REAL is set
NAT is non empty V21() V22() V23() V28() V33() V34() Element of bool REAL
bool REAL is set
{} is set
the Relation-like non-empty empty-yielding functional empty V21() V22() V23() V25() V26() V27() V28() V33() V35( {} ) FinSequence-like FinSequence-membered V47() V48() ext-real non positive non negative set is Relation-like non-empty empty-yielding functional empty V21() V22() V23() V25() V26() V27() V28() V33() V35( {} ) FinSequence-like FinSequence-membered V47() V48() ext-real non positive non negative set
1 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
{{},1} is set
NAT is non empty V21() V22() V23() V28() V33() V34() set
bool NAT is V28() set
bool NAT is V28() set
K183(NAT) is V45() set
COMPLEX is set
RAT is set
INT is set
[:1,1:] is Relation-like set
bool [:1,1:] is set
[:[:1,1:],1:] is Relation-like set
bool [:[:1,1:],1:] is set
[:[:1,1:],REAL:] is Relation-like set
bool [:[:1,1:],REAL:] is set
[:REAL,REAL:] is Relation-like set
[:[:REAL,REAL:],REAL:] is Relation-like set
bool [:[:REAL,REAL:],REAL:] is set
2 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
[:2,2:] is Relation-like set
[:[:2,2:],REAL:] is Relation-like set
bool [:[:2,2:],REAL:] is set
bool [:REAL,REAL:] is set
K386(2) is V166() L15()
the carrier of K386(2) is set
0 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
3 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
Seg 1 is non empty trivial V28() V35(1) Element of bool NAT
{1} is non empty trivial V35(1) set
Seg 2 is non empty V28() V35(2) Element of bool NAT
{1,2} is set
n is non empty ZeroStr
the carrier of n is non empty set
K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
0. n is V83(n) Element of the carrier of n
K |-> (0. n) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35(K) FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of n
K -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
n is non empty ZeroStr
K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(n,K) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
the carrier of n is non empty set
0. n is V83(n) Element of the carrier of n
K |-> (0. n) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35(K) FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of n
K -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
n is non empty addLoopStr
the carrier of n is non empty set
K is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(len K) -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
the carrier of n * is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
{ b1 where b1 is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like Element of the carrier of n * : len b1 = len K } is set
n is non empty addLoopStr
the carrier of n is non empty set
K is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K + A is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len (K + A) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(len K) -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
B2 is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
B3 is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
B2 + B3 is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
dom (B2 + B3) is V35( len K) Element of bool NAT
Seg (len K) is V28() V35( len K) Element of bool NAT
n is non empty addLoopStr
the carrier of n is non empty set
K is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K - A is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len (K - A) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(len K) -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
B2 is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
B3 is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
B2 - B3 is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
dom (B2 - B3) is V35( len K) Element of bool NAT
Seg (len K) is V28() V35( len K) Element of bool NAT
n is non empty multLoopStr
the carrier of n is non empty set
K is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
A is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
mlt (K,A) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
dom (mlt (K,A)) is Element of bool NAT
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(mlt (K,A)) . B is set
K /. B is Element of the carrier of n
A /. B is Element of the carrier of n
(K /. B) * (A /. B) is Element of the carrier of n
the multF of n is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of n, the carrier of n:], the carrier of n:] is Relation-like set
bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is set
the multF of n . ((K /. B),(A /. B)) is Element of the carrier of n
(mlt (K,A)) /. B is Element of the carrier of n
the multF of n .: (K,A) is Relation-like Function-like set
rng A is set
dom the multF of n is set
rng K is set
[:(rng K),(rng A):] is Relation-like set
dom K is Element of bool NAT
dom A is Element of bool NAT
(dom K) /\ (dom A) is Element of bool NAT
A . B is set
K . B is set
n is non empty addLoopStr
the carrier of n is non empty set
K is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K + A is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
K - A is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(K + A) . B is set
K /. B is Element of the carrier of n
A /. B is Element of the carrier of n
(K /. B) + (A /. B) is Element of the carrier of n
the addF of n is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of n, the carrier of n:], the carrier of n:] is Relation-like set
bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is set
the addF of n . ((K /. B),(A /. B)) is Element of the carrier of n
(K - A) . B is set
(K /. B) - (A /. B) is Element of the carrier of n
- (A /. B) is Element of the carrier of n
(K /. B) + (- (A /. B)) is Element of the carrier of n
the addF of n . ((K /. B),(- (A /. B))) is Element of the carrier of n
(len K) -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
B2 is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
B2 /. B is Element of the carrier of n
B2 . B is set
B3 is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
B3 /. B is Element of the carrier of n
B3 . B is set
Seg (len K) is V28() V35( len K) Element of bool NAT
len (K + A) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (len (K + A)) is V28() V35( len (K + A)) Element of bool NAT
dom (K + A) is Element of bool NAT
len (K - A) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (len (K - A)) is V28() V35( len (K - A)) Element of bool NAT
dom (K - A) is Element of bool NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
K is Element of the carrier of n
- K is Element of the carrier of n
A is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
K * A is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
- (K * A) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
(- K) * A is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
- A is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
K * (- A) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(len A) -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
B2 is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len A) FinSequence-like FinSubsequence-like Element of (len A) -tuples_on the carrier of n
K * B2 is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len A) FinSequence-like FinSubsequence-like Element of (len A) -tuples_on the carrier of n
B3 is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len A) FinSequence-like FinSubsequence-like Element of (len A) -tuples_on the carrier of n
1_ n is Element of the carrier of n
1. n is V83(n) Element of the carrier of n
- (1_ n) is Element of the carrier of n
(- (1_ n)) * B3 is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len A) FinSequence-like FinSubsequence-like Element of (len A) -tuples_on the carrier of n
(- (1_ n)) * K is Element of the carrier of n
the multF of n is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of n, the carrier of n:], the carrier of n:] is Relation-like set
bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is set
the multF of n . ((- (1_ n)),K) is Element of the carrier of n
((- (1_ n)) * K) * B2 is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len A) FinSequence-like FinSubsequence-like Element of (len A) -tuples_on the carrier of n
(1_ n) * K is Element of the carrier of n
the multF of n . ((1_ n),K) is Element of the carrier of n
- ((1_ n) * K) is Element of the carrier of n
(- ((1_ n) * K)) * B2 is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len A) FinSequence-like FinSubsequence-like Element of (len A) -tuples_on the carrier of n
(- (1_ n)) * B2 is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len A) FinSequence-like FinSubsequence-like Element of (len A) -tuples_on the carrier of n
K * ((- (1_ n)) * B2) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len A) FinSequence-like FinSubsequence-like Element of (len A) -tuples_on the carrier of n
n is non empty multLoopStr
the carrier of n is non empty set
K is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K ^ B is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
A ^ B2 is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
mlt ((K ^ B),(A ^ B2)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
mlt (K,A) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
mlt (B,B2) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
(mlt (K,A)) ^ (mlt (B,B2)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
the multF of n is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of n, the carrier of n:], the carrier of n:] is Relation-like set
bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is set
the multF of n .: ((K ^ B),(A ^ B2)) is Relation-like Function-like set
<:(K ^ B),(A ^ B2):> is Relation-like Function-like set
<:(K ^ B),(A ^ B2):> * the multF of n is Relation-like set
dom (K ^ B) is Element of bool NAT
len (K ^ B) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (len (K ^ B)) is V28() V35( len (K ^ B)) Element of bool NAT
rng (A ^ B2) is set
dom the multF of n is set
rng (K ^ B) is set
[:(rng (K ^ B)),(rng (A ^ B2)):] is Relation-like set
dom (<:(K ^ B),(A ^ B2):> * the multF of n) is set
dom (A ^ B2) is Element of bool NAT
(dom (K ^ B)) /\ (dom (A ^ B2)) is Element of bool NAT
len (A ^ B2) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(len A) + (len B2) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (len (A ^ B2)) is V28() V35( len (A ^ B2)) Element of bool NAT
dom (mlt ((K ^ B),(A ^ B2))) is Element of bool NAT
the multF of n .: (B,B2) is Relation-like Function-like set
<:B,B2:> is Relation-like Function-like set
<:B,B2:> * the multF of n is Relation-like set
rng B is set
rng B2 is set
[:(rng B),(rng B2):] is Relation-like set
dom (<:B,B2:> * the multF of n) is set
dom B is Element of bool NAT
dom B2 is Element of bool NAT
(dom B) /\ (dom B2) is Element of bool NAT
Seg (len B) is V28() V35( len B) Element of bool NAT
dom (mlt (B,B2)) is Element of bool NAT
len (mlt (B,B2)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
the multF of n .: (K,A) is Relation-like Function-like set
<:K,A:> is Relation-like Function-like set
<:K,A:> * the multF of n is Relation-like set
rng K is set
rng A is set
[:(rng K),(rng A):] is Relation-like set
dom (<:K,A:> * the multF of n) is set
dom K is Element of bool NAT
dom A is Element of bool NAT
(dom K) /\ (dom A) is Element of bool NAT
(len K) + (len B) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (len K) is V28() V35( len K) Element of bool NAT
dom (mlt (K,A)) is Element of bool NAT
len (mlt ((K ^ B),(A ^ B2))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(mlt ((K ^ B),(A ^ B2))) . B3 is set
((mlt (K,A)) ^ (mlt (B,B2))) . B3 is set
Seg (len (mlt ((K ^ B),(A ^ B2)))) is V28() V35( len (mlt ((K ^ B),(A ^ B2)))) Element of bool NAT
(K ^ B) /. B3 is Element of the carrier of n
(K ^ B) . B3 is set
(A ^ B2) /. B3 is Element of the carrier of n
(A ^ B2) . B3 is set
A . B3 is set
(mlt (K,A)) . B3 is set
K /. B3 is Element of the carrier of n
A /. B3 is Element of the carrier of n
(K /. B3) * (A /. B3) is Element of the carrier of n
the multF of n . ((K /. B3),(A /. B3)) is Element of the carrier of n
K . B3 is set
((K ^ B) /. B3) * ((A ^ B2) /. B3) is Element of the carrier of n
the multF of n . (((K ^ B) /. B3),((A ^ B2) /. B3)) is Element of the carrier of n
B3 -' (len K) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B3 - (len K) is V47() V48() ext-real set
(len K) + (B3 -' (len K)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
((len K) + (len B)) - (len K) is V47() V48() ext-real set
0 + 1 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
len (mlt (K,A)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(len (mlt (K,A))) + (B3 -' (len K)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(mlt (B,B2)) . (B3 -' (len K)) is set
B /. (B3 -' (len K)) is Element of the carrier of n
B2 /. (B3 -' (len K)) is Element of the carrier of n
(B /. (B3 -' (len K))) * (B2 /. (B3 -' (len K))) is Element of the carrier of n
the multF of n . ((B /. (B3 -' (len K))),(B2 /. (B3 -' (len K)))) is Element of the carrier of n
B . (B3 -' (len K)) is set
B2 . (B3 -' (len K)) is set
((K ^ B) /. B3) * ((A ^ B2) /. B3) is Element of the carrier of n
the multF of n . (((K ^ B) /. B3),((A ^ B2) /. B3)) is Element of the carrier of n
((K ^ B) /. B3) * ((A ^ B2) /. B3) is Element of the carrier of n
the multF of n . (((K ^ B) /. B3),((A ^ B2) /. B3)) is Element of the carrier of n
((K ^ B) /. B3) * ((A ^ B2) /. B3) is Element of the carrier of n
the multF of n . (((K ^ B) /. B3),((A ^ B2) /. B3)) is Element of the carrier of n
len (mlt (K,A)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(len (mlt (K,A))) + (len (mlt (B,B2))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
len ((mlt (K,A)) ^ (mlt (B,B2))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
K is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
mlt (K,A) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B is Element of the carrier of n
B * K is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
mlt ((B * K),A) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B * (mlt (K,A)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B * A is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
mlt (K,(B * A)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
(len K) -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
B3 is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
B2 is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
mlt (B3,B2) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
B * (mlt (B3,B2)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
K is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K "*" A is Element of the carrier of n
B is Element of the carrier of n
B * K is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
(B * K) "*" A is Element of the carrier of n
B * (K "*" A) is Element of the carrier of n
the multF of n is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of n, the carrier of n:], the carrier of n:] is Relation-like set
bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is set
the multF of n . (B,(K "*" A)) is Element of the carrier of n
mlt ((B * K),A) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
Sum (mlt ((B * K),A)) is Element of the carrier of n
mlt (K,A) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B * (mlt (K,A)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
Sum (B * (mlt (K,A))) is Element of the carrier of n
Sum (mlt (K,A)) is Element of the carrier of n
B * (Sum (mlt (K,A))) is Element of the carrier of n
the multF of n . (B,(Sum (mlt (K,A)))) is Element of the carrier of n
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
K is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K "*" A is Element of the carrier of n
B is Element of the carrier of n
B * A is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
K "*" (B * A) is Element of the carrier of n
B * (K "*" A) is Element of the carrier of n
the multF of n is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of n, the carrier of n:], the carrier of n:] is Relation-like set
bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is set
the multF of n . (B,(K "*" A)) is Element of the carrier of n
mlt (K,(B * A)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
Sum (mlt (K,(B * A))) is Element of the carrier of n
mlt (K,A) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B * (mlt (K,A)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
Sum (B * (mlt (K,A))) is Element of the carrier of n
Sum (mlt (K,A)) is Element of the carrier of n
B * (Sum (mlt (K,A))) is Element of the carrier of n
the multF of n . (B,(Sum (mlt (K,A)))) is Element of the carrier of n
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
K is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A + B is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
K "*" (A + B) is Element of the carrier of n
K "*" A is Element of the carrier of n
K "*" B is Element of the carrier of n
(K "*" A) + (K "*" B) is Element of the carrier of n
the addF of n is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of n, the carrier of n:], the carrier of n:] is Relation-like set
bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is set
the addF of n . ((K "*" A),(K "*" B)) is Element of the carrier of n
(len K) -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
mlt (K,(A + B)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
Sum (mlt (K,(A + B))) is Element of the carrier of n
B3 is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
B2 is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
mlt (B3,B2) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
B is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
mlt (B3,B) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
(mlt (B3,B2)) + (mlt (B3,B)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
Sum ((mlt (B3,B2)) + (mlt (B3,B))) is Element of the carrier of n
Sum (mlt (B3,B2)) is Element of the carrier of n
Sum (mlt (B3,B)) is Element of the carrier of n
(Sum (mlt (B3,B2))) + (Sum (mlt (B3,B))) is Element of the carrier of n
the addF of n . ((Sum (mlt (B3,B2))),(Sum (mlt (B3,B)))) is Element of the carrier of n
mlt (K,A) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
Sum (mlt (K,A)) is Element of the carrier of n
(Sum (mlt (K,A))) + (K "*" B) is Element of the carrier of n
the addF of n . ((Sum (mlt (K,A))),(K "*" B)) is Element of the carrier of n
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
K is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K ^ B is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
A ^ B2 is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
(K ^ B) "*" (A ^ B2) is Element of the carrier of n
K "*" A is Element of the carrier of n
B "*" B2 is Element of the carrier of n
(K "*" A) + (B "*" B2) is Element of the carrier of n
the addF of n is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of n, the carrier of n:], the carrier of n:] is Relation-like set
bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is set
the addF of n . ((K "*" A),(B "*" B2)) is Element of the carrier of n
mlt (K,A) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
mlt (B,B2) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
(mlt (K,A)) ^ (mlt (B,B2)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
Sum ((mlt (K,A)) ^ (mlt (B,B2))) is Element of the carrier of n
Sum (mlt (K,A)) is Element of the carrier of n
Sum (mlt (B,B2)) is Element of the carrier of n
(Sum (mlt (K,A))) + (Sum (mlt (B,B2))) is Element of the carrier of n
the addF of n . ((Sum (mlt (K,A))),(Sum (mlt (B,B2)))) is Element of the carrier of n
mlt ((K ^ B),(A ^ B2)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
Sum (mlt ((K ^ B),(A ^ B2))) is Element of the carrier of n
(Sum (mlt (K,A))) + (B "*" B2) is Element of the carrier of n
the addF of n . ((Sum (mlt (K,A))),(B "*" B2)) is Element of the carrier of n
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
n -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
0. K is V83(K) Element of the carrier of K
n |-> (0. K) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of K
A is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of K
mlt (A,(n |-> (0. K))) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of K
(K,n) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of K
(0. K) * (K,n) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of K
mlt (A,((0. K) * (K,n))) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of K
mlt (A,(K,n)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of K
(0. K) * (mlt (A,(K,n))) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of K
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
1. (n,0) is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of 0 , 0 , the carrier of n
the carrier of n is non empty non trivial set
the carrier of n * is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
0. (n,0) is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of 0 , 0 , the carrier of n
0 -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
0. n is V83(n) Element of the carrier of n
0 |-> (0. n) is Relation-like non-empty empty-yielding NAT -defined the carrier of n -valued Function-like functional empty V21() V22() V23() V25() V26() V27() V28() V33() V35( 0 ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V40() V47() V48() ext-real non positive non negative Element of 0 -tuples_on the carrier of n
0 |-> (0 |-> (0. n)) is Relation-like non-empty empty-yielding NAT -defined 0 -tuples_on the carrier of n -valued Function-like functional empty V21() V22() V23() V25() V26() V27() V28() V33() V35( 0 ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V40() V47() V48() ext-real non positive non negative Element of 0 -tuples_on (0 -tuples_on the carrier of n)
0 -tuples_on (0 -tuples_on the carrier of n) is functional non empty FinSequence-membered FinSequenceSet of 0 -tuples_on the carrier of n
len (1. (n,0)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
1. (n,0) is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of 0 , 0 , the carrier of n
0. (n,0) is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of 0 , 0 , the carrier of n
0 -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
0. n is V83(n) Element of the carrier of n
0 |-> (0. n) is Relation-like non-empty empty-yielding NAT -defined the carrier of n -valued Function-like functional empty V21() V22() V23() V25() V26() V27() V28() V33() V35( 0 ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V40() V47() V48() ext-real non positive non negative Element of 0 -tuples_on the carrier of n
0 |-> (0 |-> (0. n)) is Relation-like non-empty empty-yielding NAT -defined 0 -tuples_on the carrier of n -valued Function-like functional empty V21() V22() V23() V25() V26() V27() V28() V33() V35( 0 ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V40() V47() V48() ext-real non positive non negative Element of 0 -tuples_on (0 -tuples_on the carrier of n)
0 -tuples_on (0 -tuples_on the carrier of n) is functional non empty FinSequence-membered FinSequenceSet of 0 -tuples_on the carrier of n
K is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of 0 , 0 , the carrier of n
len K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
K is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of 0 , 0 , the carrier of n
K * K is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of 0 , 0 , the carrier of n
1. (n,0) is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of 0 , 0 , the carrier of n
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A * B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(A * B) * B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B * B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A * (B * B2) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
width B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
len B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
width A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
len B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
1. (K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A ~ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B * A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A * B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
1. (K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A ~ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(A ~) * A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A * (A ~) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B * A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A * B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
0. n is V83(n) Element of the carrier of n
K is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(n,(len K)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
(len K) -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
(len K) |-> (0. n) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
K "*" (n,(len K)) is Element of the carrier of n
B is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
mlt (B,(n,(len K))) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
Sum (mlt (B,(n,(len K)))) is Element of the carrier of n
Sum (n,(len K)) is Element of the carrier of n
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
0. n is V83(n) Element of the carrier of n
K is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(n,(len K)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
(len K) -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
(len K) |-> (0. n) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35( len K) FinSequence-like FinSubsequence-like Element of (len K) -tuples_on the carrier of n
(n,(len K)) "*" K is Element of the carrier of n
K "*" (n,(len K)) is Element of the carrier of n
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
0. n is V83(n) Element of the carrier of n
<*(0. n)*> is Relation-like NAT -defined the carrier of n -valued Function-like non empty trivial V28() V35(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of n
K is Element of the carrier of n
<*K*> is Relation-like NAT -defined the carrier of n -valued Function-like non empty trivial V28() V35(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of n
<*(0. n)*> "*" <*K*> is Element of the carrier of n
len <*K*> is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
(n,1) is Relation-like NAT -defined the carrier of n -valued Function-like non empty trivial V28() V35(1) FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of n
1 -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
1 |-> (0. n) is Relation-like NAT -defined the carrier of n -valued Function-like non empty trivial V28() V35(1) FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of n
(n,1) "*" <*K*> is Element of the carrier of n
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
0. n is V83(n) Element of the carrier of n
K |-> (0. n) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35(K) FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of n
K -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
1. n is V83(n) Element of the carrier of n
Replace ((K |-> (0. n)),A,(1. n)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(n,K,A) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
the carrier of n is non empty non trivial set
0. n is V83(n) Element of the carrier of n
K |-> (0. n) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35(K) FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of n
K -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
1. n is V83(n) Element of the carrier of n
Replace ((K |-> (0. n)),A,(1. n)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len (n,K,A) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
len (Replace ((K |-> (0. n)),A,(1. n))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
len (K |-> (0. n)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
1. n is V83(n) Element of the carrier of n
the carrier of n is non empty non trivial set
K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(n,A,K) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
0. n is V83(n) Element of the carrier of n
A |-> (0. n) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35(A) FinSequence-like FinSubsequence-like Element of A -tuples_on the carrier of n
A -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
Replace ((A |-> (0. n)),K,(1. n)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
(n,A,K) . K is set
len (A |-> (0. n)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
len (Replace ((A |-> (0. n)),K,(1. n))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(Replace ((A |-> (0. n)),K,(1. n))) /. K is Element of the carrier of n
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
0. n is V83(n) Element of the carrier of n
the carrier of n is non empty non trivial set
A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(n,B,K) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B |-> (0. n) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35(B) FinSequence-like FinSubsequence-like Element of B -tuples_on the carrier of n
B -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
1. n is V83(n) Element of the carrier of n
Replace ((B |-> (0. n)),K,(1. n)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
(n,B,K) . A is set
Seg B is V28() V35(B) Element of bool NAT
len (B |-> (0. n)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
len (Replace ((B |-> (0. n)),K,(1. n))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(Replace ((B |-> (0. n)),K,(1. n))) /. A is Element of the carrier of n
(B |-> (0. n)) /. A is Element of the carrier of n
(B |-> (0. n)) . A is set
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
1. (n,A) is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of A,A, the carrier of n
the carrier of n is non empty non trivial set
the carrier of n * is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
(1. (n,A)) . K is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,A,K) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
0. n is V83(n) Element of the carrier of n
A |-> (0. n) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35(A) FinSequence-like FinSubsequence-like Element of A -tuples_on the carrier of n
A -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
1. n is V83(n) Element of the carrier of n
Replace ((A |-> (0. n)),K,(1. n)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
[K,1] is set
Indices (1. (n,A)) is set
dom (1. (n,A)) is Element of bool NAT
width (1. (n,A)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (1. (n,A))) is V28() V35( width (1. (n,A))) Element of bool NAT
[:(dom (1. (n,A))),(Seg (width (1. (n,A)))):] is Relation-like set
(1. (n,A)) * (K,1) is Element of the carrier of n
B is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B . 1 is set
len (1. (n,A)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
rng (1. (n,A)) is set
len B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B . B2 is set
(n,A,K) . B2 is set
[K,B2] is set
(1. (n,A)) * (K,B2) is Element of the carrier of n
(1. (n,A)) * (K,K) is Element of the carrier of n
1_ n is Element of the carrier of n
B3 is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B3 . B2 is set
B3 is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B3 . B2 is set
len (n,A,K) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
1. (K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,A) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
0. K is V83(K) Element of the carrier of K
n |-> (0. K) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of K
n -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
1. K is V83(K) Element of the carrier of K
Replace ((n |-> (0. K)),A,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(1. (K,n)) * (A,B) is Element of the carrier of K
(K,n,A) . B is set
[A,B] is set
Indices (1. (K,n)) is set
dom (1. (K,n)) is Element of bool NAT
width (1. (K,n)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (1. (K,n))) is V28() V35( width (1. (K,n))) Element of bool NAT
[:(dom (1. (K,n))),(Seg (width (1. (K,n)))):] is Relation-like set
(1. (K,n)) . A is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
B2 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B2 . B is set
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
0. (K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
n -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
0. K is V83(K) Element of the carrier of K
n |-> (0. K) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of K
n |-> (n |-> (0. K)) is Relation-like NAT -defined n -tuples_on the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Function-yielding V40() Element of n -tuples_on (n -tuples_on the carrier of K)
n -tuples_on (n -tuples_on the carrier of K) is functional non empty FinSequence-membered FinSequenceSet of n -tuples_on the carrier of K
A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
0. (K,n,n) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A * (B2,B) is Element of the carrier of K
[B2,B] is set
Indices (0. (K,n)) is set
dom (0. (K,n)) is Element of bool NAT
width (0. (K,n)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (0. (K,n))) is V28() V35( width (0. (K,n))) Element of bool NAT
[:(dom (0. (K,n))),(Seg (width (0. (K,n)))):] is Relation-like set
(0. (K,n)) + (0. (K,n)) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
((0. (K,n)) + (0. (K,n))) * (B2,B) is Element of the carrier of K
(0. (K,n)) * (B2,B) is Element of the carrier of K
((0. (K,n)) * (B2,B)) + ((0. (K,n)) * (B2,B)) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is Relation-like set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the addF of K . (((0. (K,n)) * (B2,B)),((0. (K,n)) * (B2,B))) is Element of the carrier of K
((0. (K,n)) * (B2,B)) - ((0. (K,n)) * (B2,B)) is Element of the carrier of K
- ((0. (K,n)) * (B2,B)) is Element of the carrier of K
((0. (K,n)) * (B2,B)) + (- ((0. (K,n)) * (B2,B))) is Element of the carrier of K
the addF of K . (((0. (K,n)) * (B2,B)),(- ((0. (K,n)) * (B2,B)))) is Element of the carrier of K
((0. (K,n)) * (B2,B)) + (((0. (K,n)) * (B2,B)) - ((0. (K,n)) * (B2,B))) is Element of the carrier of K
the addF of K . (((0. (K,n)) * (B2,B)),(((0. (K,n)) * (B2,B)) - ((0. (K,n)) * (B2,B)))) is Element of the carrier of K
((0. (K,n)) * (B2,B)) + (0. K) is Element of the carrier of K
the addF of K . (((0. (K,n)) * (B2,B)),(0. K)) is Element of the carrier of K
len A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Indices A is set
dom A is Element of bool NAT
width A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width A) is V28() V35( width A) Element of bool NAT
[:(dom A),(Seg (width A)):] is Relation-like set
Seg n is V28() V35(n) Element of bool NAT
[:(Seg n),(Seg n):] is Relation-like set
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
[B,B2] is set
A * (B,B2) is Element of the carrier of K
(A * (B,B2)) + (A * (B,B2)) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is Relation-like set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the addF of K . ((A * (B,B2)),(A * (B,B2))) is Element of the carrier of K
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A * (B3,B2) is Element of the carrier of K
A + A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
0. (K,(len A),(width A)) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of len A, width A, the carrier of K
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
1. (K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
1. K is V83(K) Element of the carrier of K
0. K is V83(K) Element of the carrier of K
A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
Indices A is set
dom A is Element of bool NAT
width A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width A) is V28() V35( width A) Element of bool NAT
[:(dom A),(Seg (width A)):] is Relation-like set
Seg n is V28() V35(n) Element of bool NAT
[:(Seg n),(Seg n):] is Relation-like set
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A * (B,B2) is Element of the carrier of K
IFEQ (B,B2,(1. K),(0. K)) is Element of the carrier of K
[B,B2] is set
len (1. (K,n)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
width (1. (K,n)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Indices (1. (K,n)) is set
dom (1. (K,n)) is Element of bool NAT
Seg (width (1. (K,n))) is V28() V35( width (1. (K,n))) Element of bool NAT
[:(dom (1. (K,n))),(Seg (width (1. (K,n)))):] is Relation-like set
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
[B,B2] is set
A * (B,B2) is Element of the carrier of K
(1. (K,n)) * (B,B2) is Element of the carrier of K
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A * (B3,B2) is Element of the carrier of K
IFEQ (B3,B2,(1. K),(0. K)) is Element of the carrier of K
1_ K is Element of the carrier of K
len A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A * B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(A * B) @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(B @) * (A @) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
width B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
len B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
width A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
1. (K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(A @) ~ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A ~ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(A ~) @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
1. (K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B * A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A * B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(A * B) @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(B @) * (A @) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(B * A) @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(A @) * (B @) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
0. n is V83(n) Element of the carrier of n
K is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
len K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Sum K is Element of the carrier of n
A is Element of the carrier of n
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K . B is set
[:NAT, the carrier of n:] is Relation-like V28() set
bool [:NAT, the carrier of n:] is V28() set
K . 1 is set
the addF of n is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of n, the carrier of n:], the carrier of n:] is Relation-like set
bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is set
the addF of n "**" K is Element of the carrier of n
B2 is Relation-like Function-like V18( NAT , the carrier of n) Element of bool [:NAT, the carrier of n:]
B2 . 1 is Element of the carrier of n
B2 . (len K) is Element of the carrier of n
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 . B3 is Element of the carrier of n
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 . B2 is Element of the carrier of n
B2 + 1 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
B2 . (B2 + 1) is Element of the carrier of n
1 + B2 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
K . (B2 + 1) is set
the addF of n . ((B2 . B2),(K . (B2 + 1))) is set
(0. n) + (0. n) is Element of the carrier of n
the addF of n . ((0. n),(0. n)) is Element of the carrier of n
B2 . 0 is Element of the carrier of n
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 . B3 is Element of the carrier of n
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 . B2 is Element of the carrier of n
B2 + 1 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
B2 . (B2 + 1) is Element of the carrier of n
K . (B2 + 1) is set
the addF of n . ((B2 . B2),(K . (B2 + 1))) is set
A + (0. n) is Element of the carrier of n
the addF of n . (A,(0. n)) is Element of the carrier of n
K . (B2 + 1) is set
the addF of n . ((B2 . B2),(K . (B2 + 1))) is set
(0. n) + A is Element of the carrier of n
the addF of n . ((0. n),A) is Element of the carrier of n
1 + B2 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
B2 . 0 is Element of the carrier of n
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
K is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
A is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
mlt (K,A) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
dom (mlt (K,A)) is Element of bool NAT
dom K is Element of bool NAT
dom A is Element of bool NAT
(dom K) /\ (dom A) is Element of bool NAT
rng A is set
the multF of n is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of n, the carrier of n:], the carrier of n:] is Relation-like set
bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is set
dom the multF of n is set
rng K is set
the multF of n .: (K,A) is Relation-like Function-like set
[:(rng K),(rng A):] is Relation-like set
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(mlt (K,A)) . B is set
K /. B is Element of the carrier of n
A /. B is Element of the carrier of n
(K /. B) * (A /. B) is Element of the carrier of n
the multF of n . ((K /. B),(A /. B)) is Element of the carrier of n
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
0. K is V83(K) Element of the carrier of K
A is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B2) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
n |-> (0. K) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of K
n -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
1. K is V83(K) Element of the carrier of K
Replace ((n |-> (0. K)),B2,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
mlt (A,(K,n,B2)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B . B2 is set
A . B2 is set
dom A is Element of bool NAT
len (K,n,B2) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B2) /. B2 is Element of the carrier of K
(K,n,B2) . B2 is set
rng (K,n,B2) is set
the multF of K is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is Relation-like set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
dom the multF of K is set
rng A is set
[:(rng A),(rng (K,n,B2)):] is Relation-like set
the multF of K .: (A,(K,n,B2)) is Relation-like Function-like set
dom ( the multF of K .: (A,(K,n,B2))) is set
dom (K,n,B2) is Element of bool NAT
(dom A) /\ (dom (K,n,B2)) is Element of bool NAT
dom (mlt (A,(K,n,B2))) is Element of bool NAT
Seg n is V28() V35(n) Element of bool NAT
(Seg n) /\ (dom (K,n,B2)) is Element of bool NAT
(Seg n) /\ (Seg n) is Element of bool NAT
(mlt (A,(K,n,B2))) . B2 is set
A /. B2 is Element of the carrier of K
(A /. B2) * ((K,n,B2) /. B2) is Element of the carrier of K
the multF of K . ((A /. B2),((K,n,B2) /. B2)) is Element of the carrier of K
(A /. B2) * (1. K) is Element of the carrier of K
the multF of K . ((A /. B2),(1. K)) is Element of the carrier of K
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B . B3 is set
(K,n,B2) /. B3 is Element of the carrier of K
(K,n,B2) . B3 is set
(mlt (A,(K,n,B2))) . B3 is set
A /. B3 is Element of the carrier of K
(A /. B3) * ((K,n,B2) /. B3) is Element of the carrier of K
the multF of K . ((A /. B3),((K,n,B2) /. B3)) is Element of the carrier of K
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of A is non empty non trivial set
(A,n,K) is Relation-like NAT -defined the carrier of A -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of A
0. A is V83(A) Element of the carrier of A
n |-> (0. A) is Relation-like NAT -defined the carrier of A -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of A
n -tuples_on the carrier of A is functional non empty FinSequence-membered FinSequenceSet of the carrier of A
1. A is V83(A) Element of the carrier of A
Replace ((n |-> (0. A)),K,(1. A)) is Relation-like NAT -defined the carrier of A -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of A
B is Relation-like NAT -defined the carrier of A -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of A
len B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B "*" (A,n,K) is Element of the carrier of A
B . K is set
B /. K is Element of the carrier of A
mlt (B,(A,n,K)) is Relation-like NAT -defined the carrier of A -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of A
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(mlt (B,(A,n,K))) . B2 is set
len (A,n,K) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
rng (A,n,K) is set
the multF of A is Relation-like Function-like V18([: the carrier of A, the carrier of A:], the carrier of A) Element of bool [:[: the carrier of A, the carrier of A:], the carrier of A:]
[: the carrier of A, the carrier of A:] is Relation-like set
[:[: the carrier of A, the carrier of A:], the carrier of A:] is Relation-like set
bool [:[: the carrier of A, the carrier of A:], the carrier of A:] is set
dom the multF of A is set
rng B is set
[:(rng B),(rng (A,n,K)):] is Relation-like set
the multF of A .: (B,(A,n,K)) is Relation-like Function-like set
dom ( the multF of A .: (B,(A,n,K))) is set
dom B is Element of bool NAT
dom (A,n,K) is Element of bool NAT
(dom B) /\ (dom (A,n,K)) is Element of bool NAT
dom (mlt (B,(A,n,K))) is Element of bool NAT
Seg n is V28() V35(n) Element of bool NAT
(Seg n) /\ (dom (A,n,K)) is Element of bool NAT
(Seg n) /\ (Seg n) is Element of bool NAT
len (mlt (B,(A,n,K))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(mlt (B,(A,n,K))) . K is set
Sum (mlt (B,(A,n,K))) is Element of the carrier of A
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
1. n is V83(n) Element of the carrier of n
the carrier of n is non empty non trivial set
K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(n,K,A) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
0. n is V83(n) Element of the carrier of n
K |-> (0. n) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35(K) FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of n
K -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
Replace ((K |-> (0. n)),A,(1. n)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
(n,K,A) "*" (n,K,A) is Element of the carrier of n
len (n,K,A) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(n,K,A) . A is set
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
0. K is V83(K) Element of the carrier of K
A is Element of the carrier of K
A " is Element of the carrier of K
B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B * (1,1) is Element of the carrier of K
B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B2 * (1,1) is Element of the carrier of K
B ~ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
0 + 1 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
(K,n,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
n |-> (0. K) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of K
n -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
1. K is V83(K) Element of the carrier of K
Replace ((n |-> (0. K)),1,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len (K,n,1) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
len B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(A ") * (K,n,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len ((A ") * (K,n,1)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Col (B,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( len B) FinSequence-like FinSubsequence-like Element of (len B) -tuples_on the carrier of K
(len B) -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(Col (B,1)) . B3 is set
((A ") * (K,n,1)) . B3 is set
Seg n is V28() V35(n) Element of bool NAT
dom B is Element of bool NAT
[B3,1] is set
Indices B is set
width B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width B) is V28() V35( width B) Element of bool NAT
[:(dom B),(Seg (width B)):] is Relation-like set
B . B3 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
B * (B3,1) is Element of the carrier of K
(K,n,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,n,B3) . 1 is set
B2 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B2 . 1 is set
(K,n,1) /. B3 is Element of the carrier of K
(K,n,1) . B3 is set
dom ((A ") * (K,n,1)) is Element of bool NAT
(A ") * ((K,n,1) /. B3) is Element of the carrier of K
the multF of K is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is Relation-like set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the multF of K . ((A "),((K,n,1) /. B3)) is Element of the carrier of K
(A ") * (1. K) is Element of the carrier of K
the multF of K . ((A "),(1. K)) is Element of the carrier of K
(A ") * (0. K) is Element of the carrier of K
the multF of K . ((A "),(0. K)) is Element of the carrier of K
len B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (len B2) is V28() V35( len B2) Element of bool NAT
dom B2 is Element of bool NAT
width B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Line (B2,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width B2) FinSequence-like FinSubsequence-like Element of (width B2) -tuples_on the carrier of K
(width B2) -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
len (Line (B2,1)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
dom (Line (B2,1)) is V35( width B2) Element of bool NAT
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B * (1,B3) is Element of the carrier of K
B2 * (1,B3) is Element of the carrier of K
(A ") * (B2 * (1,B3)) is Element of the carrier of K
the multF of K is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is Relation-like set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the multF of K . ((A "),(B2 * (1,B3))) is Element of the carrier of K
- ((A ") * (B2 * (1,B3))) is Element of the carrier of K
A * (B * (1,B3)) is Element of the carrier of K
the multF of K . (A,(B * (1,B3))) is Element of the carrier of K
- (A * (B * (1,B3))) is Element of the carrier of K
(A ") * (- (A * (B * (1,B3)))) is Element of the carrier of K
the multF of K . ((A "),(- (A * (B * (1,B3))))) is Element of the carrier of K
- ((A ") * (- (A * (B * (1,B3))))) is Element of the carrier of K
- A is Element of the carrier of K
(- A) * (B * (1,B3)) is Element of the carrier of K
the multF of K . ((- A),(B * (1,B3))) is Element of the carrier of K
(A ") * ((- A) * (B * (1,B3))) is Element of the carrier of K
the multF of K . ((A "),((- A) * (B * (1,B3)))) is Element of the carrier of K
- ((A ") * ((- A) * (B * (1,B3)))) is Element of the carrier of K
- (A ") is Element of the carrier of K
(- (A ")) * ((- A) * (B * (1,B3))) is Element of the carrier of K
the multF of K . ((- (A ")),((- A) * (B * (1,B3)))) is Element of the carrier of K
(- (A ")) * (- A) is Element of the carrier of K
the multF of K . ((- (A ")),(- A)) is Element of the carrier of K
((- (A ")) * (- A)) * (B * (1,B3)) is Element of the carrier of K
the multF of K . (((- (A ")) * (- A)),(B * (1,B3))) is Element of the carrier of K
A * (A ") is Element of the carrier of K
the multF of K . (A,(A ")) is Element of the carrier of K
(A * (A ")) * (B * (1,B3)) is Element of the carrier of K
the multF of K . ((A * (A ")),(B * (1,B3))) is Element of the carrier of K
(1. K) * (B * (1,B3)) is Element of the carrier of K
the multF of K . ((1. K),(B * (1,B3))) is Element of the carrier of K
B2 * B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(B2 * B) * (1,B3) is Element of the carrier of K
B2 * (1,B3) is Element of the carrier of K
(A ") * (B2 * (1,B3)) is Element of the carrier of K
the multF of K is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is Relation-like set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the multF of K . ((A "),(B2 * (1,B3))) is Element of the carrier of K
((A ") * (B2 * (1,B3))) * (K,n,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
- (((A ") * (B2 * (1,B3))) * (K,n,1)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len (- (((A ") * (B2 * (1,B3))) * (K,n,1))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
- ((A ") * (B2 * (1,B3))) is Element of the carrier of K
(- ((A ") * (B2 * (1,B3)))) * (K,n,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len ((- ((A ") * (B2 * (1,B3)))) * (K,n,1)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg n is V28() V35(n) Element of bool NAT
Seg (width B2) is V28() V35( width B2) Element of bool NAT
(Line (B2,1)) /. B3 is Element of the carrier of K
(Line (B2,1)) . B3 is set
(Line (B2,1)) /. 1 is Element of the carrier of K
(Line (B2,1)) . 1 is set
Col (B,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( len B) FinSequence-like FinSubsequence-like Element of (len B) -tuples_on the carrier of K
len (Col (B,B3)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(- (((A ") * (B2 * (1,B3))) * (K,n,1))) + (K,n,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len (K,n,B3) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
C is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B2 . C is set
B . C is set
dom ((- ((A ") * (B2 * (1,B3)))) * (K,n,1)) is Element of bool NAT
(K,n,1) /. C is Element of the carrier of K
(K,n,1) . C is set
dom B is Element of bool NAT
B * (C,B3) is Element of the carrier of K
(- (((A ") * (B2 * (1,B3))) * (K,n,1))) . C is set
((- ((A ") * (B2 * (1,B3)))) * (K,n,1)) . C is set
(- ((A ") * (B2 * (1,B3)))) * ((K,n,1) /. C) is Element of the carrier of K
the multF of K . ((- ((A ") * (B2 * (1,B3)))),((K,n,1) /. C)) is Element of the carrier of K
(- (((A ") * (B2 * (1,B3))) * (K,n,1))) /. 1 is Element of the carrier of K
(K,n,1) /. 1 is Element of the carrier of K
(- ((A ") * (B2 * (1,B3)))) * ((K,n,1) /. 1) is Element of the carrier of K
the multF of K . ((- ((A ") * (B2 * (1,B3)))),((K,n,1) /. 1)) is Element of the carrier of K
(- ((A ") * (B2 * (1,B3)))) * (1. K) is Element of the carrier of K
the multF of K . ((- ((A ") * (B2 * (1,B3)))),(1. K)) is Element of the carrier of K
B2 . 1 is set
(K,n,B3) /. 1 is Element of the carrier of K
(K,n,B3) . 1 is set
B . 1 is set
(- ((A ") * (B2 * (1,B3)))) + (0. K) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . ((- ((A ") * (B2 * (1,B3)))),(0. K)) is Element of the carrier of K
[C,B3] is set
Indices B is set
width B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width B) is V28() V35( width B) Element of bool NAT
[:(dom B),(Seg (width B)):] is Relation-like set
B . C is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(K,n,C) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),C,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,n,C) . B3 is set
A3 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
A3 . B3 is set
(- ((A ") * (B2 * (1,B3)))) * (0. K) is Element of the carrier of K
the multF of K . ((- ((A ") * (B2 * (1,B3)))),(0. K)) is Element of the carrier of K
(- (((A ") * (B2 * (1,B3))) * (K,n,1))) /. C is Element of the carrier of K
(K,n,B3) /. C is Element of the carrier of K
(K,n,B3) . C is set
(0. K) + (0. K) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . ((0. K),(0. K)) is Element of the carrier of K
B2 * (1,C) is Element of the carrier of K
(A ") * (B2 * (1,C)) is Element of the carrier of K
the multF of K . ((A "),(B2 * (1,C))) is Element of the carrier of K
((A ") * (B2 * (1,C))) * (K,n,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
- (((A ") * (B2 * (1,C))) * (K,n,1)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(- (((A ") * (B2 * (1,C))) * (K,n,1))) /. C is Element of the carrier of K
(- (((A ") * (B2 * (1,C))) * (K,n,1))) . C is set
- ((A ") * (B2 * (1,C))) is Element of the carrier of K
(- ((A ") * (B2 * (1,C)))) * (0. K) is Element of the carrier of K
the multF of K . ((- ((A ") * (B2 * (1,C)))),(0. K)) is Element of the carrier of K
(K,n,C) /. C is Element of the carrier of K
(K,n,C) . C is set
(0. K) + (1. K) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . ((0. K),(1. K)) is Element of the carrier of K
len ((- (((A ") * (B2 * (1,B3))) * (K,n,1))) + (K,n,B3)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
[1,B3] is set
Indices (B2 * B) is set
dom (B2 * B) is Element of bool NAT
width (B2 * B) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (B2 * B)) is V28() V35( width (B2 * B)) Element of bool NAT
[:(dom (B2 * B)),(Seg (width (B2 * B))):] is Relation-like set
(Line (B2,1)) "*" (Col (B,B3)) is Element of the carrier of K
(Line (B2,1)) "*" (- (((A ") * (B2 * (1,B3))) * (K,n,1))) is Element of the carrier of K
(Line (B2,1)) "*" (K,n,B3) is Element of the carrier of K
((Line (B2,1)) "*" (- (((A ") * (B2 * (1,B3))) * (K,n,1)))) + ((Line (B2,1)) "*" (K,n,B3)) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . (((Line (B2,1)) "*" (- (((A ") * (B2 * (1,B3))) * (K,n,1)))),((Line (B2,1)) "*" (K,n,B3))) is Element of the carrier of K
(Line (B2,1)) "*" ((- ((A ") * (B2 * (1,B3)))) * (K,n,1)) is Element of the carrier of K
((Line (B2,1)) "*" ((- ((A ") * (B2 * (1,B3)))) * (K,n,1))) + ((Line (B2,1)) "*" (K,n,B3)) is Element of the carrier of K
the addF of K . (((Line (B2,1)) "*" ((- ((A ") * (B2 * (1,B3)))) * (K,n,1))),((Line (B2,1)) "*" (K,n,B3))) is Element of the carrier of K
(Line (B2,1)) "*" (K,n,1) is Element of the carrier of K
(- ((A ") * (B2 * (1,B3)))) * ((Line (B2,1)) "*" (K,n,1)) is Element of the carrier of K
the multF of K . ((- ((A ") * (B2 * (1,B3)))),((Line (B2,1)) "*" (K,n,1))) is Element of the carrier of K
((- ((A ") * (B2 * (1,B3)))) * ((Line (B2,1)) "*" (K,n,1))) + ((Line (B2,1)) "*" (K,n,B3)) is Element of the carrier of K
the addF of K . (((- ((A ") * (B2 * (1,B3)))) * ((Line (B2,1)) "*" (K,n,1))),((Line (B2,1)) "*" (K,n,B3))) is Element of the carrier of K
(- ((A ") * (B2 * (1,B3)))) * A is Element of the carrier of K
the multF of K . ((- ((A ") * (B2 * (1,B3)))),A) is Element of the carrier of K
((- ((A ") * (B2 * (1,B3)))) * A) + ((Line (B2,1)) "*" (K,n,B3)) is Element of the carrier of K
the addF of K . (((- ((A ") * (B2 * (1,B3)))) * A),((Line (B2,1)) "*" (K,n,B3))) is Element of the carrier of K
((A ") * (B2 * (1,B3))) * A is Element of the carrier of K
the multF of K . (((A ") * (B2 * (1,B3))),A) is Element of the carrier of K
- (((A ") * (B2 * (1,B3))) * A) is Element of the carrier of K
(- (((A ") * (B2 * (1,B3))) * A)) + ((Line (B2,1)) "*" (K,n,B3)) is Element of the carrier of K
the addF of K . ((- (((A ") * (B2 * (1,B3))) * A)),((Line (B2,1)) "*" (K,n,B3))) is Element of the carrier of K
(A ") * A is Element of the carrier of K
the multF of K . ((A "),A) is Element of the carrier of K
(B2 * (1,B3)) * ((A ") * A) is Element of the carrier of K
the multF of K . ((B2 * (1,B3)),((A ") * A)) is Element of the carrier of K
- ((B2 * (1,B3)) * ((A ") * A)) is Element of the carrier of K
(- ((B2 * (1,B3)) * ((A ") * A))) + ((Line (B2,1)) "*" (K,n,B3)) is Element of the carrier of K
the addF of K . ((- ((B2 * (1,B3)) * ((A ") * A))),((Line (B2,1)) "*" (K,n,B3))) is Element of the carrier of K
(B2 * (1,B3)) * (1. K) is Element of the carrier of K
the multF of K . ((B2 * (1,B3)),(1. K)) is Element of the carrier of K
- ((B2 * (1,B3)) * (1. K)) is Element of the carrier of K
(- ((B2 * (1,B3)) * (1. K))) + ((Line (B2,1)) "*" (K,n,B3)) is Element of the carrier of K
the addF of K . ((- ((B2 * (1,B3)) * (1. K))),((Line (B2,1)) "*" (K,n,B3))) is Element of the carrier of K
(- ((B2 * (1,B3)) * (1. K))) + ((Line (B2,1)) /. B3) is Element of the carrier of K
the addF of K . ((- ((B2 * (1,B3)) * (1. K))),((Line (B2,1)) /. B3)) is Element of the carrier of K
- (B2 * (1,B3)) is Element of the carrier of K
(- (B2 * (1,B3))) + ((Line (B2,1)) /. B3) is Element of the carrier of K
the addF of K . ((- (B2 * (1,B3))),((Line (B2,1)) /. B3)) is Element of the carrier of K
(- (B2 * (1,B3))) + (B2 * (1,B3)) is Element of the carrier of K
the addF of K . ((- (B2 * (1,B3))),(B2 * (1,B3))) is Element of the carrier of K
Seg (width B2) is V28() V35( width B2) Element of bool NAT
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(B2 * B) * (B3,B2) is Element of the carrier of K
B2 * (1,B2) is Element of the carrier of K
(A ") * (B2 * (1,B2)) is Element of the carrier of K
the multF of K is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is Relation-like set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the multF of K . ((A "),(B2 * (1,B2))) is Element of the carrier of K
((A ") * (B2 * (1,B2))) * (K,n,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
- (((A ") * (B2 * (1,B2))) * (K,n,1)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len (- (((A ") * (B2 * (1,B2))) * (K,n,1))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
- ((A ") * (B2 * (1,B2))) is Element of the carrier of K
(- ((A ") * (B2 * (1,B2)))) * (K,n,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len ((- ((A ") * (B2 * (1,B2)))) * (K,n,1)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
[B3,B2] is set
Indices B2 is set
[:(dom B2),(Seg (width B2)):] is Relation-like set
B2 . B3 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
B2 * (B3,B2) is Element of the carrier of K
B is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B . B2 is set
(K,n,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
[B3,1] is set
B2 * (B3,1) is Element of the carrier of K
C is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
C . 1 is set
Seg n is V28() V35(n) Element of bool NAT
Col (B,B2) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( len B) FinSequence-like FinSubsequence-like Element of (len B) -tuples_on the carrier of K
len (Col (B,B2)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B2) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B2,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(- (((A ") * (B2 * (1,B2))) * (K,n,1))) + (K,n,B2) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len (K,n,B2) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A3 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B3 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
F is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
A3 . F is set
B3 . F is set
dom ((- ((A ") * (B2 * (1,B2)))) * (K,n,1)) is Element of bool NAT
(K,n,1) /. F is Element of the carrier of K
(K,n,1) . F is set
dom B is Element of bool NAT
B * (F,B2) is Element of the carrier of K
(- (((A ") * (B2 * (1,B2))) * (K,n,1))) . F is set
((- ((A ") * (B2 * (1,B2)))) * (K,n,1)) . F is set
(- ((A ") * (B2 * (1,B2)))) * ((K,n,1) /. F) is Element of the carrier of K
the multF of K . ((- ((A ") * (B2 * (1,B2)))),((K,n,1) /. F)) is Element of the carrier of K
(- (((A ") * (B2 * (1,B2))) * (K,n,1))) /. F is Element of the carrier of K
(- ((A ") * (B2 * (1,B2)))) * (1. K) is Element of the carrier of K
the multF of K . ((- ((A ") * (B2 * (1,B2)))),(1. K)) is Element of the carrier of K
(K,n,B2) /. F is Element of the carrier of K
(K,n,B2) . F is set
(- ((A ") * (B2 * (1,B2)))) + (0. K) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . ((- ((A ") * (B2 * (1,B2)))),(0. K)) is Element of the carrier of K
[F,B2] is set
Indices B is set
width B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width B) is V28() V35( width B) Element of bool NAT
[:(dom B),(Seg (width B)):] is Relation-like set
B . F is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(K,n,F) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),F,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,n,F) . B2 is set
G is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
G . B2 is set
(- ((A ") * (B2 * (1,B2)))) * (0. K) is Element of the carrier of K
the multF of K . ((- ((A ") * (B2 * (1,B2)))),(0. K)) is Element of the carrier of K
(- (((A ") * (B2 * (1,B2))) * (K,n,1))) /. F is Element of the carrier of K
(K,n,B2) /. F is Element of the carrier of K
(K,n,B2) . F is set
(0. K) + (0. K) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . ((0. K),(0. K)) is Element of the carrier of K
(- ((A ") * (B2 * (1,B2)))) * (0. K) is Element of the carrier of K
the multF of K . ((- ((A ") * (B2 * (1,B2)))),(0. K)) is Element of the carrier of K
(- (((A ") * (B2 * (1,B2))) * (K,n,1))) /. F is Element of the carrier of K
(K,n,B2) /. F is Element of the carrier of K
(K,n,B2) . F is set
(0. K) + (1. K) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . ((0. K),(1. K)) is Element of the carrier of K
len ((- (((A ") * (B2 * (1,B2))) * (K,n,1))) + (K,n,B2)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Line (B2,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width B2) FinSequence-like FinSubsequence-like Element of (width B2) -tuples_on the carrier of K
len (Line (B2,B3)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(Line (B2,B3)) /. 1 is Element of the carrier of K
(Line (B2,B3)) . 1 is set
(Line (B2,B3)) /. B2 is Element of the carrier of K
(Line (B2,B3)) . B2 is set
Indices (B2 * B) is set
dom (B2 * B) is Element of bool NAT
width (B2 * B) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (B2 * B)) is V28() V35( width (B2 * B)) Element of bool NAT
[:(dom (B2 * B)),(Seg (width (B2 * B))):] is Relation-like set
(Line (B2,B3)) "*" (Col (B,B2)) is Element of the carrier of K
(Line (B2,B3)) "*" (- (((A ") * (B2 * (1,B2))) * (K,n,1))) is Element of the carrier of K
(Line (B2,B3)) "*" (K,n,B2) is Element of the carrier of K
((Line (B2,B3)) "*" (- (((A ") * (B2 * (1,B2))) * (K,n,1)))) + ((Line (B2,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . (((Line (B2,B3)) "*" (- (((A ") * (B2 * (1,B2))) * (K,n,1)))),((Line (B2,B3)) "*" (K,n,B2))) is Element of the carrier of K
(Line (B2,B3)) "*" ((- ((A ") * (B2 * (1,B2)))) * (K,n,1)) is Element of the carrier of K
((Line (B2,B3)) "*" ((- ((A ") * (B2 * (1,B2)))) * (K,n,1))) + ((Line (B2,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K . (((Line (B2,B3)) "*" ((- ((A ") * (B2 * (1,B2)))) * (K,n,1))),((Line (B2,B3)) "*" (K,n,B2))) is Element of the carrier of K
(Line (B2,B3)) "*" (K,n,1) is Element of the carrier of K
(- ((A ") * (B2 * (1,B2)))) * ((Line (B2,B3)) "*" (K,n,1)) is Element of the carrier of K
the multF of K . ((- ((A ") * (B2 * (1,B2)))),((Line (B2,B3)) "*" (K,n,1))) is Element of the carrier of K
((- ((A ") * (B2 * (1,B2)))) * ((Line (B2,B3)) "*" (K,n,1))) + ((Line (B2,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K . (((- ((A ") * (B2 * (1,B2)))) * ((Line (B2,B3)) "*" (K,n,1))),((Line (B2,B3)) "*" (K,n,B2))) is Element of the carrier of K
(- ((A ") * (B2 * (1,B2)))) * (B2 * (B3,1)) is Element of the carrier of K
the multF of K . ((- ((A ") * (B2 * (1,B2)))),(B2 * (B3,1))) is Element of the carrier of K
((- ((A ") * (B2 * (1,B2)))) * (B2 * (B3,1))) + ((Line (B2,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K . (((- ((A ") * (B2 * (1,B2)))) * (B2 * (B3,1))),((Line (B2,B3)) "*" (K,n,B2))) is Element of the carrier of K
(B2 * (1,B2)) * (A ") is Element of the carrier of K
the multF of K . ((B2 * (1,B2)),(A ")) is Element of the carrier of K
((B2 * (1,B2)) * (A ")) * (B2 * (B3,1)) is Element of the carrier of K
the multF of K . (((B2 * (1,B2)) * (A ")),(B2 * (B3,1))) is Element of the carrier of K
- (((B2 * (1,B2)) * (A ")) * (B2 * (B3,1))) is Element of the carrier of K
(- (((B2 * (1,B2)) * (A ")) * (B2 * (B3,1)))) + ((Line (B2,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K . ((- (((B2 * (1,B2)) * (A ")) * (B2 * (B3,1)))),((Line (B2,B3)) "*" (K,n,B2))) is Element of the carrier of K
(A ") * (B2 * (B3,1)) is Element of the carrier of K
the multF of K . ((A "),(B2 * (B3,1))) is Element of the carrier of K
(B2 * (1,B2)) * ((A ") * (B2 * (B3,1))) is Element of the carrier of K
the multF of K . ((B2 * (1,B2)),((A ") * (B2 * (B3,1)))) is Element of the carrier of K
- ((B2 * (1,B2)) * ((A ") * (B2 * (B3,1)))) is Element of the carrier of K
(- ((B2 * (1,B2)) * ((A ") * (B2 * (B3,1))))) + ((Line (B2,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K . ((- ((B2 * (1,B2)) * ((A ") * (B2 * (B3,1))))),((Line (B2,B3)) "*" (K,n,B2))) is Element of the carrier of K
(- ((B2 * (1,B2)) * ((A ") * (B2 * (B3,1))))) + (B2 * (B3,B2)) is Element of the carrier of K
the addF of K . ((- ((B2 * (1,B2)) * ((A ") * (B2 * (B3,1))))),(B2 * (B3,B2))) is Element of the carrier of K
(A ") * (0. K) is Element of the carrier of K
the multF of K . ((A "),(0. K)) is Element of the carrier of K
(B2 * (1,B2)) * ((A ") * (0. K)) is Element of the carrier of K
the multF of K . ((B2 * (1,B2)),((A ") * (0. K))) is Element of the carrier of K
- ((B2 * (1,B2)) * ((A ") * (0. K))) is Element of the carrier of K
(- ((B2 * (1,B2)) * ((A ") * (0. K)))) + (B2 * (B3,B2)) is Element of the carrier of K
the addF of K . ((- ((B2 * (1,B2)) * ((A ") * (0. K)))),(B2 * (B3,B2))) is Element of the carrier of K
(B2 * (1,B2)) * (0. K) is Element of the carrier of K
the multF of K . ((B2 * (1,B2)),(0. K)) is Element of the carrier of K
- ((B2 * (1,B2)) * (0. K)) is Element of the carrier of K
(- ((B2 * (1,B2)) * (0. K))) + (B2 * (B3,B2)) is Element of the carrier of K
the addF of K . ((- ((B2 * (1,B2)) * (0. K))),(B2 * (B3,B2))) is Element of the carrier of K
- (0. K) is Element of the carrier of K
(- (0. K)) + (B2 * (B3,B2)) is Element of the carrier of K
the addF of K . ((- (0. K)),(B2 * (B3,B2))) is Element of the carrier of K
(0. K) + (1. K) is Element of the carrier of K
the addF of K . ((0. K),(1. K)) is Element of the carrier of K
Indices B is set
dom B is Element of bool NAT
width B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width B) is V28() V35( width B) Element of bool NAT
[:(dom B),(Seg (width B)):] is Relation-like set
Seg n is V28() V35(n) Element of bool NAT
[:(Seg n),(Seg n):] is Relation-like set
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(B2 * B) * (B3,B2) is Element of the carrier of K
[B3,B2] is set
Indices (B2 * B) is set
dom (B2 * B) is Element of bool NAT
width (B2 * B) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (B2 * B)) is V28() V35( width (B2 * B)) Element of bool NAT
[:(dom (B2 * B)),(Seg (width (B2 * B))):] is Relation-like set
B2 * (1,B2) is Element of the carrier of K
(A ") * (B2 * (1,B2)) is Element of the carrier of K
the multF of K is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is Relation-like set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the multF of K . ((A "),(B2 * (1,B2))) is Element of the carrier of K
- ((A ") * (B2 * (1,B2))) is Element of the carrier of K
(- ((A ") * (B2 * (1,B2)))) * (K,n,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len ((- ((A ") * (B2 * (1,B2)))) * (K,n,1)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Col (B,B2) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( len B) FinSequence-like FinSubsequence-like Element of (len B) -tuples_on the carrier of K
len (Col (B,B2)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
[B3,1] is set
Indices B2 is set
[:(dom B2),(Seg (width B2)):] is Relation-like set
(K,n,B2) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B2,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len (K,n,B2) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
((A ") * (B2 * (1,B2))) * (K,n,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
- (((A ") * (B2 * (1,B2))) * (K,n,1)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len (- (((A ") * (B2 * (1,B2))) * (K,n,1))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(- (((A ") * (B2 * (1,B2))) * (K,n,1))) + (K,n,B2) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len ((- (((A ") * (B2 * (1,B2))) * (K,n,1))) + (K,n,B2)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
C is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
A3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B . A3 is set
C . A3 is set
dom ((- ((A ") * (B2 * (1,B2)))) * (K,n,1)) is Element of bool NAT
(K,n,1) /. A3 is Element of the carrier of K
(K,n,1) . A3 is set
B * (A3,B2) is Element of the carrier of K
(- (((A ") * (B2 * (1,B2))) * (K,n,1))) . A3 is set
((- ((A ") * (B2 * (1,B2)))) * (K,n,1)) . A3 is set
(- ((A ") * (B2 * (1,B2)))) * ((K,n,1) /. A3) is Element of the carrier of K
the multF of K . ((- ((A ") * (B2 * (1,B2)))),((K,n,1) /. A3)) is Element of the carrier of K
(- ((A ") * (B2 * (1,B2)))) * (1. K) is Element of the carrier of K
the multF of K . ((- ((A ") * (B2 * (1,B2)))),(1. K)) is Element of the carrier of K
(- (((A ") * (B2 * (1,B2))) * (K,n,1))) /. A3 is Element of the carrier of K
(K,n,B2) /. A3 is Element of the carrier of K
(K,n,B2) . A3 is set
((- ((A ") * (B2 * (1,B2)))) * (1. K)) + (0. K) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . (((- ((A ") * (B2 * (1,B2)))) * (1. K)),(0. K)) is Element of the carrier of K
[A3,B2] is set
B . A3 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(K,n,A3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),A3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,n,A3) . B2 is set
B3 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B3 . B2 is set
(- (((A ") * (B2 * (1,B2))) * (K,n,1))) /. A3 is Element of the carrier of K
(- ((A ") * (B2 * (1,B2)))) * (0. K) is Element of the carrier of K
the multF of K . ((- ((A ") * (B2 * (1,B2)))),(0. K)) is Element of the carrier of K
(K,n,B2) /. A3 is Element of the carrier of K
(0. K) + ((K,n,B2) /. A3) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . ((0. K),((K,n,B2) /. A3)) is Element of the carrier of K
(K,n,B2) . A3 is set
(- (((A ") * (B2 * (1,B2))) * (K,n,1))) /. A3 is Element of the carrier of K
(- ((A ") * (B2 * (1,B2)))) * (0. K) is Element of the carrier of K
the multF of K . ((- ((A ") * (B2 * (1,B2)))),(0. K)) is Element of the carrier of K
(K,n,B2) /. A3 is Element of the carrier of K
(0. K) + ((K,n,B2) /. A3) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . ((0. K),((K,n,B2) /. A3)) is Element of the carrier of K
(K,n,B2) . A3 is set
Line (B2,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width B2) FinSequence-like FinSubsequence-like Element of (width B2) -tuples_on the carrier of K
len (Line (B2,B3)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(Line (B2,B3)) /. B2 is Element of the carrier of K
(Line (B2,B3)) . B2 is set
B2 * (B3,B2) is Element of the carrier of K
(Line (B2,B3)) /. 1 is Element of the carrier of K
(Line (B2,B3)) . 1 is set
B2 * (B3,1) is Element of the carrier of K
(Line (B2,B3)) "*" (Col (B,B2)) is Element of the carrier of K
(Line (B2,B3)) "*" (- (((A ") * (B2 * (1,B2))) * (K,n,1))) is Element of the carrier of K
(Line (B2,B3)) "*" (K,n,B2) is Element of the carrier of K
((Line (B2,B3)) "*" (- (((A ") * (B2 * (1,B2))) * (K,n,1)))) + ((Line (B2,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . (((Line (B2,B3)) "*" (- (((A ") * (B2 * (1,B2))) * (K,n,1)))),((Line (B2,B3)) "*" (K,n,B2))) is Element of the carrier of K
(Line (B2,B3)) "*" ((- ((A ") * (B2 * (1,B2)))) * (K,n,1)) is Element of the carrier of K
((Line (B2,B3)) "*" ((- ((A ") * (B2 * (1,B2)))) * (K,n,1))) + ((Line (B2,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K . (((Line (B2,B3)) "*" ((- ((A ") * (B2 * (1,B2)))) * (K,n,1))),((Line (B2,B3)) "*" (K,n,B2))) is Element of the carrier of K
(Line (B2,B3)) "*" (K,n,1) is Element of the carrier of K
(- ((A ") * (B2 * (1,B2)))) * ((Line (B2,B3)) "*" (K,n,1)) is Element of the carrier of K
the multF of K . ((- ((A ") * (B2 * (1,B2)))),((Line (B2,B3)) "*" (K,n,1))) is Element of the carrier of K
((- ((A ") * (B2 * (1,B2)))) * ((Line (B2,B3)) "*" (K,n,1))) + ((Line (B2,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K . (((- ((A ") * (B2 * (1,B2)))) * ((Line (B2,B3)) "*" (K,n,1))),((Line (B2,B3)) "*" (K,n,B2))) is Element of the carrier of K
(- ((A ") * (B2 * (1,B2)))) * (B2 * (B3,1)) is Element of the carrier of K
the multF of K . ((- ((A ") * (B2 * (1,B2)))),(B2 * (B3,1))) is Element of the carrier of K
((- ((A ") * (B2 * (1,B2)))) * (B2 * (B3,1))) + ((Line (B2,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K . (((- ((A ") * (B2 * (1,B2)))) * (B2 * (B3,1))),((Line (B2,B3)) "*" (K,n,B2))) is Element of the carrier of K
(B2 * (1,B2)) * (A ") is Element of the carrier of K
the multF of K . ((B2 * (1,B2)),(A ")) is Element of the carrier of K
((B2 * (1,B2)) * (A ")) * (B2 * (B3,1)) is Element of the carrier of K
the multF of K . (((B2 * (1,B2)) * (A ")),(B2 * (B3,1))) is Element of the carrier of K
- (((B2 * (1,B2)) * (A ")) * (B2 * (B3,1))) is Element of the carrier of K
(- (((B2 * (1,B2)) * (A ")) * (B2 * (B3,1)))) + ((Line (B2,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K . ((- (((B2 * (1,B2)) * (A ")) * (B2 * (B3,1)))),((Line (B2,B3)) "*" (K,n,B2))) is Element of the carrier of K
(A ") * (B2 * (B3,1)) is Element of the carrier of K
the multF of K . ((A "),(B2 * (B3,1))) is Element of the carrier of K
(B2 * (1,B2)) * ((A ") * (B2 * (B3,1))) is Element of the carrier of K
the multF of K . ((B2 * (1,B2)),((A ") * (B2 * (B3,1)))) is Element of the carrier of K
- ((B2 * (1,B2)) * ((A ") * (B2 * (B3,1)))) is Element of the carrier of K
(- ((B2 * (1,B2)) * ((A ") * (B2 * (B3,1))))) + ((Line (B2,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K . ((- ((B2 * (1,B2)) * ((A ") * (B2 * (B3,1))))),((Line (B2,B3)) "*" (K,n,B2))) is Element of the carrier of K
(- ((B2 * (1,B2)) * ((A ") * (B2 * (B3,1))))) + (B2 * (B3,B2)) is Element of the carrier of K
the addF of K . ((- ((B2 * (1,B2)) * ((A ") * (B2 * (B3,1))))),(B2 * (B3,B2))) is Element of the carrier of K
B2 . B3 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
A3 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
A3 . 1 is set
B3 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B3 . B2 is set
(K,n,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(A ") * (0. K) is Element of the carrier of K
the multF of K . ((A "),(0. K)) is Element of the carrier of K
(B2 * (1,B2)) * ((A ") * (0. K)) is Element of the carrier of K
the multF of K . ((B2 * (1,B2)),((A ") * (0. K))) is Element of the carrier of K
- ((B2 * (1,B2)) * ((A ") * (0. K))) is Element of the carrier of K
(- ((B2 * (1,B2)) * ((A ") * (0. K)))) + (B2 * (B3,B2)) is Element of the carrier of K
the addF of K . ((- ((B2 * (1,B2)) * ((A ") * (0. K)))),(B2 * (B3,B2))) is Element of the carrier of K
(B2 * (1,B2)) * (0. K) is Element of the carrier of K
the multF of K . ((B2 * (1,B2)),(0. K)) is Element of the carrier of K
- ((B2 * (1,B2)) * (0. K)) is Element of the carrier of K
(- ((B2 * (1,B2)) * (0. K))) + (B2 * (B3,B2)) is Element of the carrier of K
the addF of K . ((- ((B2 * (1,B2)) * (0. K))),(B2 * (B3,B2))) is Element of the carrier of K
- (0. K) is Element of the carrier of K
(- (0. K)) + (B2 * (B3,B2)) is Element of the carrier of K
the addF of K . ((- (0. K)),(B2 * (B3,B2))) is Element of the carrier of K
(0. K) + (0. K) is Element of the carrier of K
the addF of K . ((0. K),(0. K)) is Element of the carrier of K
B is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
C is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
A3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B . A3 is set
C . A3 is set
(K,n,1) /. A3 is Element of the carrier of K
(K,n,1) . A3 is set
dom ((A ") * (K,n,1)) is Element of bool NAT
((A ") * (K,n,1)) . A3 is set
(A ") * ((K,n,1) /. A3) is Element of the carrier of K
the multF of K . ((A "),((K,n,1) /. A3)) is Element of the carrier of K
B * (A3,B2) is Element of the carrier of K
(A ") * (1. K) is Element of the carrier of K
the multF of K . ((A "),(1. K)) is Element of the carrier of K
[A3,B2] is set
B . A3 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(K,n,A3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),A3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,n,A3) . B2 is set
B3 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B3 . B2 is set
(A ") * (0. K) is Element of the carrier of K
the multF of K . ((A "),(0. K)) is Element of the carrier of K
Line (B2,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width B2) FinSequence-like FinSubsequence-like Element of (width B2) -tuples_on the carrier of K
len (Line (B2,B3)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(Line (B2,B3)) /. 1 is Element of the carrier of K
(Line (B2,B3)) . 1 is set
B2 * (B3,1) is Element of the carrier of K
(Line (B2,B3)) "*" (Col (B,B2)) is Element of the carrier of K
(Line (B2,B3)) "*" ((A ") * (K,n,1)) is Element of the carrier of K
(Line (B2,B3)) "*" (K,n,1) is Element of the carrier of K
(A ") * ((Line (B2,B3)) "*" (K,n,1)) is Element of the carrier of K
the multF of K . ((A "),((Line (B2,B3)) "*" (K,n,1))) is Element of the carrier of K
(A ") * (B2 * (B3,1)) is Element of the carrier of K
the multF of K . ((A "),(B2 * (B3,1))) is Element of the carrier of K
B2 . B3 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
A3 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
A3 . 1 is set
(K,n,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(A ") * (0. K) is Element of the carrier of K
the multF of K . ((A "),(0. K)) is Element of the carrier of K
len (Col (B,1)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Indices (B2 * B) is set
dom (B2 * B) is Element of bool NAT
width (B2 * B) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (B2 * B)) is V28() V35( width (B2 * B)) Element of bool NAT
[:(dom (B2 * B)),(Seg (width (B2 * B))):] is Relation-like set
(A ") * (Line (B2,1)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width B2) FinSequence-like FinSubsequence-like Element of (width B2) -tuples_on the carrier of K
len ((A ") * (Line (B2,1))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Indices B2 is set
[:(dom B2),(Seg (width B2)):] is Relation-like set
[1,1] is set
(B2 * B) * (1,1) is Element of the carrier of K
(Line (B2,1)) "*" (Col (B,1)) is Element of the carrier of K
(Line (B2,1)) "*" (K,n,1) is Element of the carrier of K
(A ") * ((Line (B2,1)) "*" (K,n,1)) is Element of the carrier of K
the multF of K is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is Relation-like set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the multF of K . ((A "),((Line (B2,1)) "*" (K,n,1))) is Element of the carrier of K
(Line (B2,1)) /. 1 is Element of the carrier of K
(A ") * ((Line (B2,1)) /. 1) is Element of the carrier of K
the multF of K . ((A "),((Line (B2,1)) /. 1)) is Element of the carrier of K
((A ") * (Line (B2,1))) /. 1 is Element of the carrier of K
((A ") * (Line (B2,1))) . 1 is set
(A ") * (B2 * (1,1)) is Element of the carrier of K
the multF of K . ((A "),(B2 * (1,1))) is Element of the carrier of K
1. (K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
[B3,B2] is set
(B2 * B) * (B3,B2) is Element of the carrier of K
(1. (K,n)) * (B3,B2) is Element of the carrier of K
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
C is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) . C is set
(B2 * B) * (B,C) is Element of the carrier of K
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
C is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) . C is set
(B2 * B) * (B,C) is Element of the carrier of K
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
C is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) . C is set
(B2 * B) * (B,C) is Element of the carrier of K
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
C is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) . C is set
A * (K,n,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len (A * (K,n,1)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Col (B2,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( len B2) FinSequence-like FinSubsequence-like Element of (len B2) -tuples_on the carrier of K
(len B2) -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(Col (B2,1)) . B3 is set
(A * (K,n,1)) . B3 is set
(K,n,1) /. B3 is Element of the carrier of K
(K,n,1) . B3 is set
dom (A * (K,n,1)) is Element of bool NAT
A * ((K,n,1) /. B3) is Element of the carrier of K
the multF of K . (A,((K,n,1) /. B3)) is Element of the carrier of K
A * (0. K) is Element of the carrier of K
the multF of K . (A,(0. K)) is Element of the carrier of K
[B3,1] is set
B2 . B3 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
B2 * (B3,1) is Element of the carrier of K
(K,n,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,n,B3) . 1 is set
B2 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B2 . 1 is set
A * (1. K) is Element of the carrier of K
the multF of K . (A,(1. K)) is Element of the carrier of K
Seg (len B) is V28() V35( len B) Element of bool NAT
Line (B,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width B) FinSequence-like FinSubsequence-like Element of (width B) -tuples_on the carrier of K
(width B) -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
len (Line (B,1)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
dom (Line (B,1)) is V35( width B) Element of bool NAT
B * B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(B * B2) * (1,B3) is Element of the carrier of K
B * (1,B3) is Element of the carrier of K
A * (B * (1,B3)) is Element of the carrier of K
the multF of K . (A,(B * (1,B3))) is Element of the carrier of K
(A * (B * (1,B3))) * (K,n,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
- ((A * (B * (1,B3))) * (K,n,1)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len (- ((A * (B * (1,B3))) * (K,n,1))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
- (A * (B * (1,B3))) is Element of the carrier of K
(- (A * (B * (1,B3)))) * (K,n,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len ((- (A * (B * (1,B3)))) * (K,n,1)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Col (B2,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( len B2) FinSequence-like FinSubsequence-like Element of (len B2) -tuples_on the carrier of K
(K,n,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(- ((A * (B * (1,B3))) * (K,n,1))) + (K,n,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len (K,n,B3) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
C is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B2 . C is set
B . C is set
(K,n,1) /. C is Element of the carrier of K
(K,n,1) . C is set
dom ((- (A * (B * (1,B3)))) * (K,n,1)) is Element of bool NAT
(- ((A * (B * (1,B3))) * (K,n,1))) . C is set
((- (A * (B * (1,B3)))) * (K,n,1)) . C is set
(- (A * (B * (1,B3)))) * ((K,n,1) /. C) is Element of the carrier of K
the multF of K . ((- (A * (B * (1,B3)))),((K,n,1) /. C)) is Element of the carrier of K
(K,n,B3) /. C is Element of the carrier of K
(K,n,B3) . C is set
(- ((A * (B * (1,B3))) * (K,n,1))) /. C is Element of the carrier of K
((- ((A * (B * (1,B3))) * (K,n,1))) /. C) + (0. K) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . (((- ((A * (B * (1,B3))) * (K,n,1))) /. C),(0. K)) is Element of the carrier of K
1_ K is Element of the carrier of K
(- (A * (B * (1,B3)))) * (1_ K) is Element of the carrier of K
the multF of K . ((- (A * (B * (1,B3)))),(1_ K)) is Element of the carrier of K
B2 * (1,B3) is Element of the carrier of K
[C,B3] is set
B2 . C is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
B2 * (C,B3) is Element of the carrier of K
A3 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
A3 . B3 is set
(K,n,C) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),C,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,n,C) . B3 is set
(- ((A * (B * (1,B3))) * (K,n,1))) /. C is Element of the carrier of K
(- (A * (B * (1,B3)))) * (0. K) is Element of the carrier of K
the multF of K . ((- (A * (B * (1,B3)))),(0. K)) is Element of the carrier of K
(K,n,B3) /. C is Element of the carrier of K
(0. K) + ((K,n,B3) /. C) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . ((0. K),((K,n,B3) /. C)) is Element of the carrier of K
(K,n,B3) . C is set
(- ((A * (B * (1,B3))) * (K,n,1))) /. C is Element of the carrier of K
(- (A * (B * (1,B3)))) * (0. K) is Element of the carrier of K
the multF of K . ((- (A * (B * (1,B3)))),(0. K)) is Element of the carrier of K
(K,n,B3) /. C is Element of the carrier of K
(0. K) + ((K,n,B3) /. C) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . ((0. K),((K,n,B3) /. C)) is Element of the carrier of K
(K,n,B3) . C is set
(Line (B,1)) /. 1 is Element of the carrier of K
(Line (B,1)) . 1 is set
len (Col (B2,B3)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
len ((- ((A * (B * (1,B3))) * (K,n,1))) + (K,n,B3)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(Line (B,1)) /. B3 is Element of the carrier of K
(Line (B,1)) . B3 is set
[1,B3] is set
Indices (B * B2) is set
dom (B * B2) is Element of bool NAT
width (B * B2) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (B * B2)) is V28() V35( width (B * B2)) Element of bool NAT
[:(dom (B * B2)),(Seg (width (B * B2))):] is Relation-like set
(Line (B,1)) "*" (Col (B2,B3)) is Element of the carrier of K
(Line (B,1)) "*" (- ((A * (B * (1,B3))) * (K,n,1))) is Element of the carrier of K
(Line (B,1)) "*" (K,n,B3) is Element of the carrier of K
((Line (B,1)) "*" (- ((A * (B * (1,B3))) * (K,n,1)))) + ((Line (B,1)) "*" (K,n,B3)) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . (((Line (B,1)) "*" (- ((A * (B * (1,B3))) * (K,n,1)))),((Line (B,1)) "*" (K,n,B3))) is Element of the carrier of K
(Line (B,1)) "*" ((- (A * (B * (1,B3)))) * (K,n,1)) is Element of the carrier of K
((Line (B,1)) "*" ((- (A * (B * (1,B3)))) * (K,n,1))) + ((Line (B,1)) "*" (K,n,B3)) is Element of the carrier of K
the addF of K . (((Line (B,1)) "*" ((- (A * (B * (1,B3)))) * (K,n,1))),((Line (B,1)) "*" (K,n,B3))) is Element of the carrier of K
(Line (B,1)) "*" (K,n,1) is Element of the carrier of K
(- (A * (B * (1,B3)))) * ((Line (B,1)) "*" (K,n,1)) is Element of the carrier of K
the multF of K . ((- (A * (B * (1,B3)))),((Line (B,1)) "*" (K,n,1))) is Element of the carrier of K
((- (A * (B * (1,B3)))) * ((Line (B,1)) "*" (K,n,1))) + ((Line (B,1)) "*" (K,n,B3)) is Element of the carrier of K
the addF of K . (((- (A * (B * (1,B3)))) * ((Line (B,1)) "*" (K,n,1))),((Line (B,1)) "*" (K,n,B3))) is Element of the carrier of K
(- (A * (B * (1,B3)))) * (A ") is Element of the carrier of K
the multF of K . ((- (A * (B * (1,B3)))),(A ")) is Element of the carrier of K
((- (A * (B * (1,B3)))) * (A ")) + ((Line (B,1)) "*" (K,n,B3)) is Element of the carrier of K
the addF of K . (((- (A * (B * (1,B3)))) * (A ")),((Line (B,1)) "*" (K,n,B3))) is Element of the carrier of K
(A * (B * (1,B3))) * (A ") is Element of the carrier of K
the multF of K . ((A * (B * (1,B3))),(A ")) is Element of the carrier of K
- ((A * (B * (1,B3))) * (A ")) is Element of the carrier of K
(- ((A * (B * (1,B3))) * (A "))) + ((Line (B,1)) "*" (K,n,B3)) is Element of the carrier of K
the addF of K . ((- ((A * (B * (1,B3))) * (A "))),((Line (B,1)) "*" (K,n,B3))) is Element of the carrier of K
A * (A ") is Element of the carrier of K
the multF of K . (A,(A ")) is Element of the carrier of K
(B * (1,B3)) * (A * (A ")) is Element of the carrier of K
the multF of K . ((B * (1,B3)),(A * (A "))) is Element of the carrier of K
- ((B * (1,B3)) * (A * (A "))) is Element of the carrier of K
(- ((B * (1,B3)) * (A * (A ")))) + ((Line (B,1)) "*" (K,n,B3)) is Element of the carrier of K
the addF of K . ((- ((B * (1,B3)) * (A * (A ")))),((Line (B,1)) "*" (K,n,B3))) is Element of the carrier of K
1_ K is Element of the carrier of K
(B * (1,B3)) * (1_ K) is Element of the carrier of K
the multF of K . ((B * (1,B3)),(1_ K)) is Element of the carrier of K
- ((B * (1,B3)) * (1_ K)) is Element of the carrier of K
(- ((B * (1,B3)) * (1_ K))) + ((Line (B,1)) "*" (K,n,B3)) is Element of the carrier of K
the addF of K . ((- ((B * (1,B3)) * (1_ K))),((Line (B,1)) "*" (K,n,B3))) is Element of the carrier of K
(B * (1,B3)) * (1. K) is Element of the carrier of K
the multF of K . ((B * (1,B3)),(1. K)) is Element of the carrier of K
- ((B * (1,B3)) * (1. K)) is Element of the carrier of K
(- ((B * (1,B3)) * (1. K))) + ((Line (B,1)) /. B3) is Element of the carrier of K
the addF of K . ((- ((B * (1,B3)) * (1. K))),((Line (B,1)) /. B3)) is Element of the carrier of K
- (B * (1,B3)) is Element of the carrier of K
(- (B * (1,B3))) + (B * (1,B3)) is Element of the carrier of K
the addF of K . ((- (B * (1,B3))),(B * (1,B3))) is Element of the carrier of K
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(B * B2) * (B3,B2) is Element of the carrier of K
B * (1,B2) is Element of the carrier of K
A * (B * (1,B2)) is Element of the carrier of K
the multF of K . (A,(B * (1,B2))) is Element of the carrier of K
(A * (B * (1,B2))) * (K,n,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
- ((A * (B * (1,B2))) * (K,n,1)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len (- ((A * (B * (1,B2))) * (K,n,1))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
- (A * (B * (1,B2))) is Element of the carrier of K
(- (A * (B * (1,B2)))) * (K,n,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len ((- (A * (B * (1,B2)))) * (K,n,1)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Col (B2,B2) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( len B2) FinSequence-like FinSubsequence-like Element of (len B2) -tuples_on the carrier of K
(K,n,B2) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B2,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(- ((A * (B * (1,B2))) * (K,n,1))) + (K,n,B2) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len (K,n,B2) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
C is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
A3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B . A3 is set
C . A3 is set
dom ((- (A * (B * (1,B2)))) * (K,n,1)) is Element of bool NAT
(K,n,1) /. A3 is Element of the carrier of K
(K,n,1) . A3 is set
B2 * (A3,B2) is Element of the carrier of K
(- ((A * (B * (1,B2))) * (K,n,1))) . A3 is set
((- (A * (B * (1,B2)))) * (K,n,1)) . A3 is set
(- (A * (B * (1,B2)))) * ((K,n,1) /. A3) is Element of the carrier of K
the multF of K . ((- (A * (B * (1,B2)))),((K,n,1) /. A3)) is Element of the carrier of K
(- ((A * (B * (1,B2))) * (K,n,1))) /. A3 is Element of the carrier of K
(- (A * (B * (1,B2)))) * (1. K) is Element of the carrier of K
the multF of K . ((- (A * (B * (1,B2)))),(1. K)) is Element of the carrier of K
(K,n,B2) /. A3 is Element of the carrier of K
(K,n,B2) . A3 is set
((- (A * (B * (1,B2)))) * (1. K)) + (0. K) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . (((- (A * (B * (1,B2)))) * (1. K)),(0. K)) is Element of the carrier of K
[A3,B2] is set
B2 . A3 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(K,n,A3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),A3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,n,A3) . B2 is set
B3 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B3 . B2 is set
(- ((A * (B * (1,B2))) * (K,n,1))) /. A3 is Element of the carrier of K
(- (A * (B * (1,B2)))) * (0. K) is Element of the carrier of K
the multF of K . ((- (A * (B * (1,B2)))),(0. K)) is Element of the carrier of K
(K,n,B2) /. A3 is Element of the carrier of K
(K,n,B2) . A3 is set
(0. K) + (0. K) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . ((0. K),(0. K)) is Element of the carrier of K
(- ((A * (B * (1,B2))) * (K,n,1))) /. A3 is Element of the carrier of K
(- (A * (B * (1,B2)))) * (0. K) is Element of the carrier of K
the multF of K . ((- (A * (B * (1,B2)))),(0. K)) is Element of the carrier of K
(K,n,B2) /. A3 is Element of the carrier of K
(K,n,B2) . A3 is set
(0. K) + (1. K) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . ((0. K),(1. K)) is Element of the carrier of K
[B3,B2] is set
B . B3 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
B * (B3,B2) is Element of the carrier of K
A3 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
A3 . B2 is set
(K,n,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len (Col (B2,B2)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
len ((- ((A * (B * (1,B2))) * (K,n,1))) + (K,n,B2)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Line (B,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width B) FinSequence-like FinSubsequence-like Element of (width B) -tuples_on the carrier of K
len (Line (B,B3)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(Line (B,B3)) /. 1 is Element of the carrier of K
(Line (B,B3)) . 1 is set
B * (B3,1) is Element of the carrier of K
(Line (B,B3)) /. B2 is Element of the carrier of K
(Line (B,B3)) . B2 is set
Indices (B * B2) is set
dom (B * B2) is Element of bool NAT
width (B * B2) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (B * B2)) is V28() V35( width (B * B2)) Element of bool NAT
[:(dom (B * B2)),(Seg (width (B * B2))):] is Relation-like set
(Line (B,B3)) "*" (Col (B2,B2)) is Element of the carrier of K
(Line (B,B3)) "*" (- ((A * (B * (1,B2))) * (K,n,1))) is Element of the carrier of K
(Line (B,B3)) "*" (K,n,B2) is Element of the carrier of K
((Line (B,B3)) "*" (- ((A * (B * (1,B2))) * (K,n,1)))) + ((Line (B,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . (((Line (B,B3)) "*" (- ((A * (B * (1,B2))) * (K,n,1)))),((Line (B,B3)) "*" (K,n,B2))) is Element of the carrier of K
(Line (B,B3)) "*" ((- (A * (B * (1,B2)))) * (K,n,1)) is Element of the carrier of K
((Line (B,B3)) "*" ((- (A * (B * (1,B2)))) * (K,n,1))) + ((Line (B,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K . (((Line (B,B3)) "*" ((- (A * (B * (1,B2)))) * (K,n,1))),((Line (B,B3)) "*" (K,n,B2))) is Element of the carrier of K
(Line (B,B3)) "*" (K,n,1) is Element of the carrier of K
(- (A * (B * (1,B2)))) * ((Line (B,B3)) "*" (K,n,1)) is Element of the carrier of K
the multF of K . ((- (A * (B * (1,B2)))),((Line (B,B3)) "*" (K,n,1))) is Element of the carrier of K
((- (A * (B * (1,B2)))) * ((Line (B,B3)) "*" (K,n,1))) + ((Line (B,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K . (((- (A * (B * (1,B2)))) * ((Line (B,B3)) "*" (K,n,1))),((Line (B,B3)) "*" (K,n,B2))) is Element of the carrier of K
(- (A * (B * (1,B2)))) * (B * (B3,1)) is Element of the carrier of K
the multF of K . ((- (A * (B * (1,B2)))),(B * (B3,1))) is Element of the carrier of K
((- (A * (B * (1,B2)))) * (B * (B3,1))) + ((Line (B,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K . (((- (A * (B * (1,B2)))) * (B * (B3,1))),((Line (B,B3)) "*" (K,n,B2))) is Element of the carrier of K
(A * (B * (1,B2))) * (B * (B3,1)) is Element of the carrier of K
the multF of K . ((A * (B * (1,B2))),(B * (B3,1))) is Element of the carrier of K
- ((A * (B * (1,B2))) * (B * (B3,1))) is Element of the carrier of K
(- ((A * (B * (1,B2))) * (B * (B3,1)))) + ((Line (B,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K . ((- ((A * (B * (1,B2))) * (B * (B3,1)))),((Line (B,B3)) "*" (K,n,B2))) is Element of the carrier of K
A * (B * (B3,1)) is Element of the carrier of K
the multF of K . (A,(B * (B3,1))) is Element of the carrier of K
(B * (1,B2)) * (A * (B * (B3,1))) is Element of the carrier of K
the multF of K . ((B * (1,B2)),(A * (B * (B3,1)))) is Element of the carrier of K
- ((B * (1,B2)) * (A * (B * (B3,1)))) is Element of the carrier of K
(- ((B * (1,B2)) * (A * (B * (B3,1))))) + ((Line (B,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K . ((- ((B * (1,B2)) * (A * (B * (B3,1))))),((Line (B,B3)) "*" (K,n,B2))) is Element of the carrier of K
(- ((B * (1,B2)) * (A * (B * (B3,1))))) + (B * (B3,B2)) is Element of the carrier of K
the addF of K . ((- ((B * (1,B2)) * (A * (B * (B3,1))))),(B * (B3,B2))) is Element of the carrier of K
[B3,1] is set
B3 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B3 . 1 is set
A * (0. K) is Element of the carrier of K
the multF of K . (A,(0. K)) is Element of the carrier of K
(B * (1,B2)) * (A * (0. K)) is Element of the carrier of K
the multF of K . ((B * (1,B2)),(A * (0. K))) is Element of the carrier of K
- ((B * (1,B2)) * (A * (0. K))) is Element of the carrier of K
(- ((B * (1,B2)) * (A * (0. K)))) + (B * (B3,B2)) is Element of the carrier of K
the addF of K . ((- ((B * (1,B2)) * (A * (0. K)))),(B * (B3,B2))) is Element of the carrier of K
(B * (1,B2)) * (0. K) is Element of the carrier of K
the multF of K . ((B * (1,B2)),(0. K)) is Element of the carrier of K
- ((B * (1,B2)) * (0. K)) is Element of the carrier of K
(- ((B * (1,B2)) * (0. K))) + (B * (B3,B2)) is Element of the carrier of K
the addF of K . ((- ((B * (1,B2)) * (0. K))),(B * (B3,B2))) is Element of the carrier of K
- (0. K) is Element of the carrier of K
(- (0. K)) + (B * (B3,B2)) is Element of the carrier of K
the addF of K . ((- (0. K)),(B * (B3,B2))) is Element of the carrier of K
(0. K) + (1. K) is Element of the carrier of K
the addF of K . ((0. K),(1. K)) is Element of the carrier of K
len (Col (B2,1)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Indices (B * B2) is set
dom (B * B2) is Element of bool NAT
width (B * B2) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (B * B2)) is V28() V35( width (B * B2)) Element of bool NAT
[:(dom (B * B2)),(Seg (width (B * B2))):] is Relation-like set
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(B * B2) * (B3,B2) is Element of the carrier of K
[B3,B2] is set
Col (B2,B2) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( len B2) FinSequence-like FinSubsequence-like Element of (len B2) -tuples_on the carrier of K
len (Col (B2,B2)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
[B3,1] is set
(K,n,B2) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B2,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len (K,n,B2) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B * (1,B2) is Element of the carrier of K
A * (B * (1,B2)) is Element of the carrier of K
the multF of K . (A,(B * (1,B2))) is Element of the carrier of K
(A * (B * (1,B2))) * (K,n,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
- ((A * (B * (1,B2))) * (K,n,1)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len (- ((A * (B * (1,B2))) * (K,n,1))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
- (A * (B * (1,B2))) is Element of the carrier of K
(- (A * (B * (1,B2)))) * (K,n,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len ((- (A * (B * (1,B2)))) * (K,n,1)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(- ((A * (B * (1,B2))) * (K,n,1))) + (K,n,B2) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len ((- ((A * (B * (1,B2))) * (K,n,1))) + (K,n,B2)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
C is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
A3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B . A3 is set
C . A3 is set
(K,n,1) /. A3 is Element of the carrier of K
(K,n,1) . A3 is set
dom ((- (A * (B * (1,B2)))) * (K,n,1)) is Element of bool NAT
(- ((A * (B * (1,B2))) * (K,n,1))) . A3 is set
((- (A * (B * (1,B2)))) * (K,n,1)) . A3 is set
(- (A * (B * (1,B2)))) * ((K,n,1) /. A3) is Element of the carrier of K
the multF of K . ((- (A * (B * (1,B2)))),((K,n,1) /. A3)) is Element of the carrier of K
B2 * (A3,B2) is Element of the carrier of K
(- ((A * (B * (1,B2))) * (K,n,1))) /. A3 is Element of the carrier of K
(- (A * (B * (1,B2)))) * (1. K) is Element of the carrier of K
the multF of K . ((- (A * (B * (1,B2)))),(1. K)) is Element of the carrier of K
(K,n,B2) /. A3 is Element of the carrier of K
(K,n,B2) . A3 is set
((- (A * (B * (1,B2)))) * (1. K)) + (0. K) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . (((- (A * (B * (1,B2)))) * (1. K)),(0. K)) is Element of the carrier of K
1_ K is Element of the carrier of K
(- (A * (B * (1,B2)))) * (1_ K) is Element of the carrier of K
the multF of K . ((- (A * (B * (1,B2)))),(1_ K)) is Element of the carrier of K
[A3,B2] is set
B2 . A3 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(K,n,A3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),A3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,n,A3) . B2 is set
B3 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B3 . B2 is set
(K,n,B2) /. A3 is Element of the carrier of K
(K,n,B2) . A3 is set
(- ((A * (B * (1,B2))) * (K,n,1))) /. A3 is Element of the carrier of K
((- ((A * (B * (1,B2))) * (K,n,1))) /. A3) + (0. K) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . (((- ((A * (B * (1,B2))) * (K,n,1))) /. A3),(0. K)) is Element of the carrier of K
(- (A * (B * (1,B2)))) * (0. K) is Element of the carrier of K
the multF of K . ((- (A * (B * (1,B2)))),(0. K)) is Element of the carrier of K
(- ((A * (B * (1,B2))) * (K,n,1))) /. A3 is Element of the carrier of K
(- (A * (B * (1,B2)))) * (0. K) is Element of the carrier of K
the multF of K . ((- (A * (B * (1,B2)))),(0. K)) is Element of the carrier of K
(K,n,B2) /. A3 is Element of the carrier of K
(K,n,B2) . A3 is set
(0. K) + (1. K) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . ((0. K),(1. K)) is Element of the carrier of K
Line (B,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width B) FinSequence-like FinSubsequence-like Element of (width B) -tuples_on the carrier of K
len (Line (B,B3)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(Line (B,B3)) /. B2 is Element of the carrier of K
(Line (B,B3)) . B2 is set
B * (B3,B2) is Element of the carrier of K
(Line (B,B3)) /. 1 is Element of the carrier of K
(Line (B,B3)) . 1 is set
B * (B3,1) is Element of the carrier of K
(Line (B,B3)) "*" (Col (B2,B2)) is Element of the carrier of K
(Line (B,B3)) "*" (- ((A * (B * (1,B2))) * (K,n,1))) is Element of the carrier of K
(Line (B,B3)) "*" (K,n,B2) is Element of the carrier of K
((Line (B,B3)) "*" (- ((A * (B * (1,B2))) * (K,n,1)))) + ((Line (B,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . (((Line (B,B3)) "*" (- ((A * (B * (1,B2))) * (K,n,1)))),((Line (B,B3)) "*" (K,n,B2))) is Element of the carrier of K
(Line (B,B3)) "*" ((- (A * (B * (1,B2)))) * (K,n,1)) is Element of the carrier of K
((Line (B,B3)) "*" ((- (A * (B * (1,B2)))) * (K,n,1))) + ((Line (B,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K . (((Line (B,B3)) "*" ((- (A * (B * (1,B2)))) * (K,n,1))),((Line (B,B3)) "*" (K,n,B2))) is Element of the carrier of K
(Line (B,B3)) "*" (K,n,1) is Element of the carrier of K
(- (A * (B * (1,B2)))) * ((Line (B,B3)) "*" (K,n,1)) is Element of the carrier of K
the multF of K . ((- (A * (B * (1,B2)))),((Line (B,B3)) "*" (K,n,1))) is Element of the carrier of K
((- (A * (B * (1,B2)))) * ((Line (B,B3)) "*" (K,n,1))) + ((Line (B,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K . (((- (A * (B * (1,B2)))) * ((Line (B,B3)) "*" (K,n,1))),((Line (B,B3)) "*" (K,n,B2))) is Element of the carrier of K
(- (A * (B * (1,B2)))) * (B * (B3,1)) is Element of the carrier of K
the multF of K . ((- (A * (B * (1,B2)))),(B * (B3,1))) is Element of the carrier of K
((- (A * (B * (1,B2)))) * (B * (B3,1))) + ((Line (B,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K . (((- (A * (B * (1,B2)))) * (B * (B3,1))),((Line (B,B3)) "*" (K,n,B2))) is Element of the carrier of K
(A * (B * (1,B2))) * (B * (B3,1)) is Element of the carrier of K
the multF of K . ((A * (B * (1,B2))),(B * (B3,1))) is Element of the carrier of K
- ((A * (B * (1,B2))) * (B * (B3,1))) is Element of the carrier of K
(- ((A * (B * (1,B2))) * (B * (B3,1)))) + ((Line (B,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K . ((- ((A * (B * (1,B2))) * (B * (B3,1)))),((Line (B,B3)) "*" (K,n,B2))) is Element of the carrier of K
A * (B * (B3,1)) is Element of the carrier of K
the multF of K . (A,(B * (B3,1))) is Element of the carrier of K
(B * (1,B2)) * (A * (B * (B3,1))) is Element of the carrier of K
the multF of K . ((B * (1,B2)),(A * (B * (B3,1)))) is Element of the carrier of K
- ((B * (1,B2)) * (A * (B * (B3,1)))) is Element of the carrier of K
(- ((B * (1,B2)) * (A * (B * (B3,1))))) + ((Line (B,B3)) "*" (K,n,B2)) is Element of the carrier of K
the addF of K . ((- ((B * (1,B2)) * (A * (B * (B3,1))))),((Line (B,B3)) "*" (K,n,B2))) is Element of the carrier of K
(- ((B * (1,B2)) * (A * (B * (B3,1))))) + (B * (B3,B2)) is Element of the carrier of K
the addF of K . ((- ((B * (1,B2)) * (A * (B * (B3,1))))),(B * (B3,B2))) is Element of the carrier of K
B . B3 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
A3 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
A3 . 1 is set
B3 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B3 . B2 is set
(K,n,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
A * (0. K) is Element of the carrier of K
the multF of K . (A,(0. K)) is Element of the carrier of K
(B * (1,B2)) * (A * (0. K)) is Element of the carrier of K
the multF of K . ((B * (1,B2)),(A * (0. K))) is Element of the carrier of K
- ((B * (1,B2)) * (A * (0. K))) is Element of the carrier of K
(- ((B * (1,B2)) * (A * (0. K)))) + (B * (B3,B2)) is Element of the carrier of K
the addF of K . ((- ((B * (1,B2)) * (A * (0. K)))),(B * (B3,B2))) is Element of the carrier of K
(B * (1,B2)) * (0. K) is Element of the carrier of K
the multF of K . ((B * (1,B2)),(0. K)) is Element of the carrier of K
- ((B * (1,B2)) * (0. K)) is Element of the carrier of K
(- ((B * (1,B2)) * (0. K))) + (B * (B3,B2)) is Element of the carrier of K
the addF of K . ((- ((B * (1,B2)) * (0. K))),(B * (B3,B2))) is Element of the carrier of K
- (0. K) is Element of the carrier of K
(- (0. K)) + (B * (B3,B2)) is Element of the carrier of K
the addF of K . ((- (0. K)),(B * (B3,B2))) is Element of the carrier of K
(0. K) + (0. K) is Element of the carrier of K
the addF of K . ((0. K),(0. K)) is Element of the carrier of K
B is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
C is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
A3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B . A3 is set
C . A3 is set
(K,n,1) /. A3 is Element of the carrier of K
(K,n,1) . A3 is set
dom (A * (K,n,1)) is Element of bool NAT
(A * (K,n,1)) . A3 is set
A * ((K,n,1) /. A3) is Element of the carrier of K
the multF of K . (A,((K,n,1) /. A3)) is Element of the carrier of K
A * (1. K) is Element of the carrier of K
the multF of K . (A,(1. K)) is Element of the carrier of K
B2 * (1,B2) is Element of the carrier of K
[A3,B2] is set
B2 . A3 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
B2 * (A3,B2) is Element of the carrier of K
(K,n,A3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),A3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,n,A3) . B2 is set
B3 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B3 . B2 is set
A * (0. K) is Element of the carrier of K
the multF of K . (A,(0. K)) is Element of the carrier of K
Line (B,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width B) FinSequence-like FinSubsequence-like Element of (width B) -tuples_on the carrier of K
len (Line (B,B3)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(Line (B,B3)) /. 1 is Element of the carrier of K
(Line (B,B3)) . 1 is set
B * (B3,1) is Element of the carrier of K
(Line (B,B3)) "*" (Col (B2,B2)) is Element of the carrier of K
(Line (B,B3)) "*" (A * (K,n,1)) is Element of the carrier of K
(Line (B,B3)) "*" (K,n,1) is Element of the carrier of K
A * ((Line (B,B3)) "*" (K,n,1)) is Element of the carrier of K
the multF of K . (A,((Line (B,B3)) "*" (K,n,1))) is Element of the carrier of K
A * (B * (B3,1)) is Element of the carrier of K
the multF of K . (A,(B * (B3,1))) is Element of the carrier of K
B . B3 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
A3 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
A3 . 1 is set
(K,n,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
A * (0. K) is Element of the carrier of K
the multF of K . (A,(0. K)) is Element of the carrier of K
A * (Line (B,1)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width B) FinSequence-like FinSubsequence-like Element of (width B) -tuples_on the carrier of K
len (A * (Line (B,1))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(B * B2) * (1,1) is Element of the carrier of K
(Line (B,1)) "*" (Col (B2,1)) is Element of the carrier of K
(Line (B,1)) "*" (K,n,1) is Element of the carrier of K
A * ((Line (B,1)) "*" (K,n,1)) is Element of the carrier of K
the multF of K . (A,((Line (B,1)) "*" (K,n,1))) is Element of the carrier of K
(Line (B,1)) /. 1 is Element of the carrier of K
A * ((Line (B,1)) /. 1) is Element of the carrier of K
the multF of K . (A,((Line (B,1)) /. 1)) is Element of the carrier of K
(A * (Line (B,1))) /. 1 is Element of the carrier of K
(A * (Line (B,1))) . 1 is set
A * (B * (1,1)) is Element of the carrier of K
the multF of K . (A,(B * (1,1))) is Element of the carrier of K
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
[B3,B2] is set
(B * B2) * (B3,B2) is Element of the carrier of K
(1. (K,n)) * (B3,B2) is Element of the carrier of K
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
C is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) . C is set
(B * B2) * (B,C) is Element of the carrier of K
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
C is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) . C is set
(B * B2) * (B,C) is Element of the carrier of K
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
C is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) . C is set
(B * B2) * (B,C) is Element of the carrier of K
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
C is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) . C is set
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
0. K is V83(K) Element of the carrier of K
A is Element of the carrier of K
A " is Element of the carrier of K
B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B * (1,1) is Element of the carrier of K
Seg n is V28() V35(n) Element of bool NAT
[:(Seg n),(Seg n):] is Relation-like set
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
[B2,B3] is set
B * (1,B3) is Element of the carrier of K
A * (B * (1,B3)) is Element of the carrier of K
the multF of K is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is Relation-like set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the multF of K . (A,(B * (1,B3))) is Element of the carrier of K
- (A * (B * (1,B3))) is Element of the carrier of K
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,A3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
n |-> (0. K) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of K
n -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
1. K is V83(K) Element of the carrier of K
Replace ((n |-> (0. K)),A3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,n,A3) . B3 is set
A3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,A3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
n |-> (0. K) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of K
n -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
1. K is V83(K) Element of the carrier of K
Replace ((n |-> (0. K)),A3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,n,A3) . B3 is set
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B2) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
n |-> (0. K) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of K
n -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
1. K is V83(K) Element of the carrier of K
Replace ((n |-> (0. K)),B2,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len (K,n,B2) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B2) /. B is Element of the carrier of K
(K,n,B2) . B is set
C is Element of the carrier of K
A3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,A3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),A3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,n,A3) . B3 is set
B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
Indices B2 is set
dom B2 is Element of bool NAT
width B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width B2) is V28() V35( width B2) Element of bool NAT
[:(dom B2),(Seg (width B2)):] is Relation-like set
0 + 1 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 * (1,B3) is Element of the carrier of K
B * (1,B3) is Element of the carrier of K
A * (B * (1,B3)) is Element of the carrier of K
the multF of K is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is Relation-like set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the multF of K . (A,(B * (1,B3))) is Element of the carrier of K
- (A * (B * (1,B3))) is Element of the carrier of K
[1,B3] is set
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 . B3 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(K,n,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
n |-> (0. K) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of K
n -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
1. K is V83(K) Element of the carrier of K
Replace ((n |-> (0. K)),B3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
[B3,1] is set
B2 * (B3,1) is Element of the carrier of K
B2 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B2 . 1 is set
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B2 . B is set
(K,n,B3) . B is set
[B3,B] is set
B2 * (B3,B) is Element of the carrier of K
C is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
C . B is set
len B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (len B2) is V28() V35( len B2) Element of bool NAT
rng B2 is set
len B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
len (K,n,B3) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
[1,1] is set
B2 * (1,1) is Element of the carrier of K
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
0. K is V83(K) Element of the carrier of K
1. K is V83(K) Element of the carrier of K
A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A * (1,1) is Element of the carrier of K
0 + 1 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
(A * (1,1)) " is Element of the carrier of K
Seg n is V28() V35(n) Element of bool NAT
[:(Seg n),(Seg n):] is Relation-like set
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
[B2,B3] is set
A * (1,B3) is Element of the carrier of K
((A * (1,1)) ") * (A * (1,B3)) is Element of the carrier of K
the multF of K is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is Relation-like set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the multF of K . (((A * (1,1)) "),(A * (1,B3))) is Element of the carrier of K
- (((A * (1,1)) ") * (A * (1,B3))) is Element of the carrier of K
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B2) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
n |-> (0. K) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of K
n -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
Replace ((n |-> (0. K)),B2,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,n,B2) /. B is Element of the carrier of K
len (K,n,B2) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,A3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),A3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,n,A3) . B3 is set
B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
Indices B2 is set
dom B2 is Element of bool NAT
width B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width B2) is V28() V35( width B2) Element of bool NAT
[:(dom B2),(Seg (width B2)):] is Relation-like set
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 . B3 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(K,n,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
n |-> (0. K) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of K
n -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
Replace ((n |-> (0. K)),B3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
[B3,1] is set
B2 * (B3,1) is Element of the carrier of K
B2 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B2 . 1 is set
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B2 . B is set
(K,n,B3) . B is set
[B3,B] is set
B2 * (B3,B) is Element of the carrier of K
C is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
C . B is set
len B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (len B2) is V28() V35( len B2) Element of bool NAT
rng B2 is set
len B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
len (K,n,B3) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
n |-> (0. K) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of K
n -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
Replace ((n |-> (0. K)),1,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
((A * (1,1)) ") * (K,n,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len (((A * (1,1)) ") * (K,n,1)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
len (K,n,1) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
[1,1] is set
B2 * (1,1) is Element of the carrier of K
len B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (len B2) is V28() V35( len B2) Element of bool NAT
Col (B2,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( len B2) FinSequence-like FinSubsequence-like Element of (len B2) -tuples_on the carrier of K
(len B2) -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(Col (B2,1)) . B3 is set
(((A * (1,1)) ") * (K,n,1)) . B3 is set
(K,n,1) /. B3 is Element of the carrier of K
(K,n,1) . B3 is set
dom (((A * (1,1)) ") * (K,n,1)) is Element of bool NAT
((A * (1,1)) ") * ((K,n,1) /. B3) is Element of the carrier of K
the multF of K is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is Relation-like set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the multF of K . (((A * (1,1)) "),((K,n,1) /. B3)) is Element of the carrier of K
((A * (1,1)) ") * (0. K) is Element of the carrier of K
the multF of K . (((A * (1,1)) "),(0. K)) is Element of the carrier of K
[B3,1] is set
B2 . B3 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
B2 * (B3,1) is Element of the carrier of K
(K,n,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,n,B3) . 1 is set
B2 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B2 . 1 is set
(K,n,1) /. 1 is Element of the carrier of K
((A * (1,1)) ") * ((K,n,1) /. 1) is Element of the carrier of K
the multF of K . (((A * (1,1)) "),((K,n,1) /. 1)) is Element of the carrier of K
((A * (1,1)) ") * (1. K) is Element of the carrier of K
the multF of K . (((A * (1,1)) "),(1. K)) is Element of the carrier of K
len A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (len A) is V28() V35( len A) Element of bool NAT
dom A is Element of bool NAT
width A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Line (A,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width A) FinSequence-like FinSubsequence-like Element of (width A) -tuples_on the carrier of K
(width A) -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
len (Line (A,1)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
dom (Line (A,1)) is V35( width A) Element of bool NAT
Seg (width A) is V28() V35( width A) Element of bool NAT
A * B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A * (B,1) is Element of the carrier of K
(A * B2) * (B,1) is Element of the carrier of K
len (Col (B2,1)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
C is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
A3 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
C . B3 is set
A3 . B3 is set
(K,n,1) /. B3 is Element of the carrier of K
(K,n,1) . B3 is set
B2 * (B3,1) is Element of the carrier of K
dom (((A * (1,1)) ") * (K,n,1)) is Element of bool NAT
(((A * (1,1)) ") * (K,n,1)) . B3 is set
((A * (1,1)) ") * ((K,n,1) /. B3) is Element of the carrier of K
the multF of K is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is Relation-like set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the multF of K . (((A * (1,1)) "),((K,n,1) /. B3)) is Element of the carrier of K
((A * (1,1)) ") * (1. K) is Element of the carrier of K
the multF of K . (((A * (1,1)) "),(1. K)) is Element of the carrier of K
((A * (1,1)) ") * (0. K) is Element of the carrier of K
the multF of K . (((A * (1,1)) "),(0. K)) is Element of the carrier of K
[B3,1] is set
B2 . B3 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(K,n,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,n,B3) . 1 is set
F is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
F . 1 is set
Line (A,B) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width A) FinSequence-like FinSubsequence-like Element of (width A) -tuples_on the carrier of K
len (Line (A,B)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(Line (A,B)) /. 1 is Element of the carrier of K
(Line (A,B)) . 1 is set
[B,1] is set
Indices (A * B2) is set
dom (A * B2) is Element of bool NAT
width (A * B2) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (A * B2)) is V28() V35( width (A * B2)) Element of bool NAT
[:(dom (A * B2)),(Seg (width (A * B2))):] is Relation-like set
(Line (A,B)) "*" (Col (B2,1)) is Element of the carrier of K
(Line (A,B)) "*" (((A * (1,1)) ") * (K,n,1)) is Element of the carrier of K
(Line (A,B)) "*" (K,n,1) is Element of the carrier of K
((A * (1,1)) ") * ((Line (A,B)) "*" (K,n,1)) is Element of the carrier of K
the multF of K is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is Relation-like set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the multF of K . (((A * (1,1)) "),((Line (A,B)) "*" (K,n,1))) is Element of the carrier of K
((A * (1,1)) ") * (A * (B,1)) is Element of the carrier of K
the multF of K . (((A * (1,1)) "),(A * (B,1))) is Element of the carrier of K
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(A * B2) * (1,B3) is Element of the carrier of K
(K,n,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),B3,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len (K,n,B3) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Col (B2,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( len B2) FinSequence-like FinSubsequence-like Element of (len B2) -tuples_on the carrier of K
A * (1,B3) is Element of the carrier of K
((A * (1,1)) ") * (A * (1,B3)) is Element of the carrier of K
the multF of K is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is Relation-like set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the multF of K . (((A * (1,1)) "),(A * (1,B3))) is Element of the carrier of K
(((A * (1,1)) ") * (A * (1,B3))) * (K,n,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
- ((((A * (1,1)) ") * (A * (1,B3))) * (K,n,1)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(- ((((A * (1,1)) ") * (A * (1,B3))) * (K,n,1))) + (K,n,B3) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
- (((A * (1,1)) ") * (A * (1,B3))) is Element of the carrier of K
(- (((A * (1,1)) ") * (A * (1,B3)))) * (K,n,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len ((- (((A * (1,1)) ") * (A * (1,B3)))) * (K,n,1)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
len (- ((((A * (1,1)) ") * (A * (1,B3))) * (K,n,1))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
[1,B3] is set
B2 is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
C is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B2 . C is set
B . C is set
dom ((- (((A * (1,1)) ") * (A * (1,B3)))) * (K,n,1)) is Element of bool NAT
(K,n,1) /. C is Element of the carrier of K
(K,n,1) . C is set
(- ((((A * (1,1)) ") * (A * (1,B3))) * (K,n,1))) . C is set
((- (((A * (1,1)) ") * (A * (1,B3)))) * (K,n,1)) . C is set
(- (((A * (1,1)) ") * (A * (1,B3)))) * ((K,n,1) /. C) is Element of the carrier of K
the multF of K . ((- (((A * (1,1)) ") * (A * (1,B3)))),((K,n,1) /. C)) is Element of the carrier of K
B2 * (C,B3) is Element of the carrier of K
(- ((((A * (1,1)) ") * (A * (1,B3))) * (K,n,1))) /. C is Element of the carrier of K
(- (((A * (1,1)) ") * (A * (1,B3)))) * (1. K) is Element of the carrier of K
the multF of K . ((- (((A * (1,1)) ") * (A * (1,B3)))),(1. K)) is Element of the carrier of K
(K,n,B3) /. C is Element of the carrier of K
(K,n,B3) . C is set
(- (((A * (1,1)) ") * (A * (1,B3)))) + (0. K) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . ((- (((A * (1,1)) ") * (A * (1,B3)))),(0. K)) is Element of the carrier of K
[C,B3] is set
(K,n,C) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),C,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
(K,n,C) . B3 is set
(- (((A * (1,1)) ") * (A * (1,B3)))) * (0. K) is Element of the carrier of K
the multF of K . ((- (((A * (1,1)) ") * (A * (1,B3)))),(0. K)) is Element of the carrier of K
(- ((((A * (1,1)) ") * (A * (1,B3))) * (K,n,1))) /. C is Element of the carrier of K
(K,n,B3) /. C is Element of the carrier of K
(K,n,B3) . C is set
(0. K) + (0. K) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . ((0. K),(0. K)) is Element of the carrier of K
(- (((A * (1,1)) ") * (A * (1,B3)))) * (0. K) is Element of the carrier of K
the multF of K . ((- (((A * (1,1)) ") * (A * (1,B3)))),(0. K)) is Element of the carrier of K
(- ((((A * (1,1)) ") * (A * (1,B3))) * (K,n,1))) /. C is Element of the carrier of K
(K,n,B3) /. C is Element of the carrier of K
(K,n,B3) . C is set
(0. K) + (1. K) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . ((0. K),(1. K)) is Element of the carrier of K
(Line (A,1)) /. 1 is Element of the carrier of K
(Line (A,1)) . 1 is set
len (Col (B2,B3)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
len ((- ((((A * (1,1)) ") * (A * (1,B3))) * (K,n,1))) + (K,n,B3)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(Line (A,1)) /. B3 is Element of the carrier of K
(Line (A,1)) . B3 is set
Indices (A * B2) is set
dom (A * B2) is Element of bool NAT
width (A * B2) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (A * B2)) is V28() V35( width (A * B2)) Element of bool NAT
[:(dom (A * B2)),(Seg (width (A * B2))):] is Relation-like set
(Line (A,1)) "*" (Col (B2,B3)) is Element of the carrier of K
(Line (A,1)) "*" (- ((((A * (1,1)) ") * (A * (1,B3))) * (K,n,1))) is Element of the carrier of K
(Line (A,1)) "*" (K,n,B3) is Element of the carrier of K
((Line (A,1)) "*" (- ((((A * (1,1)) ") * (A * (1,B3))) * (K,n,1)))) + ((Line (A,1)) "*" (K,n,B3)) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . (((Line (A,1)) "*" (- ((((A * (1,1)) ") * (A * (1,B3))) * (K,n,1)))),((Line (A,1)) "*" (K,n,B3))) is Element of the carrier of K
(Line (A,1)) "*" ((- (((A * (1,1)) ") * (A * (1,B3)))) * (K,n,1)) is Element of the carrier of K
((Line (A,1)) "*" ((- (((A * (1,1)) ") * (A * (1,B3)))) * (K,n,1))) + ((Line (A,1)) "*" (K,n,B3)) is Element of the carrier of K
the addF of K . (((Line (A,1)) "*" ((- (((A * (1,1)) ") * (A * (1,B3)))) * (K,n,1))),((Line (A,1)) "*" (K,n,B3))) is Element of the carrier of K
(Line (A,1)) "*" (K,n,1) is Element of the carrier of K
(- (((A * (1,1)) ") * (A * (1,B3)))) * ((Line (A,1)) "*" (K,n,1)) is Element of the carrier of K
the multF of K . ((- (((A * (1,1)) ") * (A * (1,B3)))),((Line (A,1)) "*" (K,n,1))) is Element of the carrier of K
((- (((A * (1,1)) ") * (A * (1,B3)))) * ((Line (A,1)) "*" (K,n,1))) + ((Line (A,1)) "*" (K,n,B3)) is Element of the carrier of K
the addF of K . (((- (((A * (1,1)) ") * (A * (1,B3)))) * ((Line (A,1)) "*" (K,n,1))),((Line (A,1)) "*" (K,n,B3))) is Element of the carrier of K
(- (((A * (1,1)) ") * (A * (1,B3)))) * (A * (1,1)) is Element of the carrier of K
the multF of K . ((- (((A * (1,1)) ") * (A * (1,B3)))),(A * (1,1))) is Element of the carrier of K
((- (((A * (1,1)) ") * (A * (1,B3)))) * (A * (1,1))) + ((Line (A,1)) "*" (K,n,B3)) is Element of the carrier of K
the addF of K . (((- (((A * (1,1)) ") * (A * (1,B3)))) * (A * (1,1))),((Line (A,1)) "*" (K,n,B3))) is Element of the carrier of K
(((A * (1,1)) ") * (A * (1,B3))) * (A * (1,1)) is Element of the carrier of K
the multF of K . ((((A * (1,1)) ") * (A * (1,B3))),(A * (1,1))) is Element of the carrier of K
- ((((A * (1,1)) ") * (A * (1,B3))) * (A * (1,1))) is Element of the carrier of K
(- ((((A * (1,1)) ") * (A * (1,B3))) * (A * (1,1)))) + ((Line (A,1)) "*" (K,n,B3)) is Element of the carrier of K
the addF of K . ((- ((((A * (1,1)) ") * (A * (1,B3))) * (A * (1,1)))),((Line (A,1)) "*" (K,n,B3))) is Element of the carrier of K
((A * (1,1)) ") * (A * (1,1)) is Element of the carrier of K
the multF of K . (((A * (1,1)) "),(A * (1,1))) is Element of the carrier of K
(A * (1,B3)) * (((A * (1,1)) ") * (A * (1,1))) is Element of the carrier of K
the multF of K . ((A * (1,B3)),(((A * (1,1)) ") * (A * (1,1)))) is Element of the carrier of K
- ((A * (1,B3)) * (((A * (1,1)) ") * (A * (1,1)))) is Element of the carrier of K
(- ((A * (1,B3)) * (((A * (1,1)) ") * (A * (1,1))))) + ((Line (A,1)) "*" (K,n,B3)) is Element of the carrier of K
the addF of K . ((- ((A * (1,B3)) * (((A * (1,1)) ") * (A * (1,1))))),((Line (A,1)) "*" (K,n,B3))) is Element of the carrier of K
(A * (1,B3)) * (1. K) is Element of the carrier of K
the multF of K . ((A * (1,B3)),(1. K)) is Element of the carrier of K
- ((A * (1,B3)) * (1. K)) is Element of the carrier of K
(- ((A * (1,B3)) * (1. K))) + ((Line (A,1)) "*" (K,n,B3)) is Element of the carrier of K
the addF of K . ((- ((A * (1,B3)) * (1. K))),((Line (A,1)) "*" (K,n,B3))) is Element of the carrier of K
(- ((A * (1,B3)) * (1. K))) + ((Line (A,1)) /. B3) is Element of the carrier of K
the addF of K . ((- ((A * (1,B3)) * (1. K))),((Line (A,1)) /. B3)) is Element of the carrier of K
- (A * (1,B3)) is Element of the carrier of K
(- (A * (1,B3))) + (A * (1,B3)) is Element of the carrier of K
the addF of K . ((- (A * (1,B3))),(A * (1,B3))) is Element of the carrier of K
Indices A is set
[:(dom A),(Seg (width A)):] is Relation-like set
Indices (A * B2) is set
dom (A * B2) is Element of bool NAT
width (A * B2) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (A * B2)) is V28() V35( width (A * B2)) Element of bool NAT
[:(dom (A * B2)),(Seg (width (A * B2))):] is Relation-like set
len (Col (B2,1)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
((A * (1,1)) ") * (Line (A,1)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width A) FinSequence-like FinSubsequence-like Element of (width A) -tuples_on the carrier of K
len (((A * (1,1)) ") * (Line (A,1))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(A * B2) * (1,1) is Element of the carrier of K
(Line (A,1)) "*" (Col (B2,1)) is Element of the carrier of K
(Line (A,1)) "*" (K,n,1) is Element of the carrier of K
((A * (1,1)) ") * ((Line (A,1)) "*" (K,n,1)) is Element of the carrier of K
the multF of K is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is Relation-like set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the multF of K . (((A * (1,1)) "),((Line (A,1)) "*" (K,n,1))) is Element of the carrier of K
(Line (A,1)) /. 1 is Element of the carrier of K
((A * (1,1)) ") * ((Line (A,1)) /. 1) is Element of the carrier of K
the multF of K . (((A * (1,1)) "),((Line (A,1)) /. 1)) is Element of the carrier of K
(((A * (1,1)) ") * (Line (A,1))) /. 1 is Element of the carrier of K
(((A * (1,1)) ") * (Line (A,1))) . 1 is set
((A * (1,1)) ") * (A * (1,1)) is Element of the carrier of K
the multF of K . (((A * (1,1)) "),(A * (1,1))) is Element of the carrier of K
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
0. K is V83(K) Element of the carrier of K
1. K is V83(K) Element of the carrier of K
A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A * (1,1) is Element of the carrier of K
A @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
0 + 1 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
[1,1] is set
Indices A is set
dom A is Element of bool NAT
width A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width A) is V28() V35( width A) Element of bool NAT
[:(dom A),(Seg (width A)):] is Relation-like set
(A @) * (1,1) is Element of the carrier of K
B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(A @) * B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
((A @) * B2) * (1,1) is Element of the carrier of K
Indices ((A @) * B2) is set
dom ((A @) * B2) is Element of bool NAT
width ((A @) * B2) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width ((A @) * B2)) is V28() V35( width ((A @) * B2)) Element of bool NAT
[:(dom ((A @) * B2)),(Seg (width ((A @) * B2))):] is Relation-like set
B2 @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(B2 @) * A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A * (1,B3) is Element of the carrier of K
((B2 @) * A) * (1,B3) is Element of the carrier of K
[1,B3] is set
(A @) * (B3,1) is Element of the carrier of K
((A @) * B2) * (B3,1) is Element of the carrier of K
[B3,1] is set
((A @) * B2) @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(((A @) * B2) @) * (1,B3) is Element of the carrier of K
(A @) @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(B2 @) * ((A @) @) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
((B2 @) * ((A @) @)) * (1,B3) is Element of the carrier of K
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
((B2 @) * A) * (B3,1) is Element of the carrier of K
[1,B3] is set
((A @) * B2) * (1,B3) is Element of the carrier of K
((A @) * B2) @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(A @) @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(B2 @) * ((A @) @) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
((B2 @) * A) * (1,1) is Element of the carrier of K
(A @) @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(B2 @) * ((A @) @) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
((B2 @) * ((A @) @)) * (1,1) is Element of the carrier of K
((A @) * B2) @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(((A @) * B2) @) * (1,1) is Element of the carrier of K
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
0. K is V83(K) Element of the carrier of K
1. K is V83(K) Element of the carrier of K
A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A * (1,1) is Element of the carrier of K
B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B * A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(B * A) * (1,1) is Element of the carrier of K
B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(B * A) * B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
((B * A) * B2) * (1,1) is Element of the carrier of K
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
((B * A) * B2) * (B3,1) is Element of the carrier of K
(B * A) * (B3,1) is Element of the carrier of K
n is non empty set
n * is functional non empty FinSequence-membered FinSequenceSet of n
K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B3 is Relation-like NAT -defined n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of K,A,n
Swap (B3,B,B2) is Relation-like NAT -defined n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of n *
rng (Swap (B3,B,B2)) is set
B2 is Relation-like NAT -defined n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of n
len B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
rng B3 is set
rng B3 is set
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
len B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
len (Swap (B3,B,B2)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
1. (n,K) is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of K,K, the carrier of n
A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
Swap ((1. (n,K)),1,A) is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
1. n is V83(n) Element of the carrier of n
0. n is V83(n) Element of the carrier of n
K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(n,K,A) is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of K,K, the carrier of n
1. (n,K) is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of K,K, the carrier of n
Swap ((1. (n,K)),1,A) is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
B is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of K,K, the carrier of n
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B * (B2,B3) is Element of the carrier of n
[B2,B3] is set
Indices B is set
dom B is Element of bool NAT
width B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width B) is V28() V35( width B) Element of bool NAT
[:(dom B),(Seg (width B)):] is Relation-like set
A -' 2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
B /. A is FinSequence-like Element of the carrier of n *
len B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B . A is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,K,A) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
K |-> (0. n) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35(K) FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of n
K -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
Replace ((K |-> (0. n)),A,(1. n)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
C is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
C . B3 is set
B /^ 1 is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A3 is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
A3 | B2 is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
<*(B /. A)*> is Relation-like NAT -defined the carrier of n * -valued Function-like non empty trivial V28() V35(1) FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
B3 is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
<*(B /. A)*> ^ B3 is Relation-like NAT -defined the carrier of n * -valued Function-like non empty V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
len (<*(B /. A)*> ^ B3) is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
len <*(B /. A)*> is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
len B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(len <*(B /. A)*>) + (len B3) is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
1 + (len B3) is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
B . B2 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
B /. 1 is FinSequence-like Element of the carrier of n *
<*(B /. 1)*> is Relation-like NAT -defined the carrier of n * -valued Function-like non empty trivial V28() V35(1) FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
(<*(B /. A)*> ^ B3) ^ <*(B /. 1)*> is Relation-like NAT -defined the carrier of n * -valued Function-like non empty V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
B /^ A is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
((<*(B /. A)*> ^ B3) ^ <*(B /. 1)*>) ^ (B /^ A) is Relation-like NAT -defined the carrier of n * -valued Function-like non empty V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
(((<*(B /. A)*> ^ B3) ^ <*(B /. 1)*>) ^ (B /^ A)) . B2 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
<*(B /. 1)*> ^ (B /^ A) is Relation-like NAT -defined the carrier of n * -valued Function-like non empty V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
(<*(B /. A)*> ^ B3) ^ (<*(B /. 1)*> ^ (B /^ A)) is Relation-like NAT -defined the carrier of n * -valued Function-like non empty V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
((<*(B /. A)*> ^ B3) ^ (<*(B /. 1)*> ^ (B /^ A))) . B2 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(<*(B /. A)*> ^ B3) . 1 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
<*(B /. A)*> . 1 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
len B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
B2 /. 1 is FinSequence-like Element of the carrier of n *
len B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 . 1 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,K,1) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
K |-> (0. n) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35(K) FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of n
K -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
Replace ((K |-> (0. n)),1,(1. n)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B . B3 is set
B . B2 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
B /. B2 is FinSequence-like Element of the carrier of n *
B2 is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
B2 /. A is FinSequence-like Element of the carrier of n *
len B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 . A is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,K,A) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
K |-> (0. n) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35(K) FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of n
K -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
Replace ((K |-> (0. n)),A,(1. n)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B . B3 is set
B . B2 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
B /. B2 is FinSequence-like Element of the carrier of n *
B2 is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
B2 /. 1 is FinSequence-like Element of the carrier of n *
len B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 . 1 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,K,1) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
K |-> (0. n) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35(K) FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of n
K -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
Replace ((K |-> (0. n)),1,(1. n)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B . B3 is set
B . B2 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
B /. B2 is FinSequence-like Element of the carrier of n *
B2 is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
B2 /. B2 is FinSequence-like Element of the carrier of n *
len B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 . B2 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,K,B2) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
K |-> (0. n) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35(K) FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of n
K -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
Replace ((K |-> (0. n)),B2,(1. n)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B . B3 is set
B . B2 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
B /. B2 is FinSequence-like Element of the carrier of n *
B2 is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
B2 /. B2 is FinSequence-like Element of the carrier of n *
len B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 . B2 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,K,B2) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
K |-> (0. n) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35(K) FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of n
K -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
Replace ((K |-> (0. n)),B2,(1. n)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B . B3 is set
B . B2 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
B /. B2 is FinSequence-like Element of the carrier of n *
B2 is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
B2 /. B2 is FinSequence-like Element of the carrier of n *
len B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 . B2 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,K,B2) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
K |-> (0. n) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35(K) FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of n
K -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
Replace ((K |-> (0. n)),B2,(1. n)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B . B3 is set
B . B2 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
B /. B2 is FinSequence-like Element of the carrier of n *
B2 is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
B2 /. B2 is FinSequence-like Element of the carrier of n *
len B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 . B2 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,K,B2) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
K |-> (0. n) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35(K) FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of n
K -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
Replace ((K |-> (0. n)),B2,(1. n)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B . B3 is set
B . B2 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
B /. B2 is FinSequence-like Element of the carrier of n *
B2 is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
B2 /. A is FinSequence-like Element of the carrier of n *
len B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 . A is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,K,A) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
K |-> (0. n) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35(K) FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of n
K -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
Replace ((K |-> (0. n)),A,(1. n)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B . B3 is set
B . B2 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
B /. B2 is FinSequence-like Element of the carrier of n *
B2 is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
B2 /. 1 is FinSequence-like Element of the carrier of n *
len B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 . 1 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
(n,K,1) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
K |-> (0. n) is Relation-like NAT -defined the carrier of n -valued Function-like V28() V35(K) FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of n
K -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
Replace ((K |-> (0. n)),1,(1. n)) is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B is Relation-like NAT -defined the carrier of n -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of n
B . B3 is set
B . B2 is Relation-like NAT -defined Function-like V28() FinSequence-like FinSubsequence-like set
B /. B2 is FinSequence-like Element of the carrier of n *
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
1. n is V83(n) Element of the carrier of n
K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(n,K,1) is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of K,K, the carrier of n
1. (n,K) is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of K,K, the carrier of n
Swap ((1. (n,K)),1,1) is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(n,K,1) * (B2,B2) is Element of the carrier of n
[B2,B2] is set
Indices (n,K,1) is set
dom (n,K,1) is Element of bool NAT
width (n,K,1) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (n,K,1)) is V28() V35( width (n,K,1)) Element of bool NAT
[:(dom (n,K,1)),(Seg (width (n,K,1))):] is Relation-like set
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
0. n is V83(n) Element of the carrier of n
K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(n,K,1) is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of K,K, the carrier of n
1. (n,K) is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of K,K, the carrier of n
Swap ((1. (n,K)),1,1) is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(n,K,1) * (B2,B3) is Element of the carrier of n
[B2,B3] is set
Indices (n,K,1) is set
dom (n,K,1) is Element of bool NAT
width (n,K,1) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (n,K,1)) is V28() V35( width (n,K,1)) Element of bool NAT
[:(dom (n,K,1)),(Seg (width (n,K,1))):] is Relation-like set
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
1. n is V83(n) Element of the carrier of n
0. n is V83(n) Element of the carrier of n
K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(n,K,A) is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of K,K, the carrier of n
1. (n,K) is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of K,K, the carrier of n
Swap ((1. (n,K)),1,A) is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
B is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of K,K, the carrier of n
Indices B is set
dom B is Element of bool NAT
width B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width B) is V28() V35( width B) Element of bool NAT
[:(dom B),(Seg (width B)):] is Relation-like set
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
[B2,B3] is set
B * (B2,B3) is Element of the carrier of n
(n,K,A) * (B2,B3) is Element of the carrier of n
Seg K is V28() V35(K) Element of bool NAT
[:(Seg K),(Seg K):] is Relation-like set
n is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of n is non empty non trivial set
the carrier of n * is functional non empty FinSequence-membered FinSequenceSet of the carrier of n
1. n is V83(n) Element of the carrier of n
0. n is V83(n) Element of the carrier of n
K is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(n,K,A) is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of K,K, the carrier of n
1. (n,K) is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of K,K, the carrier of n
Swap ((1. (n,K)),1,A) is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of n *
B is Relation-like NAT -defined the carrier of n * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of K,K, the carrier of n
Indices B is set
dom B is Element of bool NAT
width B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width B) is V28() V35( width B) Element of bool NAT
[:(dom B),(Seg (width B)):] is Relation-like set
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
[B2,B3] is set
B * (B2,B3) is Element of the carrier of n
(n,K,A) * (B2,B3) is Element of the carrier of n
Seg K is V28() V35(K) Element of bool NAT
[:(Seg K),(Seg K):] is Relation-like set
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
1. (K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
Swap ((1. (K,n)),1,B) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of K *
(K,n,B) * A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
((K,n,B) * A) * (B,B2) is Element of the carrier of K
A * (1,B2) is Element of the carrier of K
((K,n,B) * A) * (1,B2) is Element of the carrier of K
A * (B,B2) is Element of the carrier of K
width (K,n,B) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (K,n,B)) is V28() V35( width (K,n,B)) Element of bool NAT
(K,n,B) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
0. K is V83(K) Element of the carrier of K
n |-> (0. K) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of K
n -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
1. K is V83(K) Element of the carrier of K
Replace ((n |-> (0. K)),B,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(K,n,B) . B is set
(K,n,B) * (1,B) is Element of the carrier of K
C is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) * (1,C) is Element of the carrier of K
C is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) * (1,C) is Element of the carrier of K
C is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) * (1,C) is Element of the carrier of K
C is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) * (1,C) is Element of the carrier of K
C is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) * (1,C) is Element of the carrier of K
Indices ((K,n,B) * A) is set
dom ((K,n,B) * A) is Element of bool NAT
width ((K,n,B) * A) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width ((K,n,B) * A)) is V28() V35( width ((K,n,B) * A)) Element of bool NAT
[:(dom ((K,n,B) * A)),(Seg (width ((K,n,B) * A))):] is Relation-like set
Seg n is V28() V35(n) Element of bool NAT
[:(Seg n),(Seg n):] is Relation-like set
(K,n,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace ((n |-> (0. K)),1,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(K,n,1) . B is set
(K,n,B) * (B,B) is Element of the carrier of K
C is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) * (B,C) is Element of the carrier of K
C is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) * (B,C) is Element of the carrier of K
C is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) * (B,C) is Element of the carrier of K
C is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) * (B,C) is Element of the carrier of K
(K,n,1) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
Swap ((1. (K,n)),1,1) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of K *
C is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,1) * (B,C) is Element of the carrier of K
len (K,n,1) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Line ((K,n,B),B) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width (K,n,B)) FinSequence-like FinSubsequence-like Element of (width (K,n,B)) -tuples_on the carrier of K
(width (K,n,B)) -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
len A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Col (A,B2) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( len A) FinSequence-like FinSubsequence-like Element of (len A) -tuples_on the carrier of K
(len A) -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
len (Col (A,B2)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
dom A is Element of bool NAT
[1,B2] is set
[B,B2] is set
(K,n,1) "*" (Col (A,B2)) is Element of the carrier of K
(Col (A,B2)) "*" (K,n,1) is Element of the carrier of K
(Col (A,B2)) . 1 is set
len (K,n,B) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Line ((K,n,B),1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width (K,n,B)) FinSequence-like FinSubsequence-like Element of (width (K,n,B)) -tuples_on the carrier of K
(K,n,B) "*" (Col (A,B2)) is Element of the carrier of K
(Col (A,B2)) "*" (K,n,B) is Element of the carrier of K
(Col (A,B2)) . B is set
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
((K,n,B) * A) * (B2,B) is Element of the carrier of K
A * (B2,B) is Element of the carrier of K
len A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Col (A,B) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( len A) FinSequence-like FinSubsequence-like Element of (len A) -tuples_on the carrier of K
(len A) -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
len (Col (A,B)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
width (K,n,B) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (K,n,B)) is V28() V35( width (K,n,B)) Element of bool NAT
(K,n,B2) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
0. K is V83(K) Element of the carrier of K
n |-> (0. K) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of K
n -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
1. K is V83(K) Element of the carrier of K
Replace ((n |-> (0. K)),B2,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
C is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(K,n,B2) . C is set
(K,n,B) * (B2,C) is Element of the carrier of K
A3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) * (B2,A3) is Element of the carrier of K
A3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) * (B2,A3) is Element of the carrier of K
A3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) * (B2,A3) is Element of the carrier of K
A3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) * (B2,A3) is Element of the carrier of K
Seg n is V28() V35(n) Element of bool NAT
dom A is Element of bool NAT
len (K,n,B2) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Line ((K,n,B),B2) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width (K,n,B)) FinSequence-like FinSubsequence-like Element of (width (K,n,B)) -tuples_on the carrier of K
(width (K,n,B)) -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
[B2,B] is set
Indices ((K,n,B) * A) is set
dom ((K,n,B) * A) is Element of bool NAT
width ((K,n,B) * A) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width ((K,n,B) * A)) is V28() V35( width ((K,n,B) * A)) Element of bool NAT
[:(dom ((K,n,B) * A)),(Seg (width ((K,n,B) * A))):] is Relation-like set
(K,n,B2) "*" (Col (A,B)) is Element of the carrier of K
(Col (A,B)) "*" (K,n,B2) is Element of the carrier of K
(Col (A,B)) . B2 is set
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,A) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
the carrier of K is non empty non trivial set
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
1. (K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
Swap ((1. (K,n)),1,A) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of K *
(K,n,A) ~ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(K,n,A) * (K,n,A) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
Indices ((K,n,A) * (K,n,A)) is set
dom ((K,n,A) * (K,n,A)) is Element of bool NAT
width ((K,n,A) * (K,n,A)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width ((K,n,A) * (K,n,A))) is V28() V35( width ((K,n,A) * (K,n,A))) Element of bool NAT
[:(dom ((K,n,A) * (K,n,A))),(Seg (width ((K,n,A) * (K,n,A)))):] is Relation-like set
Seg n is V28() V35(n) Element of bool NAT
[:(Seg n),(Seg n):] is Relation-like set
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
[B2,B3] is set
((K,n,A) * (K,n,A)) * (B2,B3) is Element of the carrier of K
(1. (K,n)) * (B2,B3) is Element of the carrier of K
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
[B2,B] is set
Indices (1. (K,n)) is set
dom (1. (K,n)) is Element of bool NAT
width (1. (K,n)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (1. (K,n))) is V28() V35( width (1. (K,n))) Element of bool NAT
[:(dom (1. (K,n))),(Seg (width (1. (K,n)))):] is Relation-like set
(K,n,A) * (B2,B) is Element of the carrier of K
1. K is V83(K) Element of the carrier of K
(K,n,A) * (B2,B) is Element of the carrier of K
1. K is V83(K) Element of the carrier of K
(K,n,A) * (B2,B) is Element of the carrier of K
1. K is V83(K) Element of the carrier of K
(K,n,A) * (B2,B) is Element of the carrier of K
1. K is V83(K) Element of the carrier of K
(1. (K,n)) * (B2,B) is Element of the carrier of K
((K,n,A) * (K,n,A)) * (B2,B) is Element of the carrier of K
(K,n,A) * (B2,B) is Element of the carrier of K
0. K is V83(K) Element of the carrier of K
(K,n,A) * (B2,B) is Element of the carrier of K
0. K is V83(K) Element of the carrier of K
(K,n,A) * (B2,B) is Element of the carrier of K
0. K is V83(K) Element of the carrier of K
(K,n,A) * (B2,B) is Element of the carrier of K
0. K is V83(K) Element of the carrier of K
(1. (K,n)) * (B2,B) is Element of the carrier of K
((K,n,A) * (K,n,A)) * (B2,B) is Element of the carrier of K
((K,n,A) * (K,n,A)) * (B2,B) is Element of the carrier of K
(1. (K,n)) * (B2,B) is Element of the carrier of K
((K,n,A) * (K,n,A)) * (B2,B) is Element of the carrier of K
(1. (K,n)) * (B2,B) is Element of the carrier of K
(K,n,A) * (1,A) is Element of the carrier of K
1. K is V83(K) Element of the carrier of K
(K,n,A) * (1,A) is Element of the carrier of K
1. K is V83(K) Element of the carrier of K
(K,n,A) * (1,A) is Element of the carrier of K
1. K is V83(K) Element of the carrier of K
(K,n,A) * (1,A) is Element of the carrier of K
1. K is V83(K) Element of the carrier of K
(1. (K,n)) * (B2,B) is Element of the carrier of K
((K,n,A) * (K,n,A)) * (B2,B) is Element of the carrier of K
(K,n,A) * (1,B) is Element of the carrier of K
0. K is V83(K) Element of the carrier of K
(K,n,A) * (1,B) is Element of the carrier of K
0. K is V83(K) Element of the carrier of K
(K,n,A) * (1,B) is Element of the carrier of K
0. K is V83(K) Element of the carrier of K
(K,n,A) * (1,B) is Element of the carrier of K
0. K is V83(K) Element of the carrier of K
(1. (K,n)) * (B2,B) is Element of the carrier of K
((K,n,A) * (K,n,A)) * (B2,B) is Element of the carrier of K
((K,n,A) * (K,n,A)) * (B2,B) is Element of the carrier of K
(1. (K,n)) * (B2,B) is Element of the carrier of K
((K,n,A) * (K,n,A)) * (B2,B) is Element of the carrier of K
(1. (K,n)) * (B2,B) is Element of the carrier of K
((K,n,A) * (K,n,A)) * (B2,B) is Element of the carrier of K
(1. (K,n)) * (B2,B) is Element of the carrier of K
((K,n,A) * (K,n,A)) * (B2,B) is Element of the carrier of K
(1. (K,n)) * (B2,B) is Element of the carrier of K
(K,n,A) * (A,B) is Element of the carrier of K
0. K is V83(K) Element of the carrier of K
(K,n,A) * (A,B) is Element of the carrier of K
0. K is V83(K) Element of the carrier of K
(K,n,A) * (A,B) is Element of the carrier of K
0. K is V83(K) Element of the carrier of K
(K,n,A) * (A,B) is Element of the carrier of K
0. K is V83(K) Element of the carrier of K
(1. (K,n)) * (B2,B) is Element of the carrier of K
((K,n,A) * (K,n,A)) * (B2,B) is Element of the carrier of K
(1. (K,n)) * (B2,B) is Element of the carrier of K
1. K is V83(K) Element of the carrier of K
(K,n,A) * (A,B) is Element of the carrier of K
((K,n,A) * (K,n,A)) * (B2,B) is Element of the carrier of K
((K,n,A) * (K,n,A)) * (B2,B) is Element of the carrier of K
(1. (K,n)) * (B2,B) is Element of the carrier of K
((K,n,A) * (K,n,A)) * (B2,B) is Element of the carrier of K
(1. (K,n)) * (B2,B) is Element of the carrier of K
(1. (K,n)) * (B2,B) is Element of the carrier of K
0. K is V83(K) Element of the carrier of K
(K,n,1) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
Swap ((1. (K,n)),1,1) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of K *
(K,n,1) * (1,B) is Element of the carrier of K
((K,n,A) * (K,n,A)) * (B2,B) is Element of the carrier of K
(1. (K,n)) * (B,B) is Element of the carrier of K
1. K is V83(K) Element of the carrier of K
((K,n,A) * (K,n,A)) * (1,B) is Element of the carrier of K
(K,n,A) * (A,B) is Element of the carrier of K
((K,n,A) * (K,n,A)) * (B2,B) is Element of the carrier of K
(1. (K,n)) * (B2,B) is Element of the carrier of K
((K,n,A) * (K,n,A)) * (B2,B) is Element of the carrier of K
(1. (K,n)) * (B2,B) is Element of the carrier of K
((K,n,A) * (K,n,A)) * (B2,B) is Element of the carrier of K
(1. (K,n)) * (B2,B) is Element of the carrier of K
((K,n,A) * (K,n,A)) * (B2,B) is Element of the carrier of K
(1. (K,n)) * (B2,B) is Element of the carrier of K
((K,n,A) * (K,n,A)) * (B2,B) is Element of the carrier of K
(1. (K,n)) * (B2,B) is Element of the carrier of K
width (1. (K,n)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
len (1. (K,n)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
len ((K,n,A) * (K,n,A)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,A) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
1. (K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
Swap ((1. (K,n)),1,A) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of K *
(K,n,A) @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
1. K is V83(K) Element of the carrier of K
0. K is V83(K) Element of the carrier of K
Indices (K,n,A) is set
dom (K,n,A) is Element of bool NAT
width (K,n,A) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (K,n,A)) is V28() V35( width (K,n,A)) Element of bool NAT
[:(dom (K,n,A)),(Seg (width (K,n,A))):] is Relation-like set
Seg n is V28() V35(n) Element of bool NAT
[:(Seg n),(Seg n):] is Relation-like set
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
((K,n,A) @) * (B,B2) is Element of the carrier of K
[B2,B] is set
(K,n,A) * (B2,B) is Element of the carrier of K
1. K is V83(K) Element of the carrier of K
0. K is V83(K) Element of the carrier of K
Indices (K,n,A) is set
dom (K,n,A) is Element of bool NAT
width (K,n,A) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (K,n,A)) is V28() V35( width (K,n,A)) Element of bool NAT
[:(dom (K,n,A)),(Seg (width (K,n,A))):] is Relation-like set
Seg n is V28() V35(n) Element of bool NAT
[:(Seg n),(Seg n):] is Relation-like set
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
((K,n,A) @) * (B,B2) is Element of the carrier of K
[B2,B] is set
(K,n,A) * (B2,B) is Element of the carrier of K
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,n,B) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
1. (K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
Swap ((1. (K,n)),1,B) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of K *
A * (K,n,B) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(K,n,B) * (A @) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
((K,n,B) * (A @)) @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(A @) @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(K,n,B) @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
((A @) @) * ((K,n,B) @) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A * ((K,n,B) @) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(A * (K,n,B)) * (B2,B) is Element of the carrier of K
A * (B2,1) is Element of the carrier of K
(A * (K,n,B)) * (B2,1) is Element of the carrier of K
A * (B2,B) is Element of the carrier of K
[B2,1] is set
Indices A is set
dom A is Element of bool NAT
width A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width A) is V28() V35( width A) Element of bool NAT
[:(dom A),(Seg (width A)):] is Relation-like set
[B,B2] is set
Indices ((K,n,B) * (A @)) is set
dom ((K,n,B) * (A @)) is Element of bool NAT
width ((K,n,B) * (A @)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width ((K,n,B) * (A @))) is V28() V35( width ((K,n,B) * (A @))) Element of bool NAT
[:(dom ((K,n,B) * (A @))),(Seg (width ((K,n,B) * (A @)))):] is Relation-like set
((K,n,B) * (A @)) * (B,B2) is Element of the carrier of K
(A @) * (1,B2) is Element of the carrier of K
[B2,B] is set
[1,B2] is set
((K,n,B) * (A @)) * (1,B2) is Element of the carrier of K
(A @) * (B,B2) is Element of the carrier of K
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(A * (K,n,B)) * (B2,B3) is Element of the carrier of K
A * (B2,B3) is Element of the carrier of K
[B2,B3] is set
Indices A is set
dom A is Element of bool NAT
width A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width A) is V28() V35( width A) Element of bool NAT
[:(dom A),(Seg (width A)):] is Relation-like set
[B3,B2] is set
Indices ((K,n,B) * (A @)) is set
dom ((K,n,B) * (A @)) is Element of bool NAT
width ((K,n,B) * (A @)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width ((K,n,B) * (A @))) is V28() V35( width ((K,n,B) * (A @))) Element of bool NAT
[:(dom ((K,n,B) * (A @))),(Seg (width ((K,n,B) * (A @)))):] is Relation-like set
((K,n,B) * (A @)) * (B3,B2) is Element of the carrier of K
(A @) * (B3,B2) is Element of the carrier of K
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(A * (K,n,B)) * (B2,B) is Element of the carrier of K
A * (B2,1) is Element of the carrier of K
(A * (K,n,B)) * (B2,1) is Element of the carrier of K
A * (B2,B) is Element of the carrier of K
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(A * (K,n,B)) * (B3,B2) is Element of the carrier of K
A * (B3,B2) is Element of the carrier of K
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
0. (K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
n -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
0. K is V83(K) Element of the carrier of K
n |-> (0. K) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of K
n |-> (n |-> (0. K)) is Relation-like NAT -defined n -tuples_on the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Function-yielding V40() Element of n -tuples_on (n -tuples_on the carrier of K)
n -tuples_on (n -tuples_on the carrier of K) is functional non empty FinSequence-membered FinSequenceSet of n -tuples_on the carrier of K
A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
width A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
0. (K,n,n) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A * (B,B2) is Element of the carrier of K
[B,B2] is set
Indices A is set
dom A is Element of bool NAT
Seg (width A) is V28() V35( width A) Element of bool NAT
[:(dom A),(Seg (width A)):] is Relation-like set
Indices A is set
dom A is Element of bool NAT
Seg (width A) is V28() V35( width A) Element of bool NAT
[:(dom A),(Seg (width A)):] is Relation-like set
Seg n is V28() V35(n) Element of bool NAT
[:(Seg n),(Seg n):] is Relation-like set
A + A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
[B,B2] is set
A * (B,B2) is Element of the carrier of K
(A + A) * (B,B2) is Element of the carrier of K
B3 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A * (B3,B2) is Element of the carrier of K
(0. K) + (A * (B,B2)) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is Relation-like set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the addF of K . ((0. K),(A * (B,B2))) is Element of the carrier of K
len A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
0. (K,n,n) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
0. (K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
n -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
0. K is V83(K) Element of the carrier of K
n |-> (0. K) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Element of n -tuples_on the carrier of K
n |-> (n |-> (0. K)) is Relation-like NAT -defined n -tuples_on the carrier of K -valued Function-like V28() V35(n) FinSequence-like FinSubsequence-like Function-yielding V40() Element of n -tuples_on (n -tuples_on the carrier of K)
n -tuples_on (n -tuples_on the carrier of K) is functional non empty FinSequence-membered FinSequenceSet of n -tuples_on the carrier of K
1. K is V83(K) Element of the carrier of K
A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
A * (B,B2) is Element of the carrier of K
(K,n,B) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
1. (K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
Swap ((1. (K,n)),1,B) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of K *
(K,n,B) * A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(K,n,B2) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
Swap ((1. (K,n)),1,B2) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() FinSequence of the carrier of K *
((K,n,B) * A) * (K,n,B2) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(((K,n,B) * A) * (K,n,B2)) * (1,1) is Element of the carrier of K
((K,n,B) * A) * (1,B2) is Element of the carrier of K
B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
C is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B * (((K,n,B) * A) * (K,n,B2)) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(B * (((K,n,B) * A) * (K,n,B2))) * C is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
((B * (((K,n,B) * A) * (K,n,B2))) * C) * (1,1) is Element of the carrier of K
B * (K,n,B) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(K,n,B2) * C is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(B * (K,n,B)) * A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
((B * (K,n,B)) * A) * ((K,n,B2) * C) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B * ((K,n,B) * A) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(B * ((K,n,B) * A)) * ((K,n,B2) * C) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(B * ((K,n,B) * A)) * (K,n,B2) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
((B * ((K,n,B) * A)) * (K,n,B2)) * C is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
1. (K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B * A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
1. (K,B2) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2,B2, the carrier of K
B2 + 1 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
1. (K,(B2 + 1)) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
B3 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
B2 * B3 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
Indices (1. (K,(B2 + 1))) is set
dom (1. (K,(B2 + 1))) is Element of bool NAT
width (1. (K,(B2 + 1))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (1. (K,(B2 + 1)))) is V28() V35( width (1. (K,(B2 + 1)))) Element of bool NAT
[:(dom (1. (K,(B2 + 1)))),(Seg (width (1. (K,(B2 + 1))))):] is Relation-like set
Seg (B2 + 1) is non empty V28() V35(B2 + 1) Element of bool NAT
[:(Seg (B2 + 1)),(Seg (B2 + 1)):] is Relation-like set
Det B2 is Element of the carrier of K
Det B3 is Element of the carrier of K
(Det B2) * (Det B3) is Element of the carrier of K
the multF of K is Relation-like Function-like V18([: 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 Relation-like set
[:[: the carrier of K, the carrier of K:], the carrier of K:] is Relation-like set
bool [:[: the carrier of K, the carrier of K:], the carrier of K:] is set
the multF of K . ((Det B2),(Det B3)) is Element of the carrier of K
Det (1. (K,(B2 + 1))) is Element of the carrier of K
0. (K,(B2 + 1)) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
(B2 + 1) -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
0. K is V83(K) Element of the carrier of K
(B2 + 1) |-> (0. K) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35(B2 + 1) FinSequence-like FinSubsequence-like Element of (B2 + 1) -tuples_on the carrier of K
(B2 + 1) |-> ((B2 + 1) |-> (0. K)) is Relation-like NAT -defined (B2 + 1) -tuples_on the carrier of K -valued Function-like V28() V35(B2 + 1) FinSequence-like FinSubsequence-like Function-yielding V40() Element of (B2 + 1) -tuples_on ((B2 + 1) -tuples_on the carrier of K)
(B2 + 1) -tuples_on ((B2 + 1) -tuples_on the carrier of K) is functional non empty FinSequence-membered FinSequenceSet of (B2 + 1) -tuples_on the carrier of K
0. (K,(B2 + 1),(B2 + 1)) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
1_ K is Element of the carrier of K
1. K is V83(K) Element of the carrier of K
B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
C is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
B * B3 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
(B * B3) * C is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
((B * B3) * C) * (1,1) is Element of the carrier of K
C ~ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
(C ~) * B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
B ~ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
((C ~) * B2) * (B ~) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
width (((C ~) * B2) * (B ~)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
width ((B * B3) * C) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Line (((B * B3) * C),1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width ((B * B3) * C)) FinSequence-like FinSubsequence-like Element of (width ((B * B3) * C)) -tuples_on the carrier of K
(width ((B * B3) * C)) -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
len (Line (((B * B3) * C),1)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(K,(B2 + 1),1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
Replace (((B2 + 1) |-> (0. K)),1,(1. K)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of K
F is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(Line (((B * B3) * C),1)) . F is set
(K,(B2 + 1),1) . F is set
Seg (width ((B * B3) * C)) is V28() V35( width ((B * B3) * C)) Element of bool NAT
((B * B3) * C) * (1,F) is Element of the carrier of K
<*(0. K)*> is Relation-like NAT -defined the carrier of K -valued Function-like non empty trivial V28() V35(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of K
len <*(0. K)*> is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
B3 * C is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
len (B3 * C) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
F is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2,B2, the carrier of K
Indices F is set
dom F is Element of bool NAT
width F is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width F) is V28() V35( width F) Element of bool NAT
[:(dom F),(Seg (width F)):] is Relation-like set
len F is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
len C is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
G is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2,B2, the carrier of K
Indices G is set
dom G is Element of bool NAT
width G is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width G) is V28() V35( width G) Element of bool NAT
[:(dom G),(Seg (width G)):] is Relation-like set
len ((B * B3) * C) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(((C ~) * B2) * (B ~)) * ((B * B3) * C) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
B * (B3 * C) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
(((C ~) * B2) * (B ~)) * (B * (B3 * C)) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
(((C ~) * B2) * (B ~)) * B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
((((C ~) * B2) * (B ~)) * B) * (B3 * C) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
(B ~) * B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
((C ~) * B2) * ((B ~) * B) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
(((C ~) * B2) * ((B ~) * B)) * (B3 * C) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
((C ~) * B2) * (1. (K,(B2 + 1))) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
(((C ~) * B2) * (1. (K,(B2 + 1)))) * (B3 * C) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
(1. (K,(B2 + 1))) * (B3 * C) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
((C ~) * B2) * ((1. (K,(B2 + 1))) * (B3 * C)) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
((C ~) * B2) * (B3 * C) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
((C ~) * B2) * B3 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
(((C ~) * B2) * B3) * C is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
(C ~) * (1. (K,(B2 + 1))) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
((C ~) * (1. (K,(B2 + 1)))) * C is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
(1. (K,(B2 + 1))) * C is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
(C ~) * ((1. (K,(B2 + 1))) * C) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
(C ~) * C is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
len (K,(B2 + 1),1) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
G2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(((C ~) * B2) * (B ~)) * (G2,1) is Element of the carrier of K
(1. (K,(B2 + 1))) * (G2,1) is Element of the carrier of K
Col (((B * B3) * C),1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( len ((B * B3) * C)) FinSequence-like FinSubsequence-like Element of (len ((B * B3) * C)) -tuples_on the carrier of K
(len ((B * B3) * C)) -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
len (Col (((B * B3) * C),1)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B4 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(Col (((B * B3) * C),1)) . B4 is set
(K,(B2 + 1),1) . B4 is set
((B * B3) * C) * (B4,1) is Element of the carrier of K
((B * B3) * C) * (B4,1) is Element of the carrier of K
((B * B3) * C) * (B4,1) is Element of the carrier of K
((B * B3) * C) * (B4,1) is Element of the carrier of K
Seg (len ((B * B3) * C)) is V28() V35( len ((B * B3) * C)) Element of bool NAT
dom ((B * B3) * C) is Element of bool NAT
Line ((((C ~) * B2) * (B ~)),G2) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width (((C ~) * B2) * (B ~))) FinSequence-like FinSubsequence-like Element of (width (((C ~) * B2) * (B ~))) -tuples_on the carrier of K
(width (((C ~) * B2) * (B ~))) -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
len (Line ((((C ~) * B2) * (B ~)),G2)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (((C ~) * B2) * (B ~))) is V28() V35( width (((C ~) * B2) * (B ~))) Element of bool NAT
[G2,1] is set
Indices ((((C ~) * B2) * (B ~)) * ((B * B3) * C)) is set
dom ((((C ~) * B2) * (B ~)) * ((B * B3) * C)) is Element of bool NAT
width ((((C ~) * B2) * (B ~)) * ((B * B3) * C)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width ((((C ~) * B2) * (B ~)) * ((B * B3) * C))) is V28() V35( width ((((C ~) * B2) * (B ~)) * ((B * B3) * C))) Element of bool NAT
[:(dom ((((C ~) * B2) * (B ~)) * ((B * B3) * C))),(Seg (width ((((C ~) * B2) * (B ~)) * ((B * B3) * C)))):] is Relation-like set
((((C ~) * B2) * (B ~)) * ((B * B3) * C)) * (G2,1) is Element of the carrier of K
(Line ((((C ~) * B2) * (B ~)),G2)) "*" (Col (((B * B3) * C),1)) is Element of the carrier of K
(Line ((((C ~) * B2) * (B ~)),G2)) "*" (K,(B2 + 1),1) is Element of the carrier of K
(Line ((((C ~) * B2) * (B ~)),G2)) . 1 is set
G * F is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2,B2, the carrier of K
G2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B4 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(G * F) * (G2,B4) is Element of the carrier of K
IFEQ (G2,B4,(1. K),(0. K)) is Element of the carrier of K
[G2,B4] is set
Indices (G * F) is set
dom (G * F) is Element of bool NAT
width (G * F) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (G * F)) is V28() V35( width (G * F)) Element of bool NAT
[:(dom (G * F)),(Seg (width (G * F))):] is Relation-like set
dom <*(0. K)*> is non empty trivial V35(1) Element of bool NAT
B4 + 1 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
Col (((B * B3) * C),(B4 + 1)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( len ((B * B3) * C)) FinSequence-like FinSubsequence-like Element of (len ((B * B3) * C)) -tuples_on the carrier of K
(len ((B * B3) * C)) -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
((B * B3) * C) * (1,(B4 + 1)) is Element of the carrier of K
i is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(Col (((B * B3) * C),(B4 + 1))) . i is set
<*(0. K)*> . i is set
Seg (len <*(0. K)*>) is non empty V28() V35( len <*(0. K)*>) Element of bool NAT
Seg (len ((B * B3) * C)) is V28() V35( len ((B * B3) * C)) Element of bool NAT
dom ((B * B3) * C) is Element of bool NAT
Col (F,B4) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( len F) FinSequence-like FinSubsequence-like Element of (len F) -tuples_on the carrier of K
(len F) -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
len (Col (F,B4)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
G2 + 1 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
Line ((((C ~) * B2) * (B ~)),(G2 + 1)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width (((C ~) * B2) * (B ~))) FinSequence-like FinSubsequence-like Element of (width (((C ~) * B2) * (B ~))) -tuples_on the carrier of K
(width (((C ~) * B2) * (B ~))) -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
i is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(Line ((((C ~) * B2) * (B ~)),(G2 + 1))) . i is set
<*(0. K)*> . i is set
1 + B2 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
[(G2 + 1),1] is set
(((C ~) * B2) * (B ~)) * ((G2 + 1),1) is Element of the carrier of K
(1. (K,(B2 + 1))) * ((G2 + 1),1) is Element of the carrier of K
Seg (len <*(0. K)*>) is non empty V28() V35( len <*(0. K)*>) Element of bool NAT
Seg (width (((C ~) * B2) * (B ~))) is V28() V35( width (((C ~) * B2) * (B ~))) Element of bool NAT
dom (Col (F,B4)) is V35( len F) Element of bool NAT
j is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(len <*(0. K)*>) + j is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
(Col (((B * B3) * C),(B4 + 1))) . ((len <*(0. K)*>) + j) is set
(Col (F,B4)) . j is set
i is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
i -' 1 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Col (F,(i -' 1)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( len F) FinSequence-like FinSubsequence-like Element of (len F) -tuples_on the carrier of K
len (Col (F,(i -' 1))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (len (Col (F,(i -' 1)))) is V28() V35( len (Col (F,(i -' 1)))) Element of bool NAT
j + 1 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
dom ((B * B3) * C) is Element of bool NAT
[j,B4] is set
[j,(i -' 1)] is set
(i -' 1) + 1 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
((B * B3) * C) * ((j + 1),((i -' 1) + 1)) is Element of the carrier of K
F * (j,(i -' 1)) is Element of the carrier of K
Seg B2 is V28() V35(B2) Element of bool NAT
(Col (F,(i -' 1))) . j is set
Line (G,G2) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width G) FinSequence-like FinSubsequence-like Element of (width G) -tuples_on the carrier of K
(width G) -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
len (Line (G,G2)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(len <*(0. K)*>) + B2 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
dom (Line (G,G2)) is V35( width G) Element of bool NAT
i is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(len <*(0. K)*>) + i is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
(Line ((((C ~) * B2) * (B ~)),(G2 + 1))) . ((len <*(0. K)*>) + i) is set
(Line (G,G2)) . i is set
i + 1 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
Seg (len (Line (G,G2))) is V28() V35( len (Line (G,G2))) Element of bool NAT
[G2,i] is set
(((C ~) * B2) * (B ~)) * ((G2 + 1),(i + 1)) is Element of the carrier of K
G * (G2,i) is Element of the carrier of K
Seg B2 is V28() V35(B2) Element of bool NAT
Seg (width (((C ~) * B2) * (B ~))) is V28() V35( width (((C ~) * B2) * (B ~))) Element of bool NAT
(Line ((((C ~) * B2) * (B ~)),(G2 + 1))) . (i + 1) is set
len (Line ((((C ~) * B2) * (B ~)),(G2 + 1))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
dom (Line ((((C ~) * B2) * (B ~)),(G2 + 1))) is V35( width (((C ~) * B2) * (B ~))) Element of bool NAT
(len <*(0. K)*>) + (len (Line (G,G2))) is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
Seg ((len <*(0. K)*>) + (len (Line (G,G2)))) is non empty V28() V35((len <*(0. K)*>) + (len (Line (G,G2)))) Element of bool NAT
<*(0. K)*> ^ (Line (G,G2)) is Relation-like NAT -defined the carrier of K -valued Function-like non empty V28() V35(1 + (width G)) FinSequence-like FinSubsequence-like FinSequence of the carrier of K
1 + (width G) is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
[(G2 + 1),(B4 + 1)] is set
(1. (K,(B2 + 1))) * ((G2 + 1),(B4 + 1)) is Element of the carrier of K
[(G2 + 1),(B4 + 1)] is set
(1. (K,(B2 + 1))) * ((G2 + 1),(B4 + 1)) is Element of the carrier of K
(1. (K,(B2 + 1))) * ((G2 + 1),(B4 + 1)) is Element of the carrier of K
(1. (K,(B2 + 1))) * ((G2 + 1),(B4 + 1)) is Element of the carrier of K
len (Col (((B * B3) * C),(B4 + 1))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
dom (Col (((B * B3) * C),(B4 + 1))) is V35( len ((B * B3) * C)) Element of bool NAT
(len <*(0. K)*>) + (len (Col (F,B4))) is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
Seg ((len <*(0. K)*>) + (len (Col (F,B4)))) is non empty V28() V35((len <*(0. K)*>) + (len (Col (F,B4)))) Element of bool NAT
<*(0. K)*> ^ (Col (F,B4)) is Relation-like NAT -defined the carrier of K -valued Function-like non empty V28() V35(1 + (len F)) FinSequence-like FinSubsequence-like FinSequence of the carrier of K
1 + (len F) is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
[(G2 + 1),(B4 + 1)] is set
Indices ((((C ~) * B2) * (B ~)) * ((B * B3) * C)) is set
dom ((((C ~) * B2) * (B ~)) * ((B * B3) * C)) is Element of bool NAT
width ((((C ~) * B2) * (B ~)) * ((B * B3) * C)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width ((((C ~) * B2) * (B ~)) * ((B * B3) * C))) is V28() V35( width ((((C ~) * B2) * (B ~)) * ((B * B3) * C))) Element of bool NAT
[:(dom ((((C ~) * B2) * (B ~)) * ((B * B3) * C))),(Seg (width ((((C ~) * B2) * (B ~)) * ((B * B3) * C)))):] is Relation-like set
((((C ~) * B2) * (B ~)) * ((B * B3) * C)) * ((G2 + 1),(B4 + 1)) is Element of the carrier of K
(Line ((((C ~) * B2) * (B ~)),(G2 + 1))) "*" (Col (((B * B3) * C),(B4 + 1))) is Element of the carrier of K
<*(0. K)*> "*" <*(0. K)*> is Element of the carrier of K
(Line (G,G2)) "*" (Col (F,B4)) is Element of the carrier of K
(<*(0. K)*> "*" <*(0. K)*>) + ((Line (G,G2)) "*" (Col (F,B4))) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . ((<*(0. K)*> "*" <*(0. K)*>),((Line (G,G2)) "*" (Col (F,B4)))) is Element of the carrier of K
(0. K) + ((Line (G,G2)) "*" (Col (F,B4))) is Element of the carrier of K
the addF of K . ((0. K),((Line (G,G2)) "*" (Col (F,B4)))) is Element of the carrier of K
G2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2,B2, the carrier of K
F * G2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2,B2, the carrier of K
len G2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
B4 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
Indices B4 is set
dom B4 is Element of bool NAT
width B4 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width B4) is V28() V35( width B4) Element of bool NAT
[:(dom B4),(Seg (width B4)):] is Relation-like set
len B4 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Col (B4,1) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( len B4) FinSequence-like FinSubsequence-like Element of (len B4) -tuples_on the carrier of K
(len B4) -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
len (Col (B4,1)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
i is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(Col (B4,1)) . i is set
(K,(B2 + 1),1) . i is set
[i,1] is set
B4 * (i,1) is Element of the carrier of K
IFEQ (1,1,(1. K),(0. K)) is Element of the carrier of K
i -' 1 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
1 -' 1 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
G2 * ((i -' 1),(1 -' 1)) is Element of the carrier of K
IFEQ (1,1,(0. K),(G2 * ((i -' 1),(1 -' 1)))) is Element of the carrier of K
IFEQ (i,1,(IFEQ (1,1,(1. K),(0. K))),(IFEQ (1,1,(0. K),(G2 * ((i -' 1),(1 -' 1)))))) is Element of the carrier of K
B4 * (i,1) is Element of the carrier of K
IFEQ (1,1,(1. K),(0. K)) is Element of the carrier of K
i -' 1 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
1 -' 1 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
G2 * ((i -' 1),(1 -' 1)) is Element of the carrier of K
IFEQ (1,1,(0. K),(G2 * ((i -' 1),(1 -' 1)))) is Element of the carrier of K
IFEQ (i,1,(IFEQ (1,1,(1. K),(0. K))),(IFEQ (1,1,(0. K),(G2 * ((i -' 1),(1 -' 1)))))) is Element of the carrier of K
((B * B3) * C) * B4 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
width (((B * B3) * C) * B4) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Indices (((B * B3) * C) * B4) is set
dom (((B * B3) * C) * B4) is Element of bool NAT
Seg (width (((B * B3) * C) * B4)) is V28() V35( width (((B * B3) * C) * B4)) Element of bool NAT
[:(dom (((B * B3) * C) * B4)),(Seg (width (((B * B3) * C) * B4))):] is Relation-like set
len (K,(B2 + 1),1) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
i is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
j is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
[i,j] is set
(((B * B3) * C) * B4) * (i,j) is Element of the carrier of K
(1. (K,(B2 + 1))) * (i,j) is Element of the carrier of K
i -' 1 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Line (F,(i -' 1)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width F) FinSequence-like FinSubsequence-like Element of (width F) -tuples_on the carrier of K
(width F) -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
len (Line (F,(i -' 1))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
j -' 1 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Col (G2,(j -' 1)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( len G2) FinSequence-like FinSubsequence-like Element of (len G2) -tuples_on the carrier of K
(len G2) -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
len (Col (G2,(j -' 1))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Line (((B * B3) * C),i) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width ((B * B3) * C)) FinSequence-like FinSubsequence-like Element of (width ((B * B3) * C)) -tuples_on the carrier of K
len (Line (((B * B3) * C),i)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Col (B4,j) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( len B4) FinSequence-like FinSubsequence-like Element of (len B4) -tuples_on the carrier of K
len (Col (B4,j)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
i0 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Line (((B * B3) * C),i0) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width ((B * B3) * C)) FinSequence-like FinSubsequence-like Element of (width ((B * B3) * C)) -tuples_on the carrier of K
j0 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Col (B4,j0) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( len B4) FinSequence-like FinSubsequence-like Element of (len B4) -tuples_on the carrier of K
(Line (((B * B3) * C),i0)) "*" (Col (B4,j0)) is Element of the carrier of K
i0 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Line (((B * B3) * C),i0) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width ((B * B3) * C)) FinSequence-like FinSubsequence-like Element of (width ((B * B3) * C)) -tuples_on the carrier of K
j0 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Col (B4,j0) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( len B4) FinSequence-like FinSubsequence-like Element of (len B4) -tuples_on the carrier of K
(Line (((B * B3) * C),i0)) "*" (Col (B4,j0)) is Element of the carrier of K
(K,(B2 + 1),1) "*" (Col (B4,j0)) is Element of the carrier of K
(Col (B4,j0)) "*" (K,(B2 + 1),1) is Element of the carrier of K
(Col (B4,j0)) . 1 is set
B4 * (1,j) is Element of the carrier of K
IFEQ (j,1,(1. K),(0. K)) is Element of the carrier of K
G2 * ((i -' 1),(j -' 1)) is Element of the carrier of K
IFEQ (j,1,(0. K),(G2 * ((i -' 1),(j -' 1)))) is Element of the carrier of K
IFEQ (i,1,(IFEQ (j,1,(1. K),(0. K))),(IFEQ (j,1,(0. K),(G2 * ((i -' 1),(j -' 1)))))) is Element of the carrier of K
1 + 1 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
Seg (width ((B * B3) * C)) is V28() V35( width ((B * B3) * C)) Element of bool NAT
i0 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Line (((B * B3) * C),i0) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width ((B * B3) * C)) FinSequence-like FinSubsequence-like Element of (width ((B * B3) * C)) -tuples_on the carrier of K
j0 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Col (B4,j0) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( len B4) FinSequence-like FinSubsequence-like Element of (len B4) -tuples_on the carrier of K
(Line (((B * B3) * C),i0)) "*" (Col (B4,j0)) is Element of the carrier of K
(Line (((B * B3) * C),i)) "*" (K,(B2 + 1),1) is Element of the carrier of K
(Line (((B * B3) * C),i)) . 1 is set
((B * B3) * C) * (i0,1) is Element of the carrier of K
j - 1 is V47() V48() ext-real set
i - 1 is V47() V48() ext-real set
Seg B2 is V28() V35(B2) Element of bool NAT
dom (Line (F,(i -' 1))) is V35( width F) Element of bool NAT
(i -' 1) + 1 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
Line (((B * B3) * C),((i -' 1) + 1)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( width ((B * B3) * C)) FinSequence-like FinSubsequence-like Element of (width ((B * B3) * C)) -tuples_on the carrier of K
k2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(len <*(0. K)*>) + k2 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
(Line (((B * B3) * C),((i -' 1) + 1))) . ((len <*(0. K)*>) + k2) is set
(Line (F,(i -' 1))) . k2 is set
Seg (len (Line (F,(i -' 1)))) is V28() V35( len (Line (F,(i -' 1)))) Element of bool NAT
k2 + 1 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
Seg (width ((B * B3) * C)) is V28() V35( width ((B * B3) * C)) Element of bool NAT
[(i -' 1),k2] is set
((B * B3) * C) * (((i -' 1) + 1),(k2 + 1)) is Element of the carrier of K
F * ((i -' 1),k2) is Element of the carrier of K
(Line (((B * B3) * C),((i -' 1) + 1))) . (k2 + 1) is set
dom <*(0. K)*> is non empty trivial V35(1) Element of bool NAT
k2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(Line (((B * B3) * C),((i -' 1) + 1))) . k2 is set
<*(0. K)*> . k2 is set
Seg (len <*(0. K)*>) is non empty V28() V35( len <*(0. K)*>) Element of bool NAT
i0 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
((B * B3) * C) * (i0,1) is Element of the carrier of K
Seg (width ((B * B3) * C)) is V28() V35( width ((B * B3) * C)) Element of bool NAT
(Line (((B * B3) * C),i)) . k2 is set
dom (Line (((B * B3) * C),((i -' 1) + 1))) is V35( width ((B * B3) * C)) Element of bool NAT
(len <*(0. K)*>) + (len (Line (F,(i -' 1)))) is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
Seg ((len <*(0. K)*>) + (len (Line (F,(i -' 1))))) is non empty V28() V35((len <*(0. K)*>) + (len (Line (F,(i -' 1))))) Element of bool NAT
<*(0. K)*> ^ (Line (F,(i -' 1))) is Relation-like NAT -defined the carrier of K -valued Function-like non empty V28() V35(1 + (width F)) FinSequence-like FinSubsequence-like FinSequence of the carrier of K
1 + (width F) is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
(j -' 1) + 1 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
(j - 1) + 1 is V47() V48() ext-real set
[(i -' 1),(j -' 1)] is set
[:(Seg B2),(Seg B2):] is Relation-like set
Indices (F * G2) is set
dom (F * G2) is Element of bool NAT
width (F * G2) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (F * G2)) is V28() V35( width (F * G2)) Element of bool NAT
[:(dom (F * G2)),(Seg (width (F * G2))):] is Relation-like set
Col (B4,((j -' 1) + 1)) is Relation-like NAT -defined the carrier of K -valued Function-like V28() V35( len B4) FinSequence-like FinSubsequence-like Element of (len B4) -tuples_on the carrier of K
1 + B2 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
[1,j] is set
B4 * (1,j) is Element of the carrier of K
IFEQ (j,1,(1. K),(0. K)) is Element of the carrier of K
1 -' 1 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
G2 * ((1 -' 1),(j -' 1)) is Element of the carrier of K
IFEQ (j,1,(0. K),(G2 * ((1 -' 1),(j -' 1)))) is Element of the carrier of K
IFEQ (1,1,(IFEQ (j,1,(1. K),(0. K))),(IFEQ (j,1,(0. K),(G2 * ((1 -' 1),(j -' 1)))))) is Element of the carrier of K
k2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(Col (B4,((j -' 1) + 1))) . k2 is set
<*(0. K)*> . k2 is set
Seg (len <*(0. K)*>) is non empty V28() V35( len <*(0. K)*>) Element of bool NAT
Seg (len B4) is V28() V35( len B4) Element of bool NAT
(Col (B4,j)) . k2 is set
dom (Col (G2,(j -' 1))) is V35( len G2) Element of bool NAT
k2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative set
(len <*(0. K)*>) + k2 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
(Col (B4,((j -' 1) + 1))) . ((len <*(0. K)*>) + k2) is set
(Col (G2,(j -' 1))) . k2 is set
k2 + 1 is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
dom G2 is Element of bool NAT
[(k2 + 1),j] is set
B4 * ((k2 + 1),j) is Element of the carrier of K
IFEQ (j,1,(1. K),(0. K)) is Element of the carrier of K
(k2 + 1) -' 1 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
G2 * (((k2 + 1) -' 1),(j -' 1)) is Element of the carrier of K
IFEQ (j,1,(0. K),(G2 * (((k2 + 1) -' 1),(j -' 1)))) is Element of the carrier of K
IFEQ ((k2 + 1),1,(IFEQ (j,1,(1. K),(0. K))),(IFEQ (j,1,(0. K),(G2 * (((k2 + 1) -' 1),(j -' 1)))))) is Element of the carrier of K
G2 * (k2,(j -' 1)) is Element of the carrier of K
B4 * ((k2 + 1),((j -' 1) + 1)) is Element of the carrier of K
(Col (B4,((j -' 1) + 1))) . (k2 + 1) is set
dom (Col (B4,((j -' 1) + 1))) is V35( len B4) Element of bool NAT
len (Col (B4,((j -' 1) + 1))) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (len (Col (B4,((j -' 1) + 1)))) is V28() V35( len (Col (B4,((j -' 1) + 1)))) Element of bool NAT
(len <*(0. K)*>) + (len (Col (G2,(j -' 1)))) is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
Seg ((len <*(0. K)*>) + (len (Col (G2,(j -' 1))))) is non empty V28() V35((len <*(0. K)*>) + (len (Col (G2,(j -' 1))))) Element of bool NAT
<*(0. K)*> ^ (Col (G2,(j -' 1))) is Relation-like NAT -defined the carrier of K -valued Function-like non empty V28() V35(1 + (len G2)) FinSequence-like FinSubsequence-like FinSequence of the carrier of K
1 + (len G2) is non empty V21() V22() V23() V27() V28() V33() V47() V48() ext-real positive non negative Element of NAT
(i - 1) + 1 is V47() V48() ext-real set
(Line (((B * B3) * C),((i -' 1) + 1))) "*" (Col (B4,((j -' 1) + 1))) is Element of the carrier of K
<*(0. K)*> "*" <*(0. K)*> is Element of the carrier of K
(Line (F,(i -' 1))) "*" (Col (G2,(j -' 1))) is Element of the carrier of K
(<*(0. K)*> "*" <*(0. K)*>) + ((Line (F,(i -' 1))) "*" (Col (G2,(j -' 1)))) is Element of the carrier of K
the addF of K is Relation-like Function-like V18([: 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 . ((<*(0. K)*> "*" <*(0. K)*>),((Line (F,(i -' 1))) "*" (Col (G2,(j -' 1))))) is Element of the carrier of K
(0. K) + ((Line (F,(i -' 1))) "*" (Col (G2,(j -' 1)))) is Element of the carrier of K
the addF of K . ((0. K),((Line (F,(i -' 1))) "*" (Col (G2,(j -' 1))))) is Element of the carrier of K
(F * G2) * ((i -' 1),(j -' 1)) is Element of the carrier of K
(0. K) + ((F * G2) * ((i -' 1),(j -' 1))) is Element of the carrier of K
the addF of K . ((0. K),((F * G2) * ((i -' 1),(j -' 1)))) is Element of the carrier of K
(1. (K,B2)) * ((i -' 1),(j -' 1)) is Element of the carrier of K
Indices (1. (K,B2)) is set
dom (1. (K,B2)) is Element of bool NAT
width (1. (K,B2)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
Seg (width (1. (K,B2))) is V28() V35( width (1. (K,B2))) Element of bool NAT
[:(dom (1. (K,B2))),(Seg (width (1. (K,B2)))):] is Relation-like set
i0 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
j0 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(1. (K,(B2 + 1))) * (i0,j0) is Element of the carrier of K
i0 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
i0 -' 1 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
j0 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
j0 -' 1 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(1. (K,B2)) * ((i0 -' 1),(j0 -' 1)) is Element of the carrier of K
width (B ~) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(B ~) * (((B * B3) * C) * B4) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
((B ~) * (((B * B3) * C) * B4)) * B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
C * B4 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
(B * B3) * (C * B4) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
(B ~) * ((B * B3) * (C * B4)) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
((B ~) * ((B * B3) * (C * B4))) * B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
B3 * (C * B4) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
B * (B3 * (C * B4)) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
(B ~) * (B * (B3 * (C * B4))) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
((B ~) * (B * (B3 * (C * B4)))) * B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
((B ~) * B) * (B3 * (C * B4)) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
(((B ~) * B) * (B3 * (C * B4))) * B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
len (B3 * (C * B4)) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(1. (K,(B2 + 1))) * (B3 * (C * B4)) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
((1. (K,(B2 + 1))) * (B3 * (C * B4))) * B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
(B3 * (C * B4)) * B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
(C * B4) * B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
B3 * ((C * B4) * B) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
B3 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
B2 * B3 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of B2 + 1,B2 + 1, the carrier of K
1. (K,0) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of 0 , 0 , the carrier of K
B3 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of 0 , 0 , the carrier of K
B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of 0 , 0 , the carrier of K
B3 * B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of 0 , 0 , the carrier of K
0. (K,0) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of 0 , 0 , the carrier of K
0 -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
0. K is V83(K) Element of the carrier of K
0 |-> (0. K) is Relation-like non-empty empty-yielding NAT -defined the carrier of K -valued Function-like functional empty V21() V22() V23() V25() V26() V27() V28() V33() V35( 0 ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V40() V47() V48() ext-real non positive non negative Element of 0 -tuples_on the carrier of K
0 |-> (0 |-> (0. K)) is Relation-like non-empty empty-yielding NAT -defined 0 -tuples_on the carrier of K -valued Function-like functional empty V21() V22() V23() V25() V26() V27() V28() V33() V35( 0 ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V40() V47() V48() ext-real non positive non negative Element of 0 -tuples_on (0 -tuples_on the carrier of K)
0 -tuples_on (0 -tuples_on the carrier of K) is functional non empty FinSequence-membered FinSequenceSet of 0 -tuples_on the carrier of K
B2 * (0. (K,0)) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of 0 , 0 , the carrier of K
B3 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of 0 , 0 , the carrier of K
B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of 0 , 0 , the carrier of K
B3 * B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of 0 , 0 , the carrier of K
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
1. (K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B * A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A * B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A * B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
width A is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
len B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
width B is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
(A * B) @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(B @) * (A @) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(A @) * B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
width (A @) is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
len B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
width B2 is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
((A @) * B2) @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B2 @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(A @) @ is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(B2 @) * ((A @) @) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(B2 @) * A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A * A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
1. (K,0) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of 0 , 0 , the carrier of K
B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B * A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A * B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
n is V21() V22() V23() V27() V28() V33() V47() V48() ext-real non negative Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible V154() V155() V156() unital V186() V188() right-distributive left-distributive right_unital well-unital V196() left_unital doubleLoopStr
the carrier of K is non empty non trivial set
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
1. (K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A * B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B2 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B2 * A is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B2 * (1. (K,n)) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(B2 * A) * B is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B3 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
B * B3 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
(1. (K,n)) * B3 is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K
A * (B * B3) is Relation-like NAT -defined the carrier of K * -valued Function-like V28() FinSequence-like FinSubsequence-like Function-yielding V40() tabular Matrix of n,n, the carrier of K