] ((B0 . (D0 /. p)),(id REAL)) is set
I (#) ((B0 . (D0 /. p)) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
(Euclid_scalar n) . (I,((B0 . (D0 /. p)) * I)) is set
[I,((B0 . (D0 /. p)) * I)] is non empty set
{I,((B0 . (D0 /. p)) * I)} is non empty functional finite V39() set
{{I,((B0 . (D0 /. p)) * I)},{I}} is non empty finite V39() set
(Euclid_scalar n) . [I,((B0 . (D0 /. p)) * I)] is V11() V12() ext-real set
(B0 . (D0 /. p)) * x0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
x0 (#) ((B0 . (D0 /. p)) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
|(x0,((B0 . (D0 /. p)) * x0))| is V11() V12() ext-real Element of REAL
mlt (x0,((B0 . (D0 /. p)) * x0)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (x0,((B0 . (D0 /. p)) * x0)) is set
Sum (mlt (x0,((B0 . (D0 /. p)) * x0))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (x0,((B0 . (D0 /. p)) * x0))),addreal) is V11() V12() ext-real Element of REAL
|(x0,x0)| is V11() V12() ext-real Element of REAL
mlt (x0,x0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (x0,x0) is set
Sum (mlt (x0,x0)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (x0,x0)),addreal) is V11() V12() ext-real Element of REAL
(B0 . (D0 /. p)) * |(x0,x0)| is V11() V12() ext-real Element of REAL
|.x0.| is V11() V12() ext-real non negative Element of REAL
sqr x0 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
x0 (#) sqrreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
mlt (x0,x0) is Relation-like Function-like set
Sum (sqr x0) is V11() V12() ext-real Element of REAL
K608(REAL,(sqr x0),addreal) is V11() V12() ext-real Element of REAL
sqrt (Sum (sqr x0)) is V11() V12() ext-real Element of REAL
|.x0.| ^2 is V11() V12() ext-real Element of REAL
K37(|.x0.|,|.x0.|) is V11() V12() ext-real non negative set
(B0 . (D0 /. p)) * (|.x0.| ^2) is V11() V12() ext-real Element of REAL
1 ^2 is V11() V12() ext-real Element of REAL
K37(1,1) is ordinal natural V11() V12() ext-real non negative finite cardinal set
(B0 . (D0 /. p)) * (1 ^2) is V11() V12() ext-real Element of REAL
p0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
B0 . p0 is V11() V12() ext-real Element of REAL
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
RealVectSpace (Seg n) is non empty right_complementable constituted-Functions constituted-FinSeqs strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ((Seg n),REAL) is non empty functional FUNCTION_DOMAIN of Seg n, REAL
RealFuncZero (Seg n) is Relation-like Seg n -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of Funcs ((Seg n),REAL)
(Seg n) --> 0 is Relation-like Seg n -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),NAT:]
[:(Seg n),NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),NAT:] is non empty set
RealFuncAdd (Seg n) is non empty Relation-like [:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] is non empty Relation-like set
[:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty Relation-like set
bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty set
RealFuncExtMult (Seg n) is non empty Relation-like [:REAL,(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:REAL,(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
[:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial non finite set
RLSStruct(# (Funcs ((Seg n),REAL)),(RealFuncZero (Seg n)),(RealFuncAdd (Seg n)),(RealFuncExtMult (Seg n)) #) is strict RLSStruct
the carrier of (RealVectSpace (Seg n)) is non empty set
bool the carrier of (RealVectSpace (Seg n)) is non empty set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
B is Element of bool the carrier of (RealVectSpace (Seg n))
B0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
D0 is V11() V12() ext-real Element of REAL
D0 * B0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
D0 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (D0,(id REAL)) is set
B0 (#) (D0 multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
x0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
I is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
{x0,I} is non empty functional finite V39() Element of bool the carrier of (RealVectSpace (Seg n))
z0 is Element of bool the carrier of (RealVectSpace (Seg n))
p is set
D0 * I is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
the Mult of (RealVectSpace (Seg n)) is non empty Relation-like [:REAL, the carrier of (RealVectSpace (Seg n)):] -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like total quasi_total Element of bool [:[:REAL, the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):]
[:REAL, the carrier of (RealVectSpace (Seg n)):] is non empty non trivial Relation-like non finite set
[:[:REAL, the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL, the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty non trivial non finite set
the Mult of (RealVectSpace (Seg n)) . (D0,I) is set
[D0,I] is non empty set
{D0,I} is non empty finite set
{D0} is non empty trivial finite 1 -element V126() V127() V128() set
{{D0,I},{D0}} is non empty finite V39() set
the Mult of (RealVectSpace (Seg n)) . [D0,I] is set
D0 * I is Relation-like Function-like set
I (#) (D0 multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
(n) is functional FinSequence-membered () () () (n) (n) Element of bool (REAL n)
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
{ (n,b1) where b1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
card (n) is ordinal cardinal set
B is non empty ordinal natural V11() V12() ext-real positive non negative finite cardinal set
Seg B is non empty finite B -element V126() V127() V128() V129() V130() V131() Element of bool NAT
B0 is set
B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B,B) is Relation-like NAT -defined REAL -valued Function-like finite B -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL B
REAL B is non empty functional FinSequence-membered FinSequenceSet of REAL
B -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = B } is set
D0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B,D0) is Relation-like NAT -defined REAL -valued Function-like finite B -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL B
B0 is Relation-like Function-like set
dom B0 is set
rng B0 is set
(B) is non empty functional FinSequence-membered () () () (B) (B) Element of bool (REAL B)
REAL B is non empty functional FinSequence-membered FinSequenceSet of REAL
B -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = B } is set
bool (REAL B) is non empty set
{ (B,b1) where b1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT : ( 1 <= b1 & b1 <= B ) } is set
B is set
D0 is set
B0 . D0 is set
I is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B,I) is Relation-like NAT -defined REAL -valued Function-like finite B -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL B
[:(Seg B),(B):] is non empty Relation-like set
bool [:(Seg B),(B):] is non empty set
D0 is set
I is set
B0 . D0 is set
B0 . I is set
x0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
z0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B,z0) is Relation-like NAT -defined REAL -valued Function-like finite B -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL B
(B,x0) is Relation-like NAT -defined REAL -valued Function-like finite B -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL B
B is non empty Relation-like Seg B -defined (B) -valued Function-like total quasi_total finite Element of bool [:(Seg B),(B):]
D0 is set
I is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(B,I) is Relation-like NAT -defined REAL -valued Function-like finite B -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL B
B0 . I is set
card (Seg B) is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of omega
card (B) is non empty ordinal cardinal set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
(n) is functional FinSequence-membered () () () (n) (n) Element of bool (REAL n)
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
{ (n,b1) where b1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
(n) is functional finite FinSequence-membered () () () (n) (n) Element of bool (REAL n)
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
{ (n,b1) where b1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
card (n) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of omega
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
RealVectSpace (Seg n) is non empty right_complementable constituted-Functions constituted-FinSeqs strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ((Seg n),REAL) is non empty functional FUNCTION_DOMAIN of Seg n, REAL
RealFuncZero (Seg n) is Relation-like Seg n -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of Funcs ((Seg n),REAL)
(Seg n) --> 0 is Relation-like Seg n -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),NAT:]
[:(Seg n),NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),NAT:] is non empty set
RealFuncAdd (Seg n) is non empty Relation-like [:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] is non empty Relation-like set
[:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty Relation-like set
bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty set
RealFuncExtMult (Seg n) is non empty Relation-like [:REAL,(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:REAL,(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
[:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial non finite set
RLSStruct(# (Funcs ((Seg n),REAL)),(RealFuncZero (Seg n)),(RealFuncAdd (Seg n)),(RealFuncExtMult (Seg n)) #) is strict RLSStruct
the carrier of (RealVectSpace (Seg n)) is non empty set
B is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
(n,B) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B0 is Relation-like NAT -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (RealVectSpace (Seg n))
Sum B0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
len B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
len (n,B) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,B) . (len B) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(len B) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
0. (RealVectSpace (Seg n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like zero complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
the ZeroF of (RealVectSpace (Seg n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
I is set
(n,B) /. I is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
IFEQ (I,0,(0. (RealVectSpace (Seg n))),((n,B) /. I)) is set
IFIN (I,((len B) + 1),(IFEQ (I,0,(0. (RealVectSpace (Seg n))),((n,B) /. I))),(0. (RealVectSpace (Seg n)))) is set
x0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) /. x0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
IFEQ (I,0,(0. (RealVectSpace (Seg n))),((n,B) /. x0)) is set
x0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
x0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
[:NAT, the carrier of (RealVectSpace (Seg n)):] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of (RealVectSpace (Seg n)):] is non empty non trivial non finite set
I is non empty Relation-like NAT -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like total quasi_total Element of bool [:NAT, the carrier of (RealVectSpace (Seg n)):]
len B0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
x0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
x0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B0 . (x0 + 1) is set
I . (x0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
I . x0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
z0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
(I . x0) + z0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
the addF of (RealVectSpace (Seg n)) is non empty Relation-like [: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):] -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like total quasi_total Element of bool [:[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):]
[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):] is non empty Relation-like set
[:[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty Relation-like set
bool [:[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty set
the addF of (RealVectSpace (Seg n)) . ((I . x0),z0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
[(I . x0),z0] is non empty set
{(I . x0),z0} is non empty functional finite V39() set
{(I . x0)} is non empty trivial functional finite V39() 1 -element set
{{(I . x0),z0},{(I . x0)}} is non empty finite V39() set
the addF of (RealVectSpace (Seg n)) . [(I . x0),z0] is set
(I . x0) + z0 is Relation-like Function-like set
addreal .: ((I . x0),z0) is set
(n,B) /. x0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
IFEQ (x0,0,(0. (RealVectSpace (Seg n))),((n,B) /. x0)) is set
IFIN (x0,((len B) + 1),(IFEQ (x0,0,(0. (RealVectSpace (Seg n))),((n,B) /. x0))),(0. (RealVectSpace (Seg n)))) is set
(n,B) /. (x0 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
IFEQ ((x0 + 1),0,(0. (RealVectSpace (Seg n))),((n,B) /. (x0 + 1))) is set
IFIN ((x0 + 1),((len B) + 1),(IFEQ ((x0 + 1),0,(0. (RealVectSpace (Seg n))),((n,B) /. (x0 + 1)))),(0. (RealVectSpace (Seg n)))) is set
(n,B) /. 1 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
(n,B) /. x0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
IFEQ (x0,0,(0. (RealVectSpace (Seg n))),((n,B) /. x0)) is set
IFIN (x0,((len B) + 1),(IFEQ (x0,0,(0. (RealVectSpace (Seg n))),((n,B) /. x0))),(0. (RealVectSpace (Seg n)))) is set
0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) /. (x0 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
IFEQ ((x0 + 1),0,(0. (RealVectSpace (Seg n))),((n,B) /. (x0 + 1))) is set
IFIN ((x0 + 1),((len B) + 1),(IFEQ ((x0 + 1),0,(0. (RealVectSpace (Seg n))),((n,B) /. (x0 + 1)))),(0. (RealVectSpace (Seg n)))) is set
(n,B) . (x0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
B /. (x0 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
((n,B) /. x0) + (B /. (x0 + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
I . 0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
(n,B) /. 0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
IFEQ (0,0,(0. (RealVectSpace (Seg n))),((n,B) /. 0)) is set
IFIN (0,((len B) + 1),(IFEQ (0,0,(0. (RealVectSpace (Seg n))),((n,B) /. 0))),(0. (RealVectSpace (Seg n)))) is set
I . (len B0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
(n,B) /. (len B) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
IFEQ ((len B),0,(0. (RealVectSpace (Seg n))),((n,B) /. (len B))) is set
IFIN ((len B),((len B) + 1),(IFEQ ((len B),0,(0. (RealVectSpace (Seg n))),((n,B) /. (len B)))),(0. (RealVectSpace (Seg n)))) is set
len B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
0. (RealVectSpace (Seg n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like zero complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
the ZeroF of (RealVectSpace (Seg n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
NAT --> (0. (RealVectSpace (Seg n))) is non empty T-Sequence-like Relation-like NAT -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like total quasi_total Element of bool [:NAT, the carrier of (RealVectSpace (Seg n)):]
[:NAT, the carrier of (RealVectSpace (Seg n)):] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of (RealVectSpace (Seg n)):] is non empty non trivial non finite set
len B0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
I is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
x0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
I + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
B0 . (I + 1) is set
(NAT --> (0. (RealVectSpace (Seg n)))) . (I + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
(NAT --> (0. (RealVectSpace (Seg n)))) . I is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
((NAT --> (0. (RealVectSpace (Seg n)))) . I) + x0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
the addF of (RealVectSpace (Seg n)) is non empty Relation-like [: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):] -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like total quasi_total Element of bool [:[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):]
[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):] is non empty Relation-like set
[:[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty Relation-like set
bool [:[: the carrier of (RealVectSpace (Seg n)), the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty set
the addF of (RealVectSpace (Seg n)) . (((NAT --> (0. (RealVectSpace (Seg n)))) . I),x0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
[((NAT --> (0. (RealVectSpace (Seg n)))) . I),x0] is non empty set
{((NAT --> (0. (RealVectSpace (Seg n)))) . I),x0} is non empty functional finite V39() set
{((NAT --> (0. (RealVectSpace (Seg n)))) . I)} is non empty trivial functional finite V39() 1 -element set
{{((NAT --> (0. (RealVectSpace (Seg n)))) . I),x0},{((NAT --> (0. (RealVectSpace (Seg n)))) . I)}} is non empty finite V39() set
the addF of (RealVectSpace (Seg n)) . [((NAT --> (0. (RealVectSpace (Seg n)))) . I),x0] is set
((NAT --> (0. (RealVectSpace (Seg n)))) . I) + x0 is Relation-like Function-like set
addreal .: (((NAT --> (0. (RealVectSpace (Seg n)))) . I),x0) is set
(NAT --> (0. (RealVectSpace (Seg n)))) . (len B0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
0* n is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
(Seg n) --> 0 is Relation-like Seg n -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),{0}:] is non empty finite V39() set
(NAT --> (0. (RealVectSpace (Seg n)))) . 0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
len B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
[:NAT, the carrier of (RealVectSpace (Seg n)):] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of (RealVectSpace (Seg n)):] is non empty non trivial non finite set
len B0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
0. (RealVectSpace (Seg n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like zero complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
the ZeroF of (RealVectSpace (Seg n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
len B is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
[:NAT, the carrier of (RealVectSpace (Seg n)):] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of (RealVectSpace (Seg n)):] is non empty non trivial non finite set
len B0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
0. (RealVectSpace (Seg n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like zero complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
the ZeroF of (RealVectSpace (Seg n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
D0 is non empty Relation-like NAT -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like total quasi_total Element of bool [:NAT, the carrier of (RealVectSpace (Seg n)):]
D0 . (len B0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
D0 . 0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
I is non empty Relation-like NAT -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like total quasi_total Element of bool [:NAT, the carrier of (RealVectSpace (Seg n)):]
I . (len B0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
I . 0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
RealVectSpace (Seg n) is non empty right_complementable constituted-Functions constituted-FinSeqs strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ((Seg n),REAL) is non empty functional FUNCTION_DOMAIN of Seg n, REAL
RealFuncZero (Seg n) is Relation-like Seg n -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of Funcs ((Seg n),REAL)
(Seg n) --> 0 is Relation-like Seg n -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),NAT:]
[:(Seg n),NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),NAT:] is non empty set
RealFuncAdd (Seg n) is non empty Relation-like [:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] is non empty Relation-like set
[:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty Relation-like set
bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty set
RealFuncExtMult (Seg n) is non empty Relation-like [:REAL,(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:REAL,(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
[:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial non finite set
RLSStruct(# (Funcs ((Seg n),REAL)),(RealFuncZero (Seg n)),(RealFuncAdd (Seg n)),(RealFuncExtMult (Seg n)) #) is strict RLSStruct
the carrier of (RealVectSpace (Seg n)) is non empty set
bool the carrier of (RealVectSpace (Seg n)) is non empty set
(n) is functional finite FinSequence-membered () () () (n) (n) Element of bool (REAL n)
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
{ (n,b1) where b1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
B is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
B0 is Element of bool the carrier of (RealVectSpace (Seg n))
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n : ex b2 being ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT st
( 1 <= b2 & b2 <= n & b1 = (n,b2) ) } is set
D0 is set
I is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
x0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,x0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
D0 is set
I is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,I) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n : ex b2 being ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT st
( 1 <= b2 & b2 <= n & b1 = (n,b2) & not |(B,b1)| = 0 ) } is set
D0 is set
I is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
x0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,x0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,I)| is V11() V12() ext-real Element of REAL
mlt (B,I) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,I) is set
Sum (mlt (B,I)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,I)),addreal) is V11() V12() ext-real Element of REAL
(n,B) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
dom (n,B) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
len (n,B) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len (n,B)) is finite len (n,B) -element V126() V127() V128() V129() V130() V131() Element of bool NAT
D0 is Element of bool the carrier of (RealVectSpace (Seg n))
I is set
x0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,x0)| is V11() V12() ext-real Element of REAL
mlt (B,x0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,x0) is set
Sum (mlt (B,x0)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,x0)),addreal) is V11() V12() ext-real Element of REAL
z0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,z0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
z0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,z0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
[:D0,(Seg n):] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:D0,(Seg n):] is non empty set
I is Relation-like D0 -defined Seg n -valued Function-like quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:D0,(Seg n):]
x0 is set
z0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,z0)| is V11() V12() ext-real Element of REAL
mlt (B,z0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,z0) is set
Sum (mlt (B,z0)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,z0)),addreal) is V11() V12() ext-real Element of REAL
p is V11() V12() ext-real Element of REAL
p0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,p0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,(n,p0))| is V11() V12() ext-real Element of REAL
mlt (B,(n,p0)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,(n,p0)) is set
Sum (mlt (B,(n,p0))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,(n,p0))),addreal) is V11() V12() ext-real Element of REAL
[: the carrier of (RealVectSpace (Seg n)),REAL:] is non empty non trivial Relation-like non finite complex-yielding ext-real-valued real-valued set
bool [: the carrier of (RealVectSpace (Seg n)),REAL:] is non empty non trivial non finite set
x0 is non empty Relation-like the carrier of (RealVectSpace (Seg n)) -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (RealVectSpace (Seg n)),REAL:]
Funcs ( the carrier of (RealVectSpace (Seg n)),REAL) is non empty functional FUNCTION_DOMAIN of the carrier of (RealVectSpace (Seg n)), REAL
z0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
x0 . z0 is V11() V12() ext-real Element of REAL
z0 is Relation-like the carrier of (RealVectSpace (Seg n)) -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Linear_Combination of RealVectSpace (Seg n)
Carrier z0 is Element of bool the carrier of (RealVectSpace (Seg n))
p is set
{ b1 where b1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n)) : not z0 . b1 = 0 } is set
p0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
z0 . p0 is V11() V12() ext-real Element of REAL
p is Relation-like the carrier of (RealVectSpace (Seg n)) -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Linear_Combination of D0
Carrier p is Element of bool the carrier of (RealVectSpace (Seg n))
q is set
u4 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,u4)| is V11() V12() ext-real Element of REAL
mlt (B,u4) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,u4) is set
Sum (mlt (B,u4)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,u4)),addreal) is V11() V12() ext-real Element of REAL
B3 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B3) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B3 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B3) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
p . u0 is V11() V12() ext-real Element of REAL
|(B,(n,B3))| is V11() V12() ext-real Element of REAL
mlt (B,(n,B3)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,(n,B3)) is set
Sum (mlt (B,(n,B3))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,(n,B3))),addreal) is V11() V12() ext-real Element of REAL
aq is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,aq) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
{ b1 where b1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n)) : not p . b1 = 0 } is set
aq is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,aq) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
dom I is Element of bool D0
bool D0 is non empty set
q is set
u4 is set
I . q is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
I . u4 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
u0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,u0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B3 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B3) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
the Element of D0 is Element of D0
u4 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,u0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,u4)| is V11() V12() ext-real Element of REAL
mlt (B,u4) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,u4) is set
Sum (mlt (B,u4)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,u4)),addreal) is V11() V12() ext-real Element of REAL
rng I is finite V126() V127() V128() V129() V130() V131() Element of bool (Seg n)
bool (Seg n) is non empty finite V39() set
Sgm (rng I) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued FinSequence of NAT
rng (Sgm (rng I)) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
0* n is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
(Seg n) --> 0 is Relation-like Seg n -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),{0}:] is non empty finite V39() set
q is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,q) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,(n,q))| is V11() V12() ext-real Element of REAL
mlt (B,(n,q)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,(n,q)) is set
Sum (mlt (B,(n,q))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,(n,q))),addreal) is V11() V12() ext-real Element of REAL
I . (n,q) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
u4 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,u4) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,(n,q))| * (n,q) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,(n,q))| multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (|(B,(n,q))|,(id REAL)) is set
(n,q) (#) (|(B,(n,q))| multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
dom (Sgm (rng I)) is finite set
len (Sgm (rng I)) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len (Sgm (rng I))) is finite len (Sgm (rng I)) -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(Sgm (rng I)) (#) (n,B) is Relation-like NAT -defined REAL n -valued Function-like finite set
rng ((Sgm (rng I)) (#) (n,B)) is functional finite FinSequence-membered Element of bool (REAL n)
dom ((Sgm (rng I)) (#) (n,B)) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
(Sgm (rng I)) " (dom (n,B)) is finite set
dom (Sgm (rng I)) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
q is Relation-like NAT -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (RealVectSpace (Seg n))
dom q is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
(Sgm (rng I)) " (Seg n) is finite set
len q is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len q) is finite len q -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(n,(n,B)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u4 is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
(n,u4) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
Sum q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
I " is Relation-like Function-like set
(Sgm (rng I)) (#) (I ") is Relation-like NAT -defined Function-like finite set
rng ((Sgm (rng I)) (#) (I ")) is finite set
rng (I ") is set
dom ((Sgm (rng I)) (#) (I ")) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
dom (I ") is set
(Sgm (rng I)) " (dom (I ")) is finite set
(Sgm (rng I)) " (rng I) is finite set
u0 is Relation-like NAT -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (RealVectSpace (Seg n))
dom u0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
rng u0 is finite Element of bool the carrier of (RealVectSpace (Seg n))
B3 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
q . B3 is set
u0 /. B3 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
p . (u0 /. B3) is V11() V12() ext-real Element of REAL
(p . (u0 /. B3)) * (u0 /. B3) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
the Mult of (RealVectSpace (Seg n)) is non empty Relation-like [:REAL, the carrier of (RealVectSpace (Seg n)):] -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like total quasi_total Element of bool [:[:REAL, the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):]
[:REAL, the carrier of (RealVectSpace (Seg n)):] is non empty non trivial Relation-like non finite set
[:[:REAL, the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL, the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty non trivial non finite set
the Mult of (RealVectSpace (Seg n)) . ((p . (u0 /. B3)),(u0 /. B3)) is set
[(p . (u0 /. B3)),(u0 /. B3)] is non empty set
{(p . (u0 /. B3)),(u0 /. B3)} is non empty finite set
{(p . (u0 /. B3))} is non empty trivial finite 1 -element V126() V127() V128() set
{{(p . (u0 /. B3)),(u0 /. B3)},{(p . (u0 /. B3))}} is non empty finite V39() set
the Mult of (RealVectSpace (Seg n)) . [(p . (u0 /. B3)),(u0 /. B3)] is set
(p . (u0 /. B3)) * (u0 /. B3) is Relation-like Function-like set
(p . (u0 /. B3)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] ((p . (u0 /. B3)),(id REAL)) is set
(u0 /. B3) (#) ((p . (u0 /. B3)) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
(Sgm (rng I)) . B3 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
aq is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,aq) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
x3 is set
I . x3 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
I . j is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
bq is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
I . bq is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
u2 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,u2) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u2 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,u2) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u0 . B3 is set
(Sgm (rng I)) . B3 is ordinal natural V11() V12() ext-real non negative finite cardinal set
(I ") . ((Sgm (rng I)) . B3) is set
k2 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,k2) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
{ b1 where b1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n)) : not p . b1 = 0 } is set
k2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
p . k2 is V11() V12() ext-real Element of REAL
I . (n,aq) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
(I ") . (I . (n,aq)) is set
((Sgm (rng I)) (#) (I ")) . B3 is set
k2 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,k2) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(Sgm (rng I)) " is Relation-like Function-like set
((Sgm (rng I)) ") . (I . (n,aq)) is set
k2 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,k2) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(Sgm (rng I)) . (((Sgm (rng I)) ") . (I . (n,aq))) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
(I ") . ((Sgm (rng I)) . (((Sgm (rng I)) ") . (I . (n,aq)))) is set
dom ((Sgm (rng I)) ") is set
rng ((Sgm (rng I)) ") is set
p . (((Sgm (rng I)) (#) (I ")) . B3) is V11() V12() ext-real Element of REAL
p . (n,aq) is V11() V12() ext-real Element of REAL
|(B,(n,aq))| is V11() V12() ext-real Element of REAL
mlt (B,(n,aq)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,(n,aq)) is set
Sum (mlt (B,(n,aq))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,(n,aq))),addreal) is V11() V12() ext-real Element of REAL
k2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
p . k2 is V11() V12() ext-real Element of REAL
|(B,(n,aq))| * (n,aq) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,(n,aq))| multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (|(B,(n,aq))|,(id REAL)) is set
(n,aq) (#) (|(B,(n,aq))| multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
(n,B) . ((Sgm (rng I)) . B3) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((Sgm (rng I)) (#) (n,B)) . B3 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len u0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
p (#) u0 is Relation-like NAT -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (RealVectSpace (Seg n))
Sum (p (#) u0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
p0 is Relation-like the carrier of (RealVectSpace (Seg n)) -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Linear_Combination of B0
Sum p0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
n is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
REAL-US n is non empty right_complementable constituted-Functions constituted-FinSeqs Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V194() V195() L17()
the carrier of (REAL-US n) is non empty set
bool the carrier of (REAL-US n) is non empty set
(n) is functional finite FinSequence-membered () () () (n) (n) Element of bool (REAL n)
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
{ (n,b1) where b1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
B is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
B0 is Element of bool the carrier of (REAL-US n)
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n : ex b2 being ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT st
( 1 <= b2 & b2 <= n & b1 = (n,b2) ) } is set
D0 is set
I is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
x0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,x0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
D0 is set
I is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,I) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n : ex b2 being ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT st
( 1 <= b2 & b2 <= n & b1 = (n,b2) & not |(B,b1)| = 0 ) } is set
D0 is set
I is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
x0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,x0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,I)| is V11() V12() ext-real Element of REAL
mlt (B,I) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,I) is set
Sum (mlt (B,I)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,I)),addreal) is V11() V12() ext-real Element of REAL
D0 is Element of bool the carrier of (REAL-US n)
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
I is set
x0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,x0)| is V11() V12() ext-real Element of REAL
mlt (B,x0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,x0) is set
Sum (mlt (B,x0)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,x0)),addreal) is V11() V12() ext-real Element of REAL
z0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,z0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
z0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,z0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
[:D0,(Seg n):] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:D0,(Seg n):] is non empty set
I is Relation-like D0 -defined Seg n -valued Function-like quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:D0,(Seg n):]
x0 is set
z0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,z0)| is V11() V12() ext-real Element of REAL
mlt (B,z0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,z0) is set
Sum (mlt (B,z0)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,z0)),addreal) is V11() V12() ext-real Element of REAL
p is V11() V12() ext-real Element of REAL
p0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,p0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,(n,p0))| is V11() V12() ext-real Element of REAL
mlt (B,(n,p0)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,(n,p0)) is set
Sum (mlt (B,(n,p0))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,(n,p0))),addreal) is V11() V12() ext-real Element of REAL
[: the carrier of (REAL-US n),REAL:] is non empty non trivial Relation-like non finite complex-yielding ext-real-valued real-valued set
bool [: the carrier of (REAL-US n),REAL:] is non empty non trivial non finite set
x0 is non empty Relation-like the carrier of (REAL-US n) -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (REAL-US n),REAL:]
Funcs ( the carrier of (REAL-US n),REAL) is non empty functional FUNCTION_DOMAIN of the carrier of (REAL-US n), REAL
z0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
x0 . z0 is V11() V12() ext-real Element of REAL
z0 is Relation-like the carrier of (REAL-US n) -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Linear_Combination of REAL-US n
Carrier z0 is Element of bool the carrier of (REAL-US n)
p is set
{ b1 where b1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n) : not z0 . b1 = 0 } is set
p0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
z0 . p0 is V11() V12() ext-real Element of REAL
p is Relation-like the carrier of (REAL-US n) -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Linear_Combination of D0
Carrier p is Element of bool the carrier of (REAL-US n)
q is set
u4 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,u4)| is V11() V12() ext-real Element of REAL
mlt (B,u4) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,u4) is set
Sum (mlt (B,u4)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,u4)),addreal) is V11() V12() ext-real Element of REAL
B3 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B3) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B3 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B3) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
p . u0 is V11() V12() ext-real Element of REAL
|(B,(n,B3))| is V11() V12() ext-real Element of REAL
mlt (B,(n,B3)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,(n,B3)) is set
Sum (mlt (B,(n,B3))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,(n,B3))),addreal) is V11() V12() ext-real Element of REAL
aq is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,aq) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
{ b1 where b1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n) : not p . b1 = 0 } is set
aq is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,aq) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
rng I is finite V126() V127() V128() V129() V130() V131() Element of bool (Seg n)
bool (Seg n) is non empty finite V39() set
Sgm (rng I) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued FinSequence of NAT
dom (Sgm (rng I)) is finite set
len (Sgm (rng I)) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len (Sgm (rng I))) is finite len (Sgm (rng I)) -element V126() V127() V128() V129() V130() V131() Element of bool NAT
I " is Relation-like Function-like set
(Sgm (rng I)) (#) (I ") is Relation-like NAT -defined Function-like finite set
rng ((Sgm (rng I)) (#) (I ")) is finite set
rng (I ") is set
dom I is Element of bool D0
bool D0 is non empty set
q is set
u4 is set
I . q is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
I . u4 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
u0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,u0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B3 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B3) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
the Element of D0 is Element of D0
u4 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,u0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,u4)| is V11() V12() ext-real Element of REAL
mlt (B,u4) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,u4) is set
Sum (mlt (B,u4)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,u4)),addreal) is V11() V12() ext-real Element of REAL
(n,B) is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
dom (n,B) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
rng (Sgm (rng I)) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
0* n is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
(Seg n) --> 0 is Relation-like Seg n -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),{0}:] is non empty finite V39() set
q is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B) . q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (n,B) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len (n,B)) is finite len (n,B) -element V126() V127() V128() V129() V130() V131() Element of bool NAT
(n,q) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,(n,q))| is V11() V12() ext-real Element of REAL
mlt (B,(n,q)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,(n,q)) is set
Sum (mlt (B,(n,q))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,(n,q))),addreal) is V11() V12() ext-real Element of REAL
I . (n,q) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
u4 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,u4) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,(n,q))| * (n,q) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,(n,q))| multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (|(B,(n,q))|,(id REAL)) is set
(n,q) (#) (|(B,(n,q))| multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
(Sgm (rng I)) (#) (n,B) is Relation-like NAT -defined REAL n -valued Function-like finite set
rng ((Sgm (rng I)) (#) (n,B)) is functional finite FinSequence-membered Element of bool (REAL n)
dom ((Sgm (rng I)) (#) (I ")) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
dom (I ") is set
(Sgm (rng I)) " (dom (I ")) is finite set
(Sgm (rng I)) " (rng I) is finite set
dom (Sgm (rng I)) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
q is Relation-like NAT -defined the carrier of (REAL-US n) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (REAL-US n)
dom q is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
len (n,B) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len (n,B)) is finite len (n,B) -element V126() V127() V128() V129() V130() V131() Element of bool NAT
dom ((Sgm (rng I)) (#) (n,B)) is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
(Sgm (rng I)) " (Seg n) is finite set
u4 is Relation-like NAT -defined the carrier of (REAL-US n) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (REAL-US n)
dom u4 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
len u4 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len u4) is finite len u4 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
rng q is finite Element of bool the carrier of (REAL-US n)
u0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
u4 . u0 is set
q /. u0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
p . (q /. u0) is V11() V12() ext-real Element of REAL
(p . (q /. u0)) * (q /. u0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
the Mult of (REAL-US n) is non empty Relation-like [:REAL, the carrier of (REAL-US n):] -defined the carrier of (REAL-US n) -valued Function-like total quasi_total Element of bool [:[:REAL, the carrier of (REAL-US n):], the carrier of (REAL-US n):]
[:REAL, the carrier of (REAL-US n):] is non empty non trivial Relation-like non finite set
[:[:REAL, the carrier of (REAL-US n):], the carrier of (REAL-US n):] is non empty non trivial Relation-like non finite set
bool [:[:REAL, the carrier of (REAL-US n):], the carrier of (REAL-US n):] is non empty non trivial non finite set
the Mult of (REAL-US n) . ((p . (q /. u0)),(q /. u0)) is set
[(p . (q /. u0)),(q /. u0)] is non empty set
{(p . (q /. u0)),(q /. u0)} is non empty finite set
{(p . (q /. u0))} is non empty trivial finite 1 -element V126() V127() V128() set
{{(p . (q /. u0)),(q /. u0)},{(p . (q /. u0))}} is non empty finite V39() set
the Mult of (REAL-US n) . [(p . (q /. u0)),(q /. u0)] is set
(p . (q /. u0)) * (q /. u0) is Relation-like Function-like set
(p . (q /. u0)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] ((p . (q /. u0)),(id REAL)) is set
(q /. u0) (#) ((p . (q /. u0)) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
(Sgm (rng I)) . u0 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
B3 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,B3) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
bq is set
I . bq is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
x3 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
I . x3 is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
aq is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
I . aq is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
j is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,j) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
j is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,j) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
q . u0 is set
(Sgm (rng I)) . u0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
(I ") . ((Sgm (rng I)) . u0) is set
u2 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,u2) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
{ b1 where b1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n) : not p . b1 = 0 } is set
u2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
p . u2 is V11() V12() ext-real Element of REAL
I . (n,B3) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
(I ") . (I . (n,B3)) is set
((Sgm (rng I)) (#) (I ")) . u0 is set
u2 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,u2) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(Sgm (rng I)) " is Relation-like Function-like set
((Sgm (rng I)) ") . (I . (n,B3)) is set
u2 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n,u2) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(Sgm (rng I)) . (((Sgm (rng I)) ") . (I . (n,B3))) is ordinal natural V11() V12() ext-real non negative finite cardinal Element of REAL
(I ") . ((Sgm (rng I)) . (((Sgm (rng I)) ") . (I . (n,B3)))) is set
dom ((Sgm (rng I)) ") is set
rng ((Sgm (rng I)) ") is set
p . (((Sgm (rng I)) (#) (I ")) . u0) is V11() V12() ext-real Element of REAL
p . (n,B3) is V11() V12() ext-real Element of REAL
|(B,(n,B3))| is V11() V12() ext-real Element of REAL
mlt (B,(n,B3)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B,(n,B3)) is set
Sum (mlt (B,(n,B3))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B,(n,B3))),addreal) is V11() V12() ext-real Element of REAL
u2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
p . u2 is V11() V12() ext-real Element of REAL
|(B,(n,B3))| * (n,B3) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(B,(n,B3))| multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (|(B,(n,B3))|,(id REAL)) is set
(n,B3) (#) (|(B,(n,B3))| multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
(n,B) . ((Sgm (rng I)) . u0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((Sgm (rng I)) (#) (n,B)) . u0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(n,(n,B)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u0 is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
(n,u0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
Sum u4 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
len q is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
p (#) q is Relation-like NAT -defined the carrier of (REAL-US n) -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (REAL-US n)
Sum (p (#) q) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
p0 is Relation-like the carrier of (REAL-US n) -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Linear_Combination of B0
Sum p0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
RealVectSpace (Seg n) is non empty right_complementable constituted-Functions constituted-FinSeqs strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ((Seg n),REAL) is non empty functional FUNCTION_DOMAIN of Seg n, REAL
RealFuncZero (Seg n) is Relation-like Seg n -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of Funcs ((Seg n),REAL)
(Seg n) --> 0 is Relation-like Seg n -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),NAT:]
[:(Seg n),NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),NAT:] is non empty set
RealFuncAdd (Seg n) is non empty Relation-like [:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] is non empty Relation-like set
[:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty Relation-like set
bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty set
RealFuncExtMult (Seg n) is non empty Relation-like [:REAL,(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:REAL,(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
[:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial non finite set
RLSStruct(# (Funcs ((Seg n),REAL)),(RealFuncZero (Seg n)),(RealFuncAdd (Seg n)),(RealFuncExtMult (Seg n)) #) is strict RLSStruct
the carrier of (RealVectSpace (Seg n)) is non empty set
bool the carrier of (RealVectSpace (Seg n)) is non empty set
(n) is functional finite FinSequence-membered () () () (n) (n) Element of bool (REAL n)
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
{ (n,b1) where b1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
B is Element of bool the carrier of (RealVectSpace (Seg n))
Lin B is non empty right_complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of RealVectSpace (Seg n)
the carrier of (Lin B) is non empty set
{ (Sum b1) where b1 is Relation-like the carrier of (RealVectSpace (Seg n)) -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Linear_Combination of B : verum } is set
D0 is set
I is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
x0 is Relation-like the carrier of (RealVectSpace (Seg n)) -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Linear_Combination of B
Sum x0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
D0 is set
I is Relation-like the carrier of (RealVectSpace (Seg n)) -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Linear_Combination of B
Sum I is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
B is linearly-independent () () () Element of bool the carrier of (RealVectSpace (Seg n))
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
RealVectSpace (Seg n) is non empty right_complementable constituted-Functions constituted-FinSeqs strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ((Seg n),REAL) is non empty functional FUNCTION_DOMAIN of Seg n, REAL
RealFuncZero (Seg n) is Relation-like Seg n -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of Funcs ((Seg n),REAL)
(Seg n) --> 0 is Relation-like Seg n -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),NAT:]
[:(Seg n),NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),NAT:] is non empty set
RealFuncAdd (Seg n) is non empty Relation-like [:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] is non empty Relation-like set
[:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty Relation-like set
bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty set
RealFuncExtMult (Seg n) is non empty Relation-like [:REAL,(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:REAL,(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
[:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial non finite set
RLSStruct(# (Funcs ((Seg n),REAL)),(RealFuncZero (Seg n)),(RealFuncAdd (Seg n)),(RealFuncExtMult (Seg n)) #) is strict RLSStruct
the carrier of (RealVectSpace (Seg n)) is non empty set
bool the carrier of (RealVectSpace (Seg n)) is non empty set
(n) is functional finite FinSequence-membered () () () (n) (n) Element of bool (REAL n)
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
{ (n,b1) where b1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
B is Element of bool the carrier of (RealVectSpace (Seg n))
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
RealVectSpace (Seg n) is non empty right_complementable constituted-Functions constituted-FinSeqs strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital finite-dimensional RLSStruct
Funcs ((Seg n),REAL) is non empty functional FUNCTION_DOMAIN of Seg n, REAL
RealFuncZero (Seg n) is Relation-like Seg n -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of Funcs ((Seg n),REAL)
(Seg n) --> 0 is Relation-like Seg n -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),NAT:]
[:(Seg n),NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),NAT:] is non empty set
RealFuncAdd (Seg n) is non empty Relation-like [:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] is non empty Relation-like set
[:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty Relation-like set
bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty set
RealFuncExtMult (Seg n) is non empty Relation-like [:REAL,(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:REAL,(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
[:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial non finite set
RLSStruct(# (Funcs ((Seg n),REAL)),(RealFuncZero (Seg n)),(RealFuncAdd (Seg n)),(RealFuncExtMult (Seg n)) #) is strict RLSStruct
dim (RealVectSpace (Seg n)) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
the carrier of (RealVectSpace (Seg n)) is non empty set
bool the carrier of (RealVectSpace (Seg n)) is non empty set
(n) is functional finite FinSequence-membered () () () (n) (n) Element of bool (REAL n)
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
{ (n,b1) where b1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
B0 is Basis of RealVectSpace (Seg n)
card B0 is ordinal cardinal set
B is Element of bool the carrier of (RealVectSpace (Seg n))
card B is ordinal cardinal set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
RealVectSpace (Seg n) is non empty right_complementable constituted-Functions constituted-FinSeqs strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital finite-dimensional RLSStruct
Funcs ((Seg n),REAL) is non empty functional FUNCTION_DOMAIN of Seg n, REAL
RealFuncZero (Seg n) is Relation-like Seg n -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of Funcs ((Seg n),REAL)
(Seg n) --> 0 is Relation-like Seg n -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),NAT:]
[:(Seg n),NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),NAT:] is non empty set
RealFuncAdd (Seg n) is non empty Relation-like [:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] is non empty Relation-like set
[:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty Relation-like set
bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty set
RealFuncExtMult (Seg n) is non empty Relation-like [:REAL,(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:REAL,(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
[:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial non finite set
RLSStruct(# (Funcs ((Seg n),REAL)),(RealFuncZero (Seg n)),(RealFuncAdd (Seg n)),(RealFuncExtMult (Seg n)) #) is strict RLSStruct
the carrier of (RealVectSpace (Seg n)) is non empty set
bool the carrier of (RealVectSpace (Seg n)) is non empty set
B is Element of bool the carrier of (RealVectSpace (Seg n))
card B is ordinal cardinal set
(n) is functional finite FinSequence-membered () () () (n) (n) Element of bool (REAL n)
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
{ (n,b1) where b1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
B0 is Element of bool the carrier of (RealVectSpace (Seg n))
card B0 is ordinal cardinal set
Seg 0 is empty trivial proper ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional finite finite-yielding V39() cardinal 0 -element {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() () () () Element of bool NAT
RealVectSpace (Seg 0) is non empty right_complementable constituted-Functions constituted-FinSeqs strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital finite-dimensional RLSStruct
Funcs ((Seg 0),REAL) is non empty functional FUNCTION_DOMAIN of Seg 0, REAL
RealFuncZero (Seg 0) is empty trivial ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding Seg 0 -defined REAL -valued Function-like one-to-one constant functional total quasi_total finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() () () () Element of Funcs ((Seg 0),REAL)
(Seg 0) --> 0 is empty trivial non proper ordinal T-Sequence-like natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding Seg 0 -defined NAT -valued RAT -valued INT -valued Function-like one-to-one constant functional total quasi_total finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() () () () Element of bool [:(Seg 0),NAT:]
[:(Seg 0),NAT:] is empty trivial ordinal natural V11() V12() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined RAT -valued INT -valued Function-like one-to-one constant functional finite finite-yielding V39() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing V126() V127() V128() V129() V130() V131() V132() () () () set
bool [:(Seg 0),NAT:] is non empty finite V39() set
RealFuncAdd (Seg 0) is non empty Relation-like [:(Funcs ((Seg 0),REAL)),(Funcs ((Seg 0),REAL)):] -defined Funcs ((Seg 0),REAL) -valued Function-like total quasi_total Element of bool [:[:(Funcs ((Seg 0),REAL)),(Funcs ((Seg 0),REAL)):],(Funcs ((Seg 0),REAL)):]
[:(Funcs ((Seg 0),REAL)),(Funcs ((Seg 0),REAL)):] is non empty Relation-like set
[:[:(Funcs ((Seg 0),REAL)),(Funcs ((Seg 0),REAL)):],(Funcs ((Seg 0),REAL)):] is non empty Relation-like set
bool [:[:(Funcs ((Seg 0),REAL)),(Funcs ((Seg 0),REAL)):],(Funcs ((Seg 0),REAL)):] is non empty set
RealFuncExtMult (Seg 0) is non empty Relation-like [:REAL,(Funcs ((Seg 0),REAL)):] -defined Funcs ((Seg 0),REAL) -valued Function-like total quasi_total Element of bool [:[:REAL,(Funcs ((Seg 0),REAL)):],(Funcs ((Seg 0),REAL)):]
[:REAL,(Funcs ((Seg 0),REAL)):] is non empty non trivial Relation-like non finite set
[:[:REAL,(Funcs ((Seg 0),REAL)):],(Funcs ((Seg 0),REAL)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(Funcs ((Seg 0),REAL)):],(Funcs ((Seg 0),REAL)):] is non empty non trivial non finite set
RLSStruct(# (Funcs ((Seg 0),REAL)),(RealFuncZero (Seg 0)),(RealFuncAdd (Seg 0)),(RealFuncExtMult (Seg 0)) #) is strict RLSStruct
the carrier of (RealVectSpace (Seg 0)) is non empty set
bool the carrier of (RealVectSpace (Seg 0)) is non empty set
n is finite Element of bool the carrier of (RealVectSpace (Seg 0))
card n is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of omega
n is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(n) is functional finite FinSequence-membered () () () (n) (n) Element of bool (REAL n)
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
{ (n,b1) where b1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
REAL-US n is non empty right_complementable constituted-Functions constituted-FinSeqs Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V194() V195() L17()
the carrier of (REAL-US n) is non empty set
bool the carrier of (REAL-US n) is non empty set
B is Element of bool the carrier of (REAL-US n)
Lin B is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V194() V195() M37( REAL-US n)
the carrier of (Lin B) is non empty set
{ (Sum b1) where b1 is Relation-like the carrier of (REAL-US n) -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Linear_Combination of B : verum } is set
B is set
D0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
I is Relation-like the carrier of (REAL-US n) -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Linear_Combination of B
Sum I is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
B is set
D0 is Relation-like the carrier of (REAL-US n) -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Linear_Combination of B
Sum D0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (REAL-US n)
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
RealVectSpace (Seg n) is non empty right_complementable constituted-Functions constituted-FinSeqs strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital finite-dimensional RLSStruct
Funcs ((Seg n),REAL) is non empty functional FUNCTION_DOMAIN of Seg n, REAL
RealFuncZero (Seg n) is Relation-like Seg n -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of Funcs ((Seg n),REAL)
(Seg n) --> 0 is Relation-like Seg n -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),NAT:]
[:(Seg n),NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),NAT:] is non empty set
RealFuncAdd (Seg n) is non empty Relation-like [:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] is non empty Relation-like set
[:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty Relation-like set
bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty set
RealFuncExtMult (Seg n) is non empty Relation-like [:REAL,(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:REAL,(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
[:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial non finite set
RLSStruct(# (Funcs ((Seg n),REAL)),(RealFuncZero (Seg n)),(RealFuncAdd (Seg n)),(RealFuncExtMult (Seg n)) #) is strict RLSStruct
B is functional FinSequence-membered () () () (n) (n) Element of bool (REAL n)
the carrier of (RealVectSpace (Seg n)) is non empty set
bool the carrier of (RealVectSpace (Seg n)) is non empty set
B is linearly-independent () () () Element of bool the carrier of (RealVectSpace (Seg n))
I is Basis of RealVectSpace (Seg n)
card I is ordinal cardinal set
D0 is functional FinSequence-membered () () () Element of bool (REAL n)
x0 is functional FinSequence-membered () () () Element of bool (REAL n)
Lin B is non empty right_complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of RealVectSpace (Seg n)
the carrier of (Lin B) is non empty set
x0 is set
p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng p is finite set
len p is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(len p) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
p0 is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
z0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
0* n is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
n |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
(Seg n) --> 0 is Relation-like Seg n -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),{0}:]
[:(Seg n),{0}:] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),{0}:] is non empty finite V39() set
q is ordinal natural V11() V12() ext-real non negative finite cardinal set
p0 /. q is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
q + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
p0 /. (q + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
u4 is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
len u4 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
u4 . q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
u4 . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
u4 is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
len u4 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
u4 . q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
u4 . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
u4 /. q is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
u0 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
B3 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(u0,B3)| is V11() V12() ext-real Element of REAL
mlt (u0,B3) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (u0,B3) is set
Sum (mlt (u0,B3)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (u0,B3)),addreal) is V11() V12() ext-real Element of REAL
|(u0,B3)| * (p0 /. q) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(u4 /. q) - (|(u0,B3)| * (p0 /. q)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
<*((u4 /. q) - (|(u0,B3)| * (p0 /. q)))*> is non empty trivial Relation-like NAT -defined REAL n -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL n
aq is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
u4 ^ aq is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like Element of (REAL n) *
(REAL n) * is non empty functional FinSequence-membered FinSequenceSet of REAL n
Seg (len u4) is finite len u4 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
dom u4 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
bq is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
bq . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom p is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
p . (q + 1) is set
len bq is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
len aq is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
(len u4) + (len aq) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
x3 is ordinal natural V11() V12() ext-real non negative finite cardinal set
bq /. x3 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
p0 /. x3 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
x3 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
bq /. (x3 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
bq . (x3 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
j is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u2 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(j,u2)| is V11() V12() ext-real Element of REAL
mlt (j,u2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (j,u2) is set
Sum (mlt (j,u2)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (j,u2)),addreal) is V11() V12() ext-real Element of REAL
|(j,u2)| * (p0 /. x3) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(bq /. x3) - (|(j,u2)| * (p0 /. x3)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u4 . (x3 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
u4 /. (x3 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
bq . x3 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
u4 . x3 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
u4 /. x3 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
bq . (q + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(q + 1) - (len u4) is V11() V12() ext-real Element of REAL
aq . ((q + 1) - (len u4)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
((u4 /. q) - (|(u0,B3)| * (p0 /. q))) + (|(u0,B3)| * (p0 /. q)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
addreal .: (((u4 /. q) - (|(u0,B3)| * (p0 /. q))),(|(u0,B3)| * (p0 /. q))) is set
bq /. q is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
bq . q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
x3 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
j is V11() V12() ext-real Element of REAL
j * x3 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
the Mult of (RealVectSpace (Seg n)) is non empty Relation-like [:REAL, the carrier of (RealVectSpace (Seg n)):] -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like total quasi_total Element of bool [:[:REAL, the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):]
[:REAL, the carrier of (RealVectSpace (Seg n)):] is non empty non trivial Relation-like non finite set
[:[:REAL, the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL, the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty non trivial non finite set
the Mult of (RealVectSpace (Seg n)) . (j,x3) is set
[j,x3] is non empty set
{j,x3} is non empty finite set
{j} is non empty trivial finite 1 -element V126() V127() V128() set
{{j,x3},{j}} is non empty finite V39() set
the Mult of (RealVectSpace (Seg n)) . [j,x3] is set
j * x3 is Relation-like Function-like set
j multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (j,(id REAL)) is set
x3 (#) (j multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
{x3} is non empty trivial functional finite V39() 1 -element Element of bool the carrier of (RealVectSpace (Seg n))
u2 is set
Lin {x3} is non empty right_complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of RealVectSpace (Seg n)
the carrier of (Lin {x3}) is non empty set
x3 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
j is V11() V12() ext-real Element of REAL
j * x3 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
j multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (j,(id REAL)) is set
x3 (#) (j multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
u2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
j * u2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (RealVectSpace (Seg n))
the Mult of (RealVectSpace (Seg n)) is non empty Relation-like [:REAL, the carrier of (RealVectSpace (Seg n)):] -defined the carrier of (RealVectSpace (Seg n)) -valued Function-like total quasi_total Element of bool [:[:REAL, the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):]
[:REAL, the carrier of (RealVectSpace (Seg n)):] is non empty non trivial Relation-like non finite set
[:[:REAL, the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL, the carrier of (RealVectSpace (Seg n)):], the carrier of (RealVectSpace (Seg n)):] is non empty non trivial non finite set
the Mult of (RealVectSpace (Seg n)) . (j,u2) is set
[j,u2] is non empty set
{j,u2} is non empty finite set
{j} is non empty trivial finite 1 -element V126() V127() V128() set
{{j,u2},{j}} is non empty finite V39() set
the Mult of (RealVectSpace (Seg n)) . [j,u2] is set
j * u2 is Relation-like Function-like set
u2 (#) (j multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
x3 is ordinal natural V11() V12() ext-real non negative finite cardinal set
x3 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
bq . (x3 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(x3 + 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
bq . ((x3 + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(x3 + 1) + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
bq . ((x3 + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
j is set
dom p0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
p0 . (x3 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
p0 /. (x3 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
bq /. ((x3 + 1) + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
|(u0,B3)| * (p0 /. (x3 + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(bq /. ((x3 + 1) + 1)) + (|(u0,B3)| * (p0 /. (x3 + 1))) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u4 /. (x3 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
u4 . (x3 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
u4 /. (x3 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
p0 /. (x3 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
u4 /. ((x3 + 1) + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
u4 . ((x3 + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len p0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
p0 . (x3 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom p0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
j is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u2 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(j,u2)| is V11() V12() ext-real Element of REAL
mlt (j,u2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (j,u2) is set
Sum (mlt (j,u2)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (j,u2)),addreal) is V11() V12() ext-real Element of REAL
|(j,u2)| * (p0 /. (x3 + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(u4 /. (x3 + 1)) - (|(j,u2)| * (p0 /. (x3 + 1))) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(u4 /. ((x3 + 1) + 1)) + (|(j,u2)| * (p0 /. (x3 + 1))) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u4 . (x3 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
bq . (0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
bq . (q + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
x3 is V11() V12() ext-real Element of REAL
x3 * (p0 /. (q + 1)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
<*z0*> is non empty trivial Relation-like NAT -defined REAL n -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL n
u4 is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
len u4 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
u4 . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
p0 /. 1 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
u0 is V11() V12() ext-real Element of REAL
u0 * (p0 /. 1) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
dom p0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
p0 . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
u0 is ordinal natural V11() V12() ext-real non negative finite cardinal set
B3 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u4 /. u0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
aq is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
p0 /. u0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
u0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
u4 /. (u0 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
u4 . (u0 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
|(B3,aq)| is V11() V12() ext-real Element of REAL
mlt (B3,aq) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (B3,aq) is set
Sum (mlt (B3,aq)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (B3,aq)),addreal) is V11() V12() ext-real Element of REAL
|(B3,aq)| * (p0 /. u0) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(u4 /. u0) - (|(B3,aq)| * (p0 /. u0)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
p0 /. 0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
p0 /. ((len p) + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
q is Relation-like NAT -defined REAL n -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of REAL n
len q is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
q . ((len p) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
q . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
q /. (len q) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
u4 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|.u4.| is V11() V12() ext-real non negative Element of REAL
sqr u4 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
u4 (#) sqrreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
mlt (u4,u4) is Relation-like Function-like set
multreal .: (u4,u4) is set
Sum (sqr u4) is V11() V12() ext-real Element of REAL
K608(REAL,(sqr u4),addreal) is V11() V12() ext-real Element of REAL
sqrt (Sum (sqr u4)) is V11() V12() ext-real Element of REAL
1 / |.u4.| is V11() V12() ext-real non negative Element of REAL
(1 / |.u4.|) * u4 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(1 / |.u4.|) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] ((1 / |.u4.|),(id REAL)) is set
u4 (#) ((1 / |.u4.|) multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
{((1 / |.u4.|) * u4)} is non empty trivial functional finite V39() 1 -element FinSequence-membered Element of bool (REAL n)
B \/ {((1 / |.u4.|) * u4)} is non empty set
aq is ordinal natural V11() V12() ext-real non negative finite cardinal set
p0 /. aq is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
bq is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(bq,u4)| is V11() V12() ext-real Element of REAL
mlt (bq,u4) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (bq,u4) is set
Sum (mlt (bq,u4)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (bq,u4)),addreal) is V11() V12() ext-real Element of REAL
x3 is ordinal natural V11() V12() ext-real non negative finite cardinal set
q /. x3 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
x3 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
q /. (x3 + 1) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
j is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u2 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(j,u2)| is V11() V12() ext-real Element of REAL
mlt (j,u2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (j,u2) is set
Sum (mlt (j,u2)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (j,u2)),addreal) is V11() V12() ext-real Element of REAL
k2 is ordinal natural V11() V12() ext-real non negative finite cardinal set
p0 /. k2 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
p0 /. x3 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
q . (x3 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
0 + 1 is non empty ordinal natural V11() V12() ext-real positive non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
a is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
b is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(a,b)| is V11() V12() ext-real Element of REAL
mlt (a,b) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (a,b) is set
Sum (mlt (a,b)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (a,b)),addreal) is V11() V12() ext-real Element of REAL
|(a,b)| * (p0 /. x3) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
(q /. x3) - (|(a,b)| * (p0 /. x3)) is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(j,a)| is V11() V12() ext-real Element of REAL
mlt (j,a) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (j,a) is set
Sum (mlt (j,a)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (j,a)),addreal) is V11() V12() ext-real Element of REAL
|(a,b)| * b is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(a,b)| multreal is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (|(a,b)|,(id REAL)) is set
b (#) (|(a,b)| multreal) is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
|(j,(|(a,b)| * b))| is V11() V12() ext-real Element of REAL
mlt (j,(|(a,b)| * b)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (j,(|(a,b)| * b)) is set
Sum (mlt (j,(|(a,b)| * b))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (j,(|(a,b)| * b))),addreal) is V11() V12() ext-real Element of REAL
|(j,a)| - |(j,(|(a,b)| * b))| is V11() V12() ext-real Element of REAL
|(j,b)| is V11() V12() ext-real Element of REAL
mlt (j,b) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (j,b) is set
Sum (mlt (j,b)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (j,b)),addreal) is V11() V12() ext-real Element of REAL
|(a,b)| * |(j,b)| is V11() V12() ext-real Element of REAL
|(j,a)| - (|(a,b)| * |(j,b)|) is V11() V12() ext-real Element of REAL
p0 . x3 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len p0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len p0) is finite len p0 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
dom p0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
p0 . k2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len p0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len p0) is finite len p0 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
dom p0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
p0 . x3 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng p0 is functional finite FinSequence-membered Element of bool (REAL n)
|.b.| is V11() V12() ext-real non negative Element of REAL
sqr b is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
b (#) sqrreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
mlt (b,b) is Relation-like Function-like set
multreal .: (b,b) is set
Sum (sqr b) is V11() V12() ext-real Element of REAL
K608(REAL,(sqr b),addreal) is V11() V12() ext-real Element of REAL
sqrt (Sum (sqr b)) is V11() V12() ext-real Element of REAL
|.b.| ^2 is V11() V12() ext-real Element of REAL
K37(|.b.|,|.b.|) is V11() V12() ext-real non negative set
|(b,a)| is V11() V12() ext-real Element of REAL
mlt (b,a) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (b,a) is set
Sum (mlt (b,a)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (b,a)),addreal) is V11() V12() ext-real Element of REAL
|(a,b)| * 1 is V11() V12() ext-real Element of REAL
|(b,a)| - (|(a,b)| * 1) is V11() V12() ext-real Element of REAL
u2 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
k2 is ordinal natural V11() V12() ext-real non negative finite cardinal set
p0 /. k2 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
j is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(j,u2)| is V11() V12() ext-real Element of REAL
mlt (j,u2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (j,u2) is set
Sum (mlt (j,u2)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (j,u2)),addreal) is V11() V12() ext-real Element of REAL
q /. 0 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
j is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
u2 is ordinal natural V11() V12() ext-real non negative finite cardinal set
p0 /. u2 is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
x3 is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(x3,j)| is V11() V12() ext-real Element of REAL
mlt (x3,j) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (x3,j) is set
Sum (mlt (x3,j)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (x3,j)),addreal) is V11() V12() ext-real Element of REAL
aq is ordinal natural V11() V12() ext-real non negative finite cardinal set
p0 /. aq is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
bq is Relation-like NAT -defined REAL -valued Function-like finite n -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL n
|(bq,((1 / |.u4.|) * u4))| is V11() V12() ext-real Element of REAL
mlt (bq,((1 / |.u4.|) * u4)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (bq,((1 / |.u4.|) * u4)) is set
Sum (mlt (bq,((1 / |.u4.|) * u4))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (bq,((1 / |.u4.|) * u4))),addreal) is V11() V12() ext-real Element of REAL
|(bq,u4)| is V11() V12() ext-real Element of REAL
mlt (bq,u4) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (bq,u4) is set
Sum (mlt (bq,u4)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (bq,u4)),addreal) is V11() V12() ext-real Element of REAL
(1 / |.u4.|) * |(bq,u4)| is V11() V12() ext-real Element of REAL
B3 is functional FinSequence-membered Element of bool (REAL n)
aq is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
bq is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
|(aq,bq)| is V11() V12() ext-real Element of REAL
mlt (aq,bq) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
multreal .: (aq,bq) is set
Sum (mlt (aq,bq)) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (aq,bq)),addreal) is V11() V12() ext-real Element of REAL
dom p0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
x3 is set
p0 . x3 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len p0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len p0) is finite len p0 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
j is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
p0 /. j is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
dom p0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
x3 is set
p0 . x3 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len p0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len p0) is finite len p0 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
j is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
p0 /. j is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
dom p is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
q /. (len p) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
p0 /. (len p) is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
abs (1 / |.u4.|) is V11() V12() ext-real Element of REAL
|.((1 / |.u4.|) * u4).| is V11() V12() ext-real non negative Element of REAL
sqr ((1 / |.u4.|) * u4) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 / |.u4.|) * u4) (#) sqrreal is Relation-like NAT -defined REAL -valued Function-like finite complex-yielding ext-real-valued real-valued set
mlt (((1 / |.u4.|) * u4),((1 / |.u4.|) * u4)) is Relation-like Function-like set
multreal .: (((1 / |.u4.|) * u4),((1 / |.u4.|) * u4)) is set
Sum (sqr ((1 / |.u4.|) * u4)) is V11() V12() ext-real Element of REAL
K608(REAL,(sqr ((1 / |.u4.|) * u4)),addreal) is V11() V12() ext-real Element of REAL
sqrt (Sum (sqr ((1 / |.u4.|) * u4))) is V11() V12() ext-real Element of REAL
(abs (1 / |.u4.|)) * |.u4.| is V11() V12() ext-real Element of REAL
dom p0 is finite V126() V127() V128() V129() V130() V131() Element of bool NAT
x3 is set
p0 . x3 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len p0 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
Seg (len p0) is finite len p0 -element V126() V127() V128() V129() V130() V131() Element of bool NAT
j is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
p0 /. j is Relation-like NAT -defined Function-like finite n -element FinSequence-like FinSubsequence-like Element of REAL n
|(((1 / |.u4.|) * u4),((1 / |.u4.|) * u4))| is V11() V12() ext-real Element of REAL
mlt (((1 / |.u4.|) * u4),((1 / |.u4.|) * u4)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
Sum (mlt (((1 / |.u4.|) * u4),((1 / |.u4.|) * u4))) is V11() V12() ext-real Element of REAL
K608(REAL,(mlt (((1 / |.u4.|) * u4),((1 / |.u4.|) * u4))),addreal) is V11() V12() ext-real Element of REAL
Lin I is non empty right_complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of RealVectSpace (Seg n)
the carrier of (Lin I) is non empty set
n is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
REAL-US n is non empty right_complementable constituted-Functions constituted-FinSeqs Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V194() V195() L17()
the carrier of (REAL-US n) is non empty set
bool the carrier of (REAL-US n) is non empty set
(n) is functional finite FinSequence-membered () () () (n) (n) Element of bool (REAL n)
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
{ (n,b1) where b1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
B is Element of bool the carrier of (REAL-US n)
n is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
REAL-US n is non empty right_complementable constituted-Functions constituted-FinSeqs Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V194() V195() finite-dimensional L17()
dim (REAL-US n) is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT
the carrier of (REAL-US n) is non empty set
bool the carrier of (REAL-US n) is non empty set
(n) is functional finite FinSequence-membered () () () (n) (n) Element of bool (REAL n)
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
{ (n,b1) where b1 is ordinal natural V11() V12() ext-real non negative V33() V34() finite cardinal V126() V127() V128() V129() V130() V131() Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
B0 is Basis of REAL-US n
card B0 is ordinal cardinal set
B is Element of bool the carrier of (REAL-US n)
card B is ordinal cardinal set
n is ordinal natural V11() V12() ext-real non negative finite cardinal set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like Element of REAL * : len b1 = n } is set
bool (REAL n) is non empty set
B is functional FinSequence-membered () () () (n) (n) Element of bool (REAL n)
card B is ordinal cardinal set
Seg n is finite n -element V126() V127() V128() V129() V130() V131() Element of bool NAT
RealVectSpace (Seg n) is non empty right_complementable constituted-Functions constituted-FinSeqs strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital finite-dimensional RLSStruct
Funcs ((Seg n),REAL) is non empty functional FUNCTION_DOMAIN of Seg n, REAL
RealFuncZero (Seg n) is Relation-like Seg n -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of Funcs ((Seg n),REAL)
(Seg n) --> 0 is Relation-like Seg n -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(Seg n),NAT:]
[:(Seg n),NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:(Seg n),NAT:] is non empty set
RealFuncAdd (Seg n) is non empty Relation-like [:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):] is non empty Relation-like set
[:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty Relation-like set
bool [:[:(Funcs ((Seg n),REAL)),(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty set
RealFuncExtMult (Seg n) is non empty Relation-like [:REAL,(Funcs ((Seg n),REAL)):] -defined Funcs ((Seg n),REAL) -valued Function-like total quasi_total Element of bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):]
[:REAL,(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
[:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial Relation-like non finite set
bool [:[:REAL,(Funcs ((Seg n),REAL)):],(Funcs ((Seg n),REAL)):] is non empty non trivial non finite set
RLSStruct(# (Funcs ((Seg n),REAL)),(RealFuncZero (Seg n)),(RealFuncAdd (Seg n)),(RealFuncExtMult (Seg n)) #) is strict RLSStruct
the carrier of (RealVectSpace (Seg n)) is non empty set
bool the carrier of (RealVectSpace (Seg n)) is non empty set
B0 is Element of bool the carrier of (RealVectSpace (Seg n))