REAL is set
NAT is non empty V4() V5() V6() Element of bool REAL
bool REAL is set
NAT is non empty V4() V5() V6() set
bool NAT is set
bool NAT is set
1 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative Element of NAT
2 is non empty V4() V5() V6() V10() V11() V12() integer ext-real positive non negative Element of NAT
COMPLEX is set
RAT is set
INT is set
{} is empty V4() V5() V6() V8() V9() V10() V11() V12() Function-like functional integer ext-real non positive non negative set
0 is empty V4() V5() V6() V8() V9() V10() V11() V12() Function-like functional integer ext-real non positive non negative Element of NAT
K43(1) is V11() V12() integer ext-real non positive Element of REAL
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is V4() V5() V6() V10() V11() V12() integer ext-real set
n - 1 is V11() V12() integer ext-real set
(n - 1) mod K is V11() V12() integer ext-real set
1 - 1 is V11() V12() integer ext-real set
K - 1 is V11() V12() integer ext-real set
n is V4() V5() V6() V10() V11() V12() integer ext-real set
K is V4() V5() V6() V10() V11() V12() integer ext-real set
Seg K is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= K ) } is set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
p - n is V11() V12() integer ext-real set
(p - n) mod K is V11() V12() integer ext-real set
((p - n) mod K) + 1 is V11() V12() integer ext-real set
1 - K is V11() V12() integer ext-real set
K - 1 is V11() V12() integer ext-real set
- K is V11() V12() integer ext-real set
(- K) + 1 is V11() V12() integer ext-real set
- 1 is V11() V12() integer ext-real non positive set
K + (p - n) is V11() V12() integer ext-real set
K + (- 1) is V11() V12() integer ext-real set
(K - 1) + 1 is V11() V12() integer ext-real set
0 + 1 is non empty V11() V12() integer ext-real positive non negative set
n is V4() V5() V6() V10() V11() V12() integer ext-real set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
[n,p] is set
K is V4() V5() V6() V10() V11() V12() integer ext-real set
Seg K is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= K ) } is set
[:(Seg K),(Seg K):] is set
[p,n] is set
p - n is V11() V12() integer ext-real set
(p - n) mod K is V11() V12() integer ext-real set
((p - n) mod K) + 1 is V11() V12() integer ext-real set
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
1_ K is Element of the carrier of K
1. K is V49(K) Element of the carrier of K
n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(1_ K) * n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(1_ K) multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
[: the carrier of K, the carrier of K:] is set
bool [: the carrier of K, the carrier of K:] is set
the multF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
id the carrier of K is non empty Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one total Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] ((1_ K),(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,n,((1_ K) multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
dom n is set
len n is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (len n) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len n ) } is set
len ((1_ K) * n) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (len ((1_ K) * n)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len ((1_ K) * n) ) } is set
dom ((1_ K) * n) is set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
((1_ K) * n) . p is set
n . p is set
rng n is set
the multF of K [;] ((1_ K),(id the carrier of K)) is Relation-like Function-like set
dom ( the multF of K [;] ((1_ K),(id the carrier of K))) is set
((1_ K) multfield) . (n . p) is set
(id the carrier of K) . (n . p) is set
the multF of K . ((1_ K),((id the carrier of K) . (n . p))) is set
M1 is Element of the carrier of K
(1_ K) * M1 is Element of the carrier of K
the multF of K . ((1_ K),M1) is Element of the carrier of K
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
1_ K is Element of the carrier of K
1. K is V49(K) Element of the carrier of K
- (1_ K) is Element of the carrier of K
n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(- (1_ K)) * n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(- (1_ K)) multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
[: the carrier of K, the carrier of K:] is set
bool [: the carrier of K, the carrier of K:] is set
the multF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
id the carrier of K is non empty Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one total Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] ((- (1_ K)),(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,n,((- (1_ K)) multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
- n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
comp K is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,n,(comp K)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len ((- (1_ K)) * n) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (len ((- (1_ K)) * n)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len ((- (1_ K)) * n) ) } is set
len n is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (len n) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len n ) } is set
dom ((- (1_ K)) * n) is set
dom n is set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
((- (1_ K)) * n) . p is set
(- n) . p is set
rng n is set
n . p is set
the multF of K [;] ((- (1_ K)),(id the carrier of K)) is Relation-like Function-like set
dom ( the multF of K [;] ((- (1_ K)),(id the carrier of K))) is set
M1 is Element of the carrier of K
(- (1_ K)) * M1 is Element of the carrier of K
the multF of K . ((- (1_ K)),M1) is Element of the carrier of K
((- (1_ K)) * M1) + M1 is Element of the carrier of K
the addF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
the addF of K . (((- (1_ K)) * M1),M1) is Element of the carrier of K
(1_ K) * M1 is Element of the carrier of K
the multF of K . ((1_ K),M1) is Element of the carrier of K
((- (1_ K)) * M1) + ((1_ K) * M1) is Element of the carrier of K
the addF of K . (((- (1_ K)) * M1),((1_ K) * M1)) is Element of the carrier of K
(- (1_ K)) + (1_ K) is Element of the carrier of K
the addF of K . ((- (1_ K)),(1_ K)) is Element of the carrier of K
((- (1_ K)) + (1_ K)) * M1 is Element of the carrier of K
the multF of K . (((- (1_ K)) + (1_ K)),M1) is Element of the carrier of K
0. K is V49(K) Element of the carrier of K
(0. K) * M1 is Element of the carrier of K
the multF of K . ((0. K),M1) is Element of the carrier of K
- M1 is Element of the carrier of K
M1 + (- M1) is Element of the carrier of K
the addF of K . (M1,(- M1)) is Element of the carrier of K
((- (1_ K)) * M1) + (M1 + (- M1)) is Element of the carrier of K
the addF of K . (((- (1_ K)) * M1),(M1 + (- M1))) is Element of the carrier of K
(0. K) + (- M1) is Element of the carrier of K
the addF of K . ((0. K),(- M1)) is Element of the carrier of K
((- (1_ K)) * M1) + (0. K) is Element of the carrier of K
the addF of K . (((- (1_ K)) * M1),(0. K)) is Element of the carrier of K
((- (1_ K)) multfield) . (n . p) is set
(id the carrier of K) . (n . p) is set
the multF of K . ((- (1_ K)),((id the carrier of K) . (n . p))) is set
(comp K) . M1 is set
(len n) -tuples_on the carrier of K is non empty functional FinSequence-membered FinSequenceSet of the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
{ b1 where b1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like Element of the carrier of K * : len b1 = len n } is set
len (- n) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom (- n) is set
Seg (len (- n)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len (- n) ) } is set
K is set
K * is functional FinSequence-membered FinSequenceSet of K
K is set
K * is functional FinSequence-membered FinSequenceSet of K
K is non empty set
K is set
K * is functional FinSequence-membered FinSequenceSet of K
K is set
K * is functional FinSequence-membered FinSequenceSet of K
K is non empty set
K is non empty set
n is Relation-like NAT -defined K -valued Function-like FinSequence-like FinSequence of K
K * is functional FinSequence-membered FinSequenceSet of K
len n is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
p is Relation-like NAT -defined K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n,K
M1 is Relation-like NAT -defined K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n,K
Indices p is set
dom p is Element of bool NAT
width p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width p ) } is set
[:(dom p),(Seg (width p)):] is set
Indices M1 is set
dom M1 is Element of bool NAT
width M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width M1) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width M1 ) } is set
[:(dom M1),(Seg (width M1)):] is set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
[p,c6] is set
p * (p,c6) is Element of K
M1 * (p,c6) is Element of K
c6 - p is V11() V12() integer ext-real set
(c6 - p) mod (len n) is V11() V12() integer ext-real set
((c6 - p) mod (len n)) + 1 is V11() V12() integer ext-real set
n . (((c6 - p) mod (len n)) + 1) is set
K is non empty set
n is Relation-like NAT -defined K -valued Function-like FinSequence-like FinSequence of K
K * is functional FinSequence-membered FinSequenceSet of K
len n is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
p is Relation-like NAT -defined K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n,K
M1 is Relation-like NAT -defined K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n,K
Indices p is set
dom p is Element of bool NAT
width p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width p ) } is set
[:(dom p),(Seg (width p)):] is set
Indices M1 is set
dom M1 is Element of bool NAT
width M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width M1) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width M1 ) } is set
[:(dom M1),(Seg (width M1)):] is set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
[p,c6] is set
p * (p,c6) is Element of K
M1 * (p,c6) is Element of K
p - c6 is V11() V12() integer ext-real set
(p - c6) mod (len n) is V11() V12() integer ext-real set
((p - c6) mod (len n)) + 1 is V11() V12() integer ext-real set
n . (((p - c6) mod (len n)) + 1) is set
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
0. (K,1,1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of 1,1, the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
1 -tuples_on the carrier of K is non empty functional FinSequence-membered FinSequenceSet of the carrier of K
{ b1 where b1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like Element of the carrier of K * : len b1 = 1 } is set
0. K is V49(K) Element of the carrier of K
1 |-> (0. K) is Relation-like NAT -defined the carrier of K -valued Function-like V37(1) FinSequence-like Element of 1 -tuples_on the carrier of K
Seg 1 is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= 1 ) } is set
(Seg 1) --> (0. K) is Relation-like Seg 1 -defined Seg 1 -defined the carrier of K -valued {(0. K)} -valued Function-like constant total total V27( Seg 1,{(0. K)}) FinSequence-like Element of bool [:(Seg 1),{(0. K)}:]
{(0. K)} is non empty set
[:(Seg 1),{(0. K)}:] is set
bool [:(Seg 1),{(0. K)}:] is set
1 |-> (1 |-> (0. K)) is Relation-like NAT -defined 1 -tuples_on the carrier of K -valued Function-like V37(1) FinSequence-like Function-yielding V105() Element of 1 -tuples_on (1 -tuples_on the carrier of K)
1 -tuples_on (1 -tuples_on the carrier of K) is non empty functional FinSequence-membered FinSequenceSet of 1 -tuples_on the carrier of K
(1 -tuples_on the carrier of K) * is functional FinSequence-membered FinSequenceSet of 1 -tuples_on the carrier of K
{ b1 where b1 is Relation-like NAT -defined 1 -tuples_on the carrier of K -valued Function-like FinSequence-like Element of (1 -tuples_on the carrier of K) * : len b1 = 1 } is set
(Seg 1) --> (1 |-> (0. K)) is Relation-like Seg 1 -defined Seg 1 -defined 1 -tuples_on the carrier of K -valued {(1 |-> (0. K))} -valued Function-like constant total total V27( Seg 1,{(1 |-> (0. K))}) FinSequence-like Function-yielding V105() Element of bool [:(Seg 1),{(1 |-> (0. K))}:]
{(1 |-> (0. K))} is non empty functional set
[:(Seg 1),{(1 |-> (0. K))}:] is set
bool [:(Seg 1),{(1 |-> (0. K))}:] is set
0. (K,1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of 1,1, the carrier of K
p is Relation-like NAT -defined the carrier of K -valued Function-like V37(1) FinSequence-like Element of 1 -tuples_on the carrier of K
len (1 |-> (0. K)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Indices (0. (K,1)) is set
dom (0. (K,1)) is Element of bool NAT
width (0. (K,1)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (0. (K,1))) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (0. (K,1)) ) } is set
[:(dom (0. (K,1))),(Seg (width (0. (K,1)))):] is set
[:(Seg 1),(Seg 1):] is set
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
M1 is V4() V5() V6() V10() V11() V12() integer ext-real set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
[M1,p] is set
(0. (K,1)) * (M1,p) is Element of the carrier of K
M1 - p is V11() V12() integer ext-real set
(M1 - p) mod (len p) is V11() V12() integer ext-real set
((M1 - p) mod (len p)) + 1 is V11() V12() integer ext-real set
p . (((M1 - p) mod (len p)) + 1) is set
(M1 - p) mod 1 is V11() V12() integer ext-real set
((M1 - p) mod 1) + 1 is V11() V12() integer ext-real set
(Seg 1) --> (0. K) is Relation-like Seg 1 -defined Seg 1 -defined the carrier of K -valued Function-like constant total total V27( Seg 1, the carrier of K) FinSequence-like Element of bool [:(Seg 1), the carrier of K:]
[:(Seg 1), the carrier of K:] is set
bool [:(Seg 1), the carrier of K:] is set
((Seg 1) --> (0. K)) . (((M1 - p) mod 1) + 1) is set
M1 is V4() V5() V6() V10() V11() V12() integer ext-real set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
[M1,p] is set
(0. (K,1)) * (M1,p) is Element of the carrier of K
p - M1 is V11() V12() integer ext-real set
(p - M1) mod (len p) is V11() V12() integer ext-real set
((p - M1) mod (len p)) + 1 is V11() V12() integer ext-real set
p . (((p - M1) mod (len p)) + 1) is set
(p - M1) mod 1 is V11() V12() integer ext-real set
((p - M1) mod 1) + 1 is V11() V12() integer ext-real set
(Seg 1) --> (0. K) is Relation-like Seg 1 -defined Seg 1 -defined the carrier of K -valued Function-like constant total total V27( Seg 1, the carrier of K) FinSequence-like Element of bool [:(Seg 1), the carrier of K:]
[:(Seg 1), the carrier of K:] is set
bool [:(Seg 1), the carrier of K:] is set
((Seg 1) --> (0. K)) . (((p - M1) mod 1) + 1) is set
len (0. (K,1)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
0. (K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of n,n, the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
n -tuples_on the carrier of K is non empty functional FinSequence-membered FinSequenceSet of the carrier of K
{ b1 where b1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like Element of the carrier of K * : len b1 = n } is set
0. K is V49(K) Element of the carrier of K
n |-> (0. K) is Relation-like NAT -defined the carrier of K -valued Function-like V37(n) FinSequence-like Element of n -tuples_on the carrier of K
Seg n is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
(Seg n) --> (0. K) is Relation-like Seg n -defined Seg n -defined the carrier of K -valued {(0. K)} -valued Function-like constant total total V27( Seg n,{(0. K)}) FinSequence-like Element of bool [:(Seg n),{(0. K)}:]
{(0. K)} is non empty set
[:(Seg n),{(0. K)}:] is set
bool [:(Seg n),{(0. K)}:] is set
n |-> (n |-> (0. K)) is Relation-like NAT -defined n -tuples_on the carrier of K -valued Function-like V37(n) FinSequence-like Function-yielding V105() Element of n -tuples_on (n -tuples_on the carrier of K)
n -tuples_on (n -tuples_on the carrier of K) is non empty functional FinSequence-membered FinSequenceSet of n -tuples_on the carrier of K
(n -tuples_on the carrier of K) * is functional FinSequence-membered FinSequenceSet of n -tuples_on the carrier of K
{ b1 where b1 is Relation-like NAT -defined n -tuples_on the carrier of K -valued Function-like FinSequence-like Element of (n -tuples_on the carrier of K) * : len b1 = n } is set
(Seg n) --> (n |-> (0. K)) is Relation-like Seg n -defined Seg n -defined n -tuples_on the carrier of K -valued {(n |-> (0. K))} -valued Function-like constant total total V27( Seg n,{(n |-> (0. K))}) FinSequence-like Function-yielding V105() Element of bool [:(Seg n),{(n |-> (0. K))}:]
{(n |-> (0. K))} is non empty functional set
[:(Seg n),{(n |-> (0. K))}:] is set
bool [:(Seg n),{(n |-> (0. K))}:] is set
len (0. (K,n)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
0. (K,n,n) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of n,n, the carrier of K
len (n |-> (0. K)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Indices (0. (K,n)) is set
dom (0. (K,n)) is Element of bool NAT
width (0. (K,n)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (0. (K,n))) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (0. (K,n)) ) } is set
[:(dom (0. (K,n))),(Seg (width (0. (K,n)))):] is set
[:(Seg n),(Seg n):] is set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
[p,c6] is set
(0. (K,n)) * (p,c6) is Element of the carrier of K
p - c6 is V11() V12() integer ext-real set
(p - c6) mod (len (n |-> (0. K))) is V11() V12() integer ext-real set
((p - c6) mod (len (n |-> (0. K)))) + 1 is V11() V12() integer ext-real set
(n |-> (0. K)) . (((p - c6) mod (len (n |-> (0. K)))) + 1) is set
(p - c6) mod n is V11() V12() integer ext-real set
((p - c6) mod n) + 1 is V11() V12() integer ext-real set
(Seg n) --> (0. K) is Relation-like Seg n -defined Seg n -defined the carrier of K -valued Function-like constant total total V27( Seg n, the carrier of K) FinSequence-like Element of bool [:(Seg n), the carrier of K:]
[:(Seg n), the carrier of K:] is set
bool [:(Seg n), the carrier of K:] is set
((Seg n) --> (0. K)) . (((p - c6) mod (len (n |-> (0. K)))) + 1) is set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
[p,c6] is set
(0. (K,n)) * (p,c6) is Element of the carrier of K
c6 - p is V11() V12() integer ext-real set
(c6 - p) mod (len (n |-> (0. K))) is V11() V12() integer ext-real set
((c6 - p) mod (len (n |-> (0. K)))) + 1 is V11() V12() integer ext-real set
(n |-> (0. K)) . (((c6 - p) mod (len (n |-> (0. K)))) + 1) is set
(c6 - p) mod n is V11() V12() integer ext-real set
((c6 - p) mod n) + 1 is V11() V12() integer ext-real set
(Seg n) --> (0. K) is Relation-like Seg n -defined Seg n -defined the carrier of K -valued Function-like constant total total V27( Seg n, the carrier of K) FinSequence-like Element of bool [:(Seg n), the carrier of K:]
[:(Seg n), the carrier of K:] is set
bool [:(Seg n), the carrier of K:] is set
((Seg n) --> (0. K)) . (((c6 - p) mod n) + 1) is set
p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
n is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
p is Element of the carrier of K
(n,n) --> p is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of n,n, the carrier of K
n |-> p is Relation-like NAT -defined the carrier of K -valued Function-like V37(n) FinSequence-like Element of n -tuples_on the carrier of K
n -tuples_on the carrier of K is non empty functional FinSequence-membered FinSequenceSet of the carrier of K
{ b1 where b1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like Element of the carrier of K * : len b1 = n } is set
Seg n is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
(Seg n) --> p is Relation-like Seg n -defined Seg n -defined the carrier of K -valued {p} -valued Function-like constant total total V27( Seg n,{p}) FinSequence-like Element of bool [:(Seg n),{p}:]
{p} is non empty set
[:(Seg n),{p}:] is set
bool [:(Seg n),{p}:] is set
width ((n,n) --> p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len (n |-> p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Indices ((n,n) --> p) is set
dom ((n,n) --> p) is Element of bool NAT
Seg (width ((n,n) --> p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width ((n,n) --> p) ) } is set
[:(dom ((n,n) --> p)),(Seg (width ((n,n) --> p))):] is set
[:(Seg n),(Seg n):] is set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
[p,c6] is set
((n,n) --> p) * (p,c6) is Element of the carrier of K
c6 - p is V11() V12() integer ext-real set
(c6 - p) mod (len (n |-> p)) is V11() V12() integer ext-real set
((c6 - p) mod (len (n |-> p))) + 1 is V11() V12() integer ext-real set
(n |-> p) . (((c6 - p) mod (len (n |-> p))) + 1) is set
(c6 - p) mod n is V11() V12() integer ext-real set
((c6 - p) mod n) + 1 is V11() V12() integer ext-real set
(Seg n) --> p is Relation-like Seg n -defined Seg n -defined the carrier of K -valued Function-like constant total total V27( Seg n, the carrier of K) FinSequence-like Element of bool [:(Seg n), the carrier of K:]
[:(Seg n), the carrier of K:] is set
bool [:(Seg n), the carrier of K:] is set
((Seg n) --> p) . (((c6 - p) mod (len (n |-> p))) + 1) is set
p is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of n,n, the carrier of K
n |-> p is Relation-like NAT -defined the carrier of K -valued Function-like V37(n) FinSequence-like Element of n -tuples_on the carrier of K
n -tuples_on the carrier of K is non empty functional FinSequence-membered FinSequenceSet of the carrier of K
{ b1 where b1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like Element of the carrier of K * : len b1 = n } is set
Seg n is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
(Seg n) --> p is Relation-like Seg n -defined Seg n -defined the carrier of K -valued {p} -valued Function-like constant total total V27( Seg n,{p}) FinSequence-like Element of bool [:(Seg n),{p}:]
{p} is non empty set
[:(Seg n),{p}:] is set
bool [:(Seg n),{p}:] is set
len ((n,n) --> p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len (n |-> p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Indices ((n,n) --> p) is set
dom ((n,n) --> p) is Element of bool NAT
width ((n,n) --> p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width ((n,n) --> p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width ((n,n) --> p) ) } is set
[:(dom ((n,n) --> p)),(Seg (width ((n,n) --> p))):] is set
[:(Seg n),(Seg n):] is set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
c7 is V4() V5() V6() V10() V11() V12() integer ext-real set
[c6,c7] is set
((n,n) --> p) * (c6,c7) is Element of the carrier of K
c6 - c7 is V11() V12() integer ext-real set
(c6 - c7) mod (len (n |-> p)) is V11() V12() integer ext-real set
((c6 - c7) mod (len (n |-> p))) + 1 is V11() V12() integer ext-real set
(n |-> p) . (((c6 - c7) mod (len (n |-> p))) + 1) is set
(c6 - c7) mod n is V11() V12() integer ext-real set
((c6 - c7) mod n) + 1 is V11() V12() integer ext-real set
(Seg n) --> p is Relation-like Seg n -defined Seg n -defined the carrier of K -valued Function-like constant total total V27( Seg n, the carrier of K) FinSequence-like Element of bool [:(Seg n), the carrier of K:]
[:(Seg n), the carrier of K:] is set
bool [:(Seg n), the carrier of K:] is set
((Seg n) --> p) . (((c6 - c7) mod (len (n |-> p))) + 1) is set
c6 is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of n,n, the carrier of K
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
0. K is V49(K) Element of the carrier of K
(1,1) --> (0. K) is Relation-like NAT -defined the carrier of K * -valued the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular ( the carrier of K) ( the carrier of K) Matrix of 1,1, the carrier of K
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty set
n * is functional FinSequence-membered FinSequenceSet of n
p is Relation-like NAT -defined n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K,n
p @ is Relation-like NAT -defined n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K,n
width p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
M1 is Relation-like NAT -defined n -valued Function-like FinSequence-like FinSequence of n
len M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len (p @) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Indices (p @) is set
dom (p @) is Element of bool NAT
width (p @) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (p @)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (p @) ) } is set
[:(dom (p @)),(Seg (width (p @))):] is set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
[p,c6] is set
(p @) * (p,c6) is Element of n
p - c6 is V11() V12() integer ext-real set
(p - c6) mod (len M1) is V11() V12() integer ext-real set
((p - c6) mod (len M1)) + 1 is V11() V12() integer ext-real set
M1 . (((p - c6) mod (len M1)) + 1) is set
Indices p is set
dom p is Element of bool NAT
Seg (width p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width p ) } is set
[:(dom p),(Seg (width p)):] is set
Seg K is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= K ) } is set
[:(Seg K),(Seg K):] is set
[c6,p] is set
p * (c6,p) is Element of n
p is Relation-like NAT -defined n -valued Function-like FinSequence-like FinSequence of n
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty set
n * is functional FinSequence-membered FinSequenceSet of n
p is Relation-like NAT -defined n -valued Function-like FinSequence-like FinSequence of n
M1 is Relation-like NAT -defined n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K,n
Line (M1,1) is Relation-like NAT -defined n -valued Function-like V37( width M1) FinSequence-like Element of (width M1) -tuples_on n
width M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(width M1) -tuples_on n is non empty functional FinSequence-membered FinSequenceSet of n
{ b1 where b1 is Relation-like NAT -defined n -valued Function-like FinSequence-like Element of n * : len b1 = width M1 } is set
dom p is set
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (len p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len p ) } is set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
p . p is set
(Line (M1,1)) . p is set
0 + 1 is non empty V11() V12() integer ext-real positive non negative set
Seg K is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= K ) } is set
[1,p] is set
[:(Seg K),(Seg K):] is set
Indices M1 is set
dom M1 is Element of bool NAT
Seg (width M1) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width M1 ) } is set
[:(dom M1),(Seg (width M1)):] is set
M1 * (1,p) is Element of n
p - 1 is V11() V12() integer ext-real set
(p - 1) mod (len p) is V11() V12() integer ext-real set
((p - 1) mod (len p)) + 1 is V11() V12() integer ext-real set
p . (((p - 1) mod (len p)) + 1) is set
(p - 1) mod K is V11() V12() integer ext-real set
((p - 1) mod K) + 1 is V11() V12() integer ext-real set
p . (((p - 1) mod K) + 1) is set
(p - 1) + 1 is V11() V12() integer ext-real set
p . ((p - 1) + 1) is set
len (Line (M1,1)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom (Line (M1,1)) is set
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K + 1 is V11() V12() integer ext-real set
n is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
[K,n] is set
n + 1 is V11() V12() integer ext-real set
p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg p is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= p ) } is set
[:(Seg p),(Seg p):] is set
M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
c6 is non empty set
c6 * is functional FinSequence-membered FinSequenceSet of c6
c7 is Relation-like NAT -defined c6 * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of p,p,c6
c7 * (K,n) is Element of c6
c7 * (M1,p) is Element of c6
width c7 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
M3 is Relation-like NAT -defined c6 -valued Function-like FinSequence-like FinSequence of c6
len M3 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Indices c7 is set
dom c7 is Element of bool NAT
Seg (width c7) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width c7 ) } is set
[:(dom c7),(Seg (width c7)):] is set
1 + 1 is non empty V11() V12() integer ext-real positive non negative set
[M1,p] is set
p - M1 is V11() V12() integer ext-real set
(p - M1) mod (len M3) is V11() V12() integer ext-real set
((p - M1) mod (len M3)) + 1 is V11() V12() integer ext-real set
M3 . (((p - M1) mod (len M3)) + 1) is set
n - K is V11() V12() integer ext-real set
(n - K) mod (len M3) is V11() V12() integer ext-real set
((n - K) mod (len M3)) + 1 is V11() V12() integer ext-real set
M3 . (((n - K) mod (len M3)) + 1) is set
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Element of the carrier of n
M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p * M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
Indices (p * M1) is set
dom (p * M1) is Element of bool NAT
width (p * M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (p * M1)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (p * M1) ) } is set
[:(dom (p * M1)),(Seg (width (p * M1))):] is set
Seg K is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= K ) } is set
[:(Seg K),(Seg K):] is set
width M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
p is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom p is set
p * p is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
p multfield is Relation-like the carrier of n -defined the carrier of n -valued Function-like V27( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
[: the carrier of n, the carrier of n:] is set
bool [: the carrier of n, the carrier of n:] is set
the multF of n is Relation-like [: the carrier of n, the carrier of n:] -defined the carrier of n -valued Function-like V27([: the carrier of n, the carrier of n:], the carrier of n) Element of bool [:[: the carrier of n, the carrier of n:], the carrier of n:]
[:[: the carrier of n, the carrier of n:], the carrier of n:] is set
bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is set
id the carrier of n is non empty Relation-like the carrier of n -defined the carrier of n -valued Function-like one-to-one total Element of bool [: the carrier of n, the carrier of n:]
the multF of n [;] (p,(id the carrier of n)) is Relation-like the carrier of n -defined the carrier of n -valued Function-like V27( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
K191( the carrier of n, the carrier of n,p,(p multfield)) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
dom (p * p) is set
len (p * p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (len (p * p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len (p * p) ) } is set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
c7 is V4() V5() V6() V10() V11() V12() integer ext-real set
[c6,c7] is set
(p * M1) * (c6,c7) is Element of the carrier of n
c7 - c6 is V11() V12() integer ext-real set
(c7 - c6) mod (len (p * p)) is V11() V12() integer ext-real set
((c7 - c6) mod (len (p * p))) + 1 is V11() V12() integer ext-real set
(p * p) . (((c7 - c6) mod (len (p * p))) + 1) is set
(c7 - c6) mod K is V11() V12() integer ext-real set
((c7 - c6) mod K) + 1 is V11() V12() integer ext-real set
(c7 - c6) mod (len p) is V11() V12() integer ext-real set
((c7 - c6) mod (len p)) + 1 is V11() V12() integer ext-real set
Indices M1 is set
dom M1 is Element of bool NAT
Seg (width M1) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width M1 ) } is set
[:(dom M1),(Seg (width M1)):] is set
M1 * (c6,c7) is Element of the carrier of n
p * (M1 * (c6,c7)) is Element of the carrier of n
the multF of n . (p,(M1 * (c6,c7))) is Element of the carrier of n
(p multfield) . (M1 * (c6,c7)) is set
p . (((c7 - c6) mod (len p)) + 1) is set
(p multfield) . (p . (((c7 - c6) mod (len p)) + 1)) is set
p /. (((c7 - c6) mod (len p)) + 1) is Element of the carrier of n
(p multfield) . (p /. (((c7 - c6) mod (len p)) + 1)) is set
p * (p /. (((c7 - c6) mod (len p)) + 1)) is Element of the carrier of n
the multF of n . (p,(p /. (((c7 - c6) mod (len p)) + 1))) is Element of the carrier of n
(p * p) /. (((c7 - c6) mod (len p)) + 1) is Element of the carrier of n
(p * p) . (((c7 - c6) mod (len p)) + 1) is set
c6 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len c6 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p + M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
width p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
p is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Indices M1 is set
dom M1 is Element of bool NAT
width M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width M1) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width M1 ) } is set
[:(dom M1),(Seg (width M1)):] is set
Seg K is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= K ) } is set
[:(Seg K),(Seg K):] is set
Indices (p + M1) is set
dom (p + M1) is Element of bool NAT
width (p + M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (p + M1)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (p + M1) ) } is set
[:(dom (p + M1)),(Seg (width (p + M1))):] is set
dom p is set
c6 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len c6 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Indices p is set
dom p is Element of bool NAT
Seg (width p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width p ) } is set
[:(dom p),(Seg (width p)):] is set
dom c6 is set
p + c6 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
the addF of n is Relation-like [: the carrier of n, the carrier of n:] -defined the carrier of n -valued Function-like V27([: the carrier of n, the carrier of n:], the carrier of n) Element of bool [:[: the carrier of n, the carrier of n:], the carrier of n:]
[: the carrier of n, the carrier of n:] is set
[:[: the carrier of n, the carrier of n:], the carrier of n:] is set
bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is set
K188( the carrier of n, the carrier of n, the carrier of n, the addF of n,p,c6) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
dom (p + c6) is set
len (p + c6) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (len (p + c6)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len (p + c6) ) } is set
c7 is V4() V5() V6() V10() V11() V12() integer ext-real set
M3 is V4() V5() V6() V10() V11() V12() integer ext-real set
[c7,M3] is set
(p + M1) * (c7,M3) is Element of the carrier of n
M3 - c7 is V11() V12() integer ext-real set
(M3 - c7) mod (len (p + c6)) is V11() V12() integer ext-real set
((M3 - c7) mod (len (p + c6))) + 1 is V11() V12() integer ext-real set
(p + c6) . (((M3 - c7) mod (len (p + c6))) + 1) is set
p * (c7,M3) is Element of the carrier of n
M1 * (c7,M3) is Element of the carrier of n
(p * (c7,M3)) + (M1 * (c7,M3)) is Element of the carrier of n
the addF of n . ((p * (c7,M3)),(M1 * (c7,M3))) is Element of the carrier of n
(M3 - c7) mod (len c6) is V11() V12() integer ext-real set
((M3 - c7) mod (len c6)) + 1 is V11() V12() integer ext-real set
c6 . (((M3 - c7) mod (len c6)) + 1) is set
the addF of n . ((p * (c7,M3)),(c6 . (((M3 - c7) mod (len c6)) + 1))) is set
p . (((M3 - c7) mod (len (p + c6))) + 1) is set
c6 . (((M3 - c7) mod (len (p + c6))) + 1) is set
the addF of n . ((p . (((M3 - c7) mod (len (p + c6))) + 1)),(c6 . (((M3 - c7) mod (len (p + c6))) + 1))) is set
c7 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len c7 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p + M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
(p + M1) + p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Element of the carrier of n
M1 is Element of the carrier of n
p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p * p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M1 * c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
(p * p) + (M1 * c6) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Element of the carrier of n
M1 is Element of the carrier of n
p is Element of the carrier of n
c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p * c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
c7 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M1 * c7 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
(p * c6) + (M1 * c7) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M3 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p * M3 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
((p * c6) + (M1 * c7)) + (p * M3) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
- p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
width p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Indices (- p) is set
dom (- p) is Element of bool NAT
width (- p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (- p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (- p) ) } is set
[:(dom (- p)),(Seg (width (- p))):] is set
Seg K is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= K ) } is set
[:(Seg K),(Seg K):] is set
M1 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(len M1) -tuples_on the carrier of n is non empty functional FinSequence-membered FinSequenceSet of the carrier of n
{ b1 where b1 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like Element of the carrier of n * : len b1 = len M1 } is set
- M1 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
comp n is Relation-like the carrier of n -defined the carrier of n -valued Function-like V27( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
[: the carrier of n, the carrier of n:] is set
bool [: the carrier of n, the carrier of n:] is set
K191( the carrier of n, the carrier of n,M1,(comp n)) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len (- M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Indices p is set
dom p is Element of bool NAT
Seg (width p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width p ) } is set
[:(dom p),(Seg (width p)):] is set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
[p,c6] is set
(- p) * (p,c6) is Element of the carrier of n
c6 - p is V11() V12() integer ext-real set
(c6 - p) mod (len (- M1)) is V11() V12() integer ext-real set
((c6 - p) mod (len (- M1))) + 1 is V11() V12() integer ext-real set
(- M1) . (((c6 - p) mod (len (- M1))) + 1) is set
(c6 - p) mod K is V11() V12() integer ext-real set
((c6 - p) mod K) + 1 is V11() V12() integer ext-real set
(c6 - p) mod (len M1) is V11() V12() integer ext-real set
((c6 - p) mod (len M1)) + 1 is V11() V12() integer ext-real set
dom M1 is set
p * (p,c6) is Element of the carrier of n
- (p * (p,c6)) is Element of the carrier of n
(comp n) . (p * (p,c6)) is set
M1 . (((c6 - p) mod (len M1)) + 1) is set
(comp n) . (M1 . (((c6 - p) mod (len M1)) + 1)) is set
(- M1) . (((c6 - p) mod (len M1)) + 1) is set
p is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p - M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
- M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
p + (- M1) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
- M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Element of the carrier of n
M1 is Element of the carrier of n
p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p * p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M1 * c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
(p * p) - (M1 * c6) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
- (M1 * c6) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
(p * p) + (- (M1 * c6)) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
- (M1 * c6) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Element of the carrier of n
M1 is Element of the carrier of n
p is Element of the carrier of n
c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p * c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
c7 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M1 * c7 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
(p * c6) + (M1 * c7) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M3 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p * M3 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
((p * c6) + (M1 * c7)) - (p * M3) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
- (p * M3) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
((p * c6) + (M1 * c7)) + (- (p * M3)) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
- (p * M3) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Element of the carrier of n
M1 is Element of the carrier of n
p is Element of the carrier of n
c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p * c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
c7 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M1 * c7 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
(p * c6) - (M1 * c7) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
- (M1 * c7) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
(p * c6) + (- (M1 * c7)) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
M3 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p * M3 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
((p * c6) - (M1 * c7)) - (p * M3) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
- (p * M3) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
((p * c6) - (M1 * c7)) + (- (p * M3)) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
- (p * M3) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Element of the carrier of n
M1 is Element of the carrier of n
p is Element of the carrier of n
c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p * c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
c7 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M1 * c7 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
(p * c6) - (M1 * c7) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
- (M1 * c7) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
(p * c6) + (- (M1 * c7)) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
M3 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p * M3 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
((p * c6) - (M1 * c7)) + (p * M3) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty set
n * is functional FinSequence-membered FinSequenceSet of n
p is Relation-like NAT -defined n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K,n
p @ is Relation-like NAT -defined n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K,n
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
M1 is Relation-like NAT -defined n -valued Function-like FinSequence-like FinSequence of n
len M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
width p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
width (p @) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Indices (p @) is set
dom (p @) is Element of bool NAT
Seg (width (p @)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (p @) ) } is set
[:(dom (p @)),(Seg (width (p @))):] is set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
[p,c6] is set
(p @) * (p,c6) is Element of n
c6 - p is V11() V12() integer ext-real set
(c6 - p) mod (len M1) is V11() V12() integer ext-real set
((c6 - p) mod (len M1)) + 1 is V11() V12() integer ext-real set
M1 . (((c6 - p) mod (len M1)) + 1) is set
Indices p is set
dom p is Element of bool NAT
Seg (width p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width p ) } is set
[:(dom p),(Seg (width p)):] is set
Seg K is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= K ) } is set
[:(Seg K),(Seg K):] is set
[c6,p] is set
p * (c6,p) is Element of n
p is Relation-like NAT -defined n -valued Function-like FinSequence-like FinSequence of n
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty set
n * is functional FinSequence-membered FinSequenceSet of n
p is Relation-like NAT -defined n -valued Function-like FinSequence-like FinSequence of n
M1 is Relation-like NAT -defined n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K,n
Col (M1,1) is Relation-like NAT -defined n -valued Function-like V37( len M1) FinSequence-like Element of (len M1) -tuples_on n
len M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(len M1) -tuples_on n is non empty functional FinSequence-membered FinSequenceSet of n
{ b1 where b1 is Relation-like NAT -defined n -valued Function-like FinSequence-like Element of n * : len b1 = len M1 } is set
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom p is set
Seg (len p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len p ) } is set
len (Col (M1,1)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom (Col (M1,1)) is set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
p . p is set
(Col (M1,1)) . p is set
0 + 1 is non empty V11() V12() integer ext-real positive non negative set
Seg K is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= K ) } is set
[p,1] is set
[:(Seg K),(Seg K):] is set
Indices M1 is set
dom M1 is Element of bool NAT
width M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width M1) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width M1 ) } is set
[:(dom M1),(Seg (width M1)):] is set
Seg (len M1) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len M1 ) } is set
dom M1 is set
M1 * (p,1) is Element of n
p - 1 is V11() V12() integer ext-real set
(p - 1) mod (len p) is V11() V12() integer ext-real set
((p - 1) mod (len p)) + 1 is V11() V12() integer ext-real set
p . (((p - 1) mod (len p)) + 1) is set
(p - 1) + 1 is V11() V12() integer ext-real set
p . ((p - 1) + 1) is set
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K + 1 is V11() V12() integer ext-real set
n is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
[K,n] is set
n + 1 is V11() V12() integer ext-real set
p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg p is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= p ) } is set
[:(Seg p),(Seg p):] is set
M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
c6 is non empty set
c6 * is functional FinSequence-membered FinSequenceSet of c6
c7 is Relation-like NAT -defined c6 * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of p,p,c6
c7 * (K,n) is Element of c6
c7 * (M1,p) is Element of c6
Indices c7 is set
dom c7 is Element of bool NAT
width c7 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width c7) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width c7 ) } is set
[:(dom c7),(Seg (width c7)):] is set
1 + 1 is non empty V11() V12() integer ext-real positive non negative set
len c7 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
M3 is Relation-like NAT -defined c6 -valued Function-like FinSequence-like FinSequence of c6
len M3 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
[M1,p] is set
M1 - p is V11() V12() integer ext-real set
(M1 - p) mod (len M3) is V11() V12() integer ext-real set
((M1 - p) mod (len M3)) + 1 is V11() V12() integer ext-real set
M3 . (((M1 - p) mod (len M3)) + 1) is set
K - n is V11() V12() integer ext-real set
(K - n) mod (len M3) is V11() V12() integer ext-real set
((K - n) mod (len M3)) + 1 is V11() V12() integer ext-real set
M3 . (((K - n) mod (len M3)) + 1) is set
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Element of the carrier of n
M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p * M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
Indices M1 is set
dom M1 is Element of bool NAT
width M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width M1) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width M1 ) } is set
[:(dom M1),(Seg (width M1)):] is set
Seg K is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= K ) } is set
[:(Seg K),(Seg K):] is set
len M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
p is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom p is set
p * p is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
p multfield is Relation-like the carrier of n -defined the carrier of n -valued Function-like V27( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
[: the carrier of n, the carrier of n:] is set
bool [: the carrier of n, the carrier of n:] is set
the multF of n is Relation-like [: the carrier of n, the carrier of n:] -defined the carrier of n -valued Function-like V27([: the carrier of n, the carrier of n:], the carrier of n) Element of bool [:[: the carrier of n, the carrier of n:], the carrier of n:]
[:[: the carrier of n, the carrier of n:], the carrier of n:] is set
bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is set
id the carrier of n is non empty Relation-like the carrier of n -defined the carrier of n -valued Function-like one-to-one total Element of bool [: the carrier of n, the carrier of n:]
the multF of n [;] (p,(id the carrier of n)) is Relation-like the carrier of n -defined the carrier of n -valued Function-like V27( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
K191( the carrier of n, the carrier of n,p,(p multfield)) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len (p * p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom (p * p) is set
Seg (len (p * p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len (p * p) ) } is set
Indices (p * M1) is set
dom (p * M1) is Element of bool NAT
width (p * M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (p * M1)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (p * M1) ) } is set
[:(dom (p * M1)),(Seg (width (p * M1))):] is set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
c7 is V4() V5() V6() V10() V11() V12() integer ext-real set
[c6,c7] is set
(p * M1) * (c6,c7) is Element of the carrier of n
c6 - c7 is V11() V12() integer ext-real set
(c6 - c7) mod (len p) is V11() V12() integer ext-real set
((c6 - c7) mod (len p)) + 1 is V11() V12() integer ext-real set
(p * p) . (((c6 - c7) mod (len p)) + 1) is set
M1 * (c6,c7) is Element of the carrier of n
p * (M1 * (c6,c7)) is Element of the carrier of n
the multF of n . (p,(M1 * (c6,c7))) is Element of the carrier of n
(p multfield) . (M1 * (c6,c7)) is set
p . (((c6 - c7) mod (len p)) + 1) is set
(p multfield) . (p . (((c6 - c7) mod (len p)) + 1)) is set
p /. (((c6 - c7) mod (len p)) + 1) is Element of the carrier of n
(p multfield) . (p /. (((c6 - c7) mod (len p)) + 1)) is set
p * (p /. (((c6 - c7) mod (len p)) + 1)) is Element of the carrier of n
the multF of n . (p,(p /. (((c6 - c7) mod (len p)) + 1))) is Element of the carrier of n
(p * p) /. (((c6 - c7) mod (len p)) + 1) is Element of the carrier of n
len (p * M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
c6 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len c6 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p + M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
p is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Indices M1 is set
dom M1 is Element of bool NAT
width M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width M1) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width M1 ) } is set
[:(dom M1),(Seg (width M1)):] is set
Seg K is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= K ) } is set
[:(Seg K),(Seg K):] is set
Indices (p + M1) is set
dom (p + M1) is Element of bool NAT
width (p + M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (p + M1)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (p + M1) ) } is set
[:(dom (p + M1)),(Seg (width (p + M1))):] is set
len M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
c6 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len c6 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Indices p is set
dom p is Element of bool NAT
width p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width p ) } is set
[:(dom p),(Seg (width p)):] is set
len (p + M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom p is set
dom c6 is set
p + c6 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
the addF of n is Relation-like [: the carrier of n, the carrier of n:] -defined the carrier of n -valued Function-like V27([: the carrier of n, the carrier of n:], the carrier of n) Element of bool [:[: the carrier of n, the carrier of n:], the carrier of n:]
[: the carrier of n, the carrier of n:] is set
[:[: the carrier of n, the carrier of n:], the carrier of n:] is set
bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is set
K188( the carrier of n, the carrier of n, the carrier of n, the addF of n,p,c6) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
dom (p + c6) is set
len (p + c6) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (len (p + c6)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len (p + c6) ) } is set
c7 is V4() V5() V6() V10() V11() V12() integer ext-real set
M3 is V4() V5() V6() V10() V11() V12() integer ext-real set
[c7,M3] is set
(p + M1) * (c7,M3) is Element of the carrier of n
c7 - M3 is V11() V12() integer ext-real set
(c7 - M3) mod (len (p + c6)) is V11() V12() integer ext-real set
((c7 - M3) mod (len (p + c6))) + 1 is V11() V12() integer ext-real set
(p + c6) . (((c7 - M3) mod (len (p + c6))) + 1) is set
p * (c7,M3) is Element of the carrier of n
M1 * (c7,M3) is Element of the carrier of n
(p * (c7,M3)) + (M1 * (c7,M3)) is Element of the carrier of n
the addF of n . ((p * (c7,M3)),(M1 * (c7,M3))) is Element of the carrier of n
(c7 - M3) mod (len c6) is V11() V12() integer ext-real set
((c7 - M3) mod (len c6)) + 1 is V11() V12() integer ext-real set
c6 . (((c7 - M3) mod (len c6)) + 1) is set
the addF of n . ((p * (c7,M3)),(c6 . (((c7 - M3) mod (len c6)) + 1))) is set
p . (((c7 - M3) mod (len (p + c6))) + 1) is set
c6 . (((c7 - M3) mod (len (p + c6))) + 1) is set
the addF of n . ((p . (((c7 - M3) mod (len (p + c6))) + 1)),(c6 . (((c7 - M3) mod (len (p + c6))) + 1))) is set
c7 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len c7 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p + M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
(p + M1) + p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Element of the carrier of n
M1 is Element of the carrier of n
p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p * p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M1 * c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
(p * p) + (M1 * c6) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Element of the carrier of n
M1 is Element of the carrier of n
p is Element of the carrier of n
c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p * c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
c7 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M1 * c7 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
(p * c6) + (M1 * c7) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M3 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p * M3 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
((p * c6) + (M1 * c7)) + (p * M3) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
- p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
Indices p is set
dom p is Element of bool NAT
width p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width p ) } is set
[:(dom p),(Seg (width p)):] is set
Seg K is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= K ) } is set
[:(Seg K),(Seg K):] is set
Indices (- p) is set
dom (- p) is Element of bool NAT
width (- p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (- p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (- p) ) } is set
[:(dom (- p)),(Seg (width (- p))):] is set
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
M1 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(len M1) -tuples_on the carrier of n is non empty functional FinSequence-membered FinSequenceSet of the carrier of n
{ b1 where b1 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like Element of the carrier of n * : len b1 = len M1 } is set
- M1 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
comp n is Relation-like the carrier of n -defined the carrier of n -valued Function-like V27( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
[: the carrier of n, the carrier of n:] is set
bool [: the carrier of n, the carrier of n:] is set
K191( the carrier of n, the carrier of n,M1,(comp n)) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len (- p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len (- M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom M1 is set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
[p,c6] is set
(- p) * (p,c6) is Element of the carrier of n
p - c6 is V11() V12() integer ext-real set
(p - c6) mod (len (- M1)) is V11() V12() integer ext-real set
((p - c6) mod (len (- M1))) + 1 is V11() V12() integer ext-real set
(- M1) . (((p - c6) mod (len (- M1))) + 1) is set
(p - c6) mod K is V11() V12() integer ext-real set
((p - c6) mod K) + 1 is V11() V12() integer ext-real set
p * (p,c6) is Element of the carrier of n
- (p * (p,c6)) is Element of the carrier of n
(comp n) . (p * (p,c6)) is set
(p - c6) mod (len M1) is V11() V12() integer ext-real set
((p - c6) mod (len M1)) + 1 is V11() V12() integer ext-real set
M1 . (((p - c6) mod (len M1)) + 1) is set
(comp n) . (M1 . (((p - c6) mod (len M1)) + 1)) is set
(- M1) . (((p - c6) mod (len M1)) + 1) is set
p is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p - M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
- M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
p + (- M1) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
- M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Element of the carrier of n
M1 is Element of the carrier of n
p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p * p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M1 * c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
(p * p) - (M1 * c6) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
- (M1 * c6) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
(p * p) + (- (M1 * c6)) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
- (M1 * c6) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Element of the carrier of n
M1 is Element of the carrier of n
p is Element of the carrier of n
c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p * c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
c7 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M1 * c7 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
(p * c6) + (M1 * c7) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M3 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p * M3 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
((p * c6) + (M1 * c7)) - (p * M3) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
- (p * M3) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
((p * c6) + (M1 * c7)) + (- (p * M3)) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
- (p * M3) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Element of the carrier of n
M1 is Element of the carrier of n
p is Element of the carrier of n
c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p * c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
c7 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M1 * c7 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
(p * c6) - (M1 * c7) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
- (M1 * c7) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
(p * c6) + (- (M1 * c7)) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
M3 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p * M3 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
((p * c6) - (M1 * c7)) - (p * M3) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
- (p * M3) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
((p * c6) - (M1 * c7)) + (- (p * M3)) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
- (p * M3) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Element of the carrier of n
M1 is Element of the carrier of n
p is Element of the carrier of n
c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p * c6 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
c7 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M1 * c7 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
(p * c6) - (M1 * c7) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
- (M1 * c7) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
(p * c6) + (- (M1 * c7)) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
M3 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p * M3 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
((p * c6) - (M1 * c7)) + (p * M3) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
- n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
comp K is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
[: the carrier of K, the carrier of K:] is set
bool [: the carrier of K, the carrier of K:] is set
K191( the carrier of K, the carrier of K,n,(comp K)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len n is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
M1 is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
- M1 is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
Indices M1 is set
dom M1 is Element of bool NAT
width M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width M1) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width M1 ) } is set
[:(dom M1),(Seg (width M1)):] is set
Seg (len n) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len n ) } is set
[:(Seg (len n)),(Seg (len n)):] is set
Indices (- M1) is set
dom (- M1) is Element of bool NAT
width (- M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (- M1)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (- M1) ) } is set
[:(dom (- M1)),(Seg (width (- M1))):] is set
(len n) -tuples_on the carrier of K is non empty functional FinSequence-membered FinSequenceSet of the carrier of K
{ b1 where b1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like Element of the carrier of K * : len b1 = len n } is set
len (- n) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom n is set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
c7 is V4() V5() V6() V10() V11() V12() integer ext-real set
[c6,c7] is set
(- M1) * (c6,c7) is Element of the carrier of K
c7 - c6 is V11() V12() integer ext-real set
(c7 - c6) mod (len (- n)) is V11() V12() integer ext-real set
((c7 - c6) mod (len (- n))) + 1 is V11() V12() integer ext-real set
(- n) . (((c7 - c6) mod (len (- n))) + 1) is set
(c7 - c6) mod (len n) is V11() V12() integer ext-real set
((c7 - c6) mod (len n)) + 1 is V11() V12() integer ext-real set
M1 * (c6,c7) is Element of the carrier of K
- (M1 * (c6,c7)) is Element of the carrier of K
(comp K) . (M1 * (c6,c7)) is set
n . (((c7 - c6) mod (len n)) + 1) is set
(comp K) . (n . (((c7 - c6) mod (len n)) + 1)) is set
(- n) . (((c7 - c6) mod (len n)) + 1) is set
c6 is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (- n), len (- n), the carrier of K
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
- n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
comp K is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
[: the carrier of K, the carrier of K:] is set
bool [: the carrier of K, the carrier of K:] is set
K191( the carrier of K, the carrier of K,n,(comp K)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
( the carrier of K,(- n)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (- n), len (- n), the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
len (- n) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len n is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
- ( the carrier of K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
len ( the carrier of K,n) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
width ( the carrier of K,n) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Indices ( the carrier of K,n) is set
dom ( the carrier of K,n) is Element of bool NAT
Seg (width ( the carrier of K,n)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width ( the carrier of K,n) ) } is set
[:(dom ( the carrier of K,n)),(Seg (width ( the carrier of K,n))):] is set
Seg (len n) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len n ) } is set
[:(Seg (len n)),(Seg (len n)):] is set
(len n) -tuples_on the carrier of K is non empty functional FinSequence-membered FinSequenceSet of the carrier of K
{ b1 where b1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like Element of the carrier of K * : len b1 = len n } is set
M1 is V4() V5() V6() V10() V11() V12() integer ext-real set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
[M1,p] is set
( the carrier of K,(- n)) * (M1,p) is Element of the carrier of K
( the carrier of K,n) * (M1,p) is Element of the carrier of K
- (( the carrier of K,n) * (M1,p)) is Element of the carrier of K
p - M1 is V11() V12() integer ext-real set
(p - M1) mod (len n) is V11() V12() integer ext-real set
((p - M1) mod (len n)) + 1 is V11() V12() integer ext-real set
dom n is set
Indices ( the carrier of K,(- n)) is set
dom ( the carrier of K,(- n)) is Element of bool NAT
width ( the carrier of K,(- n)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width ( the carrier of K,(- n))) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width ( the carrier of K,(- n)) ) } is set
[:(dom ( the carrier of K,(- n))),(Seg (width ( the carrier of K,(- n)))):] is set
(p - M1) mod (len (- n)) is V11() V12() integer ext-real set
((p - M1) mod (len (- n))) + 1 is V11() V12() integer ext-real set
(- n) . (((p - M1) mod (len (- n))) + 1) is set
n . (((p - M1) mod (len n)) + 1) is set
(comp K) . (n . (((p - M1) mod (len n)) + 1)) is set
(comp K) . (( the carrier of K,n) * (M1,p)) is set
len ( the carrier of K,(- n)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
width ( the carrier of K,(- n)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len n is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n + p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
the addF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[: the carrier of K, the carrier of K:] is set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
K188( the carrier of K, the carrier of K, the carrier of K, the addF of K,n,p) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
p is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
dom (n + p) is set
len (n + p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (len (n + p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len (n + p) ) } is set
dom n is set
Seg (len n) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len n ) } is set
dom p is set
c6 is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
Indices c6 is set
dom c6 is Element of bool NAT
width c6 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width c6) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width c6 ) } is set
[:(dom c6),(Seg (width c6)):] is set
[:(Seg (len n)),(Seg (len n)):] is set
c6 + p is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
width (c6 + p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Indices p is set
dom p is Element of bool NAT
width p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width p ) } is set
[:(dom p),(Seg (width p)):] is set
Indices (c6 + p) is set
dom (c6 + p) is Element of bool NAT
Seg (width (c6 + p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (c6 + p) ) } is set
[:(dom (c6 + p)),(Seg (width (c6 + p))):] is set
M3 is V4() V5() V6() V10() V11() V12() integer ext-real set
c9 is V4() V5() V6() V10() V11() V12() integer ext-real set
[M3,c9] is set
(c6 + p) * (M3,c9) is Element of the carrier of K
c9 - M3 is V11() V12() integer ext-real set
(c9 - M3) mod (len (n + p)) is V11() V12() integer ext-real set
((c9 - M3) mod (len (n + p))) + 1 is V11() V12() integer ext-real set
(n + p) . (((c9 - M3) mod (len (n + p))) + 1) is set
c6 * (M3,c9) is Element of the carrier of K
p * (M3,c9) is Element of the carrier of K
(c6 * (M3,c9)) + (p * (M3,c9)) is Element of the carrier of K
the addF of K . ((c6 * (M3,c9)),(p * (M3,c9))) is Element of the carrier of K
(c9 - M3) mod (len p) is V11() V12() integer ext-real set
((c9 - M3) mod (len p)) + 1 is V11() V12() integer ext-real set
p . (((c9 - M3) mod (len p)) + 1) is set
the addF of K . ((c6 * (M3,c9)),(p . (((c9 - M3) mod (len p)) + 1))) is set
n . (((c9 - M3) mod (len (n + p))) + 1) is set
p . (((c9 - M3) mod (len (n + p))) + 1) is set
the addF of K . ((n . (((c9 - M3) mod (len (n + p))) + 1)),(p . (((c9 - M3) mod (len (n + p))) + 1))) is set
M3 is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (n + p), len (n + p), the carrier of K
width M3 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len n is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n + p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
the addF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[: the carrier of K, the carrier of K:] is set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
K188( the carrier of K, the carrier of K, the carrier of K, the addF of K,n,p) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
( the carrier of K,(n + p)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (n + p), len (n + p), the carrier of K
len (n + p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
( the carrier of K,n) + ( the carrier of K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of K *
Indices ( the carrier of K,n) is set
dom ( the carrier of K,n) is Element of bool NAT
width ( the carrier of K,n) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width ( the carrier of K,n)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width ( the carrier of K,n) ) } is set
[:(dom ( the carrier of K,n)),(Seg (width ( the carrier of K,n))):] is set
Indices ( the carrier of K,p) is set
dom ( the carrier of K,p) is Element of bool NAT
width ( the carrier of K,p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width ( the carrier of K,p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width ( the carrier of K,p) ) } is set
[:(dom ( the carrier of K,p)),(Seg (width ( the carrier of K,p))):] is set
dom n is set
Seg (len n) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len n ) } is set
dom (n + p) is set
Seg (len (n + p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len (n + p) ) } is set
[:(Seg (len n)),(Seg (len n)):] is set
dom p is set
Indices ( the carrier of K,(n + p)) is set
dom ( the carrier of K,(n + p)) is Element of bool NAT
width ( the carrier of K,(n + p)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width ( the carrier of K,(n + p))) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width ( the carrier of K,(n + p)) ) } is set
[:(dom ( the carrier of K,(n + p))),(Seg (width ( the carrier of K,(n + p)))):] is set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
[p,c6] is set
( the carrier of K,(n + p)) * (p,c6) is Element of the carrier of K
( the carrier of K,n) * (p,c6) is Element of the carrier of K
( the carrier of K,p) * (p,c6) is Element of the carrier of K
(( the carrier of K,n) * (p,c6)) + (( the carrier of K,p) * (p,c6)) is Element of the carrier of K
the addF of K . ((( the carrier of K,n) * (p,c6)),(( the carrier of K,p) * (p,c6))) is Element of the carrier of K
c6 - p is V11() V12() integer ext-real set
(c6 - p) mod (len n) is V11() V12() integer ext-real set
((c6 - p) mod (len n)) + 1 is V11() V12() integer ext-real set
(c6 - p) mod (len (n + p)) is V11() V12() integer ext-real set
((c6 - p) mod (len (n + p))) + 1 is V11() V12() integer ext-real set
(n + p) . (((c6 - p) mod (len (n + p))) + 1) is set
n . (((c6 - p) mod (len (n + p))) + 1) is set
p . (((c6 - p) mod (len (n + p))) + 1) is set
the addF of K . ((n . (((c6 - p) mod (len (n + p))) + 1)),(p . (((c6 - p) mod (len (n + p))) + 1))) is set
(c6 - p) mod (len p) is V11() V12() integer ext-real set
((c6 - p) mod (len p)) + 1 is V11() V12() integer ext-real set
p . (((c6 - p) mod (len p)) + 1) is set
the addF of K . ((( the carrier of K,n) * (p,c6)),(p . (((c6 - p) mod (len p)) + 1))) is set
len ( the carrier of K,n) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len ( the carrier of K,(n + p)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
- n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
comp K is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
[: the carrier of K, the carrier of K:] is set
bool [: the carrier of K, the carrier of K:] is set
K191( the carrier of K, the carrier of K,n,(comp K)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len n is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
M1 is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
- M1 is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
Indices M1 is set
dom M1 is Element of bool NAT
width M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width M1) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width M1 ) } is set
[:(dom M1),(Seg (width M1)):] is set
Seg (len n) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len n ) } is set
[:(Seg (len n)),(Seg (len n)):] is set
Indices (- M1) is set
dom (- M1) is Element of bool NAT
width (- M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (- M1)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (- M1) ) } is set
[:(dom (- M1)),(Seg (width (- M1))):] is set
(len n) -tuples_on the carrier of K is non empty functional FinSequence-membered FinSequenceSet of the carrier of K
{ b1 where b1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like Element of the carrier of K * : len b1 = len n } is set
len (- n) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom n is set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
c7 is V4() V5() V6() V10() V11() V12() integer ext-real set
[c6,c7] is set
(- M1) * (c6,c7) is Element of the carrier of K
c6 - c7 is V11() V12() integer ext-real set
(c6 - c7) mod (len (- n)) is V11() V12() integer ext-real set
((c6 - c7) mod (len (- n))) + 1 is V11() V12() integer ext-real set
(- n) . (((c6 - c7) mod (len (- n))) + 1) is set
(c6 - c7) mod (len n) is V11() V12() integer ext-real set
((c6 - c7) mod (len n)) + 1 is V11() V12() integer ext-real set
M1 * (c6,c7) is Element of the carrier of K
- (M1 * (c6,c7)) is Element of the carrier of K
(comp K) . (M1 * (c6,c7)) is set
n . (((c6 - c7) mod (len n)) + 1) is set
(comp K) . (n . (((c6 - c7) mod (len n)) + 1)) is set
(- n) . (((c6 - c7) mod (len n)) + 1) is set
len (- M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
c6 is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (- n), len (- n), the carrier of K
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
- n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
comp K is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
[: the carrier of K, the carrier of K:] is set
bool [: the carrier of K, the carrier of K:] is set
K191( the carrier of K, the carrier of K,n,(comp K)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
( the carrier of K,(- n)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (- n), len (- n), the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
len (- n) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len n is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
- ( the carrier of K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
dom n is set
Seg (len n) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len n ) } is set
Indices ( the carrier of K,n) is set
dom ( the carrier of K,n) is Element of bool NAT
width ( the carrier of K,n) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width ( the carrier of K,n)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width ( the carrier of K,n) ) } is set
[:(dom ( the carrier of K,n)),(Seg (width ( the carrier of K,n))):] is set
[:(Seg (len n)),(Seg (len n)):] is set
(len n) -tuples_on the carrier of K is non empty functional FinSequence-membered FinSequenceSet of the carrier of K
{ b1 where b1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like Element of the carrier of K * : len b1 = len n } is set
Indices ( the carrier of K,(- n)) is set
dom ( the carrier of K,(- n)) is Element of bool NAT
width ( the carrier of K,(- n)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width ( the carrier of K,(- n))) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width ( the carrier of K,(- n)) ) } is set
[:(dom ( the carrier of K,(- n))),(Seg (width ( the carrier of K,(- n)))):] is set
M1 is V4() V5() V6() V10() V11() V12() integer ext-real set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
[M1,p] is set
( the carrier of K,(- n)) * (M1,p) is Element of the carrier of K
( the carrier of K,n) * (M1,p) is Element of the carrier of K
- (( the carrier of K,n) * (M1,p)) is Element of the carrier of K
M1 - p is V11() V12() integer ext-real set
(M1 - p) mod (len n) is V11() V12() integer ext-real set
((M1 - p) mod (len n)) + 1 is V11() V12() integer ext-real set
(M1 - p) mod (len (- n)) is V11() V12() integer ext-real set
((M1 - p) mod (len (- n))) + 1 is V11() V12() integer ext-real set
(- n) . (((M1 - p) mod (len (- n))) + 1) is set
n . (((M1 - p) mod (len n)) + 1) is set
(comp K) . (n . (((M1 - p) mod (len n)) + 1)) is set
(comp K) . (( the carrier of K,n) * (M1,p)) is set
len ( the carrier of K,n) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len ( the carrier of K,(- n)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len n is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n + p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
the addF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[: the carrier of K, the carrier of K:] is set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
K188( the carrier of K, the carrier of K, the carrier of K, the addF of K,n,p) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
p is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
dom (n + p) is set
len (n + p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (len (n + p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len (n + p) ) } is set
dom n is set
Seg (len n) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len n ) } is set
dom p is set
c6 is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
Indices c6 is set
dom c6 is Element of bool NAT
width c6 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width c6) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width c6 ) } is set
[:(dom c6),(Seg (width c6)):] is set
[:(Seg (len n)),(Seg (len n)):] is set
c6 + p is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
len (c6 + p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Indices p is set
dom p is Element of bool NAT
width p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width p ) } is set
[:(dom p),(Seg (width p)):] is set
Indices (c6 + p) is set
dom (c6 + p) is Element of bool NAT
width (c6 + p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (c6 + p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (c6 + p) ) } is set
[:(dom (c6 + p)),(Seg (width (c6 + p))):] is set
M3 is V4() V5() V6() V10() V11() V12() integer ext-real set
c9 is V4() V5() V6() V10() V11() V12() integer ext-real set
[M3,c9] is set
(c6 + p) * (M3,c9) is Element of the carrier of K
M3 - c9 is V11() V12() integer ext-real set
(M3 - c9) mod (len (n + p)) is V11() V12() integer ext-real set
((M3 - c9) mod (len (n + p))) + 1 is V11() V12() integer ext-real set
(n + p) . (((M3 - c9) mod (len (n + p))) + 1) is set
c6 * (M3,c9) is Element of the carrier of K
p * (M3,c9) is Element of the carrier of K
(c6 * (M3,c9)) + (p * (M3,c9)) is Element of the carrier of K
the addF of K . ((c6 * (M3,c9)),(p * (M3,c9))) is Element of the carrier of K
(M3 - c9) mod (len p) is V11() V12() integer ext-real set
((M3 - c9) mod (len p)) + 1 is V11() V12() integer ext-real set
p . (((M3 - c9) mod (len p)) + 1) is set
the addF of K . ((c6 * (M3,c9)),(p . (((M3 - c9) mod (len p)) + 1))) is set
n . (((M3 - c9) mod (len (n + p))) + 1) is set
p . (((M3 - c9) mod (len (n + p))) + 1) is set
the addF of K . ((n . (((M3 - c9) mod (len (n + p))) + 1)),(p . (((M3 - c9) mod (len (n + p))) + 1))) is set
M3 is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (n + p), len (n + p), the carrier of K
len M3 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len n is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n + p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
the addF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[: the carrier of K, the carrier of K:] is set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
K188( the carrier of K, the carrier of K, the carrier of K, the addF of K,n,p) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
( the carrier of K,(n + p)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (n + p), len (n + p), the carrier of K
len (n + p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
( the carrier of K,n) + ( the carrier of K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of K *
Indices ( the carrier of K,n) is set
dom ( the carrier of K,n) is Element of bool NAT
width ( the carrier of K,n) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width ( the carrier of K,n)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width ( the carrier of K,n) ) } is set
[:(dom ( the carrier of K,n)),(Seg (width ( the carrier of K,n))):] is set
Indices ( the carrier of K,p) is set
dom ( the carrier of K,p) is Element of bool NAT
width ( the carrier of K,p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width ( the carrier of K,p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width ( the carrier of K,p) ) } is set
[:(dom ( the carrier of K,p)),(Seg (width ( the carrier of K,p))):] is set
dom n is set
Seg (len n) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len n ) } is set
dom (n + p) is set
Seg (len (n + p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len (n + p) ) } is set
[:(Seg (len n)),(Seg (len n)):] is set
dom p is set
Indices ( the carrier of K,(n + p)) is set
dom ( the carrier of K,(n + p)) is Element of bool NAT
width ( the carrier of K,(n + p)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width ( the carrier of K,(n + p))) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width ( the carrier of K,(n + p)) ) } is set
[:(dom ( the carrier of K,(n + p))),(Seg (width ( the carrier of K,(n + p)))):] is set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
[p,c6] is set
( the carrier of K,(n + p)) * (p,c6) is Element of the carrier of K
( the carrier of K,n) * (p,c6) is Element of the carrier of K
( the carrier of K,p) * (p,c6) is Element of the carrier of K
(( the carrier of K,n) * (p,c6)) + (( the carrier of K,p) * (p,c6)) is Element of the carrier of K
the addF of K . ((( the carrier of K,n) * (p,c6)),(( the carrier of K,p) * (p,c6))) is Element of the carrier of K
p - c6 is V11() V12() integer ext-real set
(p - c6) mod (len n) is V11() V12() integer ext-real set
((p - c6) mod (len n)) + 1 is V11() V12() integer ext-real set
(p - c6) mod (len (n + p)) is V11() V12() integer ext-real set
((p - c6) mod (len (n + p))) + 1 is V11() V12() integer ext-real set
(n + p) . (((p - c6) mod (len (n + p))) + 1) is set
n . (((p - c6) mod (len (n + p))) + 1) is set
p . (((p - c6) mod (len (n + p))) + 1) is set
the addF of K . ((n . (((p - c6) mod (len (n + p))) + 1)),(p . (((p - c6) mod (len (n + p))) + 1))) is set
(p - c6) mod (len p) is V11() V12() integer ext-real set
((p - c6) mod (len p)) + 1 is V11() V12() integer ext-real set
p . (((p - c6) mod (len p)) + 1) is set
the addF of K . ((( the carrier of K,n) * (p,c6)),(p . (((p - c6) mod (len p)) + 1))) is set
len ( the carrier of K,n) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len ( the carrier of K,(n + p)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
1. (n,K) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
Indices (1. (n,K)) is set
dom (1. (n,K)) is Element of bool NAT
width (1. (n,K)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (1. (n,K))) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (1. (n,K)) ) } is set
[:(dom (1. (n,K))),(Seg (width (1. (n,K)))):] is set
Seg K is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= K ) } is set
[:(Seg K),(Seg K):] is set
Col ((1. (n,K)),1) is Relation-like NAT -defined the carrier of n -valued Function-like V37( len (1. (n,K))) FinSequence-like Element of (len (1. (n,K))) -tuples_on the carrier of n
len (1. (n,K)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(len (1. (n,K))) -tuples_on the carrier of n is non empty functional FinSequence-membered FinSequenceSet of the carrier of n
{ b1 where b1 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like Element of the carrier of n * : len b1 = len (1. (n,K)) } is set
len (Col ((1. (n,K)),1)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom (1. (n,K)) is set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
[p,c6] is set
(1. (n,K)) * (p,c6) is Element of the carrier of n
p - c6 is V11() V12() integer ext-real set
(p - c6) mod (len (Col ((1. (n,K)),1))) is V11() V12() integer ext-real set
((p - c6) mod (len (Col ((1. (n,K)),1)))) + 1 is V11() V12() integer ext-real set
(Col ((1. (n,K)),1)) . (((p - c6) mod (len (Col ((1. (n,K)),1)))) + 1) is set
(p - c6) mod K is V11() V12() integer ext-real set
((p - c6) mod K) + 1 is V11() V12() integer ext-real set
1 - K is V11() V12() integer ext-real set
- K is V11() V12() integer ext-real set
(- K) + 1 is V11() V12() integer ext-real set
K - 1 is V11() V12() integer ext-real set
- 1 is V11() V12() integer ext-real non positive set
K + (p - c6) is V11() V12() integer ext-real set
K + (- 1) is V11() V12() integer ext-real set
(K - 1) + 1 is V11() V12() integer ext-real set
0 + 1 is non empty V11() V12() integer ext-real positive non negative set
[1,1] is set
(1. (n,K)) * (1,1) is Element of the carrier of n
1_ n is Element of the carrier of n
1. n is V49(n) Element of the carrier of n
(1 - K) + K is V11() V12() integer ext-real set
(p - c6) + K is V11() V12() integer ext-real set
M3 is V4() V5() V6() V10() V11() V12() integer ext-real set
[M3,1] is set
(Col ((1. (n,K)),1)) . M3 is set
(1. (n,K)) * (M3,1) is Element of the carrier of n
0. n is V49(n) Element of the carrier of n
p is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
1. (n,K) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
Line ((1. (n,K)),1) is Relation-like NAT -defined the carrier of n -valued Function-like V37( width (1. (n,K))) FinSequence-like Element of (width (1. (n,K))) -tuples_on the carrier of n
width (1. (n,K)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(width (1. (n,K))) -tuples_on the carrier of n is non empty functional FinSequence-membered FinSequenceSet of the carrier of n
{ b1 where b1 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like Element of the carrier of n * : len b1 = width (1. (n,K)) } is set
Indices (1. (n,K)) is set
dom (1. (n,K)) is Element of bool NAT
Seg (width (1. (n,K))) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (1. (n,K)) ) } is set
[:(dom (1. (n,K))),(Seg (width (1. (n,K)))):] is set
Seg K is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= K ) } is set
[:(Seg K),(Seg K):] is set
len (Line ((1. (n,K)),1)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
p is V4() V5() V6() V10() V11() V12() integer ext-real set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
[p,c6] is set
(1. (n,K)) * (p,c6) is Element of the carrier of n
c6 - p is V11() V12() integer ext-real set
(c6 - p) mod (len (Line ((1. (n,K)),1))) is V11() V12() integer ext-real set
((c6 - p) mod (len (Line ((1. (n,K)),1)))) + 1 is V11() V12() integer ext-real set
(Line ((1. (n,K)),1)) . (((c6 - p) mod (len (Line ((1. (n,K)),1)))) + 1) is set
(c6 - p) mod K is V11() V12() integer ext-real set
((c6 - p) mod K) + 1 is V11() V12() integer ext-real set
K - 1 is V11() V12() integer ext-real set
1 - K is V11() V12() integer ext-real set
- K is V11() V12() integer ext-real set
(- K) + 1 is V11() V12() integer ext-real set
- 1 is V11() V12() integer ext-real non positive set
K + (c6 - p) is V11() V12() integer ext-real set
K + (- 1) is V11() V12() integer ext-real set
(K - 1) + 1 is V11() V12() integer ext-real set
0 + 1 is non empty V11() V12() integer ext-real positive non negative set
[1,1] is set
(1. (n,K)) * (1,1) is Element of the carrier of n
1_ n is Element of the carrier of n
1. n is V49(n) Element of the carrier of n
(1 - K) + K is V11() V12() integer ext-real set
(c6 - p) + K is V11() V12() integer ext-real set
M3 is V4() V5() V6() V10() V11() V12() integer ext-real set
[1,M3] is set
(Line ((1. (n,K)),1)) . M3 is set
(1. (n,K)) * (1,M3) is Element of the carrier of n
0. n is V49(n) Element of the carrier of n
p is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Element of the carrier of K
p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n * p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
[: the carrier of K, the carrier of K:] is set
bool [: the carrier of K, the carrier of K:] is set
the multF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
id the carrier of K is non empty Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one total Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] (n,(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,p,(n multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len (n * p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
p is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
n * p is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
Indices (n * p) is set
dom (n * p) is Element of bool NAT
width (n * p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (n * p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (n * p) ) } is set
[:(dom (n * p)),(Seg (width (n * p))):] is set
Seg (len p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len p ) } is set
[:(Seg (len p)),(Seg (len p)):] is set
dom p is set
dom (n * p) is set
Seg (len (n * p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len (n * p) ) } is set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
c7 is V4() V5() V6() V10() V11() V12() integer ext-real set
[c6,c7] is set
(n * p) * (c6,c7) is Element of the carrier of K
c7 - c6 is V11() V12() integer ext-real set
(c7 - c6) mod (len (n * p)) is V11() V12() integer ext-real set
((c7 - c6) mod (len (n * p))) + 1 is V11() V12() integer ext-real set
(n * p) . (((c7 - c6) mod (len (n * p))) + 1) is set
(c7 - c6) mod (len p) is V11() V12() integer ext-real set
((c7 - c6) mod (len p)) + 1 is V11() V12() integer ext-real set
Indices p is set
dom p is Element of bool NAT
width p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width p ) } is set
[:(dom p),(Seg (width p)):] is set
p * (c6,c7) is Element of the carrier of K
n * (p * (c6,c7)) is Element of the carrier of K
the multF of K . (n,(p * (c6,c7))) is Element of the carrier of K
(n multfield) . (p * (c6,c7)) is set
p . (((c7 - c6) mod (len p)) + 1) is set
(n multfield) . (p . (((c7 - c6) mod (len p)) + 1)) is set
p /. (((c7 - c6) mod (len p)) + 1) is Element of the carrier of K
(n multfield) . (p /. (((c7 - c6) mod (len p)) + 1)) is set
n * (p /. (((c7 - c6) mod (len p)) + 1)) is Element of the carrier of K
the multF of K . (n,(p /. (((c7 - c6) mod (len p)) + 1))) is Element of the carrier of K
(n * p) /. (((c7 - c6) mod (len p)) + 1) is Element of the carrier of K
(n * p) . (((c7 - c6) mod (len p)) + 1) is set
c6 is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (n * p), len (n * p), the carrier of K
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Element of the carrier of K
p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n * p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
[: the carrier of K, the carrier of K:] is set
bool [: the carrier of K, the carrier of K:] is set
the multF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
id the carrier of K is non empty Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one total Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] (n,(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,p,(n multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
( the carrier of K,(n * p)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (n * p), len (n * p), the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
len (n * p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
n * ( the carrier of K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
Indices ( the carrier of K,p) is set
dom ( the carrier of K,p) is Element of bool NAT
width ( the carrier of K,p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width ( the carrier of K,p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width ( the carrier of K,p) ) } is set
[:(dom ( the carrier of K,p)),(Seg (width ( the carrier of K,p))):] is set
Seg (len p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len p ) } is set
[:(Seg (len p)),(Seg (len p)):] is set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
[p,c6] is set
( the carrier of K,(n * p)) * (p,c6) is Element of the carrier of K
( the carrier of K,p) * (p,c6) is Element of the carrier of K
n * (( the carrier of K,p) * (p,c6)) is Element of the carrier of K
the multF of K . (n,(( the carrier of K,p) * (p,c6))) is Element of the carrier of K
dom (n * p) is set
Seg (len (n * p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len (n * p) ) } is set
c6 - p is V11() V12() integer ext-real set
(c6 - p) mod (len p) is V11() V12() integer ext-real set
((c6 - p) mod (len p)) + 1 is V11() V12() integer ext-real set
dom p is set
Indices ( the carrier of K,(n * p)) is set
dom ( the carrier of K,(n * p)) is Element of bool NAT
width ( the carrier of K,(n * p)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width ( the carrier of K,(n * p))) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width ( the carrier of K,(n * p)) ) } is set
[:(dom ( the carrier of K,(n * p))),(Seg (width ( the carrier of K,(n * p)))):] is set
(c6 - p) mod (len (n * p)) is V11() V12() integer ext-real set
((c6 - p) mod (len (n * p))) + 1 is V11() V12() integer ext-real set
(n * p) . (((c6 - p) mod (len (n * p))) + 1) is set
(n * p) /. (((c6 - p) mod (len p)) + 1) is Element of the carrier of K
p /. (((c6 - p) mod (len p)) + 1) is Element of the carrier of K
n * (p /. (((c6 - p) mod (len p)) + 1)) is Element of the carrier of K
the multF of K . (n,(p /. (((c6 - p) mod (len p)) + 1))) is Element of the carrier of K
(n multfield) . (p /. (((c6 - p) mod (len p)) + 1)) is set
p . (((c6 - p) mod (len p)) + 1) is set
(n multfield) . (p . (((c6 - p) mod (len p)) + 1)) is set
(n multfield) . (( the carrier of K,p) * (p,c6)) is set
len ( the carrier of K,p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len ( the carrier of K,(n * p)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
width ( the carrier of K,(n * p)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Element of the carrier of K
p is Element of the carrier of K
n + p is Element of the carrier of K
the addF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[: the carrier of K, the carrier of K:] is set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the addF of K . (n,p) is Element of the carrier of K
M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
n * ( the carrier of K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
p * ( the carrier of K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
(n * ( the carrier of K,M1)) + (p * ( the carrier of K,M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
(n + p) * M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(n + p) multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
bool [: the carrier of K, the carrier of K:] is set
the multF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
id the carrier of K is non empty Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one total Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] ((n + p),(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,M1,((n + p) multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
( the carrier of K,((n + p) * M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len ((n + p) * M1), len ((n + p) * M1), the carrier of K
len ((n + p) * M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
p * M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
p multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] (p,(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,M1,(p multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len (p * M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(len M1) -tuples_on the carrier of K is non empty functional FinSequence-membered FinSequenceSet of the carrier of K
{ b1 where b1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like Element of the carrier of K * : len b1 = len M1 } is set
n * M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] (n,(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,M1,(n multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
( the carrier of K,(n * M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (n * M1), len (n * M1), the carrier of K
len (n * M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,(p * M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (p * M1), len (p * M1), the carrier of K
(n * M1) + (p * M1) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
K188( the carrier of K, the carrier of K, the carrier of K, the addF of K,(n * M1),(p * M1)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
( the carrier of K,((n * M1) + (p * M1))) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len ((n * M1) + (p * M1)), len ((n * M1) + (p * M1)), the carrier of K
len ((n * M1) + (p * M1)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Element of the carrier of K
p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
n * ( the carrier of K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
n * ( the carrier of K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
(n * ( the carrier of K,p)) + (n * ( the carrier of K,M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of K *
p + M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
the addF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[: the carrier of K, the carrier of K:] is set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
K188( the carrier of K, the carrier of K, the carrier of K, the addF of K,p,M1) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n * (p + M1) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
bool [: the carrier of K, the carrier of K:] is set
the multF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
id the carrier of K is non empty Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one total Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] (n,(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,(p + M1),(n multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
( the carrier of K,(n * (p + M1))) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (n * (p + M1)), len (n * (p + M1)), the carrier of K
len (n * (p + M1)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len ( the carrier of K,p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
width ( the carrier of K,p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len ( the carrier of K,M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
width ( the carrier of K,M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,p) + ( the carrier of K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of K *
n * (( the carrier of K,p) + ( the carrier of K,M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of K *
len (p + M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,(p + M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (p + M1), len (p + M1), the carrier of K
n * ( the carrier of K,(p + M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (p + M1), len (p + M1), the carrier of K
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Element of the carrier of K
p is Element of the carrier of K
M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
n * ( the carrier of K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
n * M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
[: the carrier of K, the carrier of K:] is set
bool [: the carrier of K, the carrier of K:] is set
the multF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
id the carrier of K is non empty Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one total Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] (n,(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,M1,(n multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
p * ( the carrier of K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
(n * ( the carrier of K,M1)) + (p * ( the carrier of K,p)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of K *
p * p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
p multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] (p,(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,p,(p multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(n * M1) + (p * p) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
the addF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
K188( the carrier of K, the carrier of K, the carrier of K, the addF of K,(n * M1),(p * p)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
( the carrier of K,((n * M1) + (p * p))) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len ((n * M1) + (p * p)), len ((n * M1) + (p * p)), the carrier of K
len ((n * M1) + (p * p)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len (p * p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,(n * M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (n * M1), len (n * M1), the carrier of K
len (n * M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,(n * M1)) + (p * ( the carrier of K,p)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of K *
( the carrier of K,(p * p)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (p * p), len (p * p), the carrier of K
( the carrier of K,(n * M1)) + ( the carrier of K,(p * p)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of K *
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Element of the carrier of K
p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n * p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
[: the carrier of K, the carrier of K:] is set
bool [: the carrier of K, the carrier of K:] is set
the multF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
id the carrier of K is non empty Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one total Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] (n,(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,p,(n multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len (n * p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
p is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
n * p is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
Indices (n * p) is set
dom (n * p) is Element of bool NAT
width (n * p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (n * p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (n * p) ) } is set
[:(dom (n * p)),(Seg (width (n * p))):] is set
Seg (len p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len p ) } is set
[:(Seg (len p)),(Seg (len p)):] is set
dom p is set
dom (n * p) is set
Seg (len (n * p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len (n * p) ) } is set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
c7 is V4() V5() V6() V10() V11() V12() integer ext-real set
[c6,c7] is set
(n * p) * (c6,c7) is Element of the carrier of K
c6 - c7 is V11() V12() integer ext-real set
(c6 - c7) mod (len (n * p)) is V11() V12() integer ext-real set
((c6 - c7) mod (len (n * p))) + 1 is V11() V12() integer ext-real set
(n * p) . (((c6 - c7) mod (len (n * p))) + 1) is set
(c6 - c7) mod (len p) is V11() V12() integer ext-real set
((c6 - c7) mod (len p)) + 1 is V11() V12() integer ext-real set
Indices p is set
dom p is Element of bool NAT
width p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width p ) } is set
[:(dom p),(Seg (width p)):] is set
p * (c6,c7) is Element of the carrier of K
n * (p * (c6,c7)) is Element of the carrier of K
the multF of K . (n,(p * (c6,c7))) is Element of the carrier of K
(n multfield) . (p * (c6,c7)) is set
p . (((c6 - c7) mod (len p)) + 1) is set
(n multfield) . (p . (((c6 - c7) mod (len p)) + 1)) is set
p /. (((c6 - c7) mod (len p)) + 1) is Element of the carrier of K
(n multfield) . (p /. (((c6 - c7) mod (len p)) + 1)) is set
n * (p /. (((c6 - c7) mod (len p)) + 1)) is Element of the carrier of K
the multF of K . (n,(p /. (((c6 - c7) mod (len p)) + 1))) is Element of the carrier of K
(n * p) /. (((c6 - c7) mod (len p)) + 1) is Element of the carrier of K
(n * p) . (((c6 - c7) mod (len p)) + 1) is set
len (n * p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
c6 is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (n * p), len (n * p), the carrier of K
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Element of the carrier of K
p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n * p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
[: the carrier of K, the carrier of K:] is set
bool [: the carrier of K, the carrier of K:] is set
the multF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
id the carrier of K is non empty Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one total Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] (n,(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,p,(n multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
( the carrier of K,(n * p)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (n * p), len (n * p), the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
len (n * p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
n * ( the carrier of K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
Indices ( the carrier of K,p) is set
dom ( the carrier of K,p) is Element of bool NAT
width ( the carrier of K,p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width ( the carrier of K,p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width ( the carrier of K,p) ) } is set
[:(dom ( the carrier of K,p)),(Seg (width ( the carrier of K,p))):] is set
Seg (len p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len p ) } is set
[:(Seg (len p)),(Seg (len p)):] is set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
[p,c6] is set
( the carrier of K,(n * p)) * (p,c6) is Element of the carrier of K
( the carrier of K,p) * (p,c6) is Element of the carrier of K
n * (( the carrier of K,p) * (p,c6)) is Element of the carrier of K
the multF of K . (n,(( the carrier of K,p) * (p,c6))) is Element of the carrier of K
dom (n * p) is set
Seg (len (n * p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len (n * p) ) } is set
p - c6 is V11() V12() integer ext-real set
(p - c6) mod (len p) is V11() V12() integer ext-real set
((p - c6) mod (len p)) + 1 is V11() V12() integer ext-real set
dom p is set
Indices ( the carrier of K,(n * p)) is set
dom ( the carrier of K,(n * p)) is Element of bool NAT
width ( the carrier of K,(n * p)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width ( the carrier of K,(n * p))) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width ( the carrier of K,(n * p)) ) } is set
[:(dom ( the carrier of K,(n * p))),(Seg (width ( the carrier of K,(n * p)))):] is set
(p - c6) mod (len (n * p)) is V11() V12() integer ext-real set
((p - c6) mod (len (n * p))) + 1 is V11() V12() integer ext-real set
(n * p) . (((p - c6) mod (len (n * p))) + 1) is set
(n * p) /. (((p - c6) mod (len p)) + 1) is Element of the carrier of K
p /. (((p - c6) mod (len p)) + 1) is Element of the carrier of K
n * (p /. (((p - c6) mod (len p)) + 1)) is Element of the carrier of K
the multF of K . (n,(p /. (((p - c6) mod (len p)) + 1))) is Element of the carrier of K
(n multfield) . (p /. (((p - c6) mod (len p)) + 1)) is set
p . (((p - c6) mod (len p)) + 1) is set
(n multfield) . (p . (((p - c6) mod (len p)) + 1)) is set
(n multfield) . (( the carrier of K,p) * (p,c6)) is set
len ( the carrier of K,p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len ( the carrier of K,(n * p)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
width ( the carrier of K,(n * p)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Element of the carrier of K
p is Element of the carrier of K
n + p is Element of the carrier of K
the addF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[: the carrier of K, the carrier of K:] is set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the addF of K . (n,p) is Element of the carrier of K
M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
n * ( the carrier of K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
p * ( the carrier of K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
(n * ( the carrier of K,M1)) + (p * ( the carrier of K,M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
(n + p) * M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(n + p) multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
bool [: the carrier of K, the carrier of K:] is set
the multF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
id the carrier of K is non empty Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one total Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] ((n + p),(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,M1,((n + p) multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
( the carrier of K,((n + p) * M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len ((n + p) * M1), len ((n + p) * M1), the carrier of K
len ((n + p) * M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
p * M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
p multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] (p,(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,M1,(p multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len (p * M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(len M1) -tuples_on the carrier of K is non empty functional FinSequence-membered FinSequenceSet of the carrier of K
{ b1 where b1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like Element of the carrier of K * : len b1 = len M1 } is set
n * M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] (n,(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,M1,(n multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
( the carrier of K,(n * M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (n * M1), len (n * M1), the carrier of K
len (n * M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,(p * M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (p * M1), len (p * M1), the carrier of K
(n * M1) + (p * M1) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
K188( the carrier of K, the carrier of K, the carrier of K, the addF of K,(n * M1),(p * M1)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
( the carrier of K,((n * M1) + (p * M1))) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len ((n * M1) + (p * M1)), len ((n * M1) + (p * M1)), the carrier of K
len ((n * M1) + (p * M1)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Element of the carrier of K
p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
n * ( the carrier of K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
n * ( the carrier of K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
(n * ( the carrier of K,p)) + (n * ( the carrier of K,M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of K *
p + M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
the addF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[: the carrier of K, the carrier of K:] is set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
K188( the carrier of K, the carrier of K, the carrier of K, the addF of K,p,M1) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n * (p + M1) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
bool [: the carrier of K, the carrier of K:] is set
the multF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
id the carrier of K is non empty Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one total Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] (n,(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,(p + M1),(n multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
( the carrier of K,(n * (p + M1))) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (n * (p + M1)), len (n * (p + M1)), the carrier of K
len (n * (p + M1)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len ( the carrier of K,p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
width ( the carrier of K,p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len ( the carrier of K,M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
width ( the carrier of K,M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,p) + ( the carrier of K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of K *
n * (( the carrier of K,p) + ( the carrier of K,M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of K *
len (p + M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,(p + M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (p + M1), len (p + M1), the carrier of K
n * ( the carrier of K,(p + M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (p + M1), len (p + M1), the carrier of K
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Element of the carrier of K
p is Element of the carrier of K
M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
n * ( the carrier of K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
n * M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
[: the carrier of K, the carrier of K:] is set
bool [: the carrier of K, the carrier of K:] is set
the multF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
id the carrier of K is non empty Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one total Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] (n,(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,M1,(n multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
p * ( the carrier of K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
(n * ( the carrier of K,M1)) + (p * ( the carrier of K,p)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of K *
p * p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
p multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] (p,(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,p,(p multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(n * M1) + (p * p) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
the addF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
K188( the carrier of K, the carrier of K, the carrier of K, the addF of K,(n * M1),(p * p)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
( the carrier of K,((n * M1) + (p * p))) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len ((n * M1) + (p * p)), len ((n * M1) + (p * p)), the carrier of K
len ((n * M1) + (p * p)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len (p * p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,(n * M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (n * M1), len (n * M1), the carrier of K
len (n * M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
( the carrier of K,(n * M1)) + (p * ( the carrier of K,p)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of K *
( the carrier of K,(p * p)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (p * p), len (p * p), the carrier of K
( the carrier of K,(n * M1)) + ( the carrier of K,(p * p)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of K *
K is set
K * is functional FinSequence-membered FinSequenceSet of K
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
len n is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
p is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
M1 is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
Indices p is set
dom p is Element of bool NAT
width p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width p ) } is set
[:(dom p),(Seg (width p)):] is set
Indices M1 is set
dom M1 is Element of bool NAT
width M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width M1) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width M1 ) } is set
[:(dom M1),(Seg (width M1)):] is set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
[p,c6] is set
p * (p,c6) is Element of the carrier of K
M1 * (p,c6) is Element of the carrier of K
c6 - p is V11() V12() integer ext-real set
(c6 - p) mod (len n) is V11() V12() integer ext-real set
((c6 - p) mod (len n)) + 1 is V11() V12() integer ext-real set
n . (((c6 - p) mod (len n)) + 1) is set
- n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
comp K is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
[: the carrier of K, the carrier of K:] is set
bool [: the carrier of K, the carrier of K:] is set
K191( the carrier of K, the carrier of K,n,(comp K)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
c6 - p is V11() V12() integer ext-real set
(c6 - p) mod (len n) is V11() V12() integer ext-real set
((c6 - p) mod (len n)) + 1 is V11() V12() integer ext-real set
(- n) . (((c6 - p) mod (len n)) + 1) is set
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Element of the carrier of n
M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p * M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
Indices (p * M1) is set
dom (p * M1) is Element of bool NAT
width (p * M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (p * M1)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (p * M1) ) } is set
[:(dom (p * M1)),(Seg (width (p * M1))):] is set
Seg K is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= K ) } is set
[:(Seg K),(Seg K):] is set
width M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
p is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom p is set
p * p is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
p multfield is Relation-like the carrier of n -defined the carrier of n -valued Function-like V27( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
[: the carrier of n, the carrier of n:] is set
bool [: the carrier of n, the carrier of n:] is set
the multF of n is Relation-like [: the carrier of n, the carrier of n:] -defined the carrier of n -valued Function-like V27([: the carrier of n, the carrier of n:], the carrier of n) Element of bool [:[: the carrier of n, the carrier of n:], the carrier of n:]
[:[: the carrier of n, the carrier of n:], the carrier of n:] is set
bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is set
id the carrier of n is non empty Relation-like the carrier of n -defined the carrier of n -valued Function-like one-to-one total Element of bool [: the carrier of n, the carrier of n:]
the multF of n [;] (p,(id the carrier of n)) is Relation-like the carrier of n -defined the carrier of n -valued Function-like V27( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
K191( the carrier of n, the carrier of n,p,(p multfield)) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
dom (p * p) is set
len (p * p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (len (p * p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len (p * p) ) } is set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
c7 is V4() V5() V6() V10() V11() V12() integer ext-real set
[c6,c7] is set
(p * M1) * (c6,c7) is Element of the carrier of n
c7 - c6 is V11() V12() integer ext-real set
(c7 - c6) mod (len (p * p)) is V11() V12() integer ext-real set
((c7 - c6) mod (len (p * p))) + 1 is V11() V12() integer ext-real set
(p * p) . (((c7 - c6) mod (len (p * p))) + 1) is set
(c7 - c6) mod K is V11() V12() integer ext-real set
((c7 - c6) mod K) + 1 is V11() V12() integer ext-real set
(c7 - c6) mod (len p) is V11() V12() integer ext-real set
((c7 - c6) mod (len p)) + 1 is V11() V12() integer ext-real set
Indices M1 is set
dom M1 is Element of bool NAT
Seg (width M1) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width M1 ) } is set
[:(dom M1),(Seg (width M1)):] is set
M1 * (c6,c7) is Element of the carrier of n
p * (M1 * (c6,c7)) is Element of the carrier of n
the multF of n . (p,(M1 * (c6,c7))) is Element of the carrier of n
(p multfield) . (M1 * (c6,c7)) is set
p . (((c7 - c6) mod (len p)) + 1) is set
(p multfield) . (p . (((c7 - c6) mod (len p)) + 1)) is set
p /. (((c7 - c6) mod (len p)) + 1) is Element of the carrier of n
(p multfield) . (p /. (((c7 - c6) mod (len p)) + 1)) is set
p * (p /. (((c7 - c6) mod (len p)) + 1)) is Element of the carrier of n
the multF of n . (p,(p /. (((c7 - c6) mod (len p)) + 1))) is Element of the carrier of n
(p * p) /. (((c7 - c6) mod (len p)) + 1) is Element of the carrier of n
(p * p) . (((c7 - c6) mod (len p)) + 1) is set
- (p * p) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
comp n is Relation-like the carrier of n -defined the carrier of n -valued Function-like V27( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
K191( the carrier of n, the carrier of n,(p * p),(comp n)) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
- p is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
K191( the carrier of n, the carrier of n,p,(comp n)) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
p * (- p) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
K191( the carrier of n, the carrier of n,(- p),(p multfield)) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len (p * (- p)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len (- p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom (p * (- p)) is set
Seg (len (- p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len (- p) ) } is set
dom (- p) is set
K -tuples_on the carrier of n is non empty functional FinSequence-membered FinSequenceSet of the carrier of n
{ b1 where b1 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like Element of the carrier of n * : len b1 = K } is set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
c7 is V4() V5() V6() V10() V11() V12() integer ext-real set
[c6,c7] is set
(p * M1) * (c6,c7) is Element of the carrier of n
c7 - c6 is V11() V12() integer ext-real set
(c7 - c6) mod (len (p * p)) is V11() V12() integer ext-real set
((c7 - c6) mod (len (p * p))) + 1 is V11() V12() integer ext-real set
(- (p * p)) . (((c7 - c6) mod (len (p * p))) + 1) is set
(c7 - c6) mod K is V11() V12() integer ext-real set
((c7 - c6) mod K) + 1 is V11() V12() integer ext-real set
(len p) -tuples_on the carrier of n is non empty functional FinSequence-membered FinSequenceSet of the carrier of n
{ b1 where b1 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like Element of the carrier of n * : len b1 = len p } is set
Indices M1 is set
dom M1 is Element of bool NAT
Seg (width M1) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width M1 ) } is set
[:(dom M1),(Seg (width M1)):] is set
M1 * (c6,c7) is Element of the carrier of n
p * (M1 * (c6,c7)) is Element of the carrier of n
the multF of n . (p,(M1 * (c6,c7))) is Element of the carrier of n
(p multfield) . (M1 * (c6,c7)) is set
(c7 - c6) mod (len p) is V11() V12() integer ext-real set
((c7 - c6) mod (len p)) + 1 is V11() V12() integer ext-real set
(- p) . (((c7 - c6) mod (len p)) + 1) is set
(p multfield) . ((- p) . (((c7 - c6) mod (len p)) + 1)) is set
(- p) /. (((c7 - c6) mod (len p)) + 1) is Element of the carrier of n
(p multfield) . ((- p) /. (((c7 - c6) mod (len p)) + 1)) is set
p * ((- p) /. (((c7 - c6) mod (len p)) + 1)) is Element of the carrier of n
the multF of n . (p,((- p) /. (((c7 - c6) mod (len p)) + 1))) is Element of the carrier of n
(p * (- p)) /. (((c7 - c6) mod (len p)) + 1) is Element of the carrier of n
(p * (- p)) . (((c7 - c6) mod (len p)) + 1) is set
1_ n is Element of the carrier of n
1. n is V49(n) Element of the carrier of n
- (1_ n) is Element of the carrier of n
(- (1_ n)) * p is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
(- (1_ n)) multfield is Relation-like the carrier of n -defined the carrier of n -valued Function-like V27( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
the multF of n [;] ((- (1_ n)),(id the carrier of n)) is Relation-like the carrier of n -defined the carrier of n -valued Function-like V27( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
K191( the carrier of n, the carrier of n,p,((- (1_ n)) multfield)) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
p * ((- (1_ n)) * p) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
K191( the carrier of n, the carrier of n,((- (1_ n)) * p),(p multfield)) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
(p * ((- (1_ n)) * p)) . (((c7 - c6) mod (len p)) + 1) is set
p * (- (1_ n)) is Element of the carrier of n
the multF of n . (p,(- (1_ n))) is Element of the carrier of n
(p * (- (1_ n))) * p is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
(p * (- (1_ n))) multfield is Relation-like the carrier of n -defined the carrier of n -valued Function-like V27( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
the multF of n [;] ((p * (- (1_ n))),(id the carrier of n)) is Relation-like the carrier of n -defined the carrier of n -valued Function-like V27( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
K191( the carrier of n, the carrier of n,p,((p * (- (1_ n))) multfield)) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
((p * (- (1_ n))) * p) . (((c7 - c6) mod (len p)) + 1) is set
p * (1_ n) is Element of the carrier of n
the multF of n . (p,(1_ n)) is Element of the carrier of n
- (p * (1_ n)) is Element of the carrier of n
(- (p * (1_ n))) * p is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
(- (p * (1_ n))) multfield is Relation-like the carrier of n -defined the carrier of n -valued Function-like V27( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
the multF of n [;] ((- (p * (1_ n))),(id the carrier of n)) is Relation-like the carrier of n -defined the carrier of n -valued Function-like V27( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
K191( the carrier of n, the carrier of n,p,((- (p * (1_ n))) multfield)) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
((- (p * (1_ n))) * p) . (((c7 - c6) mod (len p)) + 1) is set
- p is Element of the carrier of n
(- p) * p is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
(- p) multfield is Relation-like the carrier of n -defined the carrier of n -valued Function-like V27( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
the multF of n [;] ((- p),(id the carrier of n)) is Relation-like the carrier of n -defined the carrier of n -valued Function-like V27( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
K191( the carrier of n, the carrier of n,p,((- p) multfield)) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
((- p) * p) . (((c7 - c6) mod (len p)) + 1) is set
(1_ n) * p is Element of the carrier of n
the multF of n . ((1_ n),p) is Element of the carrier of n
- ((1_ n) * p) is Element of the carrier of n
(- ((1_ n) * p)) * p is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
(- ((1_ n) * p)) multfield is Relation-like the carrier of n -defined the carrier of n -valued Function-like V27( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
the multF of n [;] ((- ((1_ n) * p)),(id the carrier of n)) is Relation-like the carrier of n -defined the carrier of n -valued Function-like V27( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
K191( the carrier of n, the carrier of n,p,((- ((1_ n) * p)) multfield)) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
((- ((1_ n) * p)) * p) . (((c7 - c6) mod (len p)) + 1) is set
(- (1_ n)) * p is Element of the carrier of n
the multF of n . ((- (1_ n)),p) is Element of the carrier of n
((- (1_ n)) * p) * p is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
((- (1_ n)) * p) multfield is Relation-like the carrier of n -defined the carrier of n -valued Function-like V27( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
the multF of n [;] (((- (1_ n)) * p),(id the carrier of n)) is Relation-like the carrier of n -defined the carrier of n -valued Function-like V27( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
K191( the carrier of n, the carrier of n,p,(((- (1_ n)) * p) multfield)) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
(((- (1_ n)) * p) * p) . (((c7 - c6) mod (len p)) + 1) is set
(- (1_ n)) * (p * p) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
K191( the carrier of n, the carrier of n,(p * p),((- (1_ n)) multfield)) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
((- (1_ n)) * (p * p)) . (((c7 - c6) mod (len p)) + 1) is set
(- (p * p)) . (((c7 - c6) mod (len p)) + 1) is set
c6 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len c6 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p + M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
width p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
p is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom p is set
Seg K is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= K ) } is set
width M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
c6 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len c6 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
p + c6 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
the addF of n is Relation-like [: the carrier of n, the carrier of n:] -defined the carrier of n -valued Function-like V27([: the carrier of n, the carrier of n:], the carrier of n) Element of bool [:[: the carrier of n, the carrier of n:], the carrier of n:]
[: the carrier of n, the carrier of n:] is set
[:[: the carrier of n, the carrier of n:], the carrier of n:] is set
bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is set
K188( the carrier of n, the carrier of n, the carrier of n, the addF of n,p,c6) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
dom (p + c6) is set
len (p + c6) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (len (p + c6)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len (p + c6) ) } is set
dom c6 is set
(len p) -tuples_on the carrier of n is non empty functional FinSequence-membered FinSequenceSet of the carrier of n
{ b1 where b1 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like Element of the carrier of n * : len b1 = len p } is set
- p is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
comp n is Relation-like the carrier of n -defined the carrier of n -valued Function-like V27( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
bool [: the carrier of n, the carrier of n:] is set
K191( the carrier of n, the carrier of n,p,(comp n)) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len (- p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom (- p) is set
Indices M1 is set
dom M1 is Element of bool NAT
Seg (width M1) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width M1 ) } is set
[:(dom M1),(Seg (width M1)):] is set
[:(Seg K),(Seg K):] is set
Indices (p + M1) is set
dom (p + M1) is Element of bool NAT
width (p + M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (p + M1)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (p + M1) ) } is set
[:(dom (p + M1)),(Seg (width (p + M1))):] is set
Indices p is set
dom p is Element of bool NAT
Seg (width p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width p ) } is set
[:(dom p),(Seg (width p)):] is set
(len c6) -tuples_on the carrier of n is non empty functional FinSequence-membered FinSequenceSet of the carrier of n
{ b1 where b1 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like Element of the carrier of n * : len b1 = len c6 } is set
- c6 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
K191( the carrier of n, the carrier of n,c6,(comp n)) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len (- c6) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom (- c6) is set
- (p + c6) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
K191( the carrier of n, the carrier of n,(p + c6),(comp n)) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
c7 is V4() V5() V6() V10() V11() V12() integer ext-real set
M3 is V4() V5() V6() V10() V11() V12() integer ext-real set
[c7,M3] is set
(p + M1) * (c7,M3) is Element of the carrier of n
M3 - c7 is V11() V12() integer ext-real set
(M3 - c7) mod (len (p + c6)) is V11() V12() integer ext-real set
((M3 - c7) mod (len (p + c6))) + 1 is V11() V12() integer ext-real set
(- (p + c6)) . (((M3 - c7) mod (len (p + c6))) + 1) is set
(- p) + (- c6) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
K188( the carrier of n, the carrier of n, the carrier of n, the addF of n,(- p),(- c6)) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
dom ((- p) + (- c6)) is set
p * (c7,M3) is Element of the carrier of n
M1 * (c7,M3) is Element of the carrier of n
(p * (c7,M3)) + (M1 * (c7,M3)) is Element of the carrier of n
the addF of n . ((p * (c7,M3)),(M1 * (c7,M3))) is Element of the carrier of n
(M3 - c7) mod (len c6) is V11() V12() integer ext-real set
((M3 - c7) mod (len c6)) + 1 is V11() V12() integer ext-real set
(- c6) . (((M3 - c7) mod (len c6)) + 1) is set
the addF of n . ((p * (c7,M3)),((- c6) . (((M3 - c7) mod (len c6)) + 1))) is set
(- p) . (((M3 - c7) mod (len (p + c6))) + 1) is set
(- c6) . (((M3 - c7) mod (len (p + c6))) + 1) is set
the addF of n . (((- p) . (((M3 - c7) mod (len (p + c6))) + 1)),((- c6) . (((M3 - c7) mod (len (p + c6))) + 1))) is set
((- p) + (- c6)) . (((M3 - c7) mod (len (p + c6))) + 1) is set
c7 is V4() V5() V6() V10() V11() V12() integer ext-real set
M3 is V4() V5() V6() V10() V11() V12() integer ext-real set
[c7,M3] is set
(p + M1) * (c7,M3) is Element of the carrier of n
M3 - c7 is V11() V12() integer ext-real set
(M3 - c7) mod (len (p + c6)) is V11() V12() integer ext-real set
((M3 - c7) mod (len (p + c6))) + 1 is V11() V12() integer ext-real set
(p + c6) . (((M3 - c7) mod (len (p + c6))) + 1) is set
p * (c7,M3) is Element of the carrier of n
M1 * (c7,M3) is Element of the carrier of n
(p * (c7,M3)) + (M1 * (c7,M3)) is Element of the carrier of n
the addF of n . ((p * (c7,M3)),(M1 * (c7,M3))) is Element of the carrier of n
(M3 - c7) mod (len c6) is V11() V12() integer ext-real set
((M3 - c7) mod (len c6)) + 1 is V11() V12() integer ext-real set
c6 . (((M3 - c7) mod (len c6)) + 1) is set
the addF of n . ((p * (c7,M3)),(c6 . (((M3 - c7) mod (len c6)) + 1))) is set
p . (((M3 - c7) mod (len (p + c6))) + 1) is set
c6 . (((M3 - c7) mod (len (p + c6))) + 1) is set
the addF of n . ((p . (((M3 - c7) mod (len (p + c6))) + 1)),(c6 . (((M3 - c7) mod (len (p + c6))) + 1))) is set
c7 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len c7 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital Fanoian doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
0. K is V49(K) Element of the carrier of K
n is V4() V5() V6() V10() V11() V12() integer ext-real set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
M1 is V4() V5() V6() V10() V11() V12() integer ext-real set
[p,M1] is set
p is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of n,n, the carrier of K
Indices p is set
dom p is Element of bool NAT
width p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width p ) } is set
[:(dom p),(Seg (width p)):] is set
p * (p,M1) is Element of the carrier of K
c6 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len c6 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
M1 - p is V11() V12() integer ext-real set
(M1 - p) mod (len c6) is V11() V12() integer ext-real set
((M1 - p) mod (len c6)) + 1 is V11() V12() integer ext-real set
c6 . (((M1 - p) mod (len c6)) + 1) is set
(len c6) -tuples_on the carrier of K is non empty functional FinSequence-membered FinSequenceSet of the carrier of K
{ b1 where b1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like Element of the carrier of K * : len b1 = len c6 } is set
- c6 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
comp K is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
[: the carrier of K, the carrier of K:] is set
bool [: the carrier of K, the carrier of K:] is set
K191( the carrier of K, the carrier of K,c6,(comp K)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len (- c6) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg n is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
[:(Seg n),(Seg n):] is set
dom (- c6) is set
(- c6) . (((M1 - p) mod (len c6)) + 1) is set
(comp K) . (c6 . (((M1 - p) mod (len c6)) + 1)) is set
- (p * (p,M1)) is Element of the carrier of K
(p * (p,M1)) + (p * (p,M1)) is Element of the carrier of K
the addF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the addF of K . ((p * (p,M1)),(p * (p,M1))) is Element of the carrier of K
1_ K is Element of the carrier of K
1. K is V49(K) Element of the carrier of K
(1_ K) * (p * (p,M1)) is Element of the carrier of K
the multF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
the multF of K . ((1_ K),(p * (p,M1))) is Element of the carrier of K
((1_ K) * (p * (p,M1))) + (p * (p,M1)) is Element of the carrier of K
the addF of K . (((1_ K) * (p * (p,M1))),(p * (p,M1))) is Element of the carrier of K
((1_ K) * (p * (p,M1))) + ((1_ K) * (p * (p,M1))) is Element of the carrier of K
the addF of K . (((1_ K) * (p * (p,M1))),((1_ K) * (p * (p,M1)))) is Element of the carrier of K
(1_ K) + (1_ K) is Element of the carrier of K
the addF of K . ((1_ K),(1_ K)) is Element of the carrier of K
((1_ K) + (1_ K)) * (p * (p,M1)) is Element of the carrier of K
the multF of K . (((1_ K) + (1_ K)),(p * (p,M1))) is Element of the carrier of K
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K + 1 is V11() V12() integer ext-real set
n is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
[K,n] is set
n + 1 is V11() V12() integer ext-real set
p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg p is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= p ) } is set
[:(Seg p),(Seg p):] is set
M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
c6 is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of c6 is non empty non trivial set
the carrier of c6 * is functional FinSequence-membered FinSequenceSet of the carrier of c6
c7 is Relation-like NAT -defined the carrier of c6 * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of p,p, the carrier of c6
c7 * (M1,p) is Element of the carrier of c6
c7 * (K,n) is Element of the carrier of c6
Indices c7 is set
dom c7 is Element of bool NAT
width c7 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width c7) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width c7 ) } is set
[:(dom c7),(Seg (width c7)):] is set
1 + 1 is non empty V11() V12() integer ext-real positive non negative set
M3 is Relation-like NAT -defined the carrier of c6 -valued Function-like FinSequence-like FinSequence of the carrier of c6
len M3 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
[M1,p] is set
p - M1 is V11() V12() integer ext-real set
(p - M1) mod (len M3) is V11() V12() integer ext-real set
((p - M1) mod (len M3)) + 1 is V11() V12() integer ext-real set
M3 . (((p - M1) mod (len M3)) + 1) is set
n - K is V11() V12() integer ext-real set
(n - K) mod (len M3) is V11() V12() integer ext-real set
((n - K) mod (len M3)) + 1 is V11() V12() integer ext-real set
M3 . (((n - K) mod (len M3)) + 1) is set
Indices c7 is set
dom c7 is Element of bool NAT
width c7 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width c7) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width c7 ) } is set
[:(dom c7),(Seg (width c7)):] is set
1 + 1 is non empty V11() V12() integer ext-real positive non negative set
M3 is Relation-like NAT -defined the carrier of c6 -valued Function-like FinSequence-like FinSequence of the carrier of c6
len M3 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
[M1,p] is set
- M3 is Relation-like NAT -defined the carrier of c6 -valued Function-like FinSequence-like FinSequence of the carrier of c6
comp c6 is Relation-like the carrier of c6 -defined the carrier of c6 -valued Function-like V27( the carrier of c6, the carrier of c6) Element of bool [: the carrier of c6, the carrier of c6:]
[: the carrier of c6, the carrier of c6:] is set
bool [: the carrier of c6, the carrier of c6:] is set
K191( the carrier of c6, the carrier of c6,M3,(comp c6)) is Relation-like NAT -defined the carrier of c6 -valued Function-like FinSequence-like FinSequence of the carrier of c6
p - M1 is V11() V12() integer ext-real set
(p - M1) mod (len M3) is V11() V12() integer ext-real set
((p - M1) mod (len M3)) + 1 is V11() V12() integer ext-real set
(- M3) . (((p - M1) mod (len M3)) + 1) is set
n - K is V11() V12() integer ext-real set
(n - K) mod (len M3) is V11() V12() integer ext-real set
((n - K) mod (len M3)) + 1 is V11() V12() integer ext-real set
(- M3) . (((n - K) mod (len M3)) + 1) is set
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
- p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
Indices p is set
dom p is Element of bool NAT
width p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width p ) } is set
[:(dom p),(Seg (width p)):] is set
Seg K is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= K ) } is set
[:(Seg K),(Seg K):] is set
M1 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
- M1 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
comp n is Relation-like the carrier of n -defined the carrier of n -valued Function-like V27( the carrier of n, the carrier of n) Element of bool [: the carrier of n, the carrier of n:]
[: the carrier of n, the carrier of n:] is set
bool [: the carrier of n, the carrier of n:] is set
K191( the carrier of n, the carrier of n,M1,(comp n)) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
(len M1) -tuples_on the carrier of n is non empty functional FinSequence-membered FinSequenceSet of the carrier of n
{ b1 where b1 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like Element of the carrier of n * : len b1 = len M1 } is set
Indices (- p) is set
dom (- p) is Element of bool NAT
width (- p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (- p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (- p) ) } is set
[:(dom (- p)),(Seg (width (- p))):] is set
len (- M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
c7 is V4() V5() V6() V10() V11() V12() integer ext-real set
[c6,c7] is set
(- p) * (c6,c7) is Element of the carrier of n
c7 - c6 is V11() V12() integer ext-real set
(c7 - c6) mod (len (- M1)) is V11() V12() integer ext-real set
((c7 - c6) mod (len (- M1))) + 1 is V11() V12() integer ext-real set
(- M1) . (((c7 - c6) mod (len (- M1))) + 1) is set
(c7 - c6) mod K is V11() V12() integer ext-real set
((c7 - c6) mod K) + 1 is V11() V12() integer ext-real set
(c7 - c6) mod (len M1) is V11() V12() integer ext-real set
((c7 - c6) mod (len M1)) + 1 is V11() V12() integer ext-real set
dom M1 is set
p * (c6,c7) is Element of the carrier of n
- (p * (c6,c7)) is Element of the carrier of n
(comp n) . (p * (c6,c7)) is set
M1 . (((c7 - c6) mod (len M1)) + 1) is set
(comp n) . (M1 . (((c7 - c6) mod (len M1)) + 1)) is set
(- M1) . (((c7 - c6) mod (len M1)) + 1) is set
dom (- M1) is set
Seg (len M1) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len M1 ) } is set
- (- M1) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
K191( the carrier of n, the carrier of n,(- M1),(comp n)) is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
c7 is V4() V5() V6() V10() V11() V12() integer ext-real set
[c6,c7] is set
(- p) * (c6,c7) is Element of the carrier of n
c7 - c6 is V11() V12() integer ext-real set
(c7 - c6) mod (len (- M1)) is V11() V12() integer ext-real set
((c7 - c6) mod (len (- M1))) + 1 is V11() V12() integer ext-real set
(- (- M1)) . (((c7 - c6) mod (len (- M1))) + 1) is set
(c7 - c6) mod K is V11() V12() integer ext-real set
((c7 - c6) mod K) + 1 is V11() V12() integer ext-real set
p * (c6,c7) is Element of the carrier of n
- (p * (c6,c7)) is Element of the carrier of n
(comp n) . (p * (c6,c7)) is set
(c7 - c6) mod (len M1) is V11() V12() integer ext-real set
((c7 - c6) mod (len M1)) + 1 is V11() V12() integer ext-real set
(- M1) . (((c7 - c6) mod (len M1)) + 1) is set
(comp n) . ((- M1) . (((c7 - c6) mod (len M1)) + 1)) is set
(- (- M1)) . (((c7 - c6) mod (len M1)) + 1) is set
c6 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
len c6 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
p - M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
- M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
p + (- M1) is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of n *
- M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
K is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional FinSequence-membered FinSequenceSet of the carrier of n
p is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like FinSequence of the carrier of n
M1 is Relation-like NAT -defined the carrier of n * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of K,K, the carrier of n
Line (M1,1) is Relation-like NAT -defined the carrier of n -valued Function-like V37( width M1) FinSequence-like Element of (width M1) -tuples_on the carrier of n
width M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(width M1) -tuples_on the carrier of n is non empty functional FinSequence-membered FinSequenceSet of the carrier of n
{ b1 where b1 is Relation-like NAT -defined the carrier of n -valued Function-like FinSequence-like Element of the carrier of n * : len b1 = width M1 } is set
dom p is set
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (len p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len p ) } is set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
p . p is set
(Line (M1,1)) . p is set
0 + 1 is non empty V11() V12() integer ext-real positive non negative set
Seg K is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= K ) } is set
[1,p] is set
[:(Seg K),(Seg K):] is set
Indices M1 is set
dom M1 is Element of bool NAT
Seg (width M1) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width M1 ) } is set
[:(dom M1),(Seg (width M1)):] is set
M1 * (1,p) is Element of the carrier of n
p - 1 is V11() V12() integer ext-real set
(p - 1) mod (len p) is V11() V12() integer ext-real set
((p - 1) mod (len p)) + 1 is V11() V12() integer ext-real set
p . (((p - 1) mod (len p)) + 1) is set
(p - 1) mod K is V11() V12() integer ext-real set
((p - 1) mod K) + 1 is V11() V12() integer ext-real set
p . (((p - 1) mod K) + 1) is set
(p - 1) + 1 is V11() V12() integer ext-real set
p . ((p - 1) + 1) is set
len (Line (M1,1)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom (Line (M1,1)) is set
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
- n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
comp K is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
[: the carrier of K, the carrier of K:] is set
bool [: the carrier of K, the carrier of K:] is set
K191( the carrier of K, the carrier of K,n,(comp K)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len n is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
M1 is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
- M1 is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
Indices M1 is set
dom M1 is Element of bool NAT
width M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width M1) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width M1 ) } is set
[:(dom M1),(Seg (width M1)):] is set
Seg (len n) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len n ) } is set
[:(Seg (len n)),(Seg (len n)):] is set
Indices (- M1) is set
dom (- M1) is Element of bool NAT
width (- M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (- M1)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (- M1) ) } is set
[:(dom (- M1)),(Seg (width (- M1))):] is set
(len n) -tuples_on the carrier of K is non empty functional FinSequence-membered FinSequenceSet of the carrier of K
{ b1 where b1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like Element of the carrier of K * : len b1 = len n } is set
len (- n) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom (- n) is set
- (- n) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
K191( the carrier of K, the carrier of K,(- n),(comp K)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
c7 is V4() V5() V6() V10() V11() V12() integer ext-real set
[c6,c7] is set
(- M1) * (c6,c7) is Element of the carrier of K
c7 - c6 is V11() V12() integer ext-real set
(c7 - c6) mod (len (- n)) is V11() V12() integer ext-real set
((c7 - c6) mod (len (- n))) + 1 is V11() V12() integer ext-real set
(- (- n)) . (((c7 - c6) mod (len (- n))) + 1) is set
(c7 - c6) mod (len n) is V11() V12() integer ext-real set
((c7 - c6) mod (len n)) + 1 is V11() V12() integer ext-real set
M1 * (c6,c7) is Element of the carrier of K
- (M1 * (c6,c7)) is Element of the carrier of K
(comp K) . (M1 * (c6,c7)) is set
(- n) . (((c7 - c6) mod (len n)) + 1) is set
(comp K) . ((- n) . (((c7 - c6) mod (len n)) + 1)) is set
(- (- n)) . (((c7 - c6) mod (len n)) + 1) is set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
c7 is V4() V5() V6() V10() V11() V12() integer ext-real set
[c6,c7] is set
(- M1) * (c6,c7) is Element of the carrier of K
c7 - c6 is V11() V12() integer ext-real set
(c7 - c6) mod (len (- n)) is V11() V12() integer ext-real set
((c7 - c6) mod (len (- n))) + 1 is V11() V12() integer ext-real set
(- n) . (((c7 - c6) mod (len (- n))) + 1) is set
(c7 - c6) mod (len n) is V11() V12() integer ext-real set
((c7 - c6) mod (len n)) + 1 is V11() V12() integer ext-real set
dom n is set
M1 * (c6,c7) is Element of the carrier of K
- (M1 * (c6,c7)) is Element of the carrier of K
(comp K) . (M1 * (c6,c7)) is set
n . (((c7 - c6) mod (len n)) + 1) is set
(comp K) . (n . (((c7 - c6) mod (len n)) + 1)) is set
(- n) . (((c7 - c6) mod (len n)) + 1) is set
c6 is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (- n), len (- n), the carrier of K
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
- n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
comp K is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
[: the carrier of K, the carrier of K:] is set
bool [: the carrier of K, the carrier of K:] is set
K191( the carrier of K, the carrier of K,n,(comp K)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(K,(- n)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (- n), len (- n), the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
len (- n) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len n is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
- (K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
len (K,n) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
width (K,n) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Indices (K,n) is set
dom (K,n) is Element of bool NAT
Seg (width (K,n)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (K,n) ) } is set
[:(dom (K,n)),(Seg (width (K,n))):] is set
Seg (len n) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len n ) } is set
[:(Seg (len n)),(Seg (len n)):] is set
(len n) -tuples_on the carrier of K is non empty functional FinSequence-membered FinSequenceSet of the carrier of K
{ b1 where b1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like Element of the carrier of K * : len b1 = len n } is set
M1 is V4() V5() V6() V10() V11() V12() integer ext-real set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
[M1,p] is set
(K,(- n)) * (M1,p) is Element of the carrier of K
(K,n) * (M1,p) is Element of the carrier of K
- ((K,n) * (M1,p)) is Element of the carrier of K
p - M1 is V11() V12() integer ext-real set
(p - M1) mod (len n) is V11() V12() integer ext-real set
((p - M1) mod (len n)) + 1 is V11() V12() integer ext-real set
dom n is set
Indices (K,(- n)) is set
dom (K,(- n)) is Element of bool NAT
width (K,(- n)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (K,(- n))) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (K,(- n)) ) } is set
[:(dom (K,(- n))),(Seg (width (K,(- n)))):] is set
(p - M1) mod (len (- n)) is V11() V12() integer ext-real set
((p - M1) mod (len (- n))) + 1 is V11() V12() integer ext-real set
(- n) . (((p - M1) mod (len (- n))) + 1) is set
n . (((p - M1) mod (len n)) + 1) is set
(comp K) . (n . (((p - M1) mod (len n)) + 1)) is set
(comp K) . ((K,n) * (M1,p)) is set
p - M1 is V11() V12() integer ext-real set
(p - M1) mod (len n) is V11() V12() integer ext-real set
((p - M1) mod (len n)) + 1 is V11() V12() integer ext-real set
dom (- n) is set
Indices (K,(- n)) is set
dom (K,(- n)) is Element of bool NAT
width (K,(- n)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (K,(- n))) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (K,(- n)) ) } is set
[:(dom (K,(- n))),(Seg (width (K,(- n)))):] is set
- (- n) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
K191( the carrier of K, the carrier of K,(- n),(comp K)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(p - M1) mod (len (- n)) is V11() V12() integer ext-real set
((p - M1) mod (len (- n))) + 1 is V11() V12() integer ext-real set
(- (- n)) . (((p - M1) mod (len (- n))) + 1) is set
(- n) . (((p - M1) mod (len n)) + 1) is set
(comp K) . ((- n) . (((p - M1) mod (len n)) + 1)) is set
(comp K) . ((K,n) * (M1,p)) is set
len (K,(- n)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
width (K,(- n)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len n is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n + p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
the addF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[: the carrier of K, the carrier of K:] is set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
K188( the carrier of K, the carrier of K, the carrier of K, the addF of K,n,p) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
p is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
width p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom n is set
Seg (len n) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len n ) } is set
dom p is set
dom (n + p) is set
len (n + p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
c6 is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
Indices c6 is set
dom c6 is Element of bool NAT
width c6 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width c6) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width c6 ) } is set
[:(dom c6),(Seg (width c6)):] is set
[:(Seg (len n)),(Seg (len n)):] is set
c6 + p is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
(len p) -tuples_on the carrier of K is non empty functional FinSequence-membered FinSequenceSet of the carrier of K
{ b1 where b1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like Element of the carrier of K * : len b1 = len p } is set
- p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
comp K is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
bool [: the carrier of K, the carrier of K:] is set
K191( the carrier of K, the carrier of K,p,(comp K)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len (- p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Indices p is set
dom p is Element of bool NAT
Seg (width p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width p ) } is set
[:(dom p),(Seg (width p)):] is set
Indices (c6 + p) is set
dom (c6 + p) is Element of bool NAT
width (c6 + p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (c6 + p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (c6 + p) ) } is set
[:(dom (c6 + p)),(Seg (width (c6 + p))):] is set
Seg (len (n + p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len (n + p) ) } is set
M3 is V4() V5() V6() V10() V11() V12() integer ext-real set
c9 is V4() V5() V6() V10() V11() V12() integer ext-real set
[M3,c9] is set
(c6 + p) * (M3,c9) is Element of the carrier of K
c9 - M3 is V11() V12() integer ext-real set
(c9 - M3) mod (len (n + p)) is V11() V12() integer ext-real set
((c9 - M3) mod (len (n + p))) + 1 is V11() V12() integer ext-real set
(n + p) . (((c9 - M3) mod (len (n + p))) + 1) is set
c6 * (M3,c9) is Element of the carrier of K
p * (M3,c9) is Element of the carrier of K
(c6 * (M3,c9)) + (p * (M3,c9)) is Element of the carrier of K
the addF of K . ((c6 * (M3,c9)),(p * (M3,c9))) is Element of the carrier of K
(c9 - M3) mod (len p) is V11() V12() integer ext-real set
((c9 - M3) mod (len p)) + 1 is V11() V12() integer ext-real set
p . (((c9 - M3) mod (len p)) + 1) is set
the addF of K . ((c6 * (M3,c9)),(p . (((c9 - M3) mod (len p)) + 1))) is set
n . (((c9 - M3) mod (len (n + p))) + 1) is set
p . (((c9 - M3) mod (len (n + p))) + 1) is set
the addF of K . ((n . (((c9 - M3) mod (len (n + p))) + 1)),(p . (((c9 - M3) mod (len (n + p))) + 1))) is set
(len n) -tuples_on the carrier of K is non empty functional FinSequence-membered FinSequenceSet of the carrier of K
{ b1 where b1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like Element of the carrier of K * : len b1 = len n } is set
- n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
K191( the carrier of K, the carrier of K,n,(comp K)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len (- n) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom (- n) is set
- (n + p) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
K191( the carrier of K, the carrier of K,(n + p),(comp K)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
M3 is V4() V5() V6() V10() V11() V12() integer ext-real set
c9 is V4() V5() V6() V10() V11() V12() integer ext-real set
[M3,c9] is set
(c6 + p) * (M3,c9) is Element of the carrier of K
c9 - M3 is V11() V12() integer ext-real set
(c9 - M3) mod (len (n + p)) is V11() V12() integer ext-real set
((c9 - M3) mod (len (n + p))) + 1 is V11() V12() integer ext-real set
(- (n + p)) . (((c9 - M3) mod (len (n + p))) + 1) is set
dom (- p) is set
Seg (len p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len p ) } is set
(- n) + (- p) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
K188( the carrier of K, the carrier of K, the carrier of K, the addF of K,(- n),(- p)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
dom ((- n) + (- p)) is set
c6 * (M3,c9) is Element of the carrier of K
p * (M3,c9) is Element of the carrier of K
(c6 * (M3,c9)) + (p * (M3,c9)) is Element of the carrier of K
the addF of K . ((c6 * (M3,c9)),(p * (M3,c9))) is Element of the carrier of K
(c9 - M3) mod (len p) is V11() V12() integer ext-real set
((c9 - M3) mod (len p)) + 1 is V11() V12() integer ext-real set
(- p) . (((c9 - M3) mod (len p)) + 1) is set
the addF of K . ((c6 * (M3,c9)),((- p) . (((c9 - M3) mod (len p)) + 1))) is set
(c9 - M3) mod (len n) is V11() V12() integer ext-real set
((c9 - M3) mod (len n)) + 1 is V11() V12() integer ext-real set
(- n) . (((c9 - M3) mod (len n)) + 1) is set
the addF of K . (((- n) . (((c9 - M3) mod (len n)) + 1)),((- p) . (((c9 - M3) mod (len p)) + 1))) is set
((- n) + (- p)) . (((c9 - M3) mod (len (n + p))) + 1) is set
len (c6 + p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
M3 is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (n + p), len (n + p), the carrier of K
len M3 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len n is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len n, len n, the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
n + p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
the addF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[: the carrier of K, the carrier of K:] is set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
K188( the carrier of K, the carrier of K, the carrier of K, the addF of K,n,p) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(K,(n + p)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (n + p), len (n + p), the carrier of K
len (n + p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
(K,n) + (K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of K *
dom n is set
Seg (len n) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len n ) } is set
dom p is set
dom (n + p) is set
Indices (K,n) is set
dom (K,n) is Element of bool NAT
width (K,n) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (K,n)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (K,n) ) } is set
[:(dom (K,n)),(Seg (width (K,n))):] is set
Indices (K,(n + p)) is set
dom (K,(n + p)) is Element of bool NAT
width (K,(n + p)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (K,(n + p))) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (K,(n + p)) ) } is set
[:(dom (K,(n + p))),(Seg (width (K,(n + p)))):] is set
Indices (K,p) is set
dom (K,p) is Element of bool NAT
width (K,p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (K,p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (K,p) ) } is set
[:(dom (K,p)),(Seg (width (K,p))):] is set
Seg (len (n + p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len (n + p) ) } is set
(len n) -tuples_on the carrier of K is non empty functional FinSequence-membered FinSequenceSet of the carrier of K
{ b1 where b1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like Element of the carrier of K * : len b1 = len n } is set
- n is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
comp K is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
bool [: the carrier of K, the carrier of K:] is set
K191( the carrier of K, the carrier of K,n,(comp K)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len (- n) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
[:(Seg (len n)),(Seg (len n)):] is set
(len p) -tuples_on the carrier of K is non empty functional FinSequence-membered FinSequenceSet of the carrier of K
{ b1 where b1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like Element of the carrier of K * : len b1 = len p } is set
- p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
K191( the carrier of K, the carrier of K,p,(comp K)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len (- p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
p is V4() V5() V6() V10() V11() V12() integer ext-real set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
[p,c6] is set
(K,(n + p)) * (p,c6) is Element of the carrier of K
(K,n) * (p,c6) is Element of the carrier of K
(K,p) * (p,c6) is Element of the carrier of K
((K,n) * (p,c6)) + ((K,p) * (p,c6)) is Element of the carrier of K
the addF of K . (((K,n) * (p,c6)),((K,p) * (p,c6))) is Element of the carrier of K
c6 - p is V11() V12() integer ext-real set
(c6 - p) mod (len n) is V11() V12() integer ext-real set
((c6 - p) mod (len n)) + 1 is V11() V12() integer ext-real set
(c6 - p) mod (len (n + p)) is V11() V12() integer ext-real set
((c6 - p) mod (len (n + p))) + 1 is V11() V12() integer ext-real set
(n + p) . (((c6 - p) mod (len (n + p))) + 1) is set
n . (((c6 - p) mod (len (n + p))) + 1) is set
p . (((c6 - p) mod (len (n + p))) + 1) is set
the addF of K . ((n . (((c6 - p) mod (len (n + p))) + 1)),(p . (((c6 - p) mod (len (n + p))) + 1))) is set
(c6 - p) mod (len p) is V11() V12() integer ext-real set
((c6 - p) mod (len p)) + 1 is V11() V12() integer ext-real set
p . (((c6 - p) mod (len p)) + 1) is set
the addF of K . (((K,n) * (p,c6)),(p . (((c6 - p) mod (len p)) + 1))) is set
dom (- n) is set
dom (- p) is set
Seg (len p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len p ) } is set
(- n) + (- p) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
K188( the carrier of K, the carrier of K, the carrier of K, the addF of K,(- n),(- p)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
dom ((- n) + (- p)) is set
(c6 - p) mod (len (n + p)) is V11() V12() integer ext-real set
((c6 - p) mod (len (n + p))) + 1 is V11() V12() integer ext-real set
- (n + p) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
K191( the carrier of K, the carrier of K,(n + p),(comp K)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(- (n + p)) . (((c6 - p) mod (len (n + p))) + 1) is set
((- n) + (- p)) . (((c6 - p) mod (len (n + p))) + 1) is set
(- n) . (((c6 - p) mod (len (n + p))) + 1) is set
(- p) . (((c6 - p) mod (len (n + p))) + 1) is set
the addF of K . (((- n) . (((c6 - p) mod (len (n + p))) + 1)),((- p) . (((c6 - p) mod (len (n + p))) + 1))) is set
(c6 - p) mod (len p) is V11() V12() integer ext-real set
((c6 - p) mod (len p)) + 1 is V11() V12() integer ext-real set
(- p) . (((c6 - p) mod (len p)) + 1) is set
the addF of K . (((K,n) * (p,c6)),((- p) . (((c6 - p) mod (len p)) + 1))) is set
len (K,n) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len (K,(n + p)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Element of the carrier of K
p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n * p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
[: the carrier of K, the carrier of K:] is set
bool [: the carrier of K, the carrier of K:] is set
the multF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
id the carrier of K is non empty Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one total Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] (n,(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,p,(n multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom p is set
Seg (len p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len p ) } is set
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
p is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
n * p is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
Indices (n * p) is set
dom (n * p) is Element of bool NAT
width (n * p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (n * p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (n * p) ) } is set
[:(dom (n * p)),(Seg (width (n * p))):] is set
[:(Seg (len p)),(Seg (len p)):] is set
len (n * p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
- (n * p) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
comp K is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,(n * p),(comp K)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
- p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
K191( the carrier of K, the carrier of K,p,(comp K)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n * (- p) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
K191( the carrier of K, the carrier of K,(- p),(n multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len (n * (- p)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len (- p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom (n * (- p)) is set
Seg (len (- p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len (- p) ) } is set
dom (- p) is set
(len p) -tuples_on the carrier of K is non empty functional FinSequence-membered FinSequenceSet of the carrier of K
{ b1 where b1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like Element of the carrier of K * : len b1 = len p } is set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
c7 is V4() V5() V6() V10() V11() V12() integer ext-real set
[c6,c7] is set
(n * p) * (c6,c7) is Element of the carrier of K
c7 - c6 is V11() V12() integer ext-real set
(c7 - c6) mod (len (n * p)) is V11() V12() integer ext-real set
((c7 - c6) mod (len (n * p))) + 1 is V11() V12() integer ext-real set
(- (n * p)) . (((c7 - c6) mod (len (n * p))) + 1) is set
(c7 - c6) mod (len p) is V11() V12() integer ext-real set
((c7 - c6) mod (len p)) + 1 is V11() V12() integer ext-real set
Indices p is set
dom p is Element of bool NAT
width p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width p ) } is set
[:(dom p),(Seg (width p)):] is set
p * (c6,c7) is Element of the carrier of K
n * (p * (c6,c7)) is Element of the carrier of K
the multF of K . (n,(p * (c6,c7))) is Element of the carrier of K
(n multfield) . (p * (c6,c7)) is set
(- p) . (((c7 - c6) mod (len p)) + 1) is set
(n multfield) . ((- p) . (((c7 - c6) mod (len p)) + 1)) is set
(- p) /. (((c7 - c6) mod (len p)) + 1) is Element of the carrier of K
(n multfield) . ((- p) /. (((c7 - c6) mod (len p)) + 1)) is set
n * ((- p) /. (((c7 - c6) mod (len p)) + 1)) is Element of the carrier of K
the multF of K . (n,((- p) /. (((c7 - c6) mod (len p)) + 1))) is Element of the carrier of K
(n * (- p)) /. (((c7 - c6) mod (len p)) + 1) is Element of the carrier of K
(n * (- p)) . (((c7 - c6) mod (len p)) + 1) is set
1_ K is Element of the carrier of K
1. K is V49(K) Element of the carrier of K
- (1_ K) is Element of the carrier of K
(- (1_ K)) * p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(- (1_ K)) multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] ((- (1_ K)),(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,p,((- (1_ K)) multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n * ((- (1_ K)) * p) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
K191( the carrier of K, the carrier of K,((- (1_ K)) * p),(n multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(n * ((- (1_ K)) * p)) . (((c7 - c6) mod (len p)) + 1) is set
n * (- (1_ K)) is Element of the carrier of K
the multF of K . (n,(- (1_ K))) is Element of the carrier of K
(n * (- (1_ K))) * p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(n * (- (1_ K))) multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] ((n * (- (1_ K))),(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,p,((n * (- (1_ K))) multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
((n * (- (1_ K))) * p) . (((c7 - c6) mod (len p)) + 1) is set
n * (1_ K) is Element of the carrier of K
the multF of K . (n,(1_ K)) is Element of the carrier of K
- (n * (1_ K)) is Element of the carrier of K
(- (n * (1_ K))) * p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(- (n * (1_ K))) multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] ((- (n * (1_ K))),(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,p,((- (n * (1_ K))) multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
((- (n * (1_ K))) * p) . (((c7 - c6) mod (len p)) + 1) is set
- n is Element of the carrier of K
(- n) * p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(- n) multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] ((- n),(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,p,((- n) multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
((- n) * p) . (((c7 - c6) mod (len p)) + 1) is set
(1_ K) * n is Element of the carrier of K
the multF of K . ((1_ K),n) is Element of the carrier of K
- ((1_ K) * n) is Element of the carrier of K
(- ((1_ K) * n)) * p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(- ((1_ K) * n)) multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] ((- ((1_ K) * n)),(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,p,((- ((1_ K) * n)) multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
((- ((1_ K) * n)) * p) . (((c7 - c6) mod (len p)) + 1) is set
(- (1_ K)) * n is Element of the carrier of K
the multF of K . ((- (1_ K)),n) is Element of the carrier of K
((- (1_ K)) * n) * p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
((- (1_ K)) * n) multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] (((- (1_ K)) * n),(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,p,(((- (1_ K)) * n) multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(((- (1_ K)) * n) * p) . (((c7 - c6) mod (len p)) + 1) is set
(- (1_ K)) * (n * p) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
K191( the carrier of K, the carrier of K,(n * p),((- (1_ K)) multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
((- (1_ K)) * (n * p)) . (((c7 - c6) mod (len p)) + 1) is set
(- (n * p)) . (((c7 - c6) mod (len p)) + 1) is set
dom (n * p) is set
Seg (len (n * p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len (n * p) ) } is set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
c7 is V4() V5() V6() V10() V11() V12() integer ext-real set
[c6,c7] is set
(n * p) * (c6,c7) is Element of the carrier of K
c7 - c6 is V11() V12() integer ext-real set
(c7 - c6) mod (len (n * p)) is V11() V12() integer ext-real set
((c7 - c6) mod (len (n * p))) + 1 is V11() V12() integer ext-real set
(n * p) . (((c7 - c6) mod (len (n * p))) + 1) is set
(c7 - c6) mod (len p) is V11() V12() integer ext-real set
((c7 - c6) mod (len p)) + 1 is V11() V12() integer ext-real set
Indices p is set
dom p is Element of bool NAT
width p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width p ) } is set
[:(dom p),(Seg (width p)):] is set
p * (c6,c7) is Element of the carrier of K
n * (p * (c6,c7)) is Element of the carrier of K
the multF of K . (n,(p * (c6,c7))) is Element of the carrier of K
(n multfield) . (p * (c6,c7)) is set
p . (((c7 - c6) mod (len p)) + 1) is set
(n multfield) . (p . (((c7 - c6) mod (len p)) + 1)) is set
p /. (((c7 - c6) mod (len p)) + 1) is Element of the carrier of K
(n multfield) . (p /. (((c7 - c6) mod (len p)) + 1)) is set
n * (p /. (((c7 - c6) mod (len p)) + 1)) is Element of the carrier of K
the multF of K . (n,(p /. (((c7 - c6) mod (len p)) + 1))) is Element of the carrier of K
(n * p) /. (((c7 - c6) mod (len p)) + 1) is Element of the carrier of K
(n * p) . (((c7 - c6) mod (len p)) + 1) is set
c6 is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (n * p), len (n * p), the carrier of K
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Element of the carrier of K
p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n * p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
[: the carrier of K, the carrier of K:] is set
bool [: the carrier of K, the carrier of K:] is set
the multF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
id the carrier of K is non empty Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one total Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] (n,(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,p,(n multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(K,(n * p)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (n * p), len (n * p), the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
len (n * p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
n * (K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
Indices (K,p) is set
dom (K,p) is Element of bool NAT
width (K,p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (K,p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (K,p) ) } is set
[:(dom (K,p)),(Seg (width (K,p))):] is set
Seg (len p) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len p ) } is set
[:(Seg (len p)),(Seg (len p)):] is set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
[p,c6] is set
(K,(n * p)) * (p,c6) is Element of the carrier of K
(K,p) * (p,c6) is Element of the carrier of K
n * ((K,p) * (p,c6)) is Element of the carrier of K
the multF of K . (n,((K,p) * (p,c6))) is Element of the carrier of K
c6 - p is V11() V12() integer ext-real set
(c6 - p) mod (len p) is V11() V12() integer ext-real set
((c6 - p) mod (len p)) + 1 is V11() V12() integer ext-real set
Indices (K,(n * p)) is set
dom (K,(n * p)) is Element of bool NAT
width (K,(n * p)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Seg (width (K,(n * p))) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (K,(n * p)) ) } is set
[:(dom (K,(n * p))),(Seg (width (K,(n * p)))):] is set
dom (n * p) is set
Seg (len (n * p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len (n * p) ) } is set
dom p is set
(c6 - p) mod (len (n * p)) is V11() V12() integer ext-real set
((c6 - p) mod (len (n * p))) + 1 is V11() V12() integer ext-real set
(n * p) . (((c6 - p) mod (len (n * p))) + 1) is set
(n * p) /. (((c6 - p) mod (len p)) + 1) is Element of the carrier of K
p /. (((c6 - p) mod (len p)) + 1) is Element of the carrier of K
n * (p /. (((c6 - p) mod (len p)) + 1)) is Element of the carrier of K
the multF of K . (n,(p /. (((c6 - p) mod (len p)) + 1))) is Element of the carrier of K
(n multfield) . (p /. (((c6 - p) mod (len p)) + 1)) is set
p . (((c6 - p) mod (len p)) + 1) is set
(n multfield) . (p . (((c6 - p) mod (len p)) + 1)) is set
(n multfield) . ((K,p) * (p,c6)) is set
- p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
comp K is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,p,(comp K)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n * (- p) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
K191( the carrier of K, the carrier of K,(- p),(n multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len (n * (- p)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len (- p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
dom (n * (- p)) is set
Seg (len (- p)) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= len (- p) ) } is set
dom (- p) is set
(len p) -tuples_on the carrier of K is non empty functional FinSequence-membered FinSequenceSet of the carrier of K
{ b1 where b1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like Element of the carrier of K * : len b1 = len p } is set
(n multfield) . ((K,p) * (p,c6)) is set
(- p) . (((c6 - p) mod (len p)) + 1) is set
(n multfield) . ((- p) . (((c6 - p) mod (len p)) + 1)) is set
(- p) /. (((c6 - p) mod (len p)) + 1) is Element of the carrier of K
(n multfield) . ((- p) /. (((c6 - p) mod (len p)) + 1)) is set
n * ((- p) /. (((c6 - p) mod (len p)) + 1)) is Element of the carrier of K
the multF of K . (n,((- p) /. (((c6 - p) mod (len p)) + 1))) is Element of the carrier of K
(n * (- p)) /. (((c6 - p) mod (len p)) + 1) is Element of the carrier of K
(n * (- p)) . (((c6 - p) mod (len p)) + 1) is set
1_ K is Element of the carrier of K
1. K is V49(K) Element of the carrier of K
- (1_ K) is Element of the carrier of K
(- (1_ K)) * p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(- (1_ K)) multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] ((- (1_ K)),(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,p,((- (1_ K)) multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n * ((- (1_ K)) * p) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
K191( the carrier of K, the carrier of K,((- (1_ K)) * p),(n multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(n * ((- (1_ K)) * p)) . (((c6 - p) mod (len p)) + 1) is set
n * (- (1_ K)) is Element of the carrier of K
the multF of K . (n,(- (1_ K))) is Element of the carrier of K
(n * (- (1_ K))) * p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(n * (- (1_ K))) multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] ((n * (- (1_ K))),(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,p,((n * (- (1_ K))) multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
((n * (- (1_ K))) * p) . (((c6 - p) mod (len p)) + 1) is set
n * (1_ K) is Element of the carrier of K
the multF of K . (n,(1_ K)) is Element of the carrier of K
- (n * (1_ K)) is Element of the carrier of K
(- (n * (1_ K))) * p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(- (n * (1_ K))) multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] ((- (n * (1_ K))),(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,p,((- (n * (1_ K))) multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
((- (n * (1_ K))) * p) . (((c6 - p) mod (len p)) + 1) is set
- n is Element of the carrier of K
(- n) * p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(- n) multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] ((- n),(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,p,((- n) multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
((- n) * p) . (((c6 - p) mod (len p)) + 1) is set
(1_ K) * n is Element of the carrier of K
the multF of K . ((1_ K),n) is Element of the carrier of K
- ((1_ K) * n) is Element of the carrier of K
(- ((1_ K) * n)) * p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(- ((1_ K) * n)) multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] ((- ((1_ K) * n)),(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,p,((- ((1_ K) * n)) multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
((- ((1_ K) * n)) * p) . (((c6 - p) mod (len p)) + 1) is set
(- (1_ K)) * n is Element of the carrier of K
the multF of K . ((- (1_ K)),n) is Element of the carrier of K
((- (1_ K)) * n) * p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
((- (1_ K)) * n) multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] (((- (1_ K)) * n),(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,p,(((- (1_ K)) * n) multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(((- (1_ K)) * n) * p) . (((c6 - p) mod (len p)) + 1) is set
(- (1_ K)) * (n * p) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
K191( the carrier of K, the carrier of K,(n * p),((- (1_ K)) multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
((- (1_ K)) * (n * p)) . (((c6 - p) mod (len p)) + 1) is set
- (n * p) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
K191( the carrier of K, the carrier of K,(n * p),(comp K)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(- (n * p)) . (((c6 - p) mod (len p)) + 1) is set
len (K,p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len (K,(n * p)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
width (K,(n * p)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Element of the carrier of K
p is Element of the carrier of K
n + p is Element of the carrier of K
the addF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[: the carrier of K, the carrier of K:] is set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the addF of K . (n,p) is Element of the carrier of K
M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
n * (K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
p * (K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
(n * (K,M1)) + (p * (K,M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
(n + p) * M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(n + p) multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
bool [: the carrier of K, the carrier of K:] is set
the multF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
id the carrier of K is non empty Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one total Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] ((n + p),(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,M1,((n + p) multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(K,((n + p) * M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len ((n + p) * M1), len ((n + p) * M1), the carrier of K
len ((n + p) * M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
p * M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
p multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] (p,(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,M1,(p multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len (p * M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(len M1) -tuples_on the carrier of K is non empty functional FinSequence-membered FinSequenceSet of the carrier of K
{ b1 where b1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like Element of the carrier of K * : len b1 = len M1 } is set
n * M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] (n,(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,M1,(n multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(K,(n * M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (n * M1), len (n * M1), the carrier of K
len (n * M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(K,(n * M1)) + (p * (K,M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of K *
(K,(p * M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (p * M1), len (p * M1), the carrier of K
(K,(n * M1)) + (K,(p * M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of K *
(n * M1) + (p * M1) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
K188( the carrier of K, the carrier of K, the carrier of K, the addF of K,(n * M1),(p * M1)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(K,((n * M1) + (p * M1))) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len ((n * M1) + (p * M1)), len ((n * M1) + (p * M1)), the carrier of K
len ((n * M1) + (p * M1)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Element of the carrier of K
p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
n * (K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
n * (K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
(n * (K,p)) + (n * (K,M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of K *
p + M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
the addF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[: the carrier of K, the carrier of K:] is set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
K188( the carrier of K, the carrier of K, the carrier of K, the addF of K,p,M1) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n * (p + M1) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
bool [: the carrier of K, the carrier of K:] is set
the multF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
id the carrier of K is non empty Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one total Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] (n,(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,(p + M1),(n multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(K,(n * (p + M1))) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (n * (p + M1)), len (n * (p + M1)), the carrier of K
len (n * (p + M1)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len (K,p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
width (K,p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len (K,M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
width (K,M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(K,p) + (K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of K *
n * ((K,p) + (K,M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of K *
len (p + M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(K,(p + M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (p + M1), len (p + M1), the carrier of K
n * (K,(p + M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (p + M1), len (p + M1), the carrier of K
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n is Element of the carrier of K
p is Element of the carrier of K
M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len M1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
n * (K,M1) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len M1, len M1, the carrier of K
n * M1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
n multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
[: the carrier of K, the carrier of K:] is set
bool [: the carrier of K, the carrier of K:] is set
the multF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
[:[: the carrier of K, the carrier of K:], the carrier of K:] is set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
id the carrier of K is non empty Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one total Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] (n,(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,M1,(n multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
p * (K,p) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len p, len p, the carrier of K
(n * (K,M1)) + (p * (K,p)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of K *
p * p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
p multfield is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
the multF of K [;] (p,(id the carrier of K)) is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
K191( the carrier of K, the carrier of K,p,(p multfield)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(n * M1) + (p * p) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
the addF of K is Relation-like [: the carrier of K, the carrier of K:] -defined the carrier of K -valued Function-like V27([: the carrier of K, the carrier of K:], the carrier of K) Element of bool [:[: the carrier of K, the carrier of K:], the carrier of K:]
K188( the carrier of K, the carrier of K, the carrier of K, the addF of K,(n * M1),(p * p)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
(K,((n * M1) + (p * p))) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len ((n * M1) + (p * p)), len ((n * M1) + (p * p)), the carrier of K
len ((n * M1) + (p * p)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
len (p * p) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(K,(n * M1)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (n * M1), len (n * M1), the carrier of K
len (n * M1) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
(K,(n * M1)) + (p * (K,p)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of K *
(K,(p * p)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of len (p * p), len (p * p), the carrier of K
(K,(n * M1)) + (K,(p * p)) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular FinSequence of the carrier of K *
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital V114() V116() V119() V120() V121() right-distributive left-distributive right_unital well-unital V133() left_unital doubleLoopStr
n is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
0. (K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular ( the carrier of K) ( the carrier of K) Matrix of n,n, the carrier of K
the carrier of K is non empty non trivial set
the carrier of K * is functional FinSequence-membered FinSequenceSet of the carrier of K
n -tuples_on the carrier of K is non empty functional FinSequence-membered FinSequenceSet of the carrier of K
{ b1 where b1 is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like Element of the carrier of K * : len b1 = n } is set
0. K is V49(K) Element of the carrier of K
n |-> (0. K) is Relation-like NAT -defined the carrier of K -valued Function-like V37(n) FinSequence-like Element of n -tuples_on the carrier of K
Seg n is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
(Seg n) --> (0. K) is Relation-like Seg n -defined Seg n -defined the carrier of K -valued {(0. K)} -valued Function-like constant total total V27( Seg n,{(0. K)}) FinSequence-like Element of bool [:(Seg n),{(0. K)}:]
{(0. K)} is non empty set
[:(Seg n),{(0. K)}:] is set
bool [:(Seg n),{(0. K)}:] is set
n |-> (n |-> (0. K)) is Relation-like NAT -defined n -tuples_on the carrier of K -valued Function-like V37(n) FinSequence-like Function-yielding V105() Element of n -tuples_on (n -tuples_on the carrier of K)
n -tuples_on (n -tuples_on the carrier of K) is non empty functional FinSequence-membered FinSequenceSet of n -tuples_on the carrier of K
(n -tuples_on the carrier of K) * is functional FinSequence-membered FinSequenceSet of n -tuples_on the carrier of K
{ b1 where b1 is Relation-like NAT -defined n -tuples_on the carrier of K -valued Function-like FinSequence-like Element of (n -tuples_on the carrier of K) * : len b1 = n } is set
(Seg n) --> (n |-> (0. K)) is Relation-like Seg n -defined Seg n -defined n -tuples_on the carrier of K -valued {(n |-> (0. K))} -valued Function-like constant total total V27( Seg n,{(n |-> (0. K))}) FinSequence-like Function-yielding V105() Element of bool [:(Seg n),{(n |-> (0. K))}:]
{(n |-> (0. K))} is non empty functional set
[:(Seg n),{(n |-> (0. K))}:] is set
bool [:(Seg n),{(n |-> (0. K))}:] is set
width (0. (K,n)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
0. (K,n,n) is Relation-like NAT -defined the carrier of K * -valued Function-like FinSequence-like Function-yielding V105() tabular Matrix of n,n, the carrier of K
len (n |-> (0. K)) is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT
Indices (0. (K,n)) is set
dom (0. (K,n)) is Element of bool NAT
Seg (width (0. (K,n))) is Element of bool NAT
{ b1 where b1 is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT : ( 1 <= b1 & b1 <= width (0. (K,n)) ) } is set
[:(dom (0. (K,n))),(Seg (width (0. (K,n)))):] is set
[:(Seg n),(Seg n):] is set
- (n |-> (0. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V37(n) FinSequence-like Element of n -tuples_on the carrier of K
comp K is Relation-like the carrier of K -defined the carrier of K -valued Function-like V27( the carrier of K, the carrier of K) Element of bool [: the carrier of K, the carrier of K:]
[: the carrier of K, the carrier of K:] is set
bool [: the carrier of K, the carrier of K:] is set
K191( the carrier of K, the carrier of K,(n |-> (0. K)),(comp K)) is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
p is V4() V5() V6() V10() V11() V12() integer ext-real set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
[p,c6] is set
(0. (K,n)) * (p,c6) is Element of the carrier of K
c6 - p is V11() V12() integer ext-real set
(c6 - p) mod (len (n |-> (0. K))) is V11() V12() integer ext-real set
((c6 - p) mod (len (n |-> (0. K)))) + 1 is V11() V12() integer ext-real set
(- (n |-> (0. K))) . (((c6 - p) mod (len (n |-> (0. K)))) + 1) is set
(c6 - p) mod n is V11() V12() integer ext-real set
((c6 - p) mod n) + 1 is V11() V12() integer ext-real set
- (0. K) is Element of the carrier of K
n |-> (- (0. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V37(n) FinSequence-like Element of n -tuples_on the carrier of K
(Seg n) --> (- (0. K)) is Relation-like Seg n -defined Seg n -defined the carrier of K -valued {(- (0. K))} -valued Function-like constant total total V27( Seg n,{(- (0. K))}) FinSequence-like Element of bool [:(Seg n),{(- (0. K))}:]
{(- (0. K))} is non empty set
[:(Seg n),{(- (0. K))}:] is set
bool [:(Seg n),{(- (0. K))}:] is set
(n |-> (- (0. K))) . (((c6 - p) mod n) + 1) is set
p is V4() V5() V6() V10() V11() V12() integer ext-real set
c6 is V4() V5() V6() V10() V11() V12() integer ext-real set
[p,c6] is set
(0. (K,n)) * (p,c6) is Element of the carrier of K
c6 - p is V11() V12() integer ext-real set
(c6 - p) mod (len (n |-> (0. K))) is V11() V12() integer ext-real set
((c6 - p) mod (len (n |-> (0. K)))) + 1 is V11() V12() integer ext-real set
(n |-> (0. K)) . (((c6 - p) mod (len (n |-> (0. K)))) + 1) is set
(c6 - p) mod n is V11() V12() integer ext-real set
((c6 - p) mod n) + 1 is V11() V12() integer ext-real set
(Seg n) --> (0. K) is Relation-like Seg n -defined Seg n -defined the carrier of K -valued Function-like constant total total V27( Seg n, the carrier of K) FinSequence-like Element of bool [:(Seg n), the carrier of K:]
[:(Seg n), the carrier of K:] is set
bool [:(Seg n), the carrier of K:] is set
((Seg n) --> (0. K)) . (((c6 - p) mod n) + 1) is set
p is Relation-like NAT -defined the carrier of K -valued Function-like FinSequence-like FinSequence of the carrier of K
len p is V4() V5() V6() V10() V11() V12() integer ext-real Element of NAT