REAL is non empty V33() V167() V168() V169() V173() set
NAT is non empty epsilon-transitive epsilon-connected ordinal V33() V38() V39() V167() V168() V169() V170() V171() V172() V173() Element of bool REAL
bool REAL is V33() set
INT is non empty V33() V167() V168() V169() V170() V171() V173() set
COMPLEX is non empty V33() V167() V173() set
RAT is non empty V33() V167() V168() V169() V170() V173() set
[:COMPLEX,COMPLEX:] is V33() complex-yielding set
bool [:COMPLEX,COMPLEX:] is V33() set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is V33() complex-yielding set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is V33() set
[:REAL,REAL:] is V33() complex-yielding V158() V159() set
bool [:REAL,REAL:] is V33() set
[:[:REAL,REAL:],REAL:] is V33() complex-yielding V158() V159() set
bool [:[:REAL,REAL:],REAL:] is V33() set
[:RAT,RAT:] is RAT -valued V33() complex-yielding V158() V159() set
bool [:RAT,RAT:] is V33() set
[:[:RAT,RAT:],RAT:] is RAT -valued V33() complex-yielding V158() V159() set
bool [:[:RAT,RAT:],RAT:] is V33() set
[:INT,INT:] is RAT -valued INT -valued V33() complex-yielding V158() V159() set
bool [:INT,INT:] is V33() set
[:[:INT,INT:],INT:] is RAT -valued INT -valued V33() complex-yielding V158() V159() set
bool [:[:INT,INT:],INT:] is V33() set
[:NAT,NAT:] is RAT -valued INT -valued V33() complex-yielding V158() V159() V160() set
[:[:NAT,NAT:],NAT:] is RAT -valued INT -valued V33() complex-yielding V158() V159() V160() set
bool [:[:NAT,NAT:],NAT:] is V33() set
omega is non empty epsilon-transitive epsilon-connected ordinal V33() V38() V39() V167() V168() V169() V170() V171() V172() V173() set
bool omega is V33() set
bool NAT is V33() set
1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
{} is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural functional V33() V38() V40( {} ) FinSequence-membered ext-real non positive non negative V167() V168() V169() V170() V171() V172() V173() set
F_Real is non empty non degenerated non trivial V71() V91() V94() V114() V116() V118() V121() V122() V123() right-distributive left-distributive right_unital well-unital V135() left_unital L11()
the carrier of F_Real is non empty non trivial V167() V168() V169() set
the carrier of F_Real * is non empty functional FinSequence-membered FinSequenceSet of the carrier of F_Real
REAL * is non empty functional FinSequence-membered FinSequenceSet of REAL
3 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real functional V30() V31() V33() V38() V40( {} ) FinSequence-membered ext-real non positive non negative V167() V168() V169() V170() V171() V172() V173() Element of NAT
[:NAT,REAL:] is V33() complex-yielding V158() V159() set
bool [:NAT,REAL:] is V33() set
addreal is Relation-like [:REAL,REAL:] -defined REAL -valued Function-like V27([:REAL,REAL:], REAL ) complex-yielding V158() V159() Element of bool [:[:REAL,REAL:],REAL:]
multreal is Relation-like [:REAL,REAL:] -defined REAL -valued Function-like V27([:REAL,REAL:], REAL ) complex-yielding V158() V159() Element of bool [:[:REAL,REAL:],REAL:]
G11(REAL,addreal,multreal,1,0) is V94() L11()
Seg 1 is non empty trivial V33() V40(1) V167() V168() V169() V170() V171() V172() Element of bool NAT
{1} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
Seg 2 is non empty V33() V40(2) V167() V168() V169() V170() V171() V172() Element of bool NAT
{1,2} is non empty V167() V168() V169() V170() V171() V172() set
<*> REAL is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Relation-like NAT -defined REAL -valued Function-like functional V33() V38() V40( {} ) FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-yielding V158() V159() V160() V167() V168() V169() V170() V171() V172() V173() FinSequence of REAL
Sum (<*> REAL) is V11() real ext-real Element of REAL
P1 is set
P1 * is non empty functional FinSequence-membered FinSequenceSet of P1
P2 is Relation-like NAT -defined P1 * -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of P1 *
n2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
P2 . n2 is FinSequence-like set
dom P2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
rng P2 is set
dom P2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
<*> P1 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Relation-like NAT -defined P1 -valued Function-like functional V33() V38() V40( {} ) FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-yielding V158() V159() V160() V167() V168() V169() V170() V171() V172() V173() FinSequence of P1
dom P2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
P1 is real set
<*P1*> is non empty trivial Relation-like NAT -defined Function-like one-to-one V33() V40(1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() V161() V162() V163() V164() set
<*P1*> is non empty trivial Relation-like NAT -defined Function-like one-to-one V33() V40(1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() V161() V162() V163() V164() set
rng <*P1*> is V167() V168() V169() Element of bool REAL
P1 is non empty set
P2 is Element of P1
n2 is non empty epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real positive non negative set
n2 |-> P2 is Relation-like NAT -defined P1 -valued Function-like V33() V40(n2) FinSequence-like FinSubsequence-like Element of n2 -tuples_on P1
n2 -tuples_on P1 is non empty functional FinSequence-membered FinSequenceSet of P1
P1 * is non empty functional FinSequence-membered FinSequenceSet of P1
{ b1 where b1 is Relation-like NAT -defined P1 -valued Function-like V33() FinSequence-like FinSubsequence-like Element of P1 * : len b1 = n2 } is set
Seg n2 is non empty V33() V40(n2) V167() V168() V169() V170() V171() V172() Element of bool NAT
(Seg n2) --> P2 is Relation-like Seg n2 -defined {P2} -valued Function-like V27( Seg n2,{P2}) V33() FinSequence-like FinSubsequence-like Element of bool [:(Seg n2),{P2}:]
{P2} is non empty trivial V40(1) set
[:(Seg n2),{P2}:] is set
bool [:(Seg n2),{P2}:] is set
m is Relation-like NAT -defined P1 -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of P1
len m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom m is V167() V168() V169() V170() V171() V172() Element of bool NAT
dom (n2 |-> P2) is V40(n2) V167() V168() V169() V170() V171() V172() Element of bool NAT
n1 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
m . n1 is set
(n2 |-> P2) . n1 is set
n1 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
m . n1 is set
P1 is non empty set
P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg P2 is V33() V40(P2) V167() V168() V169() V170() V171() V172() Element of bool NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
Seg n2 is V33() V40(n2) V167() V168() V169() V170() V171() V172() Element of bool NAT
m is Element of P1
n1 is Element of P1
P is Relation-like Function-like set
dom P is set
P is Relation-like Function-like set
dom P is set
i is Relation-like NAT -defined Function-like V33() FinSequence-like FinSubsequence-like set
rng i is set
p is set
dom i is V167() V168() V169() V170() V171() V172() Element of bool NAT
p1 is set
i . p1 is set
p is Relation-like NAT -defined P1 -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of P1
len p is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
p1 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
p . p1 is set
P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
dom P1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is Relation-like NAT -defined REAL -valued Function-like V27( NAT , REAL ) complex-yielding V158() V159() Element of bool [:NAT,REAL:]
n2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
P2 . n2 is V11() real ext-real Element of REAL
n2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 . (n2 + 1) is V11() real ext-real Element of REAL
P1 . (n2 + 1) is V11() real ext-real Element of REAL
(P2 . n2) + (P1 . (n2 + 1)) is V11() real ext-real Element of REAL
n2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
P2 . n2 is V11() real ext-real Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 . m is V11() real ext-real Element of REAL
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 . (m + 1) is V11() real ext-real Element of REAL
P2 . m is V11() real ext-real Element of REAL
P2 . (m + 1) is V11() real ext-real Element of REAL
P2 . (m + 1) is V11() real ext-real Element of REAL
P2 . (m + 1) is V11() real ext-real Element of REAL
P2 . (m + 1) is V11() real ext-real Element of REAL
P2 . 0 is V11() real ext-real Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
P2 . m is V11() real ext-real Element of REAL
n2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
m is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
P2 . n2 is V11() real ext-real Element of REAL
P2 . m is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom P1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
P1 . 1 is V11() real ext-real Element of REAL
P2 is Relation-like NAT -defined REAL -valued Function-like V27( NAT , REAL ) complex-yielding V158() V159() Element of bool [:NAT,REAL:]
P2 . 1 is V11() real ext-real Element of REAL
n2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
P1 . n2 is V11() real ext-real Element of REAL
P2 . n2 is V11() real ext-real Element of REAL
n2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 . (n2 + 1) is V11() real ext-real Element of REAL
P2 . (n2 + 1) is V11() real ext-real Element of REAL
P1 . (n2 + 1) is V11() real ext-real Element of REAL
(P2 . n2) + (P1 . (n2 + 1)) is V11() real ext-real Element of REAL
P2 . (n2 + 1) is V11() real ext-real Element of REAL
P1 . (n2 + 1) is V11() real ext-real Element of REAL
P2 . (n2 + 1) is V11() real ext-real Element of REAL
P1 . (n2 + 1) is V11() real ext-real Element of REAL
P2 . (n2 + 1) is V11() real ext-real Element of REAL
P2 . (n2 + 1) is V11() real ext-real Element of REAL
P1 . 0 is V11() real ext-real Element of REAL
P2 . 0 is V11() real ext-real Element of REAL
n2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
P1 . n2 is V11() real ext-real Element of REAL
P2 . n2 is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
dom P1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
Sum P1 is V11() real ext-real Element of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
P1 . P2 is V11() real ext-real Element of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
P1 . P2 is V11() real ext-real Element of REAL
P1 . 1 is V11() real ext-real Element of REAL
m is Relation-like NAT -defined REAL -valued Function-like V27( NAT , REAL ) complex-yielding V158() V159() Element of bool [:NAT,REAL:]
m . 1 is V11() real ext-real Element of REAL
m . (len P1) is V11() real ext-real Element of REAL
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 . n2 is V11() real ext-real Element of REAL
m . n2 is V11() real ext-real Element of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 is V11() real ext-real Element of REAL
P2 is V11() real ext-real Element of REAL
n2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
m is Relation-like NAT -defined REAL -valued Function-like V27( NAT , REAL ) complex-yielding V158() V159() Element of bool [:NAT,REAL:]
n1 is set
P is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
m . P is V11() real ext-real Element of REAL
P is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
m . P is V11() real ext-real Element of REAL
P is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
m . P is V11() real ext-real Element of REAL
i is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
m . i is V11() real ext-real Element of REAL
p is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
m . p is V11() real ext-real Element of REAL
p1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
m . p1 is V11() real ext-real Element of REAL
n1 is Relation-like Function-like set
dom n1 is set
P is set
n1 . P is set
i is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
m . i is V11() real ext-real Element of REAL
P is Relation-like NAT -defined REAL -valued Function-like V27( NAT , REAL ) complex-yielding V158() V159() Element of bool [:NAT,REAL:]
i is Relation-like NAT -defined REAL -valued Function-like V27( NAT , REAL ) complex-yielding V158() V159() Element of bool [:NAT,REAL:]
p is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
i . p is V11() real ext-real Element of REAL
m . p is V11() real ext-real Element of REAL
p1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
i . p1 is V11() real ext-real Element of REAL
e3 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
m . e3 is V11() real ext-real Element of REAL
n1 is Relation-like NAT -defined REAL -valued Function-like V27( NAT , REAL ) complex-yielding V158() V159() Element of bool [:NAT,REAL:]
n1 is Relation-like NAT -defined REAL -valued Function-like V27( NAT , REAL ) complex-yielding V158() V159() Element of bool [:NAT,REAL:]
n1 . 0 is V11() real ext-real Element of REAL
P is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
n1 . P is V11() real ext-real Element of REAL
m . P is V11() real ext-real Element of REAL
i is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
n1 . i is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Sum P1 is V11() real ext-real Element of REAL
NAT --> 0 is T-Sequence-like Relation-like NAT -defined REAL -valued INT -valued RAT -valued Function-like V27( NAT , REAL ) complex-yielding V158() V159() V160() Element of bool [:NAT,REAL:]
n2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
n2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
(NAT --> 0) . (n2 + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative Element of REAL
(NAT --> 0) . n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative Element of REAL
P1 . (n2 + 1) is V11() real ext-real Element of REAL
((NAT --> 0) . n2) + (P1 . (n2 + 1)) is V11() real ext-real Element of REAL
n2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
(NAT --> 0) . n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative Element of REAL
(NAT --> 0) . 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative Element of REAL
(NAT --> 0) . (len P1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative Element of REAL
P1 . 1 is V11() real ext-real Element of REAL
P2 is Relation-like NAT -defined REAL -valued Function-like V27( NAT , REAL ) complex-yielding V158() V159() Element of bool [:NAT,REAL:]
P2 . 1 is V11() real ext-real Element of REAL
P2 . (len P1) is V11() real ext-real Element of REAL
n2 is Relation-like NAT -defined REAL -valued Function-like V27( NAT , REAL ) complex-yielding V158() V159() Element of bool [:NAT,REAL:]
n2 . 0 is V11() real ext-real Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 . (m + 1) is V11() real ext-real Element of REAL
n2 . m is V11() real ext-real Element of REAL
P1 . (m + 1) is V11() real ext-real Element of REAL
(n2 . m) + (P1 . (m + 1)) is V11() real ext-real Element of REAL
P2 . (m + 1) is V11() real ext-real Element of REAL
P2 . m is V11() real ext-real Element of REAL
(P2 . m) + (P1 . (m + 1)) is V11() real ext-real Element of REAL
n2 . (len P1) is V11() real ext-real Element of REAL
P1 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
P2 is set
P2 * is non empty functional FinSequence-membered FinSequenceSet of P2
n2 is Relation-like NAT -defined P2 -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of P2
P1 |-> n2 is Relation-like NAT -defined Function-like V33() V40(P1) FinSequence-like FinSubsequence-like set
Seg P1 is V33() V40(P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
(Seg P1) --> n2 is Relation-like Seg P1 -defined {n2} -valued Function-like V27( Seg P1,{n2}) V33() FinSequence-like FinSubsequence-like Element of bool [:(Seg P1),{n2}:]
{n2} is non empty trivial V40(1) set
[:(Seg P1),{n2}:] is set
bool [:(Seg P1),{n2}:] is set
P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg P1 is V33() V40(P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
Seg P2 is V33() V40(P2) V167() V168() V169() V170() V171() V172() Element of bool NAT
n2 is set
n2 * is non empty functional FinSequence-membered FinSequenceSet of n2
m is Relation-like NAT -defined n2 -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of n2
n1 is Relation-like NAT -defined n2 -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of n2
P1 is set
P1 * is non empty functional FinSequence-membered FinSequenceSet of P1
P2 is Relation-like NAT -defined Function-like V33() FinSequence-like FinSubsequence-like set
dom P2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
n2 is Relation-like NAT -defined P1 * -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of P1 *
rng n2 is set
m is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
dom n2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(P1,n2,n1) is Relation-like NAT -defined P1 -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of P1
P is Relation-like NAT -defined Function-like V33() FinSequence-like FinSubsequence-like set
len P is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
[:NAT,P1:] is set
bool [:NAT,P1:] is set
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 . P is set
n2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
rng P2 is set
m is set
n1 is set
P2 . n1 is set
P is Relation-like NAT -defined P1 -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of P1
len P is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P is Relation-like NAT -defined P1 -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of P1
len P is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
m is set
m is set
P1 is set
P1 * is non empty functional FinSequence-membered FinSequenceSet of P1
P2 is Relation-like NAT -defined P1 * -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of P1 *
dom P2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(P1,P2,m) is Relation-like NAT -defined P1 -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of P1
len (P1,P2,m) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(P1,P2,m) is Relation-like NAT -defined P1 -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of P1
len (P1,P2,m) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n1 is Relation-like NAT -defined P1 -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of P1
len n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
[P1,P2] is set
{P1,P2} is non empty V167() V168() V169() V170() V171() V172() set
{P1} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{P1,P2},{P1}} is non empty set
n2 is Relation-like NAT -defined Function-like V33() FinSequence-like FinSubsequence-like tabular set
Indices n2 is set
len n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len n2) is V33() V40( len n2) V167() V168() V169() V170() V171() V172() Element of bool NAT
width n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (width n2) is V33() V40( width n2) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom n2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
[:(dom n2),(Seg (width n2)):] is INT -valued RAT -valued complex-yielding V158() V159() V160() set
P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
[P1,P2] is set
{P1,P2} is non empty V167() V168() V169() V170() V171() V172() set
{P1} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{P1,P2},{P1}} is non empty set
n2 is non empty set
n2 * is non empty functional FinSequence-membered FinSequenceSet of n2
m is Relation-like NAT -defined n2 * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of n2 *
Indices m is set
dom m is V167() V168() V169() V170() V171() V172() Element of bool NAT
(n2,m,P1) is Relation-like NAT -defined n2 -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of n2
dom (n2,m,P1) is V167() V168() V169() V170() V171() V172() Element of bool NAT
width m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (width m) is V33() V40( width m) V167() V168() V169() V170() V171() V172() Element of bool NAT
len m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len m) is V33() V40( len m) V167() V168() V169() V170() V171() V172() Element of bool NAT
len (n2,m,P1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len (n2,m,P1)) is V33() V40( len (n2,m,P1)) V167() V168() V169() V170() V171() V172() Element of bool NAT
P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
[P1,P2] is set
{P1,P2} is non empty V167() V168() V169() V170() V171() V172() set
{P1} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{P1,P2},{P1}} is non empty set
n2 is non empty set
n2 * is non empty functional FinSequence-membered FinSequenceSet of n2
m is Relation-like NAT -defined n2 * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of n2 *
Indices m is set
m * (P1,P2) is Element of n2
(n2,m,P1) is Relation-like NAT -defined n2 -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of n2
(n2,m,P1) . P2 is set
n1 is Relation-like NAT -defined n2 -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of n2
n1 . P2 is set
P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
[P1,P2] is set
{P1,P2} is non empty V167() V168() V169() V170() V171() V172() set
{P1} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{P1,P2},{P1}} is non empty set
n2 is non empty set
n2 * is non empty functional FinSequence-membered FinSequenceSet of n2
m is Relation-like NAT -defined n2 * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of n2 *
Indices m is set
Col (m,P2) is Relation-like NAT -defined n2 -valued Function-like V33() V40( len m) FinSequence-like FinSubsequence-like Element of (len m) -tuples_on n2
len m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(len m) -tuples_on n2 is non empty functional FinSequence-membered FinSequenceSet of n2
{ b1 where b1 is Relation-like NAT -defined n2 -valued Function-like V33() FinSequence-like FinSubsequence-like Element of n2 * : len b1 = len m } is set
dom (Col (m,P2)) is V40( len m) V167() V168() V169() V170() V171() V172() Element of bool NAT
Line (m,P1) is Relation-like NAT -defined n2 -valued Function-like V33() V40( width m) FinSequence-like FinSubsequence-like Element of (width m) -tuples_on n2
width m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(width m) -tuples_on n2 is non empty functional FinSequence-membered FinSequenceSet of n2
{ b1 where b1 is Relation-like NAT -defined n2 -valued Function-like V33() FinSequence-like FinSubsequence-like Element of n2 * : len b1 = width m } is set
dom (Line (m,P1)) is V40( width m) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom m is V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (len m) is V33() V40( len m) V167() V168() V169() V170() V171() V172() Element of bool NAT
len (Col (m,P2)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len (Col (m,P2))) is V33() V40( len (Col (m,P2))) V167() V168() V169() V170() V171() V172() Element of bool NAT
(n2,m,P1) is Relation-like NAT -defined n2 -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of n2
dom (n2,m,P1) is V167() V168() V169() V170() V171() V172() Element of bool NAT
P1 is non empty set
P1 * is non empty functional FinSequence-membered FinSequenceSet of P1
P2 is non empty set
P2 * is non empty functional FinSequence-membered FinSequenceSet of P2
n2 is Relation-like NAT -defined P1 * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of P1 *
dom n2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
m is Relation-like NAT -defined P2 * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of P2 *
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Line (n2,n1) is Relation-like NAT -defined P1 -valued Function-like V33() V40( width n2) FinSequence-like FinSubsequence-like Element of (width n2) -tuples_on P1
width n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(width n2) -tuples_on P1 is non empty functional FinSequence-membered FinSequenceSet of P1
{ b1 where b1 is Relation-like NAT -defined P1 -valued Function-like V33() FinSequence-like FinSubsequence-like Element of P1 * : len b1 = width n2 } is set
(P1,n2,n1) is Relation-like NAT -defined P1 -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of P1
Line (m,n1) is Relation-like NAT -defined P2 -valued Function-like V33() V40( width m) FinSequence-like FinSubsequence-like Element of (width m) -tuples_on P2
width m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(width m) -tuples_on P2 is non empty functional FinSequence-membered FinSequenceSet of P2
{ b1 where b1 is Relation-like NAT -defined P2 -valued Function-like V33() FinSequence-like FinSubsequence-like Element of P2 * : len b1 = width m } is set
P1 is non empty set
P1 * is non empty functional FinSequence-membered FinSequenceSet of P1
P2 is non empty set
P2 * is non empty functional FinSequence-membered FinSequenceSet of P2
n2 is Relation-like NAT -defined P1 * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of P1 *
width n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (width n2) is V33() V40( width n2) V167() V168() V169() V170() V171() V172() Element of bool NAT
m is Relation-like NAT -defined P2 * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of P2 *
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Col (n2,n1) is Relation-like NAT -defined P1 -valued Function-like V33() V40( len n2) FinSequence-like FinSubsequence-like Element of (len n2) -tuples_on P1
len n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(len n2) -tuples_on P1 is non empty functional FinSequence-membered FinSequenceSet of P1
{ b1 where b1 is Relation-like NAT -defined P1 -valued Function-like V33() FinSequence-like FinSubsequence-like Element of P1 * : len b1 = len n2 } is set
dom (Col (n2,n1)) is V40( len n2) V167() V168() V169() V170() V171() V172() Element of bool NAT
Col (m,n1) is Relation-like NAT -defined P2 -valued Function-like V33() V40( len m) FinSequence-like FinSubsequence-like Element of (len m) -tuples_on P2
len m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(len m) -tuples_on P2 is non empty functional FinSequence-membered FinSequenceSet of P2
{ b1 where b1 is Relation-like NAT -defined P2 -valued Function-like V33() FinSequence-like FinSubsequence-like Element of P2 * : len b1 = len m } is set
P is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
(Col (n2,n1)) . P is set
(Col (m,n1)) . P is set
len (Col (n2,n1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len (Col (n2,n1))) is V33() V40( len (Col (n2,n1))) V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (len n2) is V33() V40( len n2) V167() V168() V169() V170() V171() V172() Element of bool NAT
[P,n1] is set
{P,n1} is non empty V167() V168() V169() V170() V171() V172() set
{P} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{P,n1},{P}} is non empty set
Indices n2 is set
dom n2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
n2 * (P,n1) is Element of P1
m * (P,n1) is Element of P2
len (Col (n2,n1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len (Col (n2,n1))) is V33() V40( len (Col (n2,n1))) V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (len n2) is V33() V40( len n2) V167() V168() V169() V170() V171() V172() Element of bool NAT
len (Col (m,n1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len (Col (m,n1))) is V33() V40( len (Col (m,n1))) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom (Col (m,n1)) is V40( len m) V167() V168() V169() V170() V171() V172() Element of bool NAT
P1 is non empty set
P1 * is non empty functional FinSequence-membered FinSequenceSet of P1
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
n2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
m is Relation-like NAT -defined P1 -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of P1
len m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 |-> m is Relation-like NAT -defined Function-like V33() V40(n2) FinSequence-like FinSubsequence-like set
Seg n2 is V33() V40(n2) V167() V168() V169() V170() V171() V172() Element of bool NAT
(Seg n2) --> m is Relation-like Seg n2 -defined {m} -valued Function-like V27( Seg n2,{m}) V33() FinSequence-like FinSubsequence-like Element of bool [:(Seg n2),{m}:]
{m} is non empty trivial V40(1) set
[:(Seg n2),{m}:] is set
bool [:(Seg n2),{m}:] is set
n1 is Relation-like NAT -defined P1 * -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of P1 *
len n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom n1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
P is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(P1,n1,P) is Relation-like NAT -defined P1 -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of P1
len (P1,n1,P) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P is Relation-like NAT -defined P1 * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of P1 *
rng P is set
i is Relation-like NAT -defined P1 -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of P1
len i is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom P is V167() V168() V169() V170() V171() V172() Element of bool NAT
p is set
P . p is FinSequence-like set
P1 is non empty set
P1 * is non empty functional FinSequence-membered FinSequenceSet of P1
P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg P2 is V33() V40(P2) V167() V168() V169() V170() V171() V172() Element of bool NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
m is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
Seg m is V33() V40(m) V167() V168() V169() V170() V171() V172() Element of bool NAT
n1 is Relation-like NAT -defined P1 -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of P1
len n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P is Relation-like NAT -defined P1 -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of P1
len P is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
i is Relation-like NAT -defined P1 * -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of P1 *
len i is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom i is V167() V168() V169() V170() V171() V172() Element of bool NAT
p is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(P1,i,p) is Relation-like NAT -defined P1 -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of P1
len (P1,i,p) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
p is Relation-like NAT -defined P1 * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of P1 *
rng p is set
p1 is Relation-like NAT -defined P1 -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of P1
len p1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom p is V167() V168() V169() V170() V171() V172() Element of bool NAT
e3 is set
p . e3 is FinSequence-like set
P1 is V11() real ext-real Element of REAL
P2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
Indices P2 is set
dom P2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(REAL,P2,n2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
dom (REAL,P2,n2) is V167() V168() V169() V170() V171() V172() Element of bool NAT
[n2,m] is set
{n2,m} is non empty V167() V168() V169() V170() V171() V172() set
{n2} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{n2,m},{n2}} is non empty set
P2 * (n2,m) is V11() real ext-real Element of REAL
(REAL,P2,n2) . m is V11() real ext-real Element of REAL
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
[n2,m] is set
{n2,m} is non empty V167() V168() V169() V170() V171() V172() set
{n2} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{n2,m},{n2}} is non empty set
(REAL,P2,n2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
dom (REAL,P2,n2) is V167() V168() V169() V170() V171() V172() Element of bool NAT
(REAL,P2,n2) . m is V11() real ext-real Element of REAL
P2 * (n2,m) is V11() real ext-real Element of REAL
P1 is V11() real ext-real Element of REAL
P2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
Indices P2 is set
dom P2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Line (P2,n2) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width P2) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width P2) -tuples_on REAL
width P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(width P2) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = width P2 } is set
dom (Line (P2,n2)) is V40( width P2) V167() V168() V169() V170() V171() V172() Element of bool NAT
(REAL,P2,n2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
(Line (P2,n2)) . m is V11() real ext-real Element of REAL
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(REAL,P2,n2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Line (P2,n2) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width P2) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width P2) -tuples_on REAL
dom (REAL,P2,n2) is V167() V168() V169() V170() V171() V172() Element of bool NAT
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(REAL,P2,n2) . m is V11() real ext-real Element of REAL
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(REAL,P2,n2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
dom (REAL,P2,n2) is V167() V168() V169() V170() V171() V172() Element of bool NAT
(REAL,P2,n2) . m is V11() real ext-real Element of REAL
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
[n2,m] is set
{n2,m} is non empty V167() V168() V169() V170() V171() V172() set
{n2} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{n2,m},{n2}} is non empty set
P2 * (n2,m) is V11() real ext-real Element of REAL
P1 is V11() real ext-real Element of REAL
P2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
Indices P2 is set
width P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (width P2) is V33() V40( width P2) V167() V168() V169() V170() V171() V172() Element of bool NAT
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Col (P2,m) is Relation-like NAT -defined REAL -valued Function-like V33() V40( len P2) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len P2) -tuples_on REAL
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(len P2) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = len P2 } is set
dom (Col (P2,m)) is V40( len P2) V167() V168() V169() V170() V171() V172() Element of bool NAT
Line (P2,n2) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width P2) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width P2) -tuples_on REAL
(width P2) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = width P2 } is set
len (Line (P2,n2)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len (Line (P2,n2))) is V33() V40( len (Line (P2,n2))) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom (Line (P2,n2)) is V40( width P2) V167() V168() V169() V170() V171() V172() Element of bool NAT
[n2,m] is set
{n2,m} is non empty V167() V168() V169() V170() V171() V172() set
{n2} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{n2,m},{n2}} is non empty set
dom P2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
(Line (P2,n2)) . m is V11() real ext-real Element of REAL
(Col (P2,m)) . n2 is V11() real ext-real Element of REAL
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Line (P2,n2) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width P2) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width P2) -tuples_on REAL
dom (Line (P2,n2)) is V40( width P2) V167() V168() V169() V170() V171() V172() Element of bool NAT
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(Line (P2,n2)) . m is V11() real ext-real Element of REAL
len (Line (P2,n2)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len (Line (P2,n2))) is V33() V40( len (Line (P2,n2))) V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (len P2) is V33() V40( len P2) V167() V168() V169() V170() V171() V172() Element of bool NAT
Col (P2,m) is Relation-like NAT -defined REAL -valued Function-like V33() V40( len P2) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len P2) -tuples_on REAL
len (Col (P2,m)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len (Col (P2,m))) is V33() V40( len (Col (P2,m))) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom (Col (P2,m)) is V40( len P2) V167() V168() V169() V170() V171() V172() Element of bool NAT
(Col (P2,m)) . n2 is V11() real ext-real Element of REAL
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
[n2,m] is set
{n2,m} is non empty V167() V168() V169() V170() V171() V172() set
{n2} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{n2,m},{n2}} is non empty set
P2 * (n2,m) is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of REAL *
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom P2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 . n2 is V11() real ext-real Element of REAL
(REAL,P1,n2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (REAL,P1,n2) is V11() real ext-real Element of REAL
P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom P2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
n2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom n2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (len P1) is V33() V40( len P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
m is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
P2 . m is V11() real ext-real Element of REAL
n2 . m is V11() real ext-real Element of REAL
(REAL,P1,m) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (REAL,P1,m) is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
(P1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len (P1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len P1) is V33() V40( len P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(P1) . P2 is V11() real ext-real Element of REAL
Line (P1,P2) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width P1) -tuples_on REAL
width P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(width P1) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = width P1 } is set
Sum (Line (P1,P2)) is V11() real ext-real Element of REAL
dom P1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (len (P1)) is V33() V40( len (P1)) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom (P1) is V167() V168() V169() V170() V171() V172() Element of bool NAT
(REAL,P1,P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (REAL,P1,P2) is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
width P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (width P1) is V33() V40( width P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom P2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom P2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
m is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
P2 . m is V11() real ext-real Element of REAL
n2 . m is V11() real ext-real Element of REAL
Col (P1,m) is Relation-like NAT -defined REAL -valued Function-like V33() V40( len P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len P1) -tuples_on REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(len P1) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = len P1 } is set
Sum (Col (P1,m)) is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
width P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(P1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
P1 @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
((P1 @)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width (P1 @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (P1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len ((P1 @)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
Seg (len (P1)) is V33() V40( len (P1)) V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (len P1) is V33() V40( len P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom P1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (width (P1 @)) is V33() V40( width (P1 @)) V167() V168() V169() V170() V171() V172() Element of bool NAT
((P1 @)) . P2 is V11() real ext-real Element of REAL
Col ((P1 @),P2) is Relation-like NAT -defined REAL -valued Function-like V33() V40( len (P1 @)) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len (P1 @)) -tuples_on REAL
len (P1 @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(len (P1 @)) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = len (P1 @) } is set
Sum (Col ((P1 @),P2)) is V11() real ext-real Element of REAL
Line (P1,P2) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width P1) -tuples_on REAL
(width P1) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = width P1 } is set
Sum (Line (P1,P2)) is V11() real ext-real Element of REAL
(P1) . P2 is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
(P1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
P1 @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
((P1 @)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len (P1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len ((P1 @)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (P1 @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
Seg (len ((P1 @))) is V33() V40( len ((P1 @))) V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (len (P1 @)) is V33() V40( len (P1 @)) V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (width P1) is V33() V40( width P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
(P1) . P2 is V11() real ext-real Element of REAL
Col (P1,P2) is Relation-like NAT -defined REAL -valued Function-like V33() V40( len P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len P1) -tuples_on REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(len P1) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = len P1 } is set
Sum (Col (P1,P2)) is V11() real ext-real Element of REAL
Line ((P1 @),P2) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width (P1 @)) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width (P1 @)) -tuples_on REAL
width (P1 @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(width (P1 @)) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = width (P1 @) } is set
Sum (Line ((P1 @),P2)) is V11() real ext-real Element of REAL
((P1 @)) . P2 is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
(P1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (P1) is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(P1) is V11() real ext-real Element of REAL
(P1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (P1) is V11() real ext-real Element of REAL
len (P1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
P2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() Matrix of P1, 0 , REAL
(P2) is V11() real ext-real Element of REAL
(P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (P2) is V11() real ext-real Element of REAL
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (P2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom (P2) is V167() V168() V169() V170() V171() V172() Element of bool NAT
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom P2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
(REAL,P2,n2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
rng P2 is set
len (REAL,P2,n2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(P2) . n2 is V11() real ext-real Element of REAL
Sum (REAL,P2,n2) is V11() real ext-real Element of REAL
(len (P2)) |-> 0 is Relation-like empty-yielding NAT -defined NAT -valued Function-like V33() V40( len (P2)) FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of (len (P2)) -tuples_on NAT
(len (P2)) -tuples_on NAT is non empty functional FinSequence-membered FinSequenceSet of NAT
NAT * is non empty functional FinSequence-membered FinSequenceSet of NAT
{ b1 where b1 is Relation-like NAT -defined NAT -valued Function-like V33() FinSequence-like FinSubsequence-like Element of NAT * : len b1 = len (P2) } is set
Seg (len (P2)) is V33() V40( len (P2)) V167() V168() V169() V170() V171() V172() Element of bool NAT
(Seg (len (P2))) --> 0 is Relation-like Seg (len (P2)) -defined INT -valued RAT -valued {0} -valued Function-like V27( Seg (len (P2)),{0}) V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of bool [:(Seg (len (P2))),{0}:]
{0} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
[:(Seg (len (P2))),{0}:] is INT -valued RAT -valued complex-yielding V158() V159() V160() set
bool [:(Seg (len (P2))),{0}:] is set
Sum ((len (P2)) |-> 0) is V11() real set
(len (P2)) * 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
n2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
m is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() Matrix of P2,P1, REAL
(m) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
n1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() Matrix of n2,P1, REAL
m ^ n1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() Matrix of K36(P2,n2),P1, REAL
K36(P2,n2) is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
((m ^ n1)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
(n1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
(m) ^ (n1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
dom ((m ^ n1)) is V167() V168() V169() V170() V171() V172() Element of bool NAT
len ((m ^ n1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len ((m ^ n1))) is V33() V40( len ((m ^ n1))) V167() V168() V169() V170() V171() V172() Element of bool NAT
P is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
len (m ^ n1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len (m ^ n1)) is V33() V40( len (m ^ n1)) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom (m ^ n1) is V167() V168() V169() V170() V171() V172() Element of bool NAT
dom m is V167() V168() V169() V170() V171() V172() Element of bool NAT
len m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (m) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom (m) is V167() V168() V169() V170() V171() V172() Element of bool NAT
((m ^ n1)) . P is V11() real ext-real Element of REAL
(REAL,(m ^ n1),P) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (REAL,(m ^ n1),P) is V11() real ext-real Element of REAL
(REAL,m,P) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (REAL,m,P) is V11() real ext-real Element of REAL
(m) . P is V11() real ext-real Element of REAL
((m) ^ (n1)) . P is V11() real ext-real Element of REAL
dom n1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
len m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (m) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (n1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom (n1) is V167() V168() V169() V170() V171() V172() Element of bool NAT
i is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
(len m) + i is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
i is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
(len m) + i is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
((m ^ n1)) . P is V11() real ext-real Element of REAL
(REAL,(m ^ n1),P) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (REAL,(m ^ n1),P) is V11() real ext-real Element of REAL
(REAL,n1,i) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (REAL,n1,i) is V11() real ext-real Element of REAL
(n1) . i is V11() real ext-real Element of REAL
((m) ^ (n1)) . P is V11() real ext-real Element of REAL
dom m is V167() V168() V169() V170() V171() V172() Element of bool NAT
dom n1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
len m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
((m ^ n1)) . P is V11() real ext-real Element of REAL
((m) ^ (n1)) . P is V11() real ext-real Element of REAL
((m ^ n1)) . P is V11() real ext-real Element of REAL
((m) ^ (n1)) . P is V11() real ext-real Element of REAL
len m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(len m) + (len n1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (m) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(len (m)) + (len n1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (n1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(len (m)) + (len (n1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len ((m) ^ (n1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
(P1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
P2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
(P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
(P1) + (P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
addreal .: ((P1),(P2)) is set
P1 ^^ P2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
((P1 ^^ P2)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
min ((len P1),(len P2)) is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg n2 is V33() V40(n2) V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (len P1) is V33() V40( len P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (len P2) is V33() V40( len P2) V167() V168() V169() V170() V171() V172() Element of bool NAT
(Seg (len P1)) /\ (Seg (len P2)) is V167() V168() V169() V170() V171() V172() set
dom P2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
(Seg (len P1)) /\ (dom P2) is V167() V168() V169() V170() V171() V172() set
dom P1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
(dom P1) /\ (dom P2) is V167() V168() V169() V170() V171() V172() set
dom (P1 ^^ P2) is V167() V168() V169() V170() V171() V172() Element of bool NAT
len (P1 ^^ P2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len (P1 ^^ P2)) is V33() V40( len (P1 ^^ P2)) V167() V168() V169() V170() V171() V172() Element of bool NAT
len ((P1) + (P2)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
addreal .: ((P1),(P2)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len (addreal .: ((P1),(P2))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (P1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (P2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
min ((len (P1)),(len (P2))) is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
min ((len P1),(len (P2))) is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
len ((P1 ^^ P2)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom ((P1) + (P2)) is V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (len ((P1) + (P2))) is V33() V40( len ((P1) + (P2))) V167() V168() V169() V170() V171() V172() Element of bool NAT
m is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
dom (addreal .: ((P1),(P2))) is V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (len (P1)) is V33() V40( len (P1)) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom (P1) is V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (len (P2)) is V33() V40( len (P2)) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom (P2) is V167() V168() V169() V170() V171() V172() Element of bool NAT
dom ((P1 ^^ P2)) is V167() V168() V169() V170() V171() V172() Element of bool NAT
(REAL,P1,m) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
(REAL,P2,m) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
(REAL,P1,m) ^ (REAL,P2,m) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
(REAL,(P1 ^^ P2),m) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
((P1) + (P2)) . m is V11() real ext-real Element of REAL
(addreal .: ((P1),(P2))) . m is V11() real ext-real Element of REAL
(P1) . m is V11() real ext-real Element of REAL
(P2) . m is V11() real ext-real Element of REAL
addreal . (((P1) . m),((P2) . m)) is V11() real ext-real Element of REAL
((P1) . m) + ((P2) . m) is V11() real ext-real Element of REAL
Sum (REAL,P1,m) is V11() real ext-real Element of REAL
(Sum (REAL,P1,m)) + ((P2) . m) is V11() real ext-real Element of REAL
Sum (REAL,P2,m) is V11() real ext-real Element of REAL
(Sum (REAL,P1,m)) + (Sum (REAL,P2,m)) is V11() real ext-real Element of REAL
Sum (REAL,(P1 ^^ P2),m) is V11() real ext-real Element of REAL
((P1 ^^ P2)) . m is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(P1) is V11() real ext-real Element of REAL
(P1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (P1) is V11() real ext-real Element of REAL
(P2) is V11() real ext-real Element of REAL
(P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (P2) is V11() real ext-real Element of REAL
(P1) + (P2) is V11() real ext-real Element of REAL
P1 ^^ P2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
((P1 ^^ P2)) is V11() real ext-real Element of REAL
((P1 ^^ P2)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((P1 ^^ P2)) is V11() real ext-real Element of REAL
len (P1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (P2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(len (P1)) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = len (P1) } is set
n2 is Relation-like NAT -defined REAL -valued Function-like V33() V40( len (P1)) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len (P1)) -tuples_on REAL
m is Relation-like NAT -defined REAL -valued Function-like V33() V40( len (P1)) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len (P1)) -tuples_on REAL
n2 + m is Relation-like NAT -defined REAL -valued Function-like V33() V40( len (P1)) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len (P1)) -tuples_on REAL
addreal .: (n2,m) is set
Sum (n2 + m) is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
(P1) is V11() real ext-real Element of REAL
(P1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (P1) is V11() real ext-real Element of REAL
P1 @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
((P1 @)) is V11() real ext-real Element of REAL
((P1 @)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((P1 @)) is V11() real ext-real Element of REAL
P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
<*P2*> is non empty trivial Relation-like NAT -defined REAL * -valued Function-like V33() V40(1) FinSequence-like FinSubsequence-like tabular V180() Matrix of 1, len P2, REAL
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(<*P2*>) is V11() real ext-real Element of REAL
(<*P2*>) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (<*P2*>) is V11() real ext-real Element of REAL
<*P2*> @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
((<*P2*> @)) is V11() real ext-real Element of REAL
((<*P2*> @)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((<*P2*> @)) is V11() real ext-real Element of REAL
n2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
<*n2*> is non empty trivial Relation-like NAT -defined REAL * -valued Function-like V33() V40(1) FinSequence-like FinSubsequence-like tabular V180() Matrix of 1, len n2, REAL
len n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(<*n2*>) is V11() real ext-real Element of REAL
(<*n2*>) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (<*n2*>) is V11() real ext-real Element of REAL
<*n2*> @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
((<*n2*> @)) is V11() real ext-real Element of REAL
((<*n2*> @)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((<*n2*> @)) is V11() real ext-real Element of REAL
m is V11() real ext-real Element of REAL
(m) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one V33() V40(1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() V161() V162() V163() V164() FinSequence of REAL
n2 ^ (m) is non empty Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
<*(n2 ^ (m))*> is non empty trivial Relation-like NAT -defined REAL * -valued Function-like V33() V40(1) FinSequence-like FinSubsequence-like tabular V180() Matrix of 1, len (n2 ^ (m)), REAL
len (n2 ^ (m)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
(<*(n2 ^ (m))*>) is V11() real ext-real Element of REAL
(<*(n2 ^ (m))*>) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (<*(n2 ^ (m))*>) is V11() real ext-real Element of REAL
<*(n2 ^ (m))*> @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
((<*(n2 ^ (m))*> @)) is V11() real ext-real Element of REAL
((<*(n2 ^ (m))*> @)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((<*(n2 ^ (m))*> @)) is V11() real ext-real Element of REAL
<*(m)*> is non empty trivial Relation-like NAT -defined REAL * -valued Function-like V33() V40(1) FinSequence-like FinSubsequence-like tabular V180() Matrix of 1, len (m), REAL
len (m) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
<*n2*> ^^ <*(m)*> is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len (<*n2*> ^^ <*(m)*>) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len (<*n2*> ^^ <*(m)*>)) is V33() V40( len (<*n2*> ^^ <*(m)*>)) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom (<*n2*> ^^ <*(m)*>) is V167() V168() V169() V170() V171() V172() Element of bool NAT
dom <*n2*> is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom <*(m)*> is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() Element of bool NAT
(dom <*n2*>) /\ (dom <*(m)*>) is V167() V168() V169() V170() V171() V172() set
(Seg 1) /\ (dom <*(m)*>) is V167() V168() V169() V170() V171() V172() set
(Seg 1) /\ (Seg 1) is V167() V168() V169() V170() V171() V172() set
len <*(n2 ^ (m))*> is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom <*(n2 ^ (m))*> is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (len <*(n2 ^ (m))*>) is non empty V33() V40( len <*(n2 ^ (m))*>) V167() V168() V169() V170() V171() V172() Element of bool NAT
n1 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
(REAL,<*n2*>,n1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
(REAL,<*(m)*>,n1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
(REAL,(<*n2*> ^^ <*(m)*>),n1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
P is Relation-like NAT -defined Function-like V33() FinSequence-like FinSubsequence-like set
i is Relation-like NAT -defined Function-like V33() FinSequence-like FinSubsequence-like set
P ^ i is Relation-like NAT -defined Function-like V33() FinSequence-like FinSubsequence-like set
n2 ^ i is Relation-like NAT -defined Function-like V33() FinSequence-like FinSubsequence-like set
(REAL,<*(n2 ^ (m))*>,n1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
(<*(m)*>) is V11() real ext-real Element of REAL
(<*(m)*>) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (<*(m)*>) is V11() real ext-real Element of REAL
<*(m)*> @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
((<*(m)*> @)) is V11() real ext-real Element of REAL
((<*(m)*> @)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((<*(m)*> @)) is V11() real ext-real Element of REAL
len <*(m)*> is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
width <*(m)*> is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
<*(m)*> @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len (<*(m)*> @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len <*n2*> is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
width <*n2*> is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (<*n2*> @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width (<*n2*> @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width <*(n2 ^ (m))*> is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(len n2) + (len (m)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
(len n2) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
(<*(m)*> @) @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
width (<*(m)*> @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() Matrix of len n2,1, REAL
P is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() Matrix of 1,1, REAL
n1 ^ P is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() Matrix of K36((len n2),1),1, REAL
K36((len n2),1) is non empty epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real positive non negative set
(n1 ^ P) @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
(<*n2*> @) @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
((<*n2*> @) @) ^^ ((<*(m)*> @) @) is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
(<*(n2 ^ (m))*> @) @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
(<*n2*> @) ^ (<*(m)*> @) is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like FinSequence of REAL *
len ((<*n2*> @) ^ (<*(m)*> @)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(len (<*n2*> @)) + (len (<*(m)*> @)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(width <*n2*>) + (len (<*(m)*> @)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(width <*n2*>) + (width <*(m)*>) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (<*(n2 ^ (m))*> @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
((<*n2*> ^^ <*(m)*>)) is V11() real ext-real Element of REAL
((<*n2*> ^^ <*(m)*>)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((<*n2*> ^^ <*(m)*>)) is V11() real ext-real Element of REAL
(<*(m)*>) is V11() real ext-real Element of REAL
(<*(m)*>) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (<*(m)*>) is V11() real ext-real Element of REAL
((<*n2*> @)) + (<*(m)*>) is V11() real ext-real Element of REAL
((<*(m)*> @)) is V11() real ext-real Element of REAL
((<*(m)*> @)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((<*(m)*> @)) is V11() real ext-real Element of REAL
((<*n2*> @)) + ((<*(m)*> @)) is V11() real ext-real Element of REAL
(n1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
(P) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
(n1) ^ (P) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((n1) ^ (P)) is V11() real ext-real Element of REAL
((n1 ^ P)) is V11() real ext-real Element of REAL
((n1 ^ P)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((n1 ^ P)) is V11() real ext-real Element of REAL
<*(<*> REAL)*> is non empty trivial Relation-like NAT -defined REAL * -valued Function-like V33() V40(1) FinSequence-like FinSubsequence-like tabular V180() Matrix of 1, len (<*> REAL), REAL
len (<*> REAL) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real functional V30() V31() V33() V38() V40( {} ) FinSequence-membered ext-real non positive non negative V167() V168() V169() V170() V171() V172() V173() Element of NAT
(<*(<*> REAL)*>) is V11() real ext-real Element of REAL
(<*(<*> REAL)*>) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (<*(<*> REAL)*>) is V11() real ext-real Element of REAL
<*(<*> REAL)*> @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
((<*(<*> REAL)*> @)) is V11() real ext-real Element of REAL
((<*(<*> REAL)*> @)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((<*(<*> REAL)*> @)) is V11() real ext-real Element of REAL
n2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() Matrix of 1, 0 , REAL
len n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len (n2 @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(n2) is V11() real ext-real Element of REAL
(n2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (n2) is V11() real ext-real Element of REAL
((n2 @)) is V11() real ext-real Element of REAL
((n2 @)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((n2 @)) is V11() real ext-real Element of REAL
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
P2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(n2) is V11() real ext-real Element of REAL
(n2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (n2) is V11() real ext-real Element of REAL
n2 @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
((n2 @)) is V11() real ext-real Element of REAL
((n2 @)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((n2 @)) is V11() real ext-real Element of REAL
dom n2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (len n2) is V33() V40( len n2) V167() V168() V169() V170() V171() V172() Element of bool NAT
(REAL,n2,1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
m is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
<*m*> is non empty trivial Relation-like NAT -defined REAL * -valued Function-like V33() V40(1) FinSequence-like FinSubsequence-like tabular V180() Matrix of 1, len m, REAL
len m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(REAL,n2,(P2 + 1)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
m is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() Matrix of P2 + 1, width n2, REAL
Del (m,(P2 + 1)) is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
Line (n2,(P2 + 1)) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width n2) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width n2) -tuples_on REAL
(width n2) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = width n2 } is set
n1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
<*n1*> is non empty trivial Relation-like NAT -defined REAL * -valued Function-like V33() V40(1) FinSequence-like FinSubsequence-like tabular V180() Matrix of 1, len n1, REAL
len n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() Matrix of P2, width n2, REAL
width P is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
i is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() Matrix of 1, width n2, REAL
width i is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len (P @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
i @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len (i @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Del (n2,(P2 + 1)) is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len (Del (n2,(P2 + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P ^ i is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() Matrix of K36(P2,1), width n2, REAL
K36(P2,1) is non empty epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real positive non negative set
((P ^ i)) is V11() real ext-real Element of REAL
((P ^ i)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((P ^ i)) is V11() real ext-real Element of REAL
(P) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
(i) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
(P) ^ (i) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((P) ^ (i)) is V11() real ext-real Element of REAL
((Del (n2,(P2 + 1)))) is V11() real ext-real Element of REAL
((Del (n2,(P2 + 1)))) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((Del (n2,(P2 + 1)))) is V11() real ext-real Element of REAL
(i) is V11() real ext-real Element of REAL
Sum (i) is V11() real ext-real Element of REAL
((Del (n2,(P2 + 1)))) + (i) is V11() real ext-real Element of REAL
(Del (n2,(P2 + 1))) @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
(((Del (n2,(P2 + 1))) @)) is V11() real ext-real Element of REAL
(((Del (n2,(P2 + 1))) @)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (((Del (n2,(P2 + 1))) @)) is V11() real ext-real Element of REAL
(((Del (n2,(P2 + 1))) @)) + (i) is V11() real ext-real Element of REAL
((i @)) is V11() real ext-real Element of REAL
((i @)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((i @)) is V11() real ext-real Element of REAL
(((Del (n2,(P2 + 1))) @)) + ((i @)) is V11() real ext-real Element of REAL
(P @) ^^ (i @) is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
(((P @) ^^ (i @))) is V11() real ext-real Element of REAL
(((P @) ^^ (i @))) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (((P @) ^^ (i @))) is V11() real ext-real Element of REAL
(P ^ i) @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
(((P ^ i) @)) is V11() real ext-real Element of REAL
(((P ^ i) @)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (((P ^ i) @)) is V11() real ext-real Element of REAL
P2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(P2) is V11() real ext-real Element of REAL
(P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (P2) is V11() real ext-real Element of REAL
P2 @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
((P2 @)) is V11() real ext-real Element of REAL
((P2 @)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((P2 @)) is V11() real ext-real Element of REAL
width P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (P2 @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(P2) is V11() real ext-real Element of REAL
(P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (P2) is V11() real ext-real Element of REAL
P2 @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
((P2 @)) is V11() real ext-real Element of REAL
((P2 @)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((P2 @)) is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
(P1) is V11() real ext-real Element of REAL
(P1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (P1) is V11() real ext-real Element of REAL
(P1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (P1) is V11() real ext-real Element of REAL
P1 @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
((P1 @)) is V11() real ext-real Element of REAL
((P1 @)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((P1 @)) is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
mlt (P1,P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: (P1,P2) is set
len (mlt (P1,P2)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = P1 } is set
P1 |-> 1 is Relation-like NAT -defined NAT -valued Function-like V33() V40(P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of P1 -tuples_on NAT
P1 -tuples_on NAT is non empty functional FinSequence-membered FinSequenceSet of NAT
NAT * is non empty functional FinSequence-membered FinSequenceSet of NAT
{ b1 where b1 is Relation-like NAT -defined NAT -valued Function-like V33() FinSequence-like FinSubsequence-like Element of NAT * : len b1 = P1 } is set
Seg P1 is V33() V40(P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
(Seg P1) --> 1 is Relation-like Seg P1 -defined INT -valued RAT -valued {1} -valued Function-like V27( Seg P1,{1}) V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of bool [:(Seg P1),{1}:]
[:(Seg P1),{1}:] is INT -valued RAT -valued complex-yielding V158() V159() V160() set
bool [:(Seg P1),{1}:] is set
P2 is Relation-like NAT -defined REAL -valued Function-like V33() V40(P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of P1 -tuples_on REAL
mlt ((P1 |-> 1),P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: ((P1 |-> 1),P2) is set
1 * P2 is Relation-like NAT -defined REAL -valued Function-like V33() V40(P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of P1 -tuples_on REAL
1 multreal is Relation-like REAL -defined REAL -valued Function-like V27( REAL , REAL ) complex-yielding V158() V159() Element of bool [:REAL,REAL:]
K71(REAL) is non empty Relation-like REAL -defined REAL -valued V23( REAL ) complex-yielding V158() V159() Element of bool [:REAL,REAL:]
multreal [;] (1,K71(REAL)) is set
P2 * (1 multreal) is Relation-like FinSequence-like complex-yielding V158() V159() set
P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(len P1) |-> 1 is Relation-like NAT -defined NAT -valued Function-like V33() V40( len P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of (len P1) -tuples_on NAT
(len P1) -tuples_on NAT is non empty functional FinSequence-membered FinSequenceSet of NAT
NAT * is non empty functional FinSequence-membered FinSequenceSet of NAT
{ b1 where b1 is Relation-like NAT -defined NAT -valued Function-like V33() FinSequence-like FinSubsequence-like Element of NAT * : len b1 = len P1 } is set
Seg (len P1) is V33() V40( len P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
(Seg (len P1)) --> 1 is Relation-like Seg (len P1) -defined INT -valued RAT -valued {1} -valued Function-like V27( Seg (len P1),{1}) V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of bool [:(Seg (len P1)),{1}:]
[:(Seg (len P1)),{1}:] is INT -valued RAT -valued complex-yielding V158() V159() V160() set
bool [:(Seg (len P1)),{1}:] is set
mlt (((len P1) |-> 1),P1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: (((len P1) |-> 1),P1) is set
(len P1) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = len P1 } is set
P2 is Relation-like NAT -defined REAL -valued Function-like V33() V40( len P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len P1) -tuples_on REAL
mlt (((len P1) |-> 1),P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: (((len P1) |-> 1),P2) is set
P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
dom P1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 . P2 is V11() real ext-real Element of REAL
P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 . P2 is V11() real ext-real Element of REAL
P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
dom P1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
dom P2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
mlt (P1,P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: (P1,P2) is set
dom (mlt (P1,P2)) is V167() V168() V169() V170() V171() V172() Element of bool NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(mlt (P1,P2)) . n2 is V11() real ext-real Element of REAL
P1 . n2 is V11() real ext-real Element of REAL
P2 . n2 is V11() real ext-real Element of REAL
(P1 . n2) * (P2 . n2) is V11() real ext-real Element of REAL
P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = P1 } is set
P1 -tuples_on the carrier of F_Real is non empty functional FinSequence-membered FinSequenceSet of the carrier of F_Real
{ b1 where b1 is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() FinSequence-like FinSubsequence-like Element of the carrier of F_Real * : len b1 = P1 } is set
P2 is Relation-like NAT -defined REAL -valued Function-like V33() V40(P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of P1 -tuples_on REAL
n2 is Relation-like NAT -defined REAL -valued Function-like V33() V40(P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of P1 -tuples_on REAL
mlt (P2,n2) is Relation-like NAT -defined REAL -valued Function-like V33() V40(P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of P1 -tuples_on REAL
multreal .: (P2,n2) is set
m is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() V40(P1) FinSequence-like FinSubsequence-like Element of P1 -tuples_on the carrier of F_Real
n1 is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() V40(P1) FinSequence-like FinSubsequence-like Element of P1 -tuples_on the carrier of F_Real
mlt (m,n1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() V40(P1) FinSequence-like FinSubsequence-like Element of P1 -tuples_on the carrier of F_Real
dom (mlt (P2,n2)) is V40(P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
len (mlt (P2,n2)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len (mlt (P2,n2))) is V33() V40( len (mlt (P2,n2))) V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg P1 is V33() V40(P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
len (mlt (m,n1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len (mlt (m,n1))) is V33() V40( len (mlt (m,n1))) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom (mlt (m,n1)) is V40(P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
P is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
(mlt (P2,n2)) . P is V11() real ext-real Element of REAL
(mlt (m,n1)) . P is set
P2 . P is V11() real ext-real Element of REAL
n2 . P is V11() real ext-real Element of REAL
i is V11() real ext-real Element of the carrier of F_Real
p is V11() real ext-real Element of the carrier of F_Real
i * p is V11() real ext-real Element of the carrier of F_Real
i * p is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
mlt (P1,P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: (P1,P2) is set
n2 is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of the carrier of F_Real
m is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of the carrier of F_Real
mlt (n2,m) is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of the carrier of F_Real
{ b1 where b1 is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() FinSequence-like FinSubsequence-like Element of the carrier of F_Real * : len b1 = len P1 } is set
(len P1) -tuples_on the carrier of F_Real is non empty functional FinSequence-membered FinSequenceSet of the carrier of F_Real
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of REAL * : len b1 = len P1 } is set
(len P1) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
e2 is Relation-like NAT -defined REAL -valued Function-like V33() V40( len P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len P1) -tuples_on REAL
e3 is Relation-like NAT -defined REAL -valued Function-like V33() V40( len P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len P1) -tuples_on REAL
mlt (e2,e3) is Relation-like NAT -defined REAL -valued Function-like V33() V40( len P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len P1) -tuples_on REAL
multreal .: (e2,e3) is set
i is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() V40( len P1) FinSequence-like FinSubsequence-like Element of (len P1) -tuples_on the carrier of F_Real
p is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() V40( len P1) FinSequence-like FinSubsequence-like Element of (len P1) -tuples_on the carrier of F_Real
mlt (i,p) is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() V40( len P1) FinSequence-like FinSubsequence-like Element of (len P1) -tuples_on the carrier of F_Real
P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum P1 is V11() real ext-real Element of REAL
P2 is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of the carrier of F_Real
Sum P2 is V11() real ext-real Element of the carrier of F_Real
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 is Relation-like NAT -defined REAL -valued Function-like V27( NAT , REAL ) complex-yielding V158() V159() Element of bool [:NAT,REAL:]
n2 . 0 is V11() real ext-real Element of REAL
n2 . (len P1) is V11() real ext-real Element of REAL
[:NAT, the carrier of F_Real:] is V33() complex-yielding V158() V159() set
bool [:NAT, the carrier of F_Real:] is V33() set
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
0. F_Real is V11() real V52( F_Real ) ext-real Element of the carrier of F_Real
m is Relation-like NAT -defined the carrier of F_Real -valued Function-like V27( NAT , the carrier of F_Real) complex-yielding V158() V159() Element of bool [:NAT, the carrier of F_Real:]
m . (len P2) is V11() real ext-real Element of the carrier of F_Real
m . 0 is V11() real ext-real Element of the carrier of F_Real
n1 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
n2 . n1 is V11() real ext-real Element of REAL
m . n1 is V11() real ext-real Element of REAL
P is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
n2 . P is V11() real ext-real Element of REAL
m . P is V11() real ext-real Element of REAL
P + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 . (P + 1) is V11() real ext-real Element of REAL
n2 . (P + 1) is V11() real ext-real Element of REAL
i is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
m . i is V11() real ext-real Element of the carrier of F_Real
p is V11() real ext-real Element of the carrier of F_Real
(m . i) + p is V11() real ext-real Element of the carrier of F_Real
(m . i) + p is V11() real ext-real Element of REAL
m . (P + 1) is V11() real ext-real Element of the carrier of F_Real
n2 . (P + 1) is V11() real ext-real Element of REAL
m . (P + 1) is V11() real ext-real Element of REAL
n2 . 0 is V11() real ext-real Element of REAL
m . 0 is V11() real ext-real Element of REAL
P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = P1 } is set
P1 -tuples_on the carrier of F_Real is non empty functional FinSequence-membered FinSequenceSet of the carrier of F_Real
{ b1 where b1 is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() FinSequence-like FinSubsequence-like Element of the carrier of F_Real * : len b1 = P1 } is set
P2 is Relation-like NAT -defined REAL -valued Function-like V33() V40(P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of P1 -tuples_on REAL
n2 is Relation-like NAT -defined REAL -valued Function-like V33() V40(P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of P1 -tuples_on REAL
|(P2,n2)| is real set
mlt (P2,n2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: (P2,n2) is set
Sum (mlt (P2,n2)) is V11() real ext-real Element of REAL
m is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() V40(P1) FinSequence-like FinSubsequence-like Element of P1 -tuples_on the carrier of F_Real
n1 is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() V40(P1) FinSequence-like FinSubsequence-like Element of P1 -tuples_on the carrier of F_Real
m "*" n1 is V11() real ext-real Element of the carrier of F_Real
mlt (m,n1) is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() V40(P1) FinSequence-like FinSubsequence-like Element of P1 -tuples_on the carrier of F_Real
Sum (mlt (m,n1)) is V11() real ext-real Element of the carrier of F_Real
P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
|(P1,P2)| is real set
mlt (P1,P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: (P1,P2) is set
Sum (mlt (P1,P2)) is V11() real ext-real Element of REAL
n2 is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of the carrier of F_Real
m is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of the carrier of F_Real
n2 "*" m is V11() real ext-real Element of the carrier of F_Real
mlt (n2,m) is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of the carrier of F_Real
Sum (mlt (n2,m)) is V11() real ext-real Element of the carrier of F_Real
P2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
width P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
P2 * n2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Indices P1 is set
MXR2MXF P1 is Relation-like NAT -defined the carrier of F_Real * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of the carrier of F_Real *
MXR2MXF n2 is Relation-like NAT -defined the carrier of F_Real * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of the carrier of F_Real *
MXR2MXF P2 is Relation-like NAT -defined the carrier of F_Real * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of the carrier of F_Real *
(MXR2MXF P2) * (MXR2MXF n2) is Relation-like NAT -defined the carrier of F_Real * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of the carrier of F_Real *
MXF2MXR ((MXR2MXF P2) * (MXR2MXF n2)) is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
i is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Line (P2,i) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width P2) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width P2) -tuples_on REAL
(width P2) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = width P2 } is set
p is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
[i,p] is set
{i,p} is non empty V167() V168() V169() V170() V171() V172() set
{i} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{i,p},{i}} is non empty set
P1 * (i,p) is V11() real ext-real Element of REAL
Col (n2,p) is Relation-like NAT -defined REAL -valued Function-like V33() V40( len n2) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len n2) -tuples_on REAL
(len n2) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = len n2 } is set
|((Line (P2,i)),(Col (n2,p)))| is real set
mlt ((Line (P2,i)),(Col (n2,p))) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: ((Line (P2,i)),(Col (n2,p))) is set
Sum (mlt ((Line (P2,i)),(Col (n2,p)))) is V11() real ext-real Element of REAL
Seg (width n2) is V33() V40( width n2) V167() V168() V169() V170() V171() V172() Element of bool NAT
Col ((MXR2MXF n2),p) is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() V40( len (MXR2MXF n2)) FinSequence-like FinSubsequence-like Element of (len (MXR2MXF n2)) -tuples_on the carrier of F_Real
len (MXR2MXF n2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(len (MXR2MXF n2)) -tuples_on the carrier of F_Real is non empty functional FinSequence-membered FinSequenceSet of the carrier of F_Real
{ b1 where b1 is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() FinSequence-like FinSubsequence-like Element of the carrier of F_Real * : len b1 = len (MXR2MXF n2) } is set
Seg (len P2) is V33() V40( len P2) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom P2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
Line ((MXR2MXF P2),i) is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() V40( width (MXR2MXF P2)) FinSequence-like FinSubsequence-like Element of (width (MXR2MXF P2)) -tuples_on the carrier of F_Real
width (MXR2MXF P2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(width (MXR2MXF P2)) -tuples_on the carrier of F_Real is non empty functional FinSequence-membered FinSequenceSet of the carrier of F_Real
{ b1 where b1 is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() FinSequence-like FinSubsequence-like Element of the carrier of F_Real * : len b1 = width (MXR2MXF P2) } is set
len (Line (P2,i)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (Col (n2,p)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Indices ((MXR2MXF P2) * (MXR2MXF n2)) is set
((MXR2MXF P2) * (MXR2MXF n2)) * (i,p) is V11() real ext-real Element of the carrier of F_Real
(Line ((MXR2MXF P2),i)) "*" (Col ((MXR2MXF n2),p)) is V11() real ext-real Element of the carrier of F_Real
width (MXR2MXF P1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width (MXR2MXF n2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (MXR2MXF P1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (MXR2MXF P2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Indices (MXR2MXF P1) is set
i is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
p is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
[i,p] is set
{i,p} is non empty V167() V168() V169() V170() V171() V172() set
{i} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{i,p},{i}} is non empty set
(MXR2MXF P1) * (i,p) is V11() real ext-real Element of the carrier of F_Real
Line ((MXR2MXF P2),i) is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() V40( width (MXR2MXF P2)) FinSequence-like FinSubsequence-like Element of (width (MXR2MXF P2)) -tuples_on the carrier of F_Real
width (MXR2MXF P2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(width (MXR2MXF P2)) -tuples_on the carrier of F_Real is non empty functional FinSequence-membered FinSequenceSet of the carrier of F_Real
{ b1 where b1 is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() FinSequence-like FinSubsequence-like Element of the carrier of F_Real * : len b1 = width (MXR2MXF P2) } is set
Col ((MXR2MXF n2),p) is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() V40( len (MXR2MXF n2)) FinSequence-like FinSubsequence-like Element of (len (MXR2MXF n2)) -tuples_on the carrier of F_Real
len (MXR2MXF n2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(len (MXR2MXF n2)) -tuples_on the carrier of F_Real is non empty functional FinSequence-membered FinSequenceSet of the carrier of F_Real
{ b1 where b1 is Relation-like NAT -defined the carrier of F_Real -valued Function-like V33() FinSequence-like FinSubsequence-like Element of the carrier of F_Real * : len b1 = len (MXR2MXF n2) } is set
(Line ((MXR2MXF P2),i)) "*" (Col ((MXR2MXF n2),p)) is V11() real ext-real Element of the carrier of F_Real
Seg (width (MXR2MXF n2)) is V33() V40( width (MXR2MXF n2)) V167() V168() V169() V170() V171() V172() Element of bool NAT
Col (n2,p) is Relation-like NAT -defined REAL -valued Function-like V33() V40( len n2) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len n2) -tuples_on REAL
(len n2) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = len n2 } is set
Seg (len (MXR2MXF P2)) is V33() V40( len (MXR2MXF P2)) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom (MXR2MXF P2) is V167() V168() V169() V170() V171() V172() Element of bool NAT
Line (P2,i) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width P2) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width P2) -tuples_on REAL
(width P2) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = width P2 } is set
len (Line (P2,i)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (Col (n2,p)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 * (i,p) is V11() real ext-real Element of REAL
|((Line (P2,i)),(Col (n2,p)))| is real set
mlt ((Line (P2,i)),(Col (n2,p))) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: ((Line (P2,i)),(Col (n2,p))) is set
Sum (mlt ((Line (P2,i)),(Col (n2,p)))) is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 * P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len (P2 * P1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len (P2 * P1)) is V33() V40( len (P2 * P1)) V167() V168() V169() V170() V171() V172() Element of bool NAT
LineVec2Mx P2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
(LineVec2Mx P2) * P1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
Line (((LineVec2Mx P2) * P1),1) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width ((LineVec2Mx P2) * P1)) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width ((LineVec2Mx P2) * P1)) -tuples_on REAL
width ((LineVec2Mx P2) * P1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(width ((LineVec2Mx P2) * P1)) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = width ((LineVec2Mx P2) * P1) } is set
len (Line (((LineVec2Mx P2) * P1),1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width (LineVec2Mx P2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len ((LineVec2Mx P2) * P1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (LineVec2Mx P2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len ((LineVec2Mx P2) * P1)) is V33() V40( len ((LineVec2Mx P2) * P1)) V167() V168() V169() V170() V171() V172() Element of bool NAT
[1,n2] is set
{1,n2} is non empty V167() V168() V169() V170() V171() V172() set
{{1,n2},{1}} is non empty set
Indices ((LineVec2Mx P2) * P1) is set
((LineVec2Mx P2) * P1) * (1,n2) is V11() real ext-real Element of REAL
Line ((LineVec2Mx P2),1) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width (LineVec2Mx P2)) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width (LineVec2Mx P2)) -tuples_on REAL
(width (LineVec2Mx P2)) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = width (LineVec2Mx P2) } is set
Col (P1,n2) is Relation-like NAT -defined REAL -valued Function-like V33() V40( len P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len P1) -tuples_on REAL
(len P1) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = len P1 } is set
|((Line ((LineVec2Mx P2),1)),(Col (P1,n2)))| is real set
mlt ((Line ((LineVec2Mx P2),1)),(Col (P1,n2))) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: ((Line ((LineVec2Mx P2),1)),(Col (P1,n2))) is set
Sum (mlt ((Line ((LineVec2Mx P2),1)),(Col (P1,n2)))) is V11() real ext-real Element of REAL
|(P2,(Col (P1,n2)))| is real set
mlt (P2,(Col (P1,n2))) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: (P2,(Col (P1,n2))) is set
Sum (mlt (P2,(Col (P1,n2)))) is V11() real ext-real Element of REAL
(Line (((LineVec2Mx P2) * P1),1)) . n2 is V11() real ext-real Element of REAL
(P2 * P1) . n2 is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
width P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 * P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len (P1 * P2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len (P1 * P2)) is V33() V40( len (P1 * P2)) V167() V168() V169() V170() V171() V172() Element of bool NAT
ColVec2Mx P2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
P1 * (ColVec2Mx P2) is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
Col ((P1 * (ColVec2Mx P2)),1) is Relation-like NAT -defined REAL -valued Function-like V33() V40( len (P1 * (ColVec2Mx P2))) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len (P1 * (ColVec2Mx P2))) -tuples_on REAL
len (P1 * (ColVec2Mx P2)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(len (P1 * (ColVec2Mx P2))) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = len (P1 * (ColVec2Mx P2)) } is set
len (Col ((P1 * (ColVec2Mx P2)),1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom (P1 * (ColVec2Mx P2)) is V167() V168() V169() V170() V171() V172() Element of bool NAT
(Col ((P1 * (ColVec2Mx P2)),1)) . n2 is V11() real ext-real Element of REAL
(P1 * (ColVec2Mx P2)) * (n2,1) is V11() real ext-real Element of REAL
len (ColVec2Mx P2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width (P1 * (ColVec2Mx P2)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width (ColVec2Mx P2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (width (P1 * (ColVec2Mx P2))) is V33() V40( width (P1 * (ColVec2Mx P2))) V167() V168() V169() V170() V171() V172() Element of bool NAT
[n2,1] is set
{n2,1} is non empty V167() V168() V169() V170() V171() V172() set
{n2} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{n2,1},{n2}} is non empty set
Indices (P1 * (ColVec2Mx P2)) is set
Line (P1,n2) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width P1) -tuples_on REAL
(width P1) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = width P1 } is set
Col ((ColVec2Mx P2),1) is Relation-like NAT -defined REAL -valued Function-like V33() V40( len (ColVec2Mx P2)) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len (ColVec2Mx P2)) -tuples_on REAL
(len (ColVec2Mx P2)) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = len (ColVec2Mx P2) } is set
|((Line (P1,n2)),(Col ((ColVec2Mx P2),1)))| is real set
mlt ((Line (P1,n2)),(Col ((ColVec2Mx P2),1))) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: ((Line (P1,n2)),(Col ((ColVec2Mx P2),1))) is set
Sum (mlt ((Line (P1,n2)),(Col ((ColVec2Mx P2),1)))) is V11() real ext-real Element of REAL
|((Line (P1,n2)),P2)| is real set
mlt ((Line (P1,n2)),P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: ((Line (P1,n2)),P2) is set
Sum (mlt ((Line (P1,n2)),P2)) is V11() real ext-real Element of REAL
(P1 * P2) . n2 is V11() real ext-real Element of REAL
P2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
width P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
P2 * n2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len P1) is V33() V40( len P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Line (P1,m) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width P1) -tuples_on REAL
(width P1) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = width P1 } is set
Line (P2,m) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width P2) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width P2) -tuples_on REAL
(width P2) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = width P2 } is set
(Line (P2,m)) * n2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len (Line (P2,m)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len ((Line (P2,m)) * n2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (Line (P1,m)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom (Line (P1,m)) is V40( width P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (width n2) is V33() V40( width n2) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom ((Line (P2,m)) * n2) is V167() V168() V169() V170() V171() V172() Element of bool NAT
dom P1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
n1 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
(Line (P1,m)) . n1 is V11() real ext-real Element of REAL
((Line (P2,m)) * n2) . n1 is V11() real ext-real Element of REAL
Seg (len ((Line (P2,m)) * n2)) is V33() V40( len ((Line (P2,m)) * n2)) V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (len (Line (P1,m))) is V33() V40( len (Line (P1,m))) V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (width P1) is V33() V40( width P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
[m,n1] is set
{m,n1} is non empty V167() V168() V169() V170() V171() V172() set
{m} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{m,n1},{m}} is non empty set
Indices P1 is set
(REAL,P1,m) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
(REAL,P1,m) . n1 is V11() real ext-real Element of REAL
P1 * (m,n1) is V11() real ext-real Element of REAL
Col (n2,n1) is Relation-like NAT -defined REAL -valued Function-like V33() V40( len n2) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len n2) -tuples_on REAL
(len n2) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = len n2 } is set
|((Line (P2,m)),(Col (n2,n1)))| is real set
mlt ((Line (P2,m)),(Col (n2,n1))) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: ((Line (P2,m)),(Col (n2,n1))) is set
Sum (mlt ((Line (P2,m)),(Col (n2,n1)))) is V11() real ext-real Element of REAL
Indices P1 is set
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Line (P2,m) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width P2) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width P2) -tuples_on REAL
(width P2) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = width P2 } is set
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
[m,n1] is set
{m,n1} is non empty V167() V168() V169() V170() V171() V172() set
{m} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{m,n1},{m}} is non empty set
P1 * (m,n1) is V11() real ext-real Element of REAL
Col (n2,n1) is Relation-like NAT -defined REAL -valued Function-like V33() V40( len n2) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len n2) -tuples_on REAL
(len n2) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = len n2 } is set
|((Line (P2,m)),(Col (n2,n1)))| is real set
mlt ((Line (P2,m)),(Col (n2,n1))) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: ((Line (P2,m)),(Col (n2,n1))) is set
Sum (mlt ((Line (P2,m)),(Col (n2,n1)))) is V11() real ext-real Element of REAL
dom P1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
len (Line (P2,m)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (width P1) is V33() V40( width P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
(Line (P2,m)) * n2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len ((Line (P2,m)) * n2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len ((Line (P2,m)) * n2)) is V33() V40( len ((Line (P2,m)) * n2)) V167() V168() V169() V170() V171() V172() Element of bool NAT
(REAL,P1,m) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
(REAL,P1,m) . n1 is V11() real ext-real Element of REAL
Line (P1,m) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width P1) -tuples_on REAL
(width P1) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = width P1 } is set
(Line (P1,m)) . n1 is V11() real ext-real Element of REAL
((Line (P2,m)) * n2) . n1 is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Indices n2 is set
m is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() Matrix of len n2, width n2, REAL
Indices m is set
len m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom n2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (width n2) is V33() V40( width n2) V167() V168() V169() V170() V171() V172() Element of bool NAT
[:(dom n2),(Seg (width n2)):] is INT -valued RAT -valued complex-yielding V158() V159() V160() set
dom m is V167() V168() V169() V170() V171() V172() Element of bool NAT
n1 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
P is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
[n1,P] is set
{n1,P} is non empty V167() V168() V169() V170() V171() V172() set
{n1} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{n1,P},{n1}} is non empty set
m * (n1,P) is V11() real ext-real Element of REAL
P1 . n1 is V11() real ext-real Element of REAL
n2 * (n1,P) is V11() real ext-real Element of REAL
(P1 . n1) * (n2 * (n1,P)) is V11() real ext-real Element of REAL
P2 . P is V11() real ext-real Element of REAL
((P1 . n1) * (n2 * (n1,P))) * (P2 . P) is V11() real ext-real Element of REAL
m is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom n2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (width n2) is V33() V40( width n2) V167() V168() V169() V170() V171() V172() Element of bool NAT
[:(dom n2),(Seg (width n2)):] is INT -valued RAT -valued complex-yielding V158() V159() V160() set
dom m is V167() V168() V169() V170() V171() V172() Element of bool NAT
Indices m is set
P is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
i is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
[P,i] is set
{P,i} is non empty V167() V168() V169() V170() V171() V172() set
{P} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{P,i},{P}} is non empty set
m * (P,i) is V11() real ext-real Element of REAL
P1 . P is V11() real ext-real Element of REAL
n2 * (P,i) is V11() real ext-real Element of REAL
(P1 . P) * (n2 * (P,i)) is V11() real ext-real Element of REAL
P2 . i is V11() real ext-real Element of REAL
((P1 . P) * (n2 * (P,i))) * (P2 . i) is V11() real ext-real Element of REAL
n1 * (P,i) is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(P1,P2,n2) is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
(P1,P2,n2) @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
n2 @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
(P2,P1,(n2 @)) is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len (n2 @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width (n2 @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (P2,P1,(n2 @)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width (P2,P1,(n2 @)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len ((P1,P2,n2) @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width (P1,P2,n2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width ((P1,P2,n2) @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (P1,P2,n2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Indices ((P1,P2,n2) @) is set
m is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
n1 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
[m,n1] is set
{m,n1} is non empty V167() V168() V169() V170() V171() V172() set
{m} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{m,n1},{m}} is non empty set
(P2,P1,(n2 @)) * (m,n1) is V11() real ext-real Element of REAL
((P1,P2,n2) @) * (m,n1) is V11() real ext-real Element of REAL
i is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
[i,P] is set
{i,P} is non empty V167() V168() V169() V170() V171() V172() set
{i} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{i,P},{i}} is non empty set
Indices n2 is set
Indices (P1,P2,n2) is set
[P,i] is set
{P,i} is non empty V167() V168() V169() V170() V171() V172() set
{P} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{P,i},{P}} is non empty set
Indices (n2 @) is set
(P2,P1,(n2 @)) * (P,i) is V11() real ext-real Element of REAL
P2 . P is V11() real ext-real Element of REAL
(n2 @) * (P,i) is V11() real ext-real Element of REAL
(P2 . P) * ((n2 @) * (P,i)) is V11() real ext-real Element of REAL
P1 . i is V11() real ext-real Element of REAL
((P2 . P) * ((n2 @) * (P,i))) * (P1 . i) is V11() real ext-real Element of REAL
n2 * (i,P) is V11() real ext-real Element of REAL
(P2 . P) * (n2 * (i,P)) is V11() real ext-real Element of REAL
((P2 . P) * (n2 * (i,P))) * (P1 . i) is V11() real ext-real Element of REAL
(P1 . i) * (n2 * (i,P)) is V11() real ext-real Element of REAL
((P1 . i) * (n2 * (i,P))) * (P2 . P) is V11() real ext-real Element of REAL
(P1,P2,n2) * (i,P) is V11() real ext-real Element of REAL
((P1,P2,n2) @) * (P,i) is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 * P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
|(P1,(n2 * P2))| is V11() real ext-real Element of REAL
mlt (P1,(n2 * P2)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: (P1,(n2 * P2)) is set
Sum (mlt (P1,(n2 * P2))) is V11() real ext-real Element of REAL
(P1,P2,n2) is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
((P1,P2,n2)) is V11() real ext-real Element of REAL
((P1,P2,n2)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((P1,P2,n2)) is V11() real ext-real Element of REAL
width (P1,P2,n2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len ((P1,P2,n2)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (P1,P2,n2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (n2 * P2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (mlt (P1,(n2 * P2))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n1 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
((P1,P2,n2)) . n1 is V11() real ext-real Element of REAL
(mlt (P1,(n2 * P2))) . n1 is V11() real ext-real Element of REAL
Seg (len ((P1,P2,n2))) is V33() V40( len ((P1,P2,n2))) V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (len n2) is V33() V40( len n2) V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (len (n2 * P2)) is V33() V40( len (n2 * P2)) V167() V168() V169() V170() V171() V172() Element of bool NAT
Line (n2,n1) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width n2) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width n2) -tuples_on REAL
(width n2) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = width n2 } is set
len (Line (n2,n1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Line ((P1,P2,n2),n1) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width (P1,P2,n2)) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width (P1,P2,n2)) -tuples_on REAL
(width (P1,P2,n2)) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = width (P1,P2,n2) } is set
len (Line ((P1,P2,n2),n1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
mlt ((Line (n2,n1)),P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: ((Line (n2,n1)),P2) is set
P1 . n1 is V11() real ext-real Element of REAL
(P1 . n1) * (mlt ((Line (n2,n1)),P2)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
(P1 . n1) multreal is Relation-like REAL -defined REAL -valued Function-like V27( REAL , REAL ) complex-yielding V158() V159() Element of bool [:REAL,REAL:]
K71(REAL) is non empty Relation-like REAL -defined REAL -valued V23( REAL ) complex-yielding V158() V159() Element of bool [:REAL,REAL:]
multreal [;] ((P1 . n1),K71(REAL)) is set
(mlt ((Line (n2,n1)),P2)) * ((P1 . n1) multreal) is Relation-like FinSequence-like complex-yielding V158() V159() set
P is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
((P1 . n1) * (mlt ((Line (n2,n1)),P2))) . P is V11() real ext-real Element of REAL
(Line ((P1,P2,n2),n1)) . P is V11() real ext-real Element of REAL
[n1,P] is set
{n1,P} is non empty V167() V168() V169() V170() V171() V172() set
{n1} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{n1,P},{n1}} is non empty set
Indices n2 is set
Seg (len (Line ((P1,P2,n2),n1))) is V33() V40( len (Line ((P1,P2,n2),n1))) V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (width (P1,P2,n2)) is V33() V40( width (P1,P2,n2)) V167() V168() V169() V170() V171() V172() Element of bool NAT
(mlt ((Line (n2,n1)),P2)) . P is V11() real ext-real Element of REAL
(P1 . n1) * ((mlt ((Line (n2,n1)),P2)) . P) is V11() real ext-real Element of REAL
(Line (n2,n1)) . P is V11() real ext-real Element of REAL
P2 . P is V11() real ext-real Element of REAL
((Line (n2,n1)) . P) * (P2 . P) is V11() real ext-real Element of REAL
(P1 . n1) * (((Line (n2,n1)) . P) * (P2 . P)) is V11() real ext-real Element of REAL
n2 * (n1,P) is V11() real ext-real Element of REAL
(n2 * (n1,P)) * (P2 . P) is V11() real ext-real Element of REAL
(P1 . n1) * ((n2 * (n1,P)) * (P2 . P)) is V11() real ext-real Element of REAL
(P1 . n1) * (n2 * (n1,P)) is V11() real ext-real Element of REAL
((P1 . n1) * (n2 * (n1,P))) * (P2 . P) is V11() real ext-real Element of REAL
(P1,P2,n2) * (n1,P) is V11() real ext-real Element of REAL
len (mlt ((Line (n2,n1)),P2)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len ((P1 . n1) * (mlt ((Line (n2,n1)),P2))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(n2 * P2) . n1 is V11() real ext-real Element of REAL
(P1 . n1) * ((n2 * P2) . n1) is V11() real ext-real Element of REAL
|((Line (n2,n1)),P2)| is real set
Sum (mlt ((Line (n2,n1)),P2)) is V11() real ext-real Element of REAL
(P1 . n1) * |((Line (n2,n1)),P2)| is V11() real ext-real Element of REAL
Sum ((P1 . n1) * (mlt ((Line (n2,n1)),P2))) is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(len P1) |-> 1 is Relation-like NAT -defined NAT -valued Function-like V33() V40( len P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of (len P1) -tuples_on NAT
(len P1) -tuples_on NAT is non empty functional FinSequence-membered FinSequenceSet of NAT
NAT * is non empty functional FinSequence-membered FinSequenceSet of NAT
{ b1 where b1 is Relation-like NAT -defined NAT -valued Function-like V33() FinSequence-like FinSubsequence-like Element of NAT * : len b1 = len P1 } is set
Seg (len P1) is V33() V40( len P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
(Seg (len P1)) --> 1 is Relation-like Seg (len P1) -defined INT -valued RAT -valued {1} -valued Function-like V27( Seg (len P1),{1}) V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of bool [:(Seg (len P1)),{1}:]
[:(Seg (len P1)),{1}:] is INT -valued RAT -valued complex-yielding V158() V159() V160() set
bool [:(Seg (len P1)),{1}:] is set
|(P1,((len P1) |-> 1))| is V11() real ext-real Element of REAL
mlt (P1,((len P1) |-> 1)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: (P1,((len P1) |-> 1)) is set
Sum (mlt (P1,((len P1) |-> 1))) is V11() real ext-real Element of REAL
Sum P1 is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 * n2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
|((P1 * n2),P2)| is V11() real ext-real Element of REAL
mlt ((P1 * n2),P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: ((P1 * n2),P2) is set
Sum (mlt ((P1 * n2),P2)) is V11() real ext-real Element of REAL
(P1,P2,n2) is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
((P1,P2,n2)) is V11() real ext-real Element of REAL
((P1,P2,n2)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((P1,P2,n2)) is V11() real ext-real Element of REAL
len (P1,P2,n2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
((P1,P2,n2)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len ((P1,P2,n2)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width (P1,P2,n2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (P1 * n2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (mlt ((P1 * n2),P2)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n1 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
((P1,P2,n2)) . n1 is V11() real ext-real Element of REAL
(mlt ((P1 * n2),P2)) . n1 is V11() real ext-real Element of REAL
Seg (len ((P1,P2,n2))) is V33() V40( len ((P1,P2,n2))) V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (width n2) is V33() V40( width n2) V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (len (P1 * n2)) is V33() V40( len (P1 * n2)) V167() V168() V169() V170() V171() V172() Element of bool NAT
Col (n2,n1) is Relation-like NAT -defined REAL -valued Function-like V33() V40( len n2) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len n2) -tuples_on REAL
(len n2) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = len n2 } is set
len (Col (n2,n1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Col ((P1,P2,n2),n1) is Relation-like NAT -defined REAL -valued Function-like V33() V40( len (P1,P2,n2)) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len (P1,P2,n2)) -tuples_on REAL
(len (P1,P2,n2)) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = len (P1,P2,n2) } is set
len (Col ((P1,P2,n2),n1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
mlt (P1,(Col (n2,n1))) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: (P1,(Col (n2,n1))) is set
P2 . n1 is V11() real ext-real Element of REAL
(P2 . n1) * (mlt (P1,(Col (n2,n1)))) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
(P2 . n1) multreal is Relation-like REAL -defined REAL -valued Function-like V27( REAL , REAL ) complex-yielding V158() V159() Element of bool [:REAL,REAL:]
K71(REAL) is non empty Relation-like REAL -defined REAL -valued V23( REAL ) complex-yielding V158() V159() Element of bool [:REAL,REAL:]
multreal [;] ((P2 . n1),K71(REAL)) is set
(mlt (P1,(Col (n2,n1)))) * ((P2 . n1) multreal) is Relation-like FinSequence-like complex-yielding V158() V159() set
P is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
((P2 . n1) * (mlt (P1,(Col (n2,n1))))) . P is V11() real ext-real Element of REAL
(Col ((P1,P2,n2),n1)) . P is V11() real ext-real Element of REAL
[P,n1] is set
{P,n1} is non empty V167() V168() V169() V170() V171() V172() set
{P} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{P,n1},{P}} is non empty set
Indices n2 is set
Seg (len (Col ((P1,P2,n2),n1))) is V33() V40( len (Col ((P1,P2,n2),n1))) V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (len (P1,P2,n2)) is V33() V40( len (P1,P2,n2)) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom (P1,P2,n2) is V167() V168() V169() V170() V171() V172() Element of bool NAT
dom n2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
(mlt (P1,(Col (n2,n1)))) . P is V11() real ext-real Element of REAL
(P2 . n1) * ((mlt (P1,(Col (n2,n1)))) . P) is V11() real ext-real Element of REAL
P1 . P is V11() real ext-real Element of REAL
(Col (n2,n1)) . P is V11() real ext-real Element of REAL
(P1 . P) * ((Col (n2,n1)) . P) is V11() real ext-real Element of REAL
(P2 . n1) * ((P1 . P) * ((Col (n2,n1)) . P)) is V11() real ext-real Element of REAL
n2 * (P,n1) is V11() real ext-real Element of REAL
(P1 . P) * (n2 * (P,n1)) is V11() real ext-real Element of REAL
(P2 . n1) * ((P1 . P) * (n2 * (P,n1))) is V11() real ext-real Element of REAL
(P1,P2,n2) * (P,n1) is V11() real ext-real Element of REAL
len (mlt (P1,(Col (n2,n1)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len ((P2 . n1) * (mlt (P1,(Col (n2,n1))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(P1 * n2) . n1 is V11() real ext-real Element of REAL
((P1 * n2) . n1) * (P2 . n1) is V11() real ext-real Element of REAL
|(P1,(Col (n2,n1)))| is real set
Sum (mlt (P1,(Col (n2,n1)))) is V11() real ext-real Element of REAL
|(P1,(Col (n2,n1)))| * (P2 . n1) is V11() real ext-real Element of REAL
Sum ((P2 . n1) * (mlt (P1,(Col (n2,n1))))) is V11() real ext-real Element of REAL
Sum ((P1,P2,n2)) is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 * n2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
|((P1 * n2),P2)| is V11() real ext-real Element of REAL
mlt ((P1 * n2),P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: ((P1 * n2),P2) is set
Sum (mlt ((P1 * n2),P2)) is V11() real ext-real Element of REAL
n2 * P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
|(P1,(n2 * P2))| is V11() real ext-real Element of REAL
mlt (P1,(n2 * P2)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: (P1,(n2 * P2)) is set
Sum (mlt (P1,(n2 * P2))) is V11() real ext-real Element of REAL
(P1,P2,n2) is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
((P1,P2,n2)) is V11() real ext-real Element of REAL
((P1,P2,n2)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((P1,P2,n2)) is V11() real ext-real Element of REAL
P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 * P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
|((n2 * P1),P2)| is V11() real ext-real Element of REAL
mlt ((n2 * P1),P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: ((n2 * P1),P2) is set
Sum (mlt ((n2 * P1),P2)) is V11() real ext-real Element of REAL
n2 @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
(n2 @) * P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
|(P1,((n2 @) * P2))| is V11() real ext-real Element of REAL
mlt (P1,((n2 @) * P2)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: (P1,((n2 @) * P2)) is set
Sum (mlt (P1,((n2 @) * P2))) is V11() real ext-real Element of REAL
len (n2 @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width (n2 @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 * (n2 @) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
|((P1 * (n2 @)),P2)| is V11() real ext-real Element of REAL
mlt ((P1 * (n2 @)),P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: ((P1 * (n2 @)),P2) is set
Sum (mlt ((P1 * (n2 @)),P2)) is V11() real ext-real Element of REAL
P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 * n2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
|(P1,(P2 * n2))| is V11() real ext-real Element of REAL
mlt (P1,(P2 * n2)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: (P1,(P2 * n2)) is set
Sum (mlt (P1,(P2 * n2))) is V11() real ext-real Element of REAL
n2 @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
P1 * (n2 @) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
|((P1 * (n2 @)),P2)| is V11() real ext-real Element of REAL
mlt ((P1 * (n2 @)),P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: ((P1 * (n2 @)),P2) is set
Sum (mlt ((P1 * (n2 @)),P2)) is V11() real ext-real Element of REAL
len (n2 @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width (n2 @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(n2 @) * P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
|(P1,((n2 @) * P2))| is V11() real ext-real Element of REAL
mlt (P1,((n2 @) * P2)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: (P1,((n2 @) * P2)) is set
Sum (mlt (P1,((n2 @) * P2))) is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(len P1) |-> 1 is Relation-like NAT -defined NAT -valued Function-like V33() V40( len P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of (len P1) -tuples_on NAT
(len P1) -tuples_on NAT is non empty functional FinSequence-membered FinSequenceSet of NAT
NAT * is non empty functional FinSequence-membered FinSequenceSet of NAT
{ b1 where b1 is Relation-like NAT -defined NAT -valued Function-like V33() FinSequence-like FinSubsequence-like Element of NAT * : len b1 = len P1 } is set
Seg (len P1) is V33() V40( len P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
(Seg (len P1)) --> 1 is Relation-like Seg (len P1) -defined INT -valued RAT -valued {1} -valued Function-like V27( Seg (len P1),{1}) V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of bool [:(Seg (len P1)),{1}:]
[:(Seg (len P1)),{1}:] is INT -valued RAT -valued complex-yielding V158() V159() V160() set
bool [:(Seg (len P1)),{1}:] is set
P2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 * P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len (P1 * P2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len (P1 * P2)) is V33() V40( len (P1 * P2)) V167() V168() V169() V170() V171() V172() Element of bool NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Col (P2,n2) is Relation-like NAT -defined REAL -valued Function-like V33() V40( len P2) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len P2) -tuples_on REAL
(len P2) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = len P2 } is set
len (Col (P2,n2)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(P1 * P2) . n2 is V11() real ext-real Element of REAL
|(P1,(Col (P2,n2)))| is real set
mlt (P1,(Col (P2,n2))) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: (P1,(Col (P2,n2))) is set
Sum (mlt (P1,(Col (P2,n2)))) is V11() real ext-real Element of REAL
Sum (Col (P2,n2)) is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(len P1) |-> 1 is Relation-like NAT -defined NAT -valued Function-like V33() V40( len P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of (len P1) -tuples_on NAT
(len P1) -tuples_on NAT is non empty functional FinSequence-membered FinSequenceSet of NAT
NAT * is non empty functional FinSequence-membered FinSequenceSet of NAT
{ b1 where b1 is Relation-like NAT -defined NAT -valued Function-like V33() FinSequence-like FinSubsequence-like Element of NAT * : len b1 = len P1 } is set
Seg (len P1) is V33() V40( len P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
(Seg (len P1)) --> 1 is Relation-like Seg (len P1) -defined INT -valued RAT -valued {1} -valued Function-like V27( Seg (len P1),{1}) V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of bool [:(Seg (len P1)),{1}:]
[:(Seg (len P1)),{1}:] is INT -valued RAT -valued complex-yielding V158() V159() V160() set
bool [:(Seg (len P1)),{1}:] is set
P2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
width P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 * P1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len (P2 * P1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len (P2 * P1)) is V33() V40( len (P2 * P1)) V167() V168() V169() V170() V171() V172() Element of bool NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Line (P2,n2) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width P2) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width P2) -tuples_on REAL
(width P2) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = width P2 } is set
len (Line (P2,n2)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(P2 * P1) . n2 is V11() real ext-real Element of REAL
|((Line (P2,n2)),P1)| is real set
mlt ((Line (P2,n2)),P1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: ((Line (P2,n2)),P1) is set
Sum (mlt ((Line (P2,n2)),P1)) is V11() real ext-real Element of REAL
Sum (Line (P2,n2)) is V11() real ext-real Element of REAL
P1 is non empty epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real positive non negative set
P2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg P2 is non empty V33() V40(P2) V167() V168() V169() V170() V171() V172() Element of bool NAT
n2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Sum n2 is V11() real ext-real Element of REAL
n2 . 1 is V11() real ext-real Element of REAL
m is Relation-like NAT -defined REAL -valued Function-like V27( NAT , REAL ) complex-yielding V158() V159() Element of bool [:NAT,REAL:]
m . 1 is V11() real ext-real Element of REAL
m . (len n2) is V11() real ext-real Element of REAL
n1 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
m . n1 is V11() real ext-real Element of REAL
n1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
m . (n1 + 1) is V11() real ext-real Element of REAL
m . (n1 + 1) is V11() real ext-real Element of REAL
n2 . (n1 + 1) is V11() real ext-real Element of REAL
1 + (n2 . (n1 + 1)) is V11() real ext-real Element of REAL
1 + 0 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
m . (n1 + 1) is V11() real ext-real Element of REAL
m . (n1 + 1) is V11() real ext-real Element of REAL
m . (n1 + 1) is V11() real ext-real Element of REAL
m . 0 is V11() real ext-real Element of REAL
n1 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
m . n1 is V11() real ext-real Element of REAL
dom n2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 . m is V11() real ext-real Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 . m is V11() real ext-real Element of REAL
P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom P2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
Sum P2 is V11() real ext-real Element of REAL
P1 is non empty Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() () FinSequence of REAL
dom P1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
Sum P1 is V11() real ext-real Element of REAL
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
P1 . P2 is V11() real ext-real Element of REAL
P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 . P2 is V11() real ext-real Element of REAL
P1 is non empty set
P1 * is non empty functional FinSequence-membered FinSequenceSet of P1
P2 is Relation-like non empty-yielding NAT -defined P1 * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of P1 *
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
P1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
P1 is non empty epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real positive non negative set
P2 is non empty epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real positive non negative set
n2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
n2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
P is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg P is non empty V33() V40(P) V167() V168() V169() V170() V171() V172() Element of bool NAT
i is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg i is V33() V40(i) V167() V168() V169() V170() V171() V172() Element of bool NAT
p1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len p1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
i + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
p1 . (i + 1) is V11() real ext-real Element of REAL
p1 | i is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
(1) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one V33() V40(1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() V161() V162() V163() V164() FinSequence of REAL
(p1 | i) ^ (1) is non empty Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
e3 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len e3 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom p1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
Sum p1 is V11() real ext-real Element of REAL
Sum e3 is V11() real ext-real Element of REAL
Sum (p1 | i) is V11() real ext-real Element of REAL
(Sum (p1 | i)) + 1 is V11() real ext-real Element of REAL
dom e3 is V167() V168() V169() V170() V171() V172() Element of bool NAT
e2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
e3 . e2 is V11() real ext-real Element of REAL
Seg (i + 1) is non empty V33() V40(i + 1) V167() V168() V169() V170() V171() V172() Element of bool NAT
p1 . e2 is V11() real ext-real Element of REAL
i |-> 0 is Relation-like empty-yielding NAT -defined NAT -valued Function-like V33() V40(i) FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of i -tuples_on NAT
i -tuples_on NAT is non empty functional FinSequence-membered FinSequenceSet of NAT
NAT * is non empty functional FinSequence-membered FinSequenceSet of NAT
{ b1 where b1 is Relation-like NAT -defined NAT -valued Function-like V33() FinSequence-like FinSubsequence-like Element of NAT * : len b1 = i } is set
(Seg i) --> 0 is Relation-like Seg i -defined INT -valued RAT -valued {0} -valued Function-like V27( Seg i,{0}) V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of bool [:(Seg i),{0}:]
{0} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
[:(Seg i),{0}:] is INT -valued RAT -valued complex-yielding V158() V159() V160() set
bool [:(Seg i),{0}:] is set
Sum e3 is V11() real ext-real Element of REAL
i * 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Sum (p1 | i) is V11() real ext-real Element of REAL
(Sum (p1 | i)) + 1 is V11() real ext-real Element of REAL
P |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like V33() V40(P) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of P -tuples_on REAL
P -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = P } is set
(Seg P) --> 0 is Relation-like Seg P -defined INT -valued RAT -valued {0} -valued Function-like V27( Seg P,{0}) V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of bool [:(Seg P),{0}:]
{0} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
[:(Seg P),{0}:] is INT -valued RAT -valued complex-yielding V158() V159() V160() set
bool [:(Seg P),{0}:] is set
e2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len e2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg n1 is non empty V33() V40(n1) V167() V168() V169() V170() V171() V172() Element of bool NAT
p is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg p is V33() V40(p) V167() V168() V169() V170() V171() V172() Element of bool NAT
M1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() Matrix of n1,P, REAL
Sum e2 is V11() real ext-real Element of REAL
P * 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(M1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len (M1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len M1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
i is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(M1) . i is V11() real ext-real Element of REAL
dom (M1) is V167() V168() V169() V170() V171() V172() Element of bool NAT
(REAL,M1,i) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (REAL,M1,i) is V11() real ext-real Element of REAL
(REAL,M1,i) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (REAL,M1,i) is V11() real ext-real Element of REAL
(M1) is V11() real ext-real Element of REAL
Sum (M1) is V11() real ext-real Element of REAL
i is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
i | p is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
p + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
i . (p + 1) is V11() real ext-real Element of REAL
j is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len j is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom i is V167() V168() V169() V170() V171() V172() Element of bool NAT
Sum i is V11() real ext-real Element of REAL
(i | p) ^ (1) is non empty Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((i | p) ^ (1)) is V11() real ext-real Element of REAL
Sum (i | p) is V11() real ext-real Element of REAL
(Sum (i | p)) + 1 is V11() real ext-real Element of REAL
dom j is V167() V168() V169() V170() V171() V172() Element of bool NAT
p1 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
j . p1 is V11() real ext-real Element of REAL
Seg (p + 1) is non empty V33() V40(p + 1) V167() V168() V169() V170() V171() V172() Element of bool NAT
i . p1 is V11() real ext-real Element of REAL
p |-> 0 is Relation-like empty-yielding NAT -defined NAT -valued Function-like V33() V40(p) FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of p -tuples_on NAT
p -tuples_on NAT is non empty functional FinSequence-membered FinSequenceSet of NAT
NAT * is non empty functional FinSequence-membered FinSequenceSet of NAT
{ b1 where b1 is Relation-like NAT -defined NAT -valued Function-like V33() FinSequence-like FinSubsequence-like Element of NAT * : len b1 = p } is set
(Seg p) --> 0 is Relation-like Seg p -defined INT -valued RAT -valued {0} -valued Function-like V27( Seg p,{0}) V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of bool [:(Seg p),{0}:]
[:(Seg p),{0}:] is INT -valued RAT -valued complex-yielding V158() V159() V160() set
bool [:(Seg p),{0}:] is set
Sum j is V11() real ext-real Element of REAL
p * 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(i | p) ^ (1) is non empty Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum ((i | p) ^ (1)) is V11() real ext-real Element of REAL
Sum (i | p) is V11() real ext-real Element of REAL
(Sum (i | p)) + 1 is V11() real ext-real Element of REAL
Indices M1 is set
i is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
j is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
[i,j] is set
{i,j} is non empty V167() V168() V169() V170() V171() V172() set
{i} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{i,j},{i}} is non empty set
M1 * (i,j) is V11() real ext-real Element of REAL
(REAL,M1,i) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
p1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
p1 . j is V11() real ext-real Element of REAL
len M1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom M1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
width M1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (width M1) is V33() V40( width M1) V167() V168() V169() V170() V171() V172() Element of bool NAT
[:(dom M1),(Seg (width M1)):] is INT -valued RAT -valued complex-yielding V158() V159() V160() set
n2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() Matrix of 1,1, REAL
(n2) is V11() real ext-real Element of REAL
(n2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (n2) is V11() real ext-real Element of REAL
len n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 is Relation-like non empty-yielding NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() () () () FinSequence of REAL *
P1 @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (P1 @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width (P1 @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
m is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() Matrix of width P1, len P1, REAL
Indices m is set
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
[n1,P] is set
{n1,P} is non empty V167() V168() V169() V170() V171() V172() set
{n1} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{n1,P},{n1}} is non empty set
m * (n1,P) is V11() real ext-real Element of REAL
[P,n1] is set
{P,n1} is non empty V167() V168() V169() V170() V171() V172() set
{P} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{P,n1},{P}} is non empty set
Indices P1 is set
P1 * (P,n1) is V11() real ext-real Element of REAL
(m) is V11() real ext-real Element of REAL
(m) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (m) is V11() real ext-real Element of REAL
(P1) is V11() real ext-real Element of REAL
(P1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (P1) is V11() real ext-real Element of REAL
P1 is Relation-like non empty-yielding NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() () () () FinSequence of REAL *
Indices P1 is set
P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
[P2,n2] is set
{P2,n2} is non empty V167() V168() V169() V170() V171() V172() set
{P2} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{P2,n2},{P2}} is non empty set
P1 * (P2,n2) is V11() real ext-real Element of REAL
(P1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
dom (P1) is V167() V168() V169() V170() V171() V172() Element of bool NAT
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
(P1) . P2 is V11() real ext-real Element of REAL
len (P1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len (P1)) is V33() V40( len (P1)) V167() V168() V169() V170() V171() V172() Element of bool NAT
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len P1) is V33() V40( len P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom P1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
(REAL,P1,P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
dom (REAL,P1,P2) is V167() V168() V169() V170() V171() V172() Element of bool NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
(REAL,P1,P2) . n2 is V11() real ext-real Element of REAL
Sum (REAL,P1,P2) is V11() real ext-real Element of REAL
P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(P1) . P2 is V11() real ext-real Element of REAL
(P1) is V11() real ext-real Element of REAL
Sum (P1) is V11() real ext-real Element of REAL
dom P1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(REAL,P1,P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
dom (REAL,P1,P2) is V167() V168() V169() V170() V171() V172() Element of bool NAT
Sum (REAL,P1,P2) is V11() real ext-real Element of REAL
n2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
(REAL,P1,P2) . n2 is V11() real ext-real Element of REAL
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(REAL,P1,P2) . n2 is V11() real ext-real Element of REAL
P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(REAL,P1,P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
dom (REAL,P1,P2) is V167() V168() V169() V170() V171() V172() Element of bool NAT
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len P1) is V33() V40( len P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
len (P1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len (P1)) is V33() V40( len (P1)) V167() V168() V169() V170() V171() V172() Element of bool NAT
(P1) . P2 is V11() real ext-real Element of REAL
Sum (REAL,P1,P2) is V11() real ext-real Element of REAL
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(REAL,P1,P2) . n2 is V11() real ext-real Element of REAL
P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
[P2,n2] is set
{P2,n2} is non empty V167() V168() V169() V170() V171() V172() set
{P2} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{P2,n2},{P2}} is non empty set
P1 * (P2,n2) is V11() real ext-real Element of REAL
(REAL,P1,P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len P1) is V33() V40( len P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
width P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (width P1) is V33() V40( width P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
len (REAL,P1,P2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len (REAL,P1,P2)) is V33() V40( len (REAL,P1,P2)) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom (REAL,P1,P2) is V167() V168() V169() V170() V171() V172() Element of bool NAT
m is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
m . n2 is V11() real ext-real Element of REAL
P1 is non empty epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real positive non negative set
P2 is non empty epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real positive non negative set
n2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
n2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg P2 is non empty V33() V40(P2) V167() V168() V169() V170() V171() V172() Element of bool NAT
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg m is V33() V40(m) V167() V168() V169() V170() V171() V172() Element of bool NAT
n1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
n1 . (m + 1) is V11() real ext-real Element of REAL
n1 | m is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
(1) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one V33() V40(1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() V161() V162() V163() V164() FinSequence of REAL
(n1 | m) ^ (1) is non empty Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
P1 |-> n1 is Relation-like NAT -defined Function-like V33() V40(P1) FinSequence-like FinSubsequence-like set
Seg P1 is non empty V33() V40(P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
(Seg P1) --> n1 is Relation-like Seg P1 -defined {n1} -valued Function-like V27( Seg P1,{n1}) V33() FinSequence-like FinSubsequence-like Element of bool [:(Seg P1),{n1}:]
{n1} is non empty trivial V40(1) set
[:(Seg P1),{n1}:] is set
bool [:(Seg P1),{n1}:] is set
P is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() Matrix of P1,P2, REAL
len P is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Indices P is set
i is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
p is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
[i,p] is set
{i,p} is non empty V167() V168() V169() V170() V171() V172() set
{i} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{i,p},{i}} is non empty set
P * (i,p) is V11() real ext-real Element of REAL
(REAL,P,i) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
p1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
p1 . p is V11() real ext-real Element of REAL
dom P is V167() V168() V169() V170() V171() V172() Element of bool NAT
width P is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (width P) is V33() V40( width P) V167() V168() V169() V170() V171() V172() Element of bool NAT
[:(dom P),(Seg (width P)):] is INT -valued RAT -valued complex-yielding V158() V159() V160() set
i is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len i is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom n1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
Sum n1 is V11() real ext-real Element of REAL
Sum (n1 | m) is V11() real ext-real Element of REAL
(Sum (n1 | m)) + 1 is V11() real ext-real Element of REAL
dom i is V167() V168() V169() V170() V171() V172() Element of bool NAT
p is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
i . p is V11() real ext-real Element of REAL
Seg (m + 1) is non empty V33() V40(m + 1) V167() V168() V169() V170() V171() V172() Element of bool NAT
n1 . p is V11() real ext-real Element of REAL
m |-> 0 is Relation-like empty-yielding NAT -defined NAT -valued Function-like V33() V40(m) FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of m -tuples_on NAT
m -tuples_on NAT is non empty functional FinSequence-membered FinSequenceSet of NAT
NAT * is non empty functional FinSequence-membered FinSequenceSet of NAT
{ b1 where b1 is Relation-like NAT -defined NAT -valued Function-like V33() FinSequence-like FinSubsequence-like Element of NAT * : len b1 = m } is set
(Seg m) --> 0 is Relation-like Seg m -defined INT -valued RAT -valued {0} -valued Function-like V27( Seg m,{0}) V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of bool [:(Seg m),{0}:]
{0} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
[:(Seg m),{0}:] is INT -valued RAT -valued complex-yielding V158() V159() V160() set
bool [:(Seg m),{0}:] is set
Sum i is V11() real ext-real Element of REAL
m * 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Sum (n1 | m) is V11() real ext-real Element of REAL
(Sum (n1 | m)) + 1 is V11() real ext-real Element of REAL
dom P is V167() V168() V169() V170() V171() V172() Element of bool NAT
p is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(REAL,P,p) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (REAL,P,p) is V11() real ext-real Element of REAL
P1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
P1 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
n2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() Matrix of 1,1, REAL
len n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 is Relation-like non empty-yielding NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() () () () FinSequence of REAL *
Indices P1 is set
P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
[P2,n2] is set
{P2,n2} is non empty V167() V168() V169() V170() V171() V172() set
{P2} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{P2,n2},{P2}} is non empty set
P1 * (P2,n2) is V11() real ext-real Element of REAL
dom P1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(REAL,P1,P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
dom (REAL,P1,P2) is V167() V168() V169() V170() V171() V172() Element of bool NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
(REAL,P1,P2) . n2 is V11() real ext-real Element of REAL
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(REAL,P1,P2) . n2 is V11() real ext-real Element of REAL
Sum (REAL,P1,P2) is V11() real ext-real Element of REAL
P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
[P2,n2] is set
{P2,n2} is non empty V167() V168() V169() V170() V171() V172() set
{P2} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{P2,n2},{P2}} is non empty set
P1 * (P2,n2) is V11() real ext-real Element of REAL
(REAL,P1,P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len P1) is V33() V40( len P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
width P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (width P1) is V33() V40( width P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
len (REAL,P1,P2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len (REAL,P1,P2)) is V33() V40( len (REAL,P1,P2)) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom (REAL,P1,P2) is V167() V168() V169() V170() V171() V172() Element of bool NAT
m is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
m . n2 is V11() real ext-real Element of REAL
P1 is Relation-like non empty-yielding NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
dom P1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
width P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Indices P1 is set
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
[m,n1] is set
{m,n1} is non empty V167() V168() V169() V170() V171() V172() set
{m} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{m,n1},{m}} is non empty set
P1 * (m,n1) is V11() real ext-real Element of REAL
Line (P1,n2) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width P1) -tuples_on REAL
(width P1) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = width P1 } is set
len (Line (P1,n2)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom (Line (P1,n2)) is V40( width P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(Line (P1,n2)) . m is V11() real ext-real Element of REAL
Sum (Line (P1,n2)) is V11() real ext-real Element of REAL
(REAL,P1,n2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (REAL,P1,n2) is V11() real ext-real Element of REAL
P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Line (P1,P2) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width P1) -tuples_on REAL
Sum (Line (P1,P2)) is V11() real ext-real Element of REAL
(REAL,P1,P2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (REAL,P1,P2) is V11() real ext-real Element of REAL
P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Line (P1,P2) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width P1) -tuples_on REAL
dom (Line (P1,P2)) is V40( width P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(Line (P1,P2)) . n2 is V11() real ext-real Element of REAL
P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
[P2,n2] is set
{P2,n2} is non empty V167() V168() V169() V170() V171() V172() set
{P2} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{P2,n2},{P2}} is non empty set
P1 * (P2,n2) is V11() real ext-real Element of REAL
P1 is Relation-like non empty-yielding NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() () FinSequence of REAL *
(P1) is V11() real ext-real Element of REAL
(P1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (P1) is V11() real ext-real Element of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (P1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom (P1) is V167() V168() V169() V170() V171() V172() Element of bool NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
Seg (len (P1)) is V33() V40( len (P1)) V167() V168() V169() V170() V171() V172() Element of bool NAT
Seg (len P1) is V33() V40( len P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom P1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
(REAL,P1,n2) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (REAL,P1,n2) is V11() real ext-real Element of REAL
(P1) . n2 is V11() real ext-real Element of REAL
(len P1) |-> 1 is Relation-like NAT -defined NAT -valued Function-like V33() V40( len P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of (len P1) -tuples_on NAT
(len P1) -tuples_on NAT is non empty functional FinSequence-membered FinSequenceSet of NAT
NAT * is non empty functional FinSequence-membered FinSequenceSet of NAT
{ b1 where b1 is Relation-like NAT -defined NAT -valued Function-like V33() FinSequence-like FinSubsequence-like Element of NAT * : len b1 = len P1 } is set
Seg (len P1) is V33() V40( len P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
(Seg (len P1)) --> 1 is Relation-like Seg (len P1) -defined INT -valued RAT -valued {1} -valued Function-like V27( Seg (len P1),{1}) V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of bool [:(Seg (len P1)),{1}:]
[:(Seg (len P1)),{1}:] is INT -valued RAT -valued complex-yielding V158() V159() V160() set
bool [:(Seg (len P1)),{1}:] is set
(len P1) * 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 is Relation-like non empty-yielding NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() () () () FinSequence of REAL *
(P1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (P1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Indices P1 is set
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
[m,n1] is set
{m,n1} is non empty V167() V168() V169() V170() V171() V172() set
{m} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{m,n1},{m}} is non empty set
P1 * (m,n1) is V11() real ext-real Element of REAL
dom (P1) is V167() V168() V169() V170() V171() V172() Element of bool NAT
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(P1) . m is V11() real ext-real Element of REAL
Seg (len P1) is V33() V40( len P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom P1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
Line (P1,m) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width P1) -tuples_on REAL
width P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(width P1) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = width P1 } is set
dom (Line (P1,m)) is V40( width P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
n1 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
(Line (P1,m)) . n1 is V11() real ext-real Element of REAL
Sum (Line (P1,m)) is V11() real ext-real Element of REAL
Sum (P1) is V11() real ext-real Element of REAL
(P1) is V11() real ext-real Element of REAL
(P1) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
width P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (P1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Indices P1 is set
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
[m,n1] is set
{m,n1} is non empty V167() V168() V169() V170() V171() V172() set
{m} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{m,n1},{m}} is non empty set
P1 * (m,n1) is V11() real ext-real Element of REAL
dom (P1) is V167() V168() V169() V170() V171() V172() Element of bool NAT
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(P1) . m is V11() real ext-real Element of REAL
Seg (width P1) is V33() V40( width P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
Col (P1,m) is Relation-like NAT -defined REAL -valued Function-like V33() V40( len P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len P1) -tuples_on REAL
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(len P1) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = len P1 } is set
dom (Col (P1,m)) is V40( len P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
n1 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
(Col (P1,m)) . n1 is V11() real ext-real Element of REAL
Sum (Col (P1,m)) is V11() real ext-real Element of REAL
Sum (P1) is V11() real ext-real Element of REAL
(P1) is V11() real ext-real Element of REAL
Sum (P1) is V11() real ext-real Element of REAL
P1 is Relation-like non empty-yielding NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
P1 @ is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
width P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width (P1 @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len (P1 @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 is Relation-like non empty-yielding NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() () () () FinSequence of REAL *
P1 @ is Relation-like non empty-yielding NAT -defined REAL * -valued REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
P1 is non empty Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() () FinSequence of REAL
len P1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 is Relation-like non empty-yielding NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() () () () FinSequence of REAL *
len n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 * n2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len (P1 * n2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom (P1 * n2) is V167() V168() V169() V170() V171() V172() Element of bool NAT
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(P1 * n2) . m is V11() real ext-real Element of REAL
Seg (len (P1 * n2)) is V33() V40( len (P1 * n2)) V167() V168() V169() V170() V171() V172() Element of bool NAT
Col (n2,m) is Relation-like NAT -defined REAL -valued Function-like V33() V40( len n2) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len n2) -tuples_on REAL
(len n2) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = len n2 } is set
|(P1,(Col (n2,m)))| is real set
mlt (P1,(Col (n2,m))) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: (P1,(Col (n2,m))) is set
Sum (mlt (P1,(Col (n2,m)))) is V11() real ext-real Element of REAL
Indices n2 is set
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
[n1,P] is set
{n1,P} is non empty V167() V168() V169() V170() V171() V172() set
{n1} is non empty trivial V40(1) V167() V168() V169() V170() V171() V172() set
{{n1,P},{n1}} is non empty set
n2 * (n1,P) is V11() real ext-real Element of REAL
Seg (width n2) is V33() V40( width n2) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom (Col (n2,m)) is V40( len n2) V167() V168() V169() V170() V171() V172() Element of bool NAT
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(Col (n2,m)) . n1 is V11() real ext-real Element of REAL
dom P1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 . n1 is V11() real ext-real Element of REAL
dom (mlt (P1,(Col (n2,m)))) is V167() V168() V169() V170() V171() V172() Element of bool NAT
n1 is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
(mlt (P1,(Col (n2,m)))) . n1 is V11() real ext-real Element of REAL
(width n2) |-> 1 is Relation-like NAT -defined REAL -valued Function-like V33() V40( width n2) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width n2) -tuples_on REAL
(width n2) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = width n2 } is set
Seg (width n2) is V33() V40( width n2) V167() V168() V169() V170() V171() V172() Element of bool NAT
(Seg (width n2)) --> 1 is Relation-like Seg (width n2) -defined INT -valued RAT -valued {1} -valued Function-like V27( Seg (width n2),{1}) V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of bool [:(Seg (width n2)),{1}:]
[:(Seg (width n2)),{1}:] is INT -valued RAT -valued complex-yielding V158() V159() V160() set
bool [:(Seg (width n2)),{1}:] is set
len ((width n2) |-> 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
n2 @ is Relation-like non empty-yielding NAT -defined REAL * -valued REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len (n2 @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width (n2 @) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
((width n2) |-> 1) * (n2 @) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
len (((width n2) |-> 1) * (n2 @)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
dom (((width n2) |-> 1) * (n2 @)) is V167() V168() V169() V170() V171() V172() Element of bool NAT
P is epsilon-transitive epsilon-connected ordinal natural V33() V38() ext-real non negative set
(((width n2) |-> 1) * (n2 @)) . P is V11() real ext-real Element of REAL
Seg (len (((width n2) |-> 1) * (n2 @))) is V33() V40( len (((width n2) |-> 1) * (n2 @))) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom n2 is V167() V168() V169() V170() V171() V172() Element of bool NAT
Col ((n2 @),P) is Relation-like NAT -defined REAL -valued Function-like V33() V40( len (n2 @)) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (len (n2 @)) -tuples_on REAL
(len (n2 @)) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = len (n2 @) } is set
Sum (Col ((n2 @),P)) is V11() real ext-real Element of REAL
Line (n2,P) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width n2) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width n2) -tuples_on REAL
Sum (Line (n2,P)) is V11() real ext-real Element of REAL
(REAL,n2,P) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
Sum (REAL,n2,P) is V11() real ext-real Element of REAL
(len P1) |-> 1 is Relation-like NAT -defined NAT -valued Function-like V33() V40( len P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of (len P1) -tuples_on NAT
(len P1) -tuples_on NAT is non empty functional FinSequence-membered FinSequenceSet of NAT
NAT * is non empty functional FinSequence-membered FinSequenceSet of NAT
{ b1 where b1 is Relation-like NAT -defined NAT -valued Function-like V33() FinSequence-like FinSubsequence-like Element of NAT * : len b1 = len P1 } is set
Seg (len P1) is non empty V33() V40( len P1) V167() V168() V169() V170() V171() V172() Element of bool NAT
(Seg (len P1)) --> 1 is Relation-like Seg (len P1) -defined INT -valued RAT -valued {1} -valued Function-like V27( Seg (len P1),{1}) V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() V160() Element of bool [:(Seg (len P1)),{1}:]
[:(Seg (len P1)),{1}:] is INT -valued RAT -valued complex-yielding V158() V159() V160() set
bool [:(Seg (len P1)),{1}:] is set
Sum (P1 * n2) is V11() real ext-real Element of REAL
|((P1 * n2),((width n2) |-> 1))| is V11() real ext-real Element of REAL
mlt ((P1 * n2),((width n2) |-> 1)) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: ((P1 * n2),((width n2) |-> 1)) is set
Sum (mlt ((P1 * n2),((width n2) |-> 1))) is V11() real ext-real Element of REAL
|(P1,(((width n2) |-> 1) * (n2 @)))| is V11() real ext-real Element of REAL
mlt (P1,(((width n2) |-> 1) * (n2 @))) is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL
multreal .: (P1,(((width n2) |-> 1) * (n2 @))) is set
Sum (mlt (P1,(((width n2) |-> 1) * (n2 @)))) is V11() real ext-real Element of REAL
Sum P1 is V11() real ext-real Element of REAL
P1 is Relation-like non empty-yielding NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() () () () FinSequence of REAL *
width P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P2 is Relation-like non empty-yielding NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() () () () FinSequence of REAL *
len P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P1 * P2 is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() FinSequence of REAL *
len (P1 * P2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
len P1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width (P1 * P2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
width P2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
P is Relation-like NAT -defined REAL * -valued Function-like V33() FinSequence-like FinSubsequence-like tabular V180() Matrix of len P1, width P2, REAL
dom P is V167() V168() V169() V170() V171() V172() Element of bool NAT
i is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Line (P,i) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width P) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width P) -tuples_on REAL
width P is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
(width P) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = width P } is set
len P is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real non negative V167() V168() V169() V170() V171() V172() Element of NAT
Seg (len P) is V33() V40( len P) V167() V168() V169() V170() V171() V172() Element of bool NAT
dom P1 is V167() V168() V169() V170() V171() V172() Element of bool NAT
Line (P1,i) is Relation-like NAT -defined REAL -valued Function-like V33() V40( width P1) FinSequence-like FinSubsequence-like complex-yielding V158() V159() Element of (width P1) -tuples_on REAL
(width P1) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = width P1 } is set
p is non empty Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() () FinSequence of REAL
len p is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() V33() V38() ext-real positive non negative V167() V168() V169() V170() V171() V172() Element of NAT
p * P2 is Relation-like NAT -defined REAL -valued Function-like V33() FinSequence-like FinSubsequence-like complex-yielding V158() V159() FinSequence of REAL