:: MATRIX_3 semantic presentation

REAL is set

NAT is non empty non trivial V34() V35() V36() V48() V53() V54() Element of bool REAL

bool REAL is non empty cup-closed diff-closed preBoolean set

{} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V34() V35() V36() V38() V39() V40() V41() ext-real non positive non negative V45() V48() V49() V52() V53() V55( {} ) FinSequence-like FinSubsequence-like FinSequence-membered set

COMPLEX is set

NAT is non empty non trivial V34() V35() V36() V48() V53() V54() set

bool NAT is non empty non trivial cup-closed diff-closed preBoolean V48() set

bool NAT is non empty non trivial cup-closed diff-closed preBoolean V48() set

Fin NAT is non empty cup-closed diff-closed preBoolean set

1 is non empty V34() V35() V36() V40() V41() ext-real positive non negative V45() V48() V53() Element of NAT

[:1,1:] is Relation-like non empty V48() set

bool [:1,1:] is non empty cup-closed diff-closed preBoolean V48() V52() set

[:[:1,1:],1:] is Relation-like non empty V48() set

bool [:[:1,1:],1:] is non empty cup-closed diff-closed preBoolean V48() V52() set

2 is non empty V34() V35() V36() V40() V41() ext-real positive non negative V45() V48() V53() Element of NAT

{{},1} is non empty V48() V52() set

3 is non empty V34() V35() V36() V40() V41() ext-real positive non negative V45() V48() V53() Element of NAT

0 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V34() V35() V36() V38() V39() V40() V41() ext-real non positive non negative V45() V48() V49() V52() V53() V55( {} ) FinSequence-like FinSubsequence-like FinSequence-membered Element of NAT

Seg 1 is non empty trivial V48() V55(1) Element of bool NAT

{1} is non empty trivial V48() V52() V55(1) set

Seg 2 is non empty V48() V55(2) Element of bool NAT

{1,2} is non empty V48() V52() set

[1,1] is V23() set

Permutations 1 is non empty permutational set

idseq 1 is Relation-like NAT -defined Function-like constant non empty trivial V48() V55(1) FinSequence-like FinSubsequence-like set

id (Seg 1) is Relation-like Seg 1 -defined Seg 1 -valued V6() V8() V9() V13() Function-like one-to-one non empty total V26( Seg 1, Seg 1) V27( Seg 1) V28( Seg 1, Seg 1) V48() Element of bool [:(Seg 1),(Seg 1):]

[:(Seg 1),(Seg 1):] is Relation-like non empty V48() set

bool [:(Seg 1),(Seg 1):] is non empty cup-closed diff-closed preBoolean V48() V52() set

{(idseq 1)} is functional non empty trivial V48() V52() V55(1) set

M is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

n is non empty non degenerated non trivial right_complementable almost_left_invertible V111() V123() associative commutative Abelian add-associative right_zeroed right-distributive left-distributive right_unital well-unital V144() left_unital doubleLoopStr

the carrier of n is non empty non trivial set

M -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

{ b

K is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

0. n is V68(n) Element of the carrier of n

M |-> (0. n) is Relation-like NAT -defined the carrier of n -valued Function-like V48() V55(M) FinSequence-like FinSubsequence-like Element of M -tuples_on the carrier of n

Seg M is V48() V55(M) Element of bool NAT

(Seg M) --> (0. n) is Relation-like Seg M -defined {(0. n)} -valued Function-like total V26( Seg M,{(0. n)}) V48() FinSequence-like FinSubsequence-like Element of bool [:(Seg M),{(0. n)}:]

{(0. n)} is non empty trivial V48() V55(1) set

[:(Seg M),{(0. n)}:] is Relation-like V48() set

bool [:(Seg M),{(0. n)}:] is non empty cup-closed diff-closed preBoolean V48() V52() set

K |-> (M |-> (0. n)) is Relation-like NAT -defined M -tuples_on the carrier of n -valued Function-like V48() V55(K) FinSequence-like FinSubsequence-like Element of K -tuples_on (M -tuples_on the carrier of n)

K -tuples_on (M -tuples_on the carrier of n) is functional non empty FinSequence-membered FinSequenceSet of M -tuples_on the carrier of n

(M -tuples_on the carrier of n) * is functional non empty FinSequence-membered FinSequenceSet of M -tuples_on the carrier of n

{ b

Seg K is V48() V55(K) Element of bool NAT

(Seg K) --> (M |-> (0. n)) is Relation-like Seg K -defined {(M |-> (0. n))} -valued Function-like total V26( Seg K,{(M |-> (0. n))}) V48() FinSequence-like FinSubsequence-like Element of bool [:(Seg K),{(M |-> (0. n))}:]

{(M |-> (0. n))} is functional non empty trivial V48() V52() V55(1) set

[:(Seg K),{(M |-> (0. n))}:] is Relation-like V48() set

bool [:(Seg K),{(M |-> (0. n))}:] is non empty cup-closed diff-closed preBoolean V48() V52() set

n is non empty non degenerated non trivial right_complementable almost_left_invertible V111() V123() associative commutative Abelian add-associative right_zeroed right-distributive left-distributive right_unital well-unital V144() 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 V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

len K is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width K is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Indices K is set

dom K is V48() Element of bool NAT

Seg (width K) is V48() V55( width K) Element of bool NAT

[:(dom K),(Seg (width K)):] is Relation-like V48() set

p1 is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular Matrix of len K, width K, the carrier of n

Indices p1 is set

dom p1 is V48() Element of bool NAT

width p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Seg (width p1) is V48() V55( width p1) Element of bool NAT

[:(dom p1),(Seg (width p1)):] is Relation-like V48() set

p2 is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular Matrix of len K, width K, the carrier of n

Indices p2 is set

dom p2 is V48() Element of bool NAT

width p2 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Seg (width p2) is V48() V55( width p2) Element of bool NAT

[:(dom p2),(Seg (width p2)):] is Relation-like V48() set

Seg (len K) is V48() V55( len K) Element of bool NAT

[:(Seg (len K)),(Seg (width K)):] is Relation-like V48() set

len p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

len p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

len p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

len p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

i is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

len i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

p is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

[p,i] is V23() set

i * (p,i) is Element of the carrier of n

K * (p,i) is Element of the carrier of n

- (K * (p,i)) is Element of the carrier of n

M is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

len M is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width M is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

p1 is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

len p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

i is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular Matrix of len K, width K, the carrier of n

Indices i is set

dom i is V48() Element of bool NAT

width i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Seg (width i) is V48() V55( width i) Element of bool NAT

[:(dom i),(Seg (width i)):] is Relation-like V48() set

Seg (len K) is V48() V55( len K) Element of bool NAT

[:(Seg (len K)),(Seg (width K)):] is Relation-like V48() set

p is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular Matrix of len K, width K, the carrier of n

Indices p is set

dom p is V48() Element of bool NAT

width p is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Seg (width p) is V48() V55( width p) Element of bool NAT

[:(dom p),(Seg (width p)):] is Relation-like V48() set

[:(Seg (len K)),(Seg (width p)):] is Relation-like V48() set

i is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular Matrix of len K, width K, the carrier of n

Indices i is set

dom i is V48() Element of bool NAT

width i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Seg (width i) is V48() V55( width i) Element of bool NAT

[:(dom i),(Seg (width i)):] is Relation-like V48() set

[:(Seg (len K)),(Seg (width i)):] is Relation-like V48() set

len p is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

len i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

j is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

c

[j,c

p * (j,c

K * (j,c

- (K * (j,c

i * (j,c

n is non empty non degenerated non trivial right_complementable almost_left_invertible V111() V123() associative commutative Abelian add-associative right_zeroed right-distributive left-distributive right_unital well-unital V144() 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 V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

len K is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width K is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Indices K is set

dom K is V48() Element of bool NAT

Seg (width K) is V48() V55( width K) Element of bool NAT

[:(dom K),(Seg (width K)):] is Relation-like V48() set

M is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

i is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular Matrix of len K, width K, the carrier of n

Indices i is set

dom i is V48() Element of bool NAT

width i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Seg (width i) is V48() V55( width i) Element of bool NAT

[:(dom i),(Seg (width i)):] is Relation-like V48() set

p2 is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular Matrix of len K, width K, the carrier of n

Indices p2 is set

dom p2 is V48() Element of bool NAT

width p2 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Seg (width p2) is V48() V55( width p2) Element of bool NAT

[:(dom p2),(Seg (width p2)):] is Relation-like V48() set

Seg (len K) is V48() V55( len K) Element of bool NAT

[:(Seg (len K)),(Seg (width K)):] is Relation-like V48() set

len i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

len i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

len i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

len i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

p is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

len p is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width p is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

j is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

[i,j] is V23() set

p * (i,j) is Element of the carrier of n

K * (i,j) is Element of the carrier of n

M * (i,j) is Element of the carrier of n

(K * (i,j)) + (M * (i,j)) is Element of the carrier of n

the addF of n is Relation-like [: the carrier of n, the carrier of n:] -defined the carrier of n -valued Function-like non empty total V26([: the carrier of n, the carrier of n:], the carrier of n) commutative associative 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 non empty set

[:[: the carrier of n, the carrier of n:], the carrier of n:] is Relation-like non empty set

bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is non empty cup-closed diff-closed preBoolean set

the addF of n . ((K * (i,j)),(M * (i,j))) is Element of the carrier of n

[(K * (i,j)),(M * (i,j))] is V23() set

the addF of n . [(K * (i,j)),(M * (i,j))] is set

p2 is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

len p2 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width p2 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

i is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

len i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

j is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular Matrix of len K, width K, the carrier of n

Indices j is set

dom j is V48() Element of bool NAT

width j is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Seg (width j) is V48() V55( width j) Element of bool NAT

[:(dom j),(Seg (width j)):] is Relation-like V48() set

Seg (len K) is V48() V55( len K) Element of bool NAT

[:(Seg (len K)),(Seg (width K)):] is Relation-like V48() set

i is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular Matrix of len K, width K, the carrier of n

Indices i is set

dom i is V48() Element of bool NAT

width i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Seg (width i) is V48() V55( width i) Element of bool NAT

[:(dom i),(Seg (width i)):] is Relation-like V48() set

[:(Seg (len K)),(Seg (width i)):] is Relation-like V48() set

p is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular Matrix of len K, width K, the carrier of n

Indices p is set

dom p is V48() Element of bool NAT

width p is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Seg (width p) is V48() V55( width p) Element of bool NAT

[:(dom p),(Seg (width p)):] is Relation-like V48() set

[:(Seg (len K)),(Seg (width p)):] is Relation-like V48() set

len i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

len p is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

c

h is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

[c

i * (c

K * (c

M * (c

(K * (c

the addF of n is Relation-like [: the carrier of n, the carrier of n:] -defined the carrier of n -valued Function-like non empty total V26([: the carrier of n, the carrier of n:], the carrier of n) commutative associative 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 non empty set

[:[: the carrier of n, the carrier of n:], the carrier of n:] is Relation-like non empty set

bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is non empty cup-closed diff-closed preBoolean set

the addF of n . ((K * (c

[(K * (c

the addF of n . [(K * (c

p * (c

n is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

K is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

M is non empty non degenerated non trivial right_complementable almost_left_invertible V111() V123() associative commutative Abelian add-associative right_zeroed right-distributive left-distributive right_unital well-unital V144() left_unital doubleLoopStr

(M,n,K) is Relation-like NAT -defined the carrier of M * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular Matrix of n,K, the carrier of M

the carrier of M is non empty non trivial set

the carrier of M * is functional non empty FinSequence-membered FinSequenceSet of the carrier of M

K -tuples_on the carrier of M is functional non empty FinSequence-membered FinSequenceSet of the carrier of M

{ b

0. M is V68(M) Element of the carrier of M

K |-> (0. M) is Relation-like NAT -defined the carrier of M -valued Function-like V48() V55(K) FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of M

Seg K is V48() V55(K) Element of bool NAT

(Seg K) --> (0. M) is Relation-like Seg K -defined {(0. M)} -valued Function-like total V26( Seg K,{(0. M)}) V48() FinSequence-like FinSubsequence-like Element of bool [:(Seg K),{(0. M)}:]

{(0. M)} is non empty trivial V48() V55(1) set

[:(Seg K),{(0. M)}:] is Relation-like V48() set

bool [:(Seg K),{(0. M)}:] is non empty cup-closed diff-closed preBoolean V48() V52() set

n |-> (K |-> (0. M)) is Relation-like NAT -defined K -tuples_on the carrier of M -valued Function-like V48() V55(n) FinSequence-like FinSubsequence-like Element of n -tuples_on (K -tuples_on the carrier of M)

n -tuples_on (K -tuples_on the carrier of M) is functional non empty FinSequence-membered FinSequenceSet of K -tuples_on the carrier of M

(K -tuples_on the carrier of M) * is functional non empty FinSequence-membered FinSequenceSet of K -tuples_on the carrier of M

{ b

Seg n is V48() V55(n) Element of bool NAT

(Seg n) --> (K |-> (0. M)) is Relation-like Seg n -defined {(K |-> (0. M))} -valued Function-like total V26( Seg n,{(K |-> (0. M))}) V48() FinSequence-like FinSubsequence-like Element of bool [:(Seg n),{(K |-> (0. M))}:]

{(K |-> (0. M))} is functional non empty trivial V48() V52() V55(1) set

[:(Seg n),{(K |-> (0. M))}:] is Relation-like V48() set

bool [:(Seg n),{(K |-> (0. M))}:] is non empty cup-closed diff-closed preBoolean V48() V52() set

Indices (M,n,K) is set

dom (M,n,K) is V48() Element of bool NAT

width (M,n,K) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Seg (width (M,n,K)) is V48() V55( width (M,n,K)) Element of bool NAT

[:(dom (M,n,K)),(Seg (width (M,n,K))):] is Relation-like V48() set

p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

p2 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

[p1,p2] is V23() set

(M,n,K) * (p1,p2) is Element of the carrier of M

[:(Seg n),(Seg (width (M,n,K))):] is Relation-like V48() set

[:(Seg n),(Seg K):] is Relation-like V48() set

i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

i |-> (0. M) is Relation-like NAT -defined the carrier of M -valued Function-like V48() V55(i) FinSequence-like FinSubsequence-like Element of i -tuples_on the carrier of M

i -tuples_on the carrier of M is functional non empty FinSequence-membered FinSequenceSet of the carrier of M

{ b

Seg i is V48() V55(i) Element of bool NAT

(Seg i) --> (0. M) is Relation-like Seg i -defined {(0. M)} -valued Function-like total V26( Seg i,{(0. M)}) V48() FinSequence-like FinSubsequence-like Element of bool [:(Seg i),{(0. M)}:]

[:(Seg i),{(0. M)}:] is Relation-like V48() set

bool [:(Seg i),{(0. M)}:] is non empty cup-closed diff-closed preBoolean V48() V52() set

(i |-> (0. M)) . p2 is set

(M,n,K) . p1 is Relation-like NAT -defined Function-like V48() FinSequence-like FinSubsequence-like set

n is non empty non degenerated non trivial right_complementable almost_left_invertible V111() V123() associative commutative Abelian add-associative right_zeroed right-distributive left-distributive right_unital well-unital V144() 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 V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

len K is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

M is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

len M is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width K is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width M is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

(n,K,M) is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

(n,M,K) is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

width (n,K,M) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width (n,M,K) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

len (n,K,M) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

dom K is V48() Element of bool NAT

dom (n,K,M) is V48() Element of bool NAT

Indices K is set

Seg (width K) is V48() V55( width K) Element of bool NAT

[:(dom K),(Seg (width K)):] is Relation-like V48() set

Indices (n,K,M) is set

Seg (width (n,K,M)) is V48() V55( width (n,K,M)) Element of bool NAT

[:(dom (n,K,M)),(Seg (width (n,K,M))):] is Relation-like V48() set

dom M is V48() Element of bool NAT

Indices M is set

Seg (width M) is V48() V55( width M) Element of bool NAT

[:(dom M),(Seg (width M)):] is Relation-like V48() set

p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

p2 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

[p1,p2] is V23() set

(n,K,M) * (p1,p2) is Element of the carrier of n

M * (p1,p2) is Element of the carrier of n

K * (p1,p2) is Element of the carrier of n

(M * (p1,p2)) + (K * (p1,p2)) is Element of the carrier of n

the addF of n is Relation-like [: the carrier of n, the carrier of n:] -defined the carrier of n -valued Function-like non empty total V26([: the carrier of n, the carrier of n:], the carrier of n) commutative associative 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 non empty set

[:[: the carrier of n, the carrier of n:], the carrier of n:] is Relation-like non empty set

bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is non empty cup-closed diff-closed preBoolean set

the addF of n . ((M * (p1,p2)),(K * (p1,p2))) is Element of the carrier of n

[(M * (p1,p2)),(K * (p1,p2))] is V23() set

the addF of n . [(M * (p1,p2)),(K * (p1,p2))] is set

(n,M,K) * (p1,p2) is Element of the carrier of n

len (n,M,K) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

n is non empty non degenerated non trivial right_complementable almost_left_invertible V111() V123() associative commutative Abelian add-associative right_zeroed right-distributive left-distributive right_unital well-unital V144() 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 V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

len K is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

M is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

len M is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width K is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width M is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

(n,K,M) is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

p1 is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

(n,(n,K,M),p1) is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

(n,M,p1) is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

(n,K,(n,M,p1)) is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

dom K is V48() Element of bool NAT

dom M is V48() Element of bool NAT

Indices M is set

Seg (width M) is V48() V55( width M) Element of bool NAT

[:(dom M),(Seg (width M)):] is Relation-like V48() set

Seg (width K) is V48() V55( width K) Element of bool NAT

[:(dom K),(Seg (width K)):] is Relation-like V48() set

Indices K is set

width (n,(n,K,M),p1) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width (n,K,M) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

len (n,K,(n,M,p1)) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width (n,K,(n,M,p1)) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

len (n,K,M) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

len (n,(n,K,M),p1) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

dom (n,(n,K,M),p1) is V48() Element of bool NAT

Indices (n,(n,K,M),p1) is set

Seg (width (n,(n,K,M),p1)) is V48() V55( width (n,(n,K,M),p1)) Element of bool NAT

[:(dom (n,(n,K,M),p1)),(Seg (width (n,(n,K,M),p1))):] is Relation-like V48() set

dom (n,K,M) is V48() Element of bool NAT

Indices (n,K,M) is set

Seg (width (n,K,M)) is V48() V55( width (n,K,M)) Element of bool NAT

[:(dom (n,K,M)),(Seg (width (n,K,M))):] is Relation-like V48() set

p2 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

[p2,i] is V23() set

(n,(n,K,M),p1) * (p2,i) is Element of the carrier of n

(n,K,M) * (p2,i) is Element of the carrier of n

p1 * (p2,i) is Element of the carrier of n

((n,K,M) * (p2,i)) + (p1 * (p2,i)) is Element of the carrier of n

the addF of n is Relation-like [: the carrier of n, the carrier of n:] -defined the carrier of n -valued Function-like non empty total V26([: the carrier of n, the carrier of n:], the carrier of n) commutative associative 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 non empty set

[:[: the carrier of n, the carrier of n:], the carrier of n:] is Relation-like non empty set

bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is non empty cup-closed diff-closed preBoolean set

the addF of n . (((n,K,M) * (p2,i)),(p1 * (p2,i))) is Element of the carrier of n

[((n,K,M) * (p2,i)),(p1 * (p2,i))] is V23() set

the addF of n . [((n,K,M) * (p2,i)),(p1 * (p2,i))] is set

K * (p2,i) is Element of the carrier of n

M * (p2,i) is Element of the carrier of n

(K * (p2,i)) + (M * (p2,i)) is Element of the carrier of n

the addF of n . ((K * (p2,i)),(M * (p2,i))) is Element of the carrier of n

[(K * (p2,i)),(M * (p2,i))] is V23() set

the addF of n . [(K * (p2,i)),(M * (p2,i))] is set

((K * (p2,i)) + (M * (p2,i))) + (p1 * (p2,i)) is Element of the carrier of n

the addF of n . (((K * (p2,i)) + (M * (p2,i))),(p1 * (p2,i))) is Element of the carrier of n

[((K * (p2,i)) + (M * (p2,i))),(p1 * (p2,i))] is V23() set

the addF of n . [((K * (p2,i)) + (M * (p2,i))),(p1 * (p2,i))] is set

(M * (p2,i)) + (p1 * (p2,i)) is Element of the carrier of n

the addF of n . ((M * (p2,i)),(p1 * (p2,i))) is Element of the carrier of n

[(M * (p2,i)),(p1 * (p2,i))] is V23() set

the addF of n . [(M * (p2,i)),(p1 * (p2,i))] is set

(K * (p2,i)) + ((M * (p2,i)) + (p1 * (p2,i))) is Element of the carrier of n

the addF of n . ((K * (p2,i)),((M * (p2,i)) + (p1 * (p2,i)))) is Element of the carrier of n

[(K * (p2,i)),((M * (p2,i)) + (p1 * (p2,i)))] is V23() set

the addF of n . [(K * (p2,i)),((M * (p2,i)) + (p1 * (p2,i)))] is set

(n,M,p1) * (p2,i) is Element of the carrier of n

(K * (p2,i)) + ((n,M,p1) * (p2,i)) is Element of the carrier of n

the addF of n . ((K * (p2,i)),((n,M,p1) * (p2,i))) is Element of the carrier of n

[(K * (p2,i)),((n,M,p1) * (p2,i))] is V23() set

the addF of n . [(K * (p2,i)),((n,M,p1) * (p2,i))] is set

(n,K,(n,M,p1)) * (p2,i) is Element of the carrier of n

n is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

K is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

M is non empty non degenerated non trivial right_complementable almost_left_invertible V111() V123() associative commutative Abelian add-associative right_zeroed right-distributive left-distributive right_unital well-unital V144() left_unital doubleLoopStr

the carrier of M is non empty non trivial set

the carrier of M * is functional non empty FinSequence-membered FinSequenceSet of the carrier of M

(M,n,K) is Relation-like NAT -defined the carrier of M * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular Matrix of n,K, the carrier of M

K -tuples_on the carrier of M is functional non empty FinSequence-membered FinSequenceSet of the carrier of M

{ b

0. M is V68(M) Element of the carrier of M

K |-> (0. M) is Relation-like NAT -defined the carrier of M -valued Function-like V48() V55(K) FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of M

Seg K is V48() V55(K) Element of bool NAT

(Seg K) --> (0. M) is Relation-like Seg K -defined {(0. M)} -valued Function-like total V26( Seg K,{(0. M)}) V48() FinSequence-like FinSubsequence-like Element of bool [:(Seg K),{(0. M)}:]

{(0. M)} is non empty trivial V48() V55(1) set

[:(Seg K),{(0. M)}:] is Relation-like V48() set

bool [:(Seg K),{(0. M)}:] is non empty cup-closed diff-closed preBoolean V48() V52() set

n |-> (K |-> (0. M)) is Relation-like NAT -defined K -tuples_on the carrier of M -valued Function-like V48() V55(n) FinSequence-like FinSubsequence-like Element of n -tuples_on (K -tuples_on the carrier of M)

n -tuples_on (K -tuples_on the carrier of M) is functional non empty FinSequence-membered FinSequenceSet of K -tuples_on the carrier of M

(K -tuples_on the carrier of M) * is functional non empty FinSequence-membered FinSequenceSet of K -tuples_on the carrier of M

{ b

Seg n is V48() V55(n) Element of bool NAT

(Seg n) --> (K |-> (0. M)) is Relation-like Seg n -defined {(K |-> (0. M))} -valued Function-like total V26( Seg n,{(K |-> (0. M))}) V48() FinSequence-like FinSubsequence-like Element of bool [:(Seg n),{(K |-> (0. M))}:]

{(K |-> (0. M))} is functional non empty trivial V48() V52() V55(1) set

[:(Seg n),{(K |-> (0. M))}:] is Relation-like V48() set

bool [:(Seg n),{(K |-> (0. M))}:] is non empty cup-closed diff-closed preBoolean V48() V52() set

p1 is Relation-like NAT -defined the carrier of M * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular Matrix of n,K, the carrier of M

(M,p1,(M,n,K)) is Relation-like NAT -defined the carrier of M * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of M *

width p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width (M,p1,(M,n,K)) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Indices p1 is set

dom p1 is V48() Element of bool NAT

Seg (width p1) is V48() V55( width p1) Element of bool NAT

[:(dom p1),(Seg (width p1)):] is Relation-like V48() set

[:(Seg n),(Seg K):] is Relation-like V48() set

len p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

len (M,p1,(M,n,K)) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

dom (M,p1,(M,n,K)) is V48() Element of bool NAT

Indices (M,p1,(M,n,K)) is set

Seg (width (M,p1,(M,n,K))) is V48() V55( width (M,p1,(M,n,K))) Element of bool NAT

[:(dom (M,p1,(M,n,K))),(Seg (width (M,p1,(M,n,K)))):] is Relation-like V48() set

Indices (M,n,K) is set

dom (M,n,K) is V48() Element of bool NAT

width (M,n,K) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Seg (width (M,n,K)) is V48() V55( width (M,n,K)) Element of bool NAT

[:(dom (M,n,K)),(Seg (width (M,n,K))):] is Relation-like V48() set

p2 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

[p2,i] is V23() set

(M,p1,(M,n,K)) * (p2,i) is Element of the carrier of M

p1 * (p2,i) is Element of the carrier of M

(M,n,K) * (p2,i) is Element of the carrier of M

(p1 * (p2,i)) + ((M,n,K) * (p2,i)) is Element of the carrier of M

the addF of M is Relation-like [: the carrier of M, the carrier of M:] -defined the carrier of M -valued Function-like non empty total V26([: the carrier of M, the carrier of M:], the carrier of M) commutative associative Element of bool [:[: the carrier of M, the carrier of M:], the carrier of M:]

[: the carrier of M, the carrier of M:] is Relation-like non empty set

[:[: the carrier of M, the carrier of M:], the carrier of M:] is Relation-like non empty set

bool [:[: the carrier of M, the carrier of M:], the carrier of M:] is non empty cup-closed diff-closed preBoolean set

the addF of M . ((p1 * (p2,i)),((M,n,K) * (p2,i))) is Element of the carrier of M

[(p1 * (p2,i)),((M,n,K) * (p2,i))] is V23() set

the addF of M . [(p1 * (p2,i)),((M,n,K) * (p2,i))] is set

(p1 * (p2,i)) + (0. M) is Element of the carrier of M

the addF of M . ((p1 * (p2,i)),(0. M)) is Element of the carrier of M

[(p1 * (p2,i)),(0. M)] is V23() set

the addF of M . [(p1 * (p2,i)),(0. M)] is set

width p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width (M,p1,(M,n,K)) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

len p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

len (M,p1,(M,n,K)) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

dom p1 is V48() Element of bool NAT

dom (M,p1,(M,n,K)) is V48() Element of bool NAT

Indices p1 is set

Seg (width p1) is V48() V55( width p1) Element of bool NAT

[:(dom p1),(Seg (width p1)):] is Relation-like V48() set

Indices (M,p1,(M,n,K)) is set

Seg (width (M,p1,(M,n,K))) is V48() V55( width (M,p1,(M,n,K))) Element of bool NAT

[:(dom (M,p1,(M,n,K))),(Seg (width (M,p1,(M,n,K)))):] is Relation-like V48() set

p2 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

[p2,i] is V23() set

(M,p1,(M,n,K)) * (p2,i) is Element of the carrier of M

p1 * (p2,i) is Element of the carrier of M

n is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

K is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

M is non empty non degenerated non trivial right_complementable almost_left_invertible V111() V123() associative commutative Abelian add-associative right_zeroed right-distributive left-distributive right_unital well-unital V144() left_unital doubleLoopStr

the carrier of M is non empty non trivial set

the carrier of M * is functional non empty FinSequence-membered FinSequenceSet of the carrier of M

(M,n,K) is Relation-like NAT -defined the carrier of M * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular Matrix of n,K, the carrier of M

K -tuples_on the carrier of M is functional non empty FinSequence-membered FinSequenceSet of the carrier of M

{ b

0. M is V68(M) Element of the carrier of M

K |-> (0. M) is Relation-like NAT -defined the carrier of M -valued Function-like V48() V55(K) FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of M

Seg K is V48() V55(K) Element of bool NAT

(Seg K) --> (0. M) is Relation-like Seg K -defined {(0. M)} -valued Function-like total V26( Seg K,{(0. M)}) V48() FinSequence-like FinSubsequence-like Element of bool [:(Seg K),{(0. M)}:]

{(0. M)} is non empty trivial V48() V55(1) set

[:(Seg K),{(0. M)}:] is Relation-like V48() set

bool [:(Seg K),{(0. M)}:] is non empty cup-closed diff-closed preBoolean V48() V52() set

n |-> (K |-> (0. M)) is Relation-like NAT -defined K -tuples_on the carrier of M -valued Function-like V48() V55(n) FinSequence-like FinSubsequence-like Element of n -tuples_on (K -tuples_on the carrier of M)

n -tuples_on (K -tuples_on the carrier of M) is functional non empty FinSequence-membered FinSequenceSet of K -tuples_on the carrier of M

(K -tuples_on the carrier of M) * is functional non empty FinSequence-membered FinSequenceSet of K -tuples_on the carrier of M

{ b

Seg n is V48() V55(n) Element of bool NAT

(Seg n) --> (K |-> (0. M)) is Relation-like Seg n -defined {(K |-> (0. M))} -valued Function-like total V26( Seg n,{(K |-> (0. M))}) V48() FinSequence-like FinSubsequence-like Element of bool [:(Seg n),{(K |-> (0. M))}:]

{(K |-> (0. M))} is functional non empty trivial V48() V52() V55(1) set

[:(Seg n),{(K |-> (0. M))}:] is Relation-like V48() set

bool [:(Seg n),{(K |-> (0. M))}:] is non empty cup-closed diff-closed preBoolean V48() V52() set

p1 is Relation-like NAT -defined the carrier of M * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular Matrix of n,K, the carrier of M

(M,p1) is Relation-like NAT -defined the carrier of M * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of M *

(M,p1,(M,p1)) is Relation-like NAT -defined the carrier of M * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of M *

width (M,p1) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

len (M,p1,(M,p1)) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

len p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width (M,p1,(M,p1)) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

len (M,p1) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

len (M,n,K) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width (M,n,K) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

dom p1 is V48() Element of bool NAT

dom (M,p1) is V48() Element of bool NAT

dom (M,p1,(M,p1)) is V48() Element of bool NAT

Indices p1 is set

Seg (width p1) is V48() V55( width p1) Element of bool NAT

[:(dom p1),(Seg (width p1)):] is Relation-like V48() set

Indices (M,p1) is set

Seg (width (M,p1)) is V48() V55( width (M,p1)) Element of bool NAT

[:(dom (M,p1)),(Seg (width (M,p1))):] is Relation-like V48() set

Indices (M,p1,(M,p1)) is set

Seg (width (M,p1,(M,p1))) is V48() V55( width (M,p1,(M,p1))) Element of bool NAT

[:(dom (M,p1,(M,p1))),(Seg (width (M,p1,(M,p1)))):] is Relation-like V48() set

Seg (width (M,p1)) is V48() V55( width (M,p1)) Element of bool NAT

Seg 0 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty proper V34() V35() V36() V38() V39() V40() V41() ext-real non positive non negative V45() V48() V49() V52() V53() V55( 0 ) V55( {} ) FinSequence-like FinSubsequence-like FinSequence-membered Element of bool NAT

dom (M,p1) is V48() Element of bool NAT

Indices (M,p1) is set

[:(dom (M,p1)),(Seg (width (M,p1))):] is Relation-like V48() set

[:(Seg 0),(Seg (width (M,p1))):] is Relation-like V48() set

[:(Seg 0),(Seg 0):] is Relation-like V48() set

dom (M,p1,(M,p1)) is V48() Element of bool NAT

Indices (M,p1,(M,p1)) is set

Seg (width (M,p1,(M,p1))) is V48() V55( width (M,p1,(M,p1))) Element of bool NAT

[:(dom (M,p1,(M,p1))),(Seg (width (M,p1,(M,p1)))):] is Relation-like V48() set

len (M,n,K) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width (M,n,K) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Indices p1 is set

dom p1 is V48() Element of bool NAT

Seg (width p1) is V48() V55( width p1) Element of bool NAT

[:(dom p1),(Seg (width p1)):] is Relation-like V48() set

len (M,n,K) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width (M,n,K) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Indices p1 is set

dom p1 is V48() Element of bool NAT

Seg (width p1) is V48() V55( width p1) Element of bool NAT

[:(dom p1),(Seg (width p1)):] is Relation-like V48() set

Indices (M,p1) is set

dom (M,p1) is V48() Element of bool NAT

Seg (width (M,p1)) is V48() V55( width (M,p1)) Element of bool NAT

[:(dom (M,p1)),(Seg (width (M,p1))):] is Relation-like V48() set

Indices (M,p1,(M,p1)) is set

dom (M,p1,(M,p1)) is V48() Element of bool NAT

Seg (width (M,p1,(M,p1))) is V48() V55( width (M,p1,(M,p1))) Element of bool NAT

[:(dom (M,p1,(M,p1))),(Seg (width (M,p1,(M,p1)))):] is Relation-like V48() set

len (M,n,K) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width (M,n,K) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Indices p1 is set

dom p1 is V48() Element of bool NAT

Seg (width p1) is V48() V55( width p1) Element of bool NAT

[:(dom p1),(Seg (width p1)):] is Relation-like V48() set

Indices (M,p1) is set

dom (M,p1) is V48() Element of bool NAT

Seg (width (M,p1)) is V48() V55( width (M,p1)) Element of bool NAT

[:(dom (M,p1)),(Seg (width (M,p1))):] is Relation-like V48() set

Indices (M,p1,(M,p1)) is set

dom (M,p1,(M,p1)) is V48() Element of bool NAT

Seg (width (M,p1,(M,p1))) is V48() V55( width (M,p1,(M,p1))) Element of bool NAT

[:(dom (M,p1,(M,p1))),(Seg (width (M,p1,(M,p1)))):] is Relation-like V48() set

Indices (M,n,K) is set

dom (M,n,K) is V48() Element of bool NAT

Seg (width (M,n,K)) is V48() V55( width (M,n,K)) Element of bool NAT

[:(dom (M,n,K)),(Seg (width (M,n,K))):] is Relation-like V48() set

p2 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

[p2,i] is V23() set

(M,p1,(M,p1)) * (p2,i) is Element of the carrier of M

p1 * (p2,i) is Element of the carrier of M

(M,p1) * (p2,i) is Element of the carrier of M

(p1 * (p2,i)) + ((M,p1) * (p2,i)) is Element of the carrier of M

the addF of M is Relation-like [: the carrier of M, the carrier of M:] -defined the carrier of M -valued Function-like non empty total V26([: the carrier of M, the carrier of M:], the carrier of M) commutative associative Element of bool [:[: the carrier of M, the carrier of M:], the carrier of M:]

[: the carrier of M, the carrier of M:] is Relation-like non empty set

[:[: the carrier of M, the carrier of M:], the carrier of M:] is Relation-like non empty set

bool [:[: the carrier of M, the carrier of M:], the carrier of M:] is non empty cup-closed diff-closed preBoolean set

the addF of M . ((p1 * (p2,i)),((M,p1) * (p2,i))) is Element of the carrier of M

[(p1 * (p2,i)),((M,p1) * (p2,i))] is V23() set

the addF of M . [(p1 * (p2,i)),((M,p1) * (p2,i))] is set

- (p1 * (p2,i)) is Element of the carrier of M

(p1 * (p2,i)) + (- (p1 * (p2,i))) is Element of the carrier of M

the addF of M . ((p1 * (p2,i)),(- (p1 * (p2,i)))) is Element of the carrier of M

[(p1 * (p2,i)),(- (p1 * (p2,i)))] is V23() set

the addF of M . [(p1 * (p2,i)),(- (p1 * (p2,i)))] is set

(M,n,K) * (p2,i) is Element of the carrier of M

n is non empty non degenerated non trivial right_complementable almost_left_invertible V111() V123() associative commutative Abelian add-associative right_zeroed right-distributive left-distributive right_unital well-unital V144() 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 V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

width K is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

M is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

len M is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

len K is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width M is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

p1 is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular Matrix of len K, width M, the carrier of n

Indices p1 is set

dom p1 is V48() Element of bool NAT

width p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Seg (width p1) is V48() V55( width p1) Element of bool NAT

[:(dom p1),(Seg (width p1)):] is Relation-like V48() set

len p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

p2 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

[p2,i] is V23() set

p1 * (p2,i) is Element of the carrier of n

Line (K,p2) is Relation-like NAT -defined the carrier of n -valued Function-like V48() V55( width K) FinSequence-like FinSubsequence-like Element of (width K) -tuples_on the carrier of n

(width K) -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n

{ b

Col (M,i) is Relation-like NAT -defined the carrier of n -valued Function-like V48() V55( len M) FinSequence-like FinSubsequence-like Element of (len M) -tuples_on the carrier of n

(len M) -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n

{ b

(Line (K,p2)) "*" (Col (M,i)) is Element of the carrier of n

p1 is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

len p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Indices p1 is set

dom p1 is V48() Element of bool NAT

Seg (width p1) is V48() V55( width p1) Element of bool NAT

[:(dom p1),(Seg (width p1)):] is Relation-like V48() set

p2 is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

len p2 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width p2 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Indices p2 is set

dom p2 is V48() Element of bool NAT

Seg (width p2) is V48() V55( width p2) Element of bool NAT

[:(dom p2),(Seg (width p2)):] is Relation-like V48() set

i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

p is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

[i,p] is V23() set

p1 * (i,p) is Element of the carrier of n

Line (K,i) is Relation-like NAT -defined the carrier of n -valued Function-like V48() V55( width K) FinSequence-like FinSubsequence-like Element of (width K) -tuples_on the carrier of n

(width K) -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n

{ b

Col (M,p) is Relation-like NAT -defined the carrier of n -valued Function-like V48() V55( len M) FinSequence-like FinSubsequence-like Element of (len M) -tuples_on the carrier of n

(len M) -tuples_on the carrier of n is functional non empty FinSequence-membered FinSequenceSet of the carrier of n

{ b

(Line (K,i)) "*" (Col (M,p)) is Element of the carrier of n

p2 * (i,p) is Element of the carrier of n

p1 is non empty non degenerated non trivial right_complementable almost_left_invertible V111() V123() associative commutative Abelian add-associative right_zeroed right-distributive left-distributive right_unital well-unital V144() left_unital doubleLoopStr

the carrier of p1 is non empty non trivial set

the carrier of p1 * is functional non empty FinSequence-membered FinSequenceSet of the carrier of p1

n is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

K is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

p2 is Relation-like NAT -defined the carrier of p1 * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular Matrix of n,K, the carrier of p1

width p2 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

M is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

i is Relation-like NAT -defined the carrier of p1 * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular Matrix of width p2,M, the carrier of p1

(p1,p2,i) is Relation-like NAT -defined the carrier of p1 * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of p1 *

len p2 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

len i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

len (p1,p2,i) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width (p1,p2,i) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

n is non empty non degenerated non trivial right_complementable almost_left_invertible V111() V123() associative commutative Abelian add-associative right_zeroed right-distributive left-distributive right_unital well-unital V144() 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 V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

len K is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width K is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Indices K is set

dom K is V48() Element of bool NAT

Seg (width K) is V48() V55( width K) Element of bool NAT

[:(dom K),(Seg (width K)):] is Relation-like V48() set

M is Element of the carrier of n

p1 is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular Matrix of len K, width K, the carrier of n

Indices p1 is set

dom p1 is V48() Element of bool NAT

width p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Seg (width p1) is V48() V55( width p1) Element of bool NAT

[:(dom p1),(Seg (width p1)):] is Relation-like V48() set

len p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

p2 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

[p2,i] is V23() set

p1 * (p2,i) is Element of the carrier of n

K * (p2,i) is Element of the carrier of n

M * (K * (p2,i)) is Element of the carrier of n

the multF of n is Relation-like [: the carrier of n, the carrier of n:] -defined the carrier of n -valued Function-like non empty total V26([: the carrier of n, the carrier of n:], the carrier of n) commutative 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 non empty set

[:[: the carrier of n, the carrier of n:], the carrier of n:] is Relation-like non empty set

bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is non empty cup-closed diff-closed preBoolean set

the multF of n . (M,(K * (p2,i))) is Element of the carrier of n

[M,(K * (p2,i))] is V23() set

the multF of n . [M,(K * (p2,i))] is set

p1 is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

len p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

p2 is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

len p2 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

width p2 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

dom p1 is V48() Element of bool NAT

Indices p1 is set

Seg (width p1) is V48() V55( width p1) Element of bool NAT

[:(dom p1),(Seg (width p1)):] is Relation-like V48() set

i is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

p is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

[i,p] is V23() set

p1 * (i,p) is Element of the carrier of n

K * (i,p) is Element of the carrier of n

M * (K * (i,p)) is Element of the carrier of n

the multF of n is Relation-like [: the carrier of n, the carrier of n:] -defined the carrier of n -valued Function-like non empty total V26([: the carrier of n, the carrier of n:], the carrier of n) commutative 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 non empty set

[:[: the carrier of n, the carrier of n:], the carrier of n:] is Relation-like non empty set

bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is non empty cup-closed diff-closed preBoolean set

the multF of n . (M,(K * (i,p))) is Element of the carrier of n

[M,(K * (i,p))] is V23() set

the multF of n . [M,(K * (i,p))] is set

p2 * (i,p) is Element of the carrier of n

n is non empty non degenerated non trivial right_complementable almost_left_invertible V111() V123() associative commutative Abelian add-associative right_zeroed right-distributive left-distributive right_unital well-unital V144() 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 V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

M is Element of the carrier of n

(n,K,M) is Relation-like NAT -defined the carrier of n * -valued Function-like V48() FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of n *

n is non empty non degenerated non trivial right_complementable almost_left_invertible V111() V123() associative commutative Abelian add-associative right_zeroed right-distributive left-distributive right_unital well-unital V144() 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 V48() FinSequence-like FinSubsequence-like FinSequence of the carrier of n

len K is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

M is Relation-like NAT -defined the carrier of n -valued Function-like V48() FinSequence-like FinSubsequence-like FinSequence of the carrier of n

len M is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

mlt (K,M) is Relation-like NAT -defined the carrier of n -valued Function-like V48() FinSequence-like FinSubsequence-like FinSequence of the carrier of n

len (mlt (K,M)) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

p1 is Relation-like NAT -defined the carrier of n -valued Function-like V48() FinSequence-like FinSubsequence-like FinSequence of the carrier of n

the multF of n is Relation-like [: the carrier of n, the carrier of n:] -defined the carrier of n -valued Function-like non empty total V26([: the carrier of n, the carrier of n:], the carrier of n) commutative 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 non empty set

[:[: the carrier of n, the carrier of n:], the carrier of n:] is Relation-like non empty set

bool [:[: the carrier of n, the carrier of n:], the carrier of n:] is non empty cup-closed diff-closed preBoolean set

the multF of n .: (K,M) is Relation-like NAT -defined the carrier of n -valued Function-like V48() FinSequence-like FinSubsequence-like FinSequence of the carrier of n

n is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

K is non empty non degenerated non trivial right_complementable almost_left_invertible V111() V123() associative commutative Abelian add-associative right_zeroed right-distributive left-distributive right_unital well-unital V144() left_unital doubleLoopStr

1. (K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like V48() FinSequence-like FinSubsequence-like 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

Indices (1. (K,n)) is set

dom (1. (K,n)) is V48() Element of bool NAT

width (1. (K,n)) is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() Element of NAT

Seg (width (1. (K,n))) is V48() V55( width (1. (K,n))) Element of bool NAT

[:(dom (1. (K,n))),(Seg (width (1. (K,n)))):] is Relation-like V48() set

1. K is V68(K) Element of the carrier of K

M is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

Line ((1. (K,n)),M) is Relation-like NAT -defined the carrier of K -valued Function-like V48() V55( width (1. (K,n))) FinSequence-like FinSubsequence-like Element of (width (1. (K,n))) -tuples_on the carrier of K

(width (1. (K,n))) -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K

{ b

p1 is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

[M,p1] is V23() set

(Line ((1. (K,n)),M)) . p1 is set

(1. (K,n)) * (M,p1) is Element of the carrier of K

n is V34() V35() V36() V40() V41() ext-real non negative V45() V48() V53() set

K is non empty non degenerated non trivial right_complementable almost_left_invertible V111() V123() associative commutative Abelian add-associative right_zeroed right-distributive left-distributive right_unital well-unital V144() left_unital doubleLoopStr

1. (K,n) is Relation-like NAT -defined the carrier of K * -valued Function-like V48() FinSequence-like FinSubsequence-like 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

Indices (1. (K,n)) is set

dom (1. (K,n)) is V48() Element of bool NAT