:: VECTSP11 semantic presentation

REAL is set
NAT is non empty non trivial V25() V26() V27() non finite cardinal limit_cardinal Element of bool REAL
bool REAL is set
K704() is strict algebraic-closed doubleLoopStr
the carrier of K704() is set
NAT is non empty non trivial V25() V26() V27() non finite cardinal limit_cardinal set
bool NAT is non trivial non finite set
bool NAT is non trivial non finite set
K95(NAT) is V24() set
INT is set
COMPLEX is set
RAT is set
{} is Function-like functional empty V25() V26() V27() V29() V30() V31() finite V36() cardinal {} -element FinSequence-membered V46() ext-real non positive non negative V165() set
the Function-like functional empty V25() V26() V27() V29() V30() V31() finite V36() cardinal {} -element FinSequence-membered V46() ext-real non positive non negative V165() set is Function-like functional empty V25() V26() V27() V29() V30() V31() finite V36() cardinal {} -element FinSequence-membered V46() ext-real non positive non negative V165() set
2 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
0 is Function-like functional empty V25() V26() V27() V29() V30() V31() finite V36() cardinal {} -element FinSequence-membered V46() ext-real non positive non negative V165() Element of NAT
K516(0,1,2) is finite set
[:K516(0,1,2),K516(0,1,2):] is finite set
[:[:K516(0,1,2),K516(0,1,2):],K516(0,1,2):] is finite set
bool [:[:K516(0,1,2),K516(0,1,2):],K516(0,1,2):] is finite V36() set
bool [:K516(0,1,2),K516(0,1,2):] is finite V36() set
[:REAL,REAL:] is set
bool [:REAL,REAL:] is set
K652() is non empty strict multMagma
the carrier of K652() is non empty set
<REAL,+> is non empty strict unital Group-like associative commutative left-invertible right-invertible invertible left-cancelable right-cancelable V232() multMagma
K658() is non empty strict associative commutative left-cancelable right-cancelable V232() SubStr of <REAL,+>
<NAT,+> is non empty strict unital associative commutative left-cancelable right-cancelable V232() uniquely-decomposable SubStr of K658()
<REAL,*> is non empty strict unital associative commutative multMagma
<NAT,*> is non empty strict unital associative commutative uniquely-decomposable SubStr of <REAL,*>
[:NAT,REAL:] is set
bool [:NAT,REAL:] is set
1 -tuples_on NAT is functional non empty FinSequence-membered FinSequenceSet of NAT
[:COMPLEX,COMPLEX:] is set
bool [:COMPLEX,COMPLEX:] is set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is set
[:[:REAL,REAL:],REAL:] is set
bool [:[:REAL,REAL:],REAL:] is set
[:RAT,RAT:] is set
bool [:RAT,RAT:] is set
[:[:RAT,RAT:],RAT:] is set
bool [:[:RAT,RAT:],RAT:] is set
[:INT,INT:] is set
bool [:INT,INT:] is set
[:[:INT,INT:],INT:] is set
bool [:[:INT,INT:],INT:] is set
[:NAT,NAT:] is non trivial non finite set
[:[:NAT,NAT:],NAT:] is non trivial non finite set
bool [:[:NAT,NAT:],NAT:] is non trivial non finite set
3 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
card {} is Function-like functional empty V25() V26() V27() V29() V30() V31() finite V36() cardinal {} -element FinSequence-membered V46() ext-real non positive non negative V165() set
K is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
K -tuples_on NAT is functional non empty FinSequence-membered FinSequenceSet of NAT
V1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
V1 -tuples_on NAT is functional non empty FinSequence-membered FinSequenceSet of NAT
V2 is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of V2 is non empty non trivial set
the carrier of V2 * is functional non empty FinSequence-membered FinSequenceSet of the carrier of V2
A is Relation-like NAT -defined the carrier of V2 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of V2 *
Indices A is set
B is Relation-like NAT -defined the carrier of V2 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of V2 *
A + B is Relation-like NAT -defined the carrier of V2 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of V2 *
L is Relation-like NAT -defined NAT -valued Function-like finite K -element FinSequence-like FinSubsequence-like V177() Element of K -tuples_on NAT
rng L is finite set
F is Relation-like NAT -defined NAT -valued Function-like finite V1 -element FinSequence-like FinSubsequence-like V177() Element of V1 -tuples_on NAT
rng F is finite set
[:(rng L),(rng F):] is finite set
Segm ((A + B),L,F) is Relation-like NAT -defined the carrier of V2 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K,V1, the carrier of V2
Segm (A,L,F) is Relation-like NAT -defined the carrier of V2 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K,V1, the carrier of V2
Segm (B,L,F) is Relation-like NAT -defined the carrier of V2 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K,V1, the carrier of V2
(Segm (A,L,F)) + (Segm (B,L,F)) is Relation-like NAT -defined the carrier of V2 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K,V1, the carrier of V2
Indices (Segm (A,L,F)) is set
Indices (Segm (B,L,F)) is set
f is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
D is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
[f,D] is set
{f,D} is non empty finite V36() set
{f} is non empty trivial finite V36() 1 -element set
{{f,D},{f}} is non empty finite V36() set
Indices (Segm ((A + B),L,F)) is set
L . f is set
F . D is set
[(L . f),(F . D)] is set
{(L . f),(F . D)} is non empty finite set
{(L . f)} is non empty trivial finite 1 -element set
{{(L . f),(F . D)},{(L . f)}} is non empty finite V36() set
(Segm ((A + B),L,F)) * (f,D) is Element of the carrier of V2
C is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
FA is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(A + B) * (C,FA) is Element of the carrier of V2
A * (C,FA) is Element of the carrier of V2
B * (C,FA) is Element of the carrier of V2
(A * (C,FA)) + (B * (C,FA)) is Element of the carrier of V2
(Segm (A,L,F)) * (f,D) is Element of the carrier of V2
((Segm (A,L,F)) * (f,D)) + (B * (C,FA)) is Element of the carrier of V2
(Segm (B,L,F)) * (f,D) is Element of the carrier of V2
((Segm (A,L,F)) * (f,D)) + ((Segm (B,L,F)) * (f,D)) is Element of the carrier of V2
((Segm (A,L,F)) + (Segm (B,L,F))) * (f,D) is Element of the carrier of V2
K is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
Seg K is finite K -element without_zero Element of bool NAT
{ b₁ where b₁ is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT : ( 1 <= b₁ & b₁ <= K ) } is set
V1 is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of V1 is non empty non trivial set
1. (V1,K) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K,K, the carrier of V1
the carrier of V1 * is functional non empty FinSequence-membered FinSequenceSet of the carrier of V1
V2 is finite without_zero Element of bool NAT
Segm ((1. (V1,K)),V2,V2) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card V2, card V2, the carrier of V1
card V2 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
Sgm V2 is Relation-like NAT -defined NAT -valued Function-like finite card V2 -element FinSequence-like FinSubsequence-like V177() Element of (card V2) -tuples_on NAT
(card V2) -tuples_on NAT is functional non empty FinSequence-membered FinSequenceSet of NAT
Segm ((1. (V1,K)),(Sgm V2),(Sgm V2)) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card V2, card V2, the carrier of V1
1. (V1,(card V2)) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card V2, card V2, the carrier of V1
L is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
F is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
[L,F] is set
{L,F} is non empty finite V36() set
{L} is non empty trivial finite V36() 1 -element set
{{L,F},{L}} is non empty finite V36() set
Indices (1. (V1,(card V2))) is set
rng (Sgm V2) is finite set
(Sgm V2) . L is set
(Sgm V2) . F is set
Indices (Segm ((1. (V1,K)),V2,V2)) is set
(Segm ((1. (V1,K)),V2,V2)) * (L,F) is Element of the carrier of V1
f is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
D is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(1. (V1,K)) * (f,D) is Element of the carrier of V1
Indices (1. (V1,K)) is set
[:(Seg K),(Seg K):] is finite set
[:V2,V2:] is finite set
[((Sgm V2) . L),((Sgm V2) . F)] is set
{((Sgm V2) . L),((Sgm V2) . F)} is non empty finite set
{((Sgm V2) . L)} is non empty trivial finite 1 -element set
{{((Sgm V2) . L),((Sgm V2) . F)},{((Sgm V2) . L)}} is non empty finite V36() set
Seg (card V2) is finite card V2 -element without_zero Element of bool NAT
{ b₁ where b₁ is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT : ( 1 <= b₁ & b₁ <= card V2 ) } is set
[:(Seg (card V2)),(Seg (card V2)):] is finite set
dom (Sgm V2) is finite card V2 -element Element of bool NAT
1_ V1 is Element of the carrier of V1
1. V1 is V65(V1) Element of the carrier of V1
the OneF of V1 is Element of the carrier of V1
(1. (V1,(card V2))) * (L,F) is Element of the carrier of V1
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed 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
V1 is Relation-like NAT -defined the carrier of K * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of K *
Indices V1 is set
V2 is Relation-like NAT -defined the carrier of K * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of K *
V1 + V2 is Relation-like NAT -defined the carrier of K * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of K *
A is finite without_zero Element of bool NAT
B is finite without_zero Element of bool NAT
[:A,B:] is finite set
Segm ((V1 + V2),A,B) is Relation-like NAT -defined the carrier of K * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card A, card B, the carrier of K
card A is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
card B is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
Sgm A is Relation-like NAT -defined NAT -valued Function-like finite card A -element FinSequence-like FinSubsequence-like V177() Element of (card A) -tuples_on NAT
(card A) -tuples_on NAT is functional non empty FinSequence-membered FinSequenceSet of NAT
Sgm B is Relation-like NAT -defined NAT -valued Function-like finite card B -element FinSequence-like FinSubsequence-like V177() Element of (card B) -tuples_on NAT
(card B) -tuples_on NAT is functional non empty FinSequence-membered FinSequenceSet of NAT
Segm ((V1 + V2),(Sgm A),(Sgm B)) is Relation-like NAT -defined the carrier of K * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card A, card B, the carrier of K
Segm (V1,A,B) is Relation-like NAT -defined the carrier of K * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card A, card B, the carrier of K
Segm (V1,(Sgm A),(Sgm B)) is Relation-like NAT -defined the carrier of K * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card A, card B, the carrier of K
Segm (V2,A,B) is Relation-like NAT -defined the carrier of K * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card A, card B, the carrier of K
Segm (V2,(Sgm A),(Sgm B)) is Relation-like NAT -defined the carrier of K * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card A, card B, the carrier of K
(Segm (V1,A,B)) + (Segm (V2,A,B)) is Relation-like NAT -defined the carrier of K * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card A, card B, the carrier of K
rng (Sgm B) is finite set
L is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
Seg L is finite L -element without_zero Element of bool NAT
{ b₁ where b₁ is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT : ( 1 <= b₁ & b₁ <= L ) } is set
rng (Sgm A) is finite set
L is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
Seg L is finite L -element without_zero Element of bool NAT
{ b₁ where b₁ is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT : ( 1 <= b₁ & b₁ <= L ) } is set
K is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
Seg K is finite K -element without_zero Element of bool NAT
{ b₁ where b₁ is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT : ( 1 <= b₁ & b₁ <= K ) } is set
K -' 1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
V1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
V2 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
A is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of A is non empty non trivial set
the carrier of A * is functional non empty FinSequence-membered FinSequenceSet of the carrier of A
B is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K,K, the carrier of A
L is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K,K, the carrier of A
B + L is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K,K, the carrier of A
Delete ((B + L),V1,V2) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K -' 1,K -' 1, the carrier of A
Delete (B,V1,V2) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K -' 1,K -' 1, the carrier of A
Delete (L,V1,V2) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K -' 1,K -' 1, the carrier of A
(Delete (B,V1,V2)) + (Delete (L,V1,V2)) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K -' 1,K -' 1, the carrier of A
{V1} is non empty trivial finite V36() 1 -element Element of bool NAT
(Seg K) \ {V1} is finite without_zero Element of bool NAT
{V2} is non empty trivial finite V36() 1 -element Element of bool NAT
(Seg K) \ {V2} is finite without_zero Element of bool NAT
[:((Seg K) \ {V1}),((Seg K) \ {V2}):] is finite set
[:(Seg K),(Seg K):] is finite set
Indices B is set
Deleting ((B + L),V1,V2) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of A *
Segm ((B + L),((Seg K) \ {V1}),((Seg K) \ {V2})) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card ((Seg K) \ {V1}), card ((Seg K) \ {V2}), the carrier of A
card ((Seg K) \ {V1}) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
card ((Seg K) \ {V2}) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
Sgm ((Seg K) \ {V1}) is Relation-like NAT -defined NAT -valued Function-like finite card ((Seg K) \ {V1}) -element FinSequence-like FinSubsequence-like V177() Element of (card ((Seg K) \ {V1})) -tuples_on NAT
(card ((Seg K) \ {V1})) -tuples_on NAT is functional non empty FinSequence-membered FinSequenceSet of NAT
Sgm ((Seg K) \ {V2}) is Relation-like NAT -defined NAT -valued Function-like finite card ((Seg K) \ {V2}) -element FinSequence-like FinSubsequence-like V177() Element of (card ((Seg K) \ {V2})) -tuples_on NAT
(card ((Seg K) \ {V2})) -tuples_on NAT is functional non empty FinSequence-membered FinSequenceSet of NAT
Segm ((B + L),(Sgm ((Seg K) \ {V1})),(Sgm ((Seg K) \ {V2}))) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card ((Seg K) \ {V1}), card ((Seg K) \ {V2}), the carrier of A
Segm (B,((Seg K) \ {V1}),((Seg K) \ {V2})) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card ((Seg K) \ {V1}), card ((Seg K) \ {V2}), the carrier of A
Segm (B,(Sgm ((Seg K) \ {V1})),(Sgm ((Seg K) \ {V2}))) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card ((Seg K) \ {V1}), card ((Seg K) \ {V2}), the carrier of A
Segm (L,((Seg K) \ {V1}),((Seg K) \ {V2})) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card ((Seg K) \ {V1}), card ((Seg K) \ {V2}), the carrier of A
Segm (L,(Sgm ((Seg K) \ {V1})),(Sgm ((Seg K) \ {V2}))) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card ((Seg K) \ {V1}), card ((Seg K) \ {V2}), the carrier of A
(Segm (B,((Seg K) \ {V1}),((Seg K) \ {V2}))) + (Segm (L,((Seg K) \ {V1}),((Seg K) \ {V2}))) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card ((Seg K) \ {V1}), card ((Seg K) \ {V2}), the carrier of A
Deleting (B,V1,V2) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of A *
(Deleting (B,V1,V2)) + (Segm (L,((Seg K) \ {V1}),((Seg K) \ {V2}))) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of A *
Deleting (L,V1,V2) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of A *
(Deleting (B,V1,V2)) + (Deleting (L,V1,V2)) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of A *
(Delete (B,V1,V2)) + (Deleting (L,V1,V2)) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K -' 1,K -' 1, the carrier of A
K is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
Seg K is finite K -element without_zero Element of bool NAT
{ b₁ where b₁ is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT : ( 1 <= b₁ & b₁ <= K ) } is set
K -' 1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
V1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
V2 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
A is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of A is non empty non trivial set
the carrier of A * is functional non empty FinSequence-membered FinSequenceSet of the carrier of A
B is Element of the carrier of A
L is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K,K, the carrier of A
B * L is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K,K, the carrier of A
Delete ((B * L),V1,V2) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K -' 1,K -' 1, the carrier of A
Delete (L,V1,V2) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K -' 1,K -' 1, the carrier of A
B * (Delete (L,V1,V2)) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K -' 1,K -' 1, the carrier of A
{V1} is non empty trivial finite V36() 1 -element Element of bool NAT
(Seg K) \ {V1} is finite without_zero Element of bool NAT
{V2} is non empty trivial finite V36() 1 -element Element of bool NAT
(Seg K) \ {V2} is finite without_zero Element of bool NAT
[:((Seg K) \ {V1}),((Seg K) \ {V2}):] is finite set
[:(Seg K),(Seg K):] is finite set
Indices L is set
Deleting ((B * L),V1,V2) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of A *
Segm ((B * L),((Seg K) \ {V1}),((Seg K) \ {V2})) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card ((Seg K) \ {V1}), card ((Seg K) \ {V2}), the carrier of A
card ((Seg K) \ {V1}) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
card ((Seg K) \ {V2}) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
Sgm ((Seg K) \ {V1}) is Relation-like NAT -defined NAT -valued Function-like finite card ((Seg K) \ {V1}) -element FinSequence-like FinSubsequence-like V177() Element of (card ((Seg K) \ {V1})) -tuples_on NAT
(card ((Seg K) \ {V1})) -tuples_on NAT is functional non empty FinSequence-membered FinSequenceSet of NAT
Sgm ((Seg K) \ {V2}) is Relation-like NAT -defined NAT -valued Function-like finite card ((Seg K) \ {V2}) -element FinSequence-like FinSubsequence-like V177() Element of (card ((Seg K) \ {V2})) -tuples_on NAT
(card ((Seg K) \ {V2})) -tuples_on NAT is functional non empty FinSequence-membered FinSequenceSet of NAT
Segm ((B * L),(Sgm ((Seg K) \ {V1})),(Sgm ((Seg K) \ {V2}))) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card ((Seg K) \ {V1}), card ((Seg K) \ {V2}), the carrier of A
Segm (L,((Seg K) \ {V1}),((Seg K) \ {V2})) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card ((Seg K) \ {V1}), card ((Seg K) \ {V2}), the carrier of A
Segm (L,(Sgm ((Seg K) \ {V1})),(Sgm ((Seg K) \ {V2}))) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card ((Seg K) \ {V1}), card ((Seg K) \ {V2}), the carrier of A
B * (Segm (L,((Seg K) \ {V1}),((Seg K) \ {V2}))) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card ((Seg K) \ {V1}), card ((Seg K) \ {V2}), the carrier of A
Deleting (L,V1,V2) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of A *
B * (Deleting (L,V1,V2)) is Relation-like NAT -defined the carrier of A * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of A *
K is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
V1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
Seg V1 is finite V1 -element without_zero Element of bool NAT
{ b₁ where b₁ is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT : ( 1 <= b₁ & b₁ <= V1 ) } is set
V1 -' 1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
V2 is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
1. (V2,V1) is Relation-like NAT -defined the carrier of V2 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of V1,V1, the carrier of V2
the carrier of V2 is non empty non trivial set
the carrier of V2 * is functional non empty FinSequence-membered FinSequenceSet of the carrier of V2
Delete ((1. (V2,V1)),K,K) is Relation-like NAT -defined the carrier of V2 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of V1 -' 1,V1 -' 1, the carrier of V2
1. (V2,(V1 -' 1)) is Relation-like NAT -defined the carrier of V2 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of V1 -' 1,V1 -' 1, the carrier of V2
V1 - 1 is V46() ext-real V165() set
card (Seg V1) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
(V1 -' 1) + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
{K} is non empty trivial finite V36() 1 -element Element of bool NAT
(Seg V1) \ {K} is finite without_zero Element of bool NAT
card ((Seg V1) \ {K}) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
Deleting ((1. (V2,V1)),K,K) is Relation-like NAT -defined the carrier of V2 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular FinSequence of the carrier of V2 *
Segm ((1. (V2,V1)),((Seg V1) \ {K}),((Seg V1) \ {K})) is Relation-like NAT -defined the carrier of V2 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card ((Seg V1) \ {K}), card ((Seg V1) \ {K}), the carrier of V2
Sgm ((Seg V1) \ {K}) is Relation-like NAT -defined NAT -valued Function-like finite card ((Seg V1) \ {K}) -element FinSequence-like FinSubsequence-like V177() Element of (card ((Seg V1) \ {K})) -tuples_on NAT
(card ((Seg V1) \ {K})) -tuples_on NAT is functional non empty FinSequence-membered FinSequenceSet of NAT
Segm ((1. (V2,V1)),(Sgm ((Seg V1) \ {K})),(Sgm ((Seg V1) \ {K}))) is Relation-like NAT -defined the carrier of V2 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of card ((Seg V1) \ {K}), card ((Seg V1) \ {K}), the carrier of V2
K is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
K + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
V1 is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of V1 is non empty non trivial set
the carrier of V1 * is functional non empty FinSequence-membered FinSequenceSet of the carrier of V1
[:NAT, the carrier of V1:] is non trivial non finite set
bool [:NAT, the carrier of V1:] is non trivial non finite set
V2 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
V2 + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
(V2 + 1) + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
B is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of V2 + 1,V2 + 1, the carrier of V1
L is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of V2 + 1,V2 + 1, the carrier of V1
(V2 + 1) + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
Seg (V2 + 1) is non empty finite V2 + 1 -element without_zero Element of bool NAT
{ b₁ where b₁ is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT : ( 1 <= b₁ & b₁ <= V2 + 1 ) } is set
F is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
F + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
D is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) Element of bool [:NAT, the carrier of V1:]
len D is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
D is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) Element of bool [:NAT, the carrier of V1:]
len D is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
[(V2 + 1),(F + 1)] is Element of [:NAT,NAT:]
{(V2 + 1),(F + 1)} is non empty finite V36() set
{(V2 + 1)} is non empty trivial finite V36() 1 -element set
{{(V2 + 1),(F + 1)},{(V2 + 1)}} is non empty finite V36() set
[:(Seg (V2 + 1)),(Seg (V2 + 1)):] is finite set
power V1 is Relation-like [: the carrier of V1,NAT:] -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [:[: the carrier of V1,NAT:], the carrier of V1:]
[: the carrier of V1,NAT:] is non trivial non finite set
[:[: the carrier of V1,NAT:], the carrier of V1:] is non trivial non finite set
bool [:[: the carrier of V1,NAT:], the carrier of V1:] is non trivial non finite set
1_ V1 is Element of the carrier of V1
1. V1 is V65(V1) Element of the carrier of V1
the OneF of V1 is Element of the carrier of V1
- (1_ V1) is Element of the carrier of V1
(F + 1) + (V2 + 1) is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
(power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1))) is Element of the carrier of V1
Delete (L,(V2 + 1),(F + 1)) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of (V2 + 1) -' 1,(V2 + 1) -' 1, the carrier of V1
(V2 + 1) -' 1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
Delete (B,(V2 + 1),(F + 1)) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of (V2 + 1) -' 1,(V2 + 1) -' 1, the carrier of V1
B * ((V2 + 1),(F + 1)) is Element of the carrier of V1
(B * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1)))) is Element of the carrier of V1
L * ((V2 + 1),(F + 1)) is Element of the carrier of V1
(L * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1)))) is Element of the carrier of V1
<%((B * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1))))),((L * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1)))))%> is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) Element of bool [:NAT, the carrier of V1:]
Indices L is set
F9 is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) Element of bool [:NAT, the carrier of V1:]
len F9 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
F9 *' <%((B * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1))))),((L * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1)))))%> is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) Element of bool [:NAT, the carrier of V1:]
D + (F9 *' <%((B * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1))))),((L * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1)))))%>) is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) Element of bool [:NAT, the carrier of V1:]
SA is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) Element of bool [:NAT, the carrier of V1:]
len SA is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
len <%((B * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1))))),((L * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1)))))%> is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
(len F9) + (len <%((B * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1))))),((L * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1)))))%>) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
(V2 + 1) + 2 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
((len F9) + (len <%((B * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1))))),((L * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1)))))%>)) -' 1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
((V2 + 1) + 2) -' 1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
V2 + 2 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
(V2 + 2) + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
((V2 + 2) + 1) -' 1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
len (F9 *' <%((B * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1))))),((L * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1)))))%>) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
SB is Element of the carrier of V1
eval (SA,SB) is Element of the carrier of V1
SB * L is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of V2 + 1,V2 + 1, the carrier of V1
B + (SB * L) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of V2 + 1,V2 + 1, the carrier of V1
LaplaceExpL ((B + (SB * L)),(V2 + 1)) is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
(LaplaceExpL ((B + (SB * L)),(V2 + 1))) | (F + 1) is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
Seg (F + 1) is non empty finite F + 1 -element without_zero Element of bool NAT
{ b₁ where b₁ is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT : ( 1 <= b₁ & b₁ <= F + 1 ) } is set
(LaplaceExpL ((B + (SB * L)),(V2 + 1))) | (Seg (F + 1)) is Relation-like NAT -defined Function-like finite FinSubsequence-like set
Sum ((LaplaceExpL ((B + (SB * L)),(V2 + 1))) | (F + 1)) is Element of the carrier of V1
the addF of V1 is Relation-like [: the carrier of V1, the carrier of V1:] -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [:[: the carrier of V1, the carrier of V1:], the carrier of V1:]
[: the carrier of V1, the carrier of V1:] is set
[:[: the carrier of V1, the carrier of V1:], the carrier of V1:] is set
bool [:[: the carrier of V1, the carrier of V1:], the carrier of V1:] is set
K132( the carrier of V1,((LaplaceExpL ((B + (SB * L)),(V2 + 1))) | (F + 1)), the addF of V1) is Element of the carrier of V1
Indices B is set
((L * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1))))) * SB is Element of the carrier of V1
((B * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1))))) + (((L * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1))))) * SB) is Element of the carrier of V1
(L * ((V2 + 1),(F + 1))) * SB is Element of the carrier of V1
((L * ((V2 + 1),(F + 1))) * SB) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1)))) is Element of the carrier of V1
((B * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1))))) + (((L * ((V2 + 1),(F + 1))) * SB) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1))))) is Element of the carrier of V1
(B * ((V2 + 1),(F + 1))) + ((L * ((V2 + 1),(F + 1))) * SB) is Element of the carrier of V1
((B * ((V2 + 1),(F + 1))) + ((L * ((V2 + 1),(F + 1))) * SB)) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1)))) is Element of the carrier of V1
(SB * L) * ((V2 + 1),(F + 1)) is Element of the carrier of V1
(B * ((V2 + 1),(F + 1))) + ((SB * L) * ((V2 + 1),(F + 1))) is Element of the carrier of V1
((B * ((V2 + 1),(F + 1))) + ((SB * L) * ((V2 + 1),(F + 1)))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1)))) is Element of the carrier of V1
(B + (SB * L)) * ((V2 + 1),(F + 1)) is Element of the carrier of V1
((B + (SB * L)) * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1)))) is Element of the carrier of V1
len (LaplaceExpL ((B + (SB * L)),(V2 + 1))) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
dom (LaplaceExpL ((B + (SB * L)),(V2 + 1))) is finite Element of bool NAT
(LaplaceExpL ((B + (SB * L)),(V2 + 1))) | F is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
Seg F is finite F -element without_zero Element of bool NAT
{ b₁ where b₁ is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(LaplaceExpL ((B + (SB * L)),(V2 + 1))) | (Seg F) is Relation-like NAT -defined Function-like finite FinSubsequence-like set
(LaplaceExpL ((B + (SB * L)),(V2 + 1))) . (F + 1) is set
<*((LaplaceExpL ((B + (SB * L)),(V2 + 1))) . (F + 1))*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
[1,((LaplaceExpL ((B + (SB * L)),(V2 + 1))) . (F + 1))] is set
{1,((LaplaceExpL ((B + (SB * L)),(V2 + 1))) . (F + 1))} is non empty finite set
{1} is non empty trivial finite V36() 1 -element set
{{1,((LaplaceExpL ((B + (SB * L)),(V2 + 1))) . (F + 1))},{1}} is non empty finite V36() set
{[1,((LaplaceExpL ((B + (SB * L)),(V2 + 1))) . (F + 1))]} is Function-like non empty trivial finite 1 -element set
((LaplaceExpL ((B + (SB * L)),(V2 + 1))) | F) ^ <*((LaplaceExpL ((B + (SB * L)),(V2 + 1))) . (F + 1))*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
SB * (Delete (L,(V2 + 1),(F + 1))) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of (V2 + 1) -' 1,(V2 + 1) -' 1, the carrier of V1
(Delete (B,(V2 + 1),(F + 1))) + (SB * (Delete (L,(V2 + 1),(F + 1)))) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of (V2 + 1) -' 1,(V2 + 1) -' 1, the carrier of V1
Delete ((SB * L),(V2 + 1),(F + 1)) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of (V2 + 1) -' 1,(V2 + 1) -' 1, the carrier of V1
(Delete (B,(V2 + 1),(F + 1))) + (Delete ((SB * L),(V2 + 1),(F + 1))) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of (V2 + 1) -' 1,(V2 + 1) -' 1, the carrier of V1
Delete ((B + (SB * L)),(V2 + 1),(F + 1)) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of (V2 + 1) -' 1,(V2 + 1) -' 1, the carrier of V1
eval ((F9 *' <%((B * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1))))),((L * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1)))))%>),SB) is Element of the carrier of V1
eval (F9,SB) is Element of the carrier of V1
eval (<%((B * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1))))),((L * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1)))))%>,SB) is Element of the carrier of V1
(eval (F9,SB)) * (eval (<%((B * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1))))),((L * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1)))))%>,SB)) is Element of the carrier of V1
Det ((Delete (B,(V2 + 1),(F + 1))) + (SB * (Delete (L,(V2 + 1),(F + 1))))) is Element of the carrier of V1
(Det ((Delete (B,(V2 + 1),(F + 1))) + (SB * (Delete (L,(V2 + 1),(F + 1)))))) * (eval (<%((B * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1))))),((L * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1)))))%>,SB)) is Element of the carrier of V1
Minor ((B + (SB * L)),(V2 + 1),(F + 1)) is Element of the carrier of V1
Det (Delete ((B + (SB * L)),(V2 + 1),(F + 1))) is Element of the carrier of V1
(Minor ((B + (SB * L)),(V2 + 1),(F + 1))) * (((B + (SB * L)) * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1))))) is Element of the carrier of V1
Cofactor ((B + (SB * L)),(V2 + 1),(F + 1)) is Element of the carrier of V1
(V2 + 1) + (F + 1) is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() set
(power V1) . ((- (1_ V1)),((V2 + 1) + (F + 1))) is Element of the carrier of V1
((power V1) . ((- (1_ V1)),((V2 + 1) + (F + 1)))) * (Minor ((B + (SB * L)),(V2 + 1),(F + 1))) is Element of the carrier of V1
((B + (SB * L)) * ((V2 + 1),(F + 1))) * (Cofactor ((B + (SB * L)),(V2 + 1),(F + 1))) is Element of the carrier of V1
Sum ((LaplaceExpL ((B + (SB * L)),(V2 + 1))) | F) is Element of the carrier of V1
K132( the carrier of V1,((LaplaceExpL ((B + (SB * L)),(V2 + 1))) | F), the addF of V1) is Element of the carrier of V1
(Sum ((LaplaceExpL ((B + (SB * L)),(V2 + 1))) | F)) + (eval ((F9 *' <%((B * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1))))),((L * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1)))))%>),SB)) is Element of the carrier of V1
eval (D,SB) is Element of the carrier of V1
(eval (D,SB)) + (eval ((F9 *' <%((B * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1))))),((L * ((V2 + 1),(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + (V2 + 1)))))%>),SB)) is Element of the carrier of V1
0_. V1 is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) with_roots Element of bool [:NAT, the carrier of V1:]
F is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) with_roots Element of bool [:NAT, the carrier of V1:]
len F is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
f is Element of the carrier of V1
eval (F,f) is Element of the carrier of V1
f * L is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of V2 + 1,V2 + 1, the carrier of V1
B + (f * L) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of V2 + 1,V2 + 1, the carrier of V1
LaplaceExpL ((B + (f * L)),(V2 + 1)) is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
(LaplaceExpL ((B + (f * L)),(V2 + 1))) | {} is Relation-like NAT -defined the carrier of V1 -valued Function-like one-to-one constant functional empty V25() V26() V27() V29() V30() V31() finite finite-yielding V36() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V46() ext-real non positive non negative V165() FinSequence of the carrier of V1
Seg {} is Function-like functional empty V25() V26() V27() V29() V30() V31() finite V36() cardinal {} -element {} -element FinSequence-membered without_zero V46() ext-real non positive non negative V165() Element of bool NAT
{ b₁ where b₁ is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT : ( 1 <= b₁ & b₁ <= {} ) } is set
(LaplaceExpL ((B + (f * L)),(V2 + 1))) | (Seg {}) is Relation-like NAT -defined Function-like finite FinSubsequence-like set
Sum ((LaplaceExpL ((B + (f * L)),(V2 + 1))) | {}) is Element of the carrier of V1
the addF of V1 is Relation-like [: the carrier of V1, the carrier of V1:] -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [:[: the carrier of V1, the carrier of V1:], the carrier of V1:]
[: the carrier of V1, the carrier of V1:] is set
[:[: the carrier of V1, the carrier of V1:], the carrier of V1:] is set
bool [:[: the carrier of V1, the carrier of V1:], the carrier of V1:] is set
K132( the carrier of V1,((LaplaceExpL ((B + (f * L)),(V2 + 1))) | {}), the addF of V1) is Element of the carrier of V1
<*> the carrier of V1 is Relation-like NAT -defined the carrier of V1 -valued Function-like one-to-one constant functional empty V25() V26() V27() V29() V30() V31() finite finite-yielding V36() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V46() ext-real non positive non negative V165() FinSequence of the carrier of V1
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
F is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) Element of bool [:NAT, the carrier of V1:]
len F is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
f is Element of the carrier of V1
eval (F,f) is Element of the carrier of V1
f * L is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of V2 + 1,V2 + 1, the carrier of V1
B + (f * L) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of V2 + 1,V2 + 1, the carrier of V1
Det (B + (f * L)) is Element of the carrier of V1
LaplaceExpL ((B + (f * L)),(V2 + 1)) is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
len (LaplaceExpL ((B + (f * L)),(V2 + 1))) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
(LaplaceExpL ((B + (f * L)),(V2 + 1))) | (V2 + 1) is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
(LaplaceExpL ((B + (f * L)),(V2 + 1))) | (Seg (V2 + 1)) is Relation-like NAT -defined Function-like finite FinSubsequence-like set
Sum ((LaplaceExpL ((B + (f * L)),(V2 + 1))) | (V2 + 1)) is Element of the carrier of V1
the addF of V1 is Relation-like [: the carrier of V1, the carrier of V1:] -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [:[: the carrier of V1, the carrier of V1:], the carrier of V1:]
[: the carrier of V1, the carrier of V1:] is set
[:[: the carrier of V1, the carrier of V1:], the carrier of V1:] is set
bool [:[: the carrier of V1, the carrier of V1:], the carrier of V1:] is set
K132( the carrier of V1,((LaplaceExpL ((B + (f * L)),(V2 + 1))) | (V2 + 1)), the addF of V1) is Element of the carrier of V1
Sum (LaplaceExpL ((B + (f * L)),(V2 + 1))) is Element of the carrier of V1
K132( the carrier of V1,(LaplaceExpL ((B + (f * L)),(V2 + 1))), the addF of V1) is Element of the carrier of V1
{} + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
V2 is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of {} , {} , the carrier of V1
A is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of {} , {} , the carrier of V1
1_. V1 is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) Element of bool [:NAT, the carrier of V1:]
B is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) Element of bool [:NAT, the carrier of V1:]
len B is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
L is Element of the carrier of V1
eval (B,L) is Element of the carrier of V1
L * A is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of {} , {} , the carrier of V1
V2 + (L * A) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of {} , {} , the carrier of V1
Det (V2 + (L * A)) is Element of the carrier of V1
1_ V1 is Element of the carrier of V1
1. V1 is V65(V1) Element of the carrier of V1
the OneF of V1 is Element of the carrier of V1
V2 is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K,K, the carrier of V1
A is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K,K, the carrier of V1
K is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
K + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
V1 is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of V1 is non empty non trivial set
the carrier of V1 * is functional non empty FinSequence-membered FinSequenceSet of the carrier of V1
[:NAT, the carrier of V1:] is non trivial non finite set
bool [:NAT, the carrier of V1:] is non trivial non finite set
1. (V1,K) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K,K, the carrier of V1
V2 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
V2 + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
1. (V1,V2) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of V2,V2, the carrier of V1
(V2 + 1) + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
1. (V1,(V2 + 1)) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of V2 + 1,V2 + 1, the carrier of V1
B is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of V2 + 1,V2 + 1, the carrier of V1
Indices (1. (V1,(V2 + 1))) is set
Indices B is set
(V2 + 1) + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
(V2 + 1) -' 1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
Seg (V2 + 1) is non empty finite V2 + 1 -element without_zero Element of bool NAT
{ b₁ where b₁ is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT : ( 1 <= b₁ & b₁ <= V2 + 1 ) } is set
[:(Seg (V2 + 1)),(Seg (V2 + 1)):] is finite set
F is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
F + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
power V1 is Relation-like [: the carrier of V1,NAT:] -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [:[: the carrier of V1,NAT:], the carrier of V1:]
[: the carrier of V1,NAT:] is non trivial non finite set
[:[: the carrier of V1,NAT:], the carrier of V1:] is non trivial non finite set
bool [:[: the carrier of V1,NAT:], the carrier of V1:] is non trivial non finite set
1_ V1 is Element of the carrier of V1
1. V1 is V65(V1) Element of the carrier of V1
the OneF of V1 is Element of the carrier of V1
- (1_ V1) is Element of the carrier of V1
(F + 1) + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
(power V1) . ((- (1_ V1)),((F + 1) + 1)) is Element of the carrier of V1
B * (1,(F + 1)) is Element of the carrier of V1
(B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))) is Element of the carrier of V1
(1. (V1,(V2 + 1))) * (1,(F + 1)) is Element of the carrier of V1
((1. (V1,(V2 + 1))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))) is Element of the carrier of V1
<%((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))),(((1. (V1,(V2 + 1))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))))%> is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) Element of bool [:NAT, the carrier of V1:]
[1,(F + 1)] is Element of [:NAT,NAT:]
{1,(F + 1)} is non empty finite V36() set
{1} is non empty trivial finite V36() 1 -element set
{{1,(F + 1)},{1}} is non empty finite V36() set
(- (1_ V1)) * (- (1_ V1)) is Element of the carrier of V1
(1_ V1) * (1_ V1) is Element of the carrier of V1
2 -' 1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
2 - 1 is V46() ext-real V165() set
<%((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))),(((1. (V1,(V2 + 1))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))))%> . 1 is Element of the carrier of V1
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
len <%((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))),(((1. (V1,(V2 + 1))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))))%> is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
Delete (B,1,1) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of (V2 + 1) -' 1,(V2 + 1) -' 1, the carrier of V1
FA is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) Element of bool [:NAT, the carrier of V1:]
len FA is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
<%((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))),(((1. (V1,(V2 + 1))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))))%> *' FA is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) Element of bool [:NAT, the carrier of V1:]
FB is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) Element of bool [:NAT, the carrier of V1:]
len FB is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
FA . V2 is set
(len <%((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))),(((1. (V1,(V2 + 1))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))))%>) -' 1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
<%((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))),(((1. (V1,(V2 + 1))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))))%> . ((len <%((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))),(((1. (V1,(V2 + 1))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))))%>) -' 1) is Element of the carrier of V1
(len FA) -' 1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
FA . ((len FA) -' 1) is Element of the carrier of V1
(<%((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))),(((1. (V1,(V2 + 1))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))))%> . ((len <%((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))),(((1. (V1,(V2 + 1))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))))%>) -' 1)) * (FA . ((len FA) -' 1)) is Element of the carrier of V1
(V2 + 1) + 2 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
((V2 + 1) + 2) - 1 is V46() ext-real V165() set
SS is Element of the carrier of V1
eval (FB,SS) is Element of the carrier of V1
SS * (1. (V1,(V2 + 1))) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of V2 + 1,V2 + 1, the carrier of V1
B + (SS * (1. (V1,(V2 + 1)))) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of V2 + 1,V2 + 1, the carrier of V1
LaplaceExpL ((B + (SS * (1. (V1,(V2 + 1))))),1) is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
(LaplaceExpL ((B + (SS * (1. (V1,(V2 + 1))))),1)) | (F + 1) is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
Seg (F + 1) is non empty finite F + 1 -element without_zero Element of bool NAT
{ b₁ where b₁ is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT : ( 1 <= b₁ & b₁ <= F + 1 ) } is set
(LaplaceExpL ((B + (SS * (1. (V1,(V2 + 1))))),1)) | (Seg (F + 1)) is Relation-like NAT -defined Function-like finite FinSubsequence-like set
Sum ((LaplaceExpL ((B + (SS * (1. (V1,(V2 + 1))))),1)) | (F + 1)) is Element of the carrier of V1
the addF of V1 is Relation-like [: the carrier of V1, the carrier of V1:] -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [:[: the carrier of V1, the carrier of V1:], the carrier of V1:]
[: the carrier of V1, the carrier of V1:] is set
[:[: the carrier of V1, the carrier of V1:], the carrier of V1:] is set
bool [:[: the carrier of V1, the carrier of V1:], the carrier of V1:] is set
K132( the carrier of V1,((LaplaceExpL ((B + (SS * (1. (V1,(V2 + 1))))),1)) | (F + 1)), the addF of V1) is Element of the carrier of V1
SS * (1. (V1,V2)) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of V2,V2, the carrier of V1
(Delete (B,1,1)) + (SS * (1. (V1,V2))) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of (V2 + 1) -' 1,(V2 + 1) -' 1, the carrier of V1
Delete ((1. (V1,(V2 + 1))),1,1) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of (V2 + 1) -' 1,(V2 + 1) -' 1, the carrier of V1
SS * (Delete ((1. (V1,(V2 + 1))),1,1)) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of (V2 + 1) -' 1,(V2 + 1) -' 1, the carrier of V1
(Delete (B,1,1)) + (SS * (Delete ((1. (V1,(V2 + 1))),1,1))) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of (V2 + 1) -' 1,(V2 + 1) -' 1, the carrier of V1
Delete ((SS * (1. (V1,(V2 + 1)))),1,1) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of (V2 + 1) -' 1,(V2 + 1) -' 1, the carrier of V1
(Delete (B,1,1)) + (Delete ((SS * (1. (V1,(V2 + 1)))),1,1)) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of (V2 + 1) -' 1,(V2 + 1) -' 1, the carrier of V1
Delete ((B + (SS * (1. (V1,(V2 + 1))))),1,1) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of (V2 + 1) -' 1,(V2 + 1) -' 1, the carrier of V1
(((1. (V1,(V2 + 1))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))) * SS is Element of the carrier of V1
((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))) + ((((1. (V1,(V2 + 1))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))) * SS) is Element of the carrier of V1
((1. (V1,(V2 + 1))) * (1,(F + 1))) * SS is Element of the carrier of V1
(((1. (V1,(V2 + 1))) * (1,(F + 1))) * SS) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))) is Element of the carrier of V1
((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))) + ((((1. (V1,(V2 + 1))) * (1,(F + 1))) * SS) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))) is Element of the carrier of V1
(B * (1,(F + 1))) + (((1. (V1,(V2 + 1))) * (1,(F + 1))) * SS) is Element of the carrier of V1
((B * (1,(F + 1))) + (((1. (V1,(V2 + 1))) * (1,(F + 1))) * SS)) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))) is Element of the carrier of V1
(SS * (1. (V1,(V2 + 1)))) * (1,(F + 1)) is Element of the carrier of V1
(B * (1,(F + 1))) + ((SS * (1. (V1,(V2 + 1)))) * (1,(F + 1))) is Element of the carrier of V1
((B * (1,(F + 1))) + ((SS * (1. (V1,(V2 + 1)))) * (1,(F + 1)))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))) is Element of the carrier of V1
(B + (SS * (1. (V1,(V2 + 1))))) * (1,(F + 1)) is Element of the carrier of V1
((B + (SS * (1. (V1,(V2 + 1))))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))) is Element of the carrier of V1
dom (LaplaceExpL ((B + (SS * (1. (V1,(V2 + 1))))),1)) is finite Element of bool NAT
len (LaplaceExpL ((B + (SS * (1. (V1,(V2 + 1))))),1)) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
Seg (len (LaplaceExpL ((B + (SS * (1. (V1,(V2 + 1))))),1))) is finite len (LaplaceExpL ((B + (SS * (1. (V1,(V2 + 1))))),1)) -element without_zero Element of bool NAT
{ b₁ where b₁ is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT : ( 1 <= b₁ & b₁ <= len (LaplaceExpL ((B + (SS * (1. (V1,(V2 + 1))))),1)) ) } is set
eval ((<%((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))),(((1. (V1,(V2 + 1))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))))%> *' FA),SS) is Element of the carrier of V1
eval (<%((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))),(((1. (V1,(V2 + 1))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))))%>,SS) is Element of the carrier of V1
eval (FA,SS) is Element of the carrier of V1
(eval (<%((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))),(((1. (V1,(V2 + 1))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))))%>,SS)) * (eval (FA,SS)) is Element of the carrier of V1
Det ((Delete (B,1,1)) + (SS * (1. (V1,V2)))) is Element of the carrier of V1
(eval (<%((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))),(((1. (V1,(V2 + 1))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))))%>,SS)) * (Det ((Delete (B,1,1)) + (SS * (1. (V1,V2))))) is Element of the carrier of V1
Minor ((B + (SS * (1. (V1,(V2 + 1))))),1,1) is Element of the carrier of V1
Det (Delete ((B + (SS * (1. (V1,(V2 + 1))))),1,1)) is Element of the carrier of V1
(B + (SS * (1. (V1,(V2 + 1))))) * (1,1) is Element of the carrier of V1
((B + (SS * (1. (V1,(V2 + 1))))) * (1,1)) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))) is Element of the carrier of V1
(Minor ((B + (SS * (1. (V1,(V2 + 1))))),1,1)) * (((B + (SS * (1. (V1,(V2 + 1))))) * (1,1)) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))) is Element of the carrier of V1
Cofactor ((B + (SS * (1. (V1,(V2 + 1))))),1,1) is Element of the carrier of V1
1 + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() set
(power V1) . ((- (1_ V1)),(1 + 1)) is Element of the carrier of V1
((power V1) . ((- (1_ V1)),(1 + 1))) * (Minor ((B + (SS * (1. (V1,(V2 + 1))))),1,1)) is Element of the carrier of V1
((B + (SS * (1. (V1,(V2 + 1))))) * (1,1)) * (Cofactor ((B + (SS * (1. (V1,(V2 + 1))))),1,1)) is Element of the carrier of V1
(LaplaceExpL ((B + (SS * (1. (V1,(V2 + 1))))),1)) . 1 is set
(LaplaceExpL ((B + (SS * (1. (V1,(V2 + 1))))),1)) /. 1 is Element of the carrier of V1
<*((LaplaceExpL ((B + (SS * (1. (V1,(V2 + 1))))),1)) /. 1)*> is Relation-like NAT -defined the carrier of V1 -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of V1
1 -tuples_on the carrier of V1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of V1
[1,((LaplaceExpL ((B + (SS * (1. (V1,(V2 + 1))))),1)) /. 1)] is set
{1,((LaplaceExpL ((B + (SS * (1. (V1,(V2 + 1))))),1)) /. 1)} is non empty finite set
{{1,((LaplaceExpL ((B + (SS * (1. (V1,(V2 + 1))))),1)) /. 1)},{1}} is non empty finite V36() set
{[1,((LaplaceExpL ((B + (SS * (1. (V1,(V2 + 1))))),1)) /. 1)]} is Function-like non empty trivial finite 1 -element set
Sum <*((LaplaceExpL ((B + (SS * (1. (V1,(V2 + 1))))),1)) /. 1)*> is Element of the carrier of V1
K132( the carrier of V1,<*((LaplaceExpL ((B + (SS * (1. (V1,(V2 + 1))))),1)) /. 1)*>, the addF of V1) is Element of the carrier of V1
<*(eval ((<%((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))),(((1. (V1,(V2 + 1))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))))%> *' FA),SS))*> is Relation-like NAT -defined the carrier of V1 -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of V1
[1,(eval ((<%((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))),(((1. (V1,(V2 + 1))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))))%> *' FA),SS))] is set
{1,(eval ((<%((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))),(((1. (V1,(V2 + 1))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))))%> *' FA),SS))} is non empty finite set
{{1,(eval ((<%((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))),(((1. (V1,(V2 + 1))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))))%> *' FA),SS))},{1}} is non empty finite V36() set
{[1,(eval ((<%((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))),(((1. (V1,(V2 + 1))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))))%> *' FA),SS))]} is Function-like non empty trivial finite 1 -element set
Sum <*(eval ((<%((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))),(((1. (V1,(V2 + 1))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))))%> *' FA),SS))*> is Element of the carrier of V1
K132( the carrier of V1,<*(eval ((<%((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))),(((1. (V1,(V2 + 1))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))))%> *' FA),SS))*>, the addF of V1) is Element of the carrier of V1
Delete (B,1,(F + 1)) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of (V2 + 1) -' 1,(V2 + 1) -' 1, the carrier of V1
Delete ((1. (V1,(V2 + 1))),1,(F + 1)) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of (V2 + 1) -' 1,(V2 + 1) -' 1, the carrier of V1
FA is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) Element of bool [:NAT, the carrier of V1:]
len FA is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
FB is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) Element of bool [:NAT, the carrier of V1:]
len FB is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
FB is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) Element of bool [:NAT, the carrier of V1:]
len FB is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))) * FA is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) Element of bool [:NAT, the carrier of V1:]
FB + (((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))) * FA) is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) Element of bool [:NAT, the carrier of V1:]
SS is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) Element of bool [:NAT, the carrier of V1:]
len SS is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
len (((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))) * FA) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
max ((len (((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))) * FA)),(len FB)) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
F9 is Element of the carrier of V1
eval (SS,F9) is Element of the carrier of V1
F9 * (1. (V1,(V2 + 1))) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of V2 + 1,V2 + 1, the carrier of V1
B + (F9 * (1. (V1,(V2 + 1)))) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of V2 + 1,V2 + 1, the carrier of V1
LaplaceExpL ((B + (F9 * (1. (V1,(V2 + 1))))),1) is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
(LaplaceExpL ((B + (F9 * (1. (V1,(V2 + 1))))),1)) | (F + 1) is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
Seg (F + 1) is non empty finite F + 1 -element without_zero Element of bool NAT
{ b₁ where b₁ is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT : ( 1 <= b₁ & b₁ <= F + 1 ) } is set
(LaplaceExpL ((B + (F9 * (1. (V1,(V2 + 1))))),1)) | (Seg (F + 1)) is Relation-like NAT -defined Function-like finite FinSubsequence-like set
Sum ((LaplaceExpL ((B + (F9 * (1. (V1,(V2 + 1))))),1)) | (F + 1)) is Element of the carrier of V1
the addF of V1 is Relation-like [: the carrier of V1, the carrier of V1:] -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [:[: the carrier of V1, the carrier of V1:], the carrier of V1:]
[: the carrier of V1, the carrier of V1:] is set
[:[: the carrier of V1, the carrier of V1:], the carrier of V1:] is set
bool [:[: the carrier of V1, the carrier of V1:], the carrier of V1:] is set
K132( the carrier of V1,((LaplaceExpL ((B + (F9 * (1. (V1,(V2 + 1))))),1)) | (F + 1)), the addF of V1) is Element of the carrier of V1
dom (LaplaceExpL ((B + (F9 * (1. (V1,(V2 + 1))))),1)) is finite Element of bool NAT
len (LaplaceExpL ((B + (F9 * (1. (V1,(V2 + 1))))),1)) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
Seg (len (LaplaceExpL ((B + (F9 * (1. (V1,(V2 + 1))))),1))) is finite len (LaplaceExpL ((B + (F9 * (1. (V1,(V2 + 1))))),1)) -element without_zero Element of bool NAT
{ b₁ where b₁ is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT : ( 1 <= b₁ & b₁ <= len (LaplaceExpL ((B + (F9 * (1. (V1,(V2 + 1))))),1)) ) } is set
(LaplaceExpL ((B + (F9 * (1. (V1,(V2 + 1))))),1)) | F is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
Seg F is finite F -element without_zero Element of bool NAT
{ b₁ where b₁ is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(LaplaceExpL ((B + (F9 * (1. (V1,(V2 + 1))))),1)) | (Seg F) is Relation-like NAT -defined Function-like finite FinSubsequence-like set
(LaplaceExpL ((B + (F9 * (1. (V1,(V2 + 1))))),1)) . (F + 1) is set
<*((LaplaceExpL ((B + (F9 * (1. (V1,(V2 + 1))))),1)) . (F + 1))*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
[1,((LaplaceExpL ((B + (F9 * (1. (V1,(V2 + 1))))),1)) . (F + 1))] is set
{1,((LaplaceExpL ((B + (F9 * (1. (V1,(V2 + 1))))),1)) . (F + 1))} is non empty finite set
{{1,((LaplaceExpL ((B + (F9 * (1. (V1,(V2 + 1))))),1)) . (F + 1))},{1}} is non empty finite V36() set
{[1,((LaplaceExpL ((B + (F9 * (1. (V1,(V2 + 1))))),1)) . (F + 1))]} is Function-like non empty trivial finite 1 -element set
((LaplaceExpL ((B + (F9 * (1. (V1,(V2 + 1))))),1)) | F) ^ <*((LaplaceExpL ((B + (F9 * (1. (V1,(V2 + 1))))),1)) . (F + 1))*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
(B * (1,(F + 1))) + (0. V1) is Element of the carrier of V1
((B * (1,(F + 1))) + (0. V1)) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))) is Element of the carrier of V1
F9 * (0. V1) is Element of the carrier of V1
(B * (1,(F + 1))) + (F9 * (0. V1)) is Element of the carrier of V1
((B * (1,(F + 1))) + (F9 * (0. V1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))) is Element of the carrier of V1
F9 * ((1. (V1,(V2 + 1))) * (1,(F + 1))) is Element of the carrier of V1
(B * (1,(F + 1))) + (F9 * ((1. (V1,(V2 + 1))) * (1,(F + 1)))) is Element of the carrier of V1
((B * (1,(F + 1))) + (F9 * ((1. (V1,(V2 + 1))) * (1,(F + 1))))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))) is Element of the carrier of V1
(F9 * (1. (V1,(V2 + 1)))) * (1,(F + 1)) is Element of the carrier of V1
(B * (1,(F + 1))) + ((F9 * (1. (V1,(V2 + 1)))) * (1,(F + 1))) is Element of the carrier of V1
((B * (1,(F + 1))) + ((F9 * (1. (V1,(V2 + 1)))) * (1,(F + 1)))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))) is Element of the carrier of V1
(B + (F9 * (1. (V1,(V2 + 1))))) * (1,(F + 1)) is Element of the carrier of V1
((B + (F9 * (1. (V1,(V2 + 1))))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1))) is Element of the carrier of V1
F9 * (Delete ((1. (V1,(V2 + 1))),1,(F + 1))) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of (V2 + 1) -' 1,(V2 + 1) -' 1, the carrier of V1
(Delete (B,1,(F + 1))) + (F9 * (Delete ((1. (V1,(V2 + 1))),1,(F + 1)))) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of (V2 + 1) -' 1,(V2 + 1) -' 1, the carrier of V1
Delete ((F9 * (1. (V1,(V2 + 1)))),1,(F + 1)) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of (V2 + 1) -' 1,(V2 + 1) -' 1, the carrier of V1
(Delete (B,1,(F + 1))) + (Delete ((F9 * (1. (V1,(V2 + 1)))),1,(F + 1))) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of (V2 + 1) -' 1,(V2 + 1) -' 1, the carrier of V1
Delete ((B + (F9 * (1. (V1,(V2 + 1))))),1,(F + 1)) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of (V2 + 1) -' 1,(V2 + 1) -' 1, the carrier of V1
eval ((((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))) * FA),F9) is Element of the carrier of V1
eval (FA,F9) is Element of the carrier of V1
((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))) * (eval (FA,F9)) is Element of the carrier of V1
Minor ((B + (F9 * (1. (V1,(V2 + 1))))),1,(F + 1)) is Element of the carrier of V1
Det (Delete ((B + (F9 * (1. (V1,(V2 + 1))))),1,(F + 1))) is Element of the carrier of V1
(Minor ((B + (F9 * (1. (V1,(V2 + 1))))),1,(F + 1))) * (((B + (F9 * (1. (V1,(V2 + 1))))) * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))) is Element of the carrier of V1
Cofactor ((B + (F9 * (1. (V1,(V2 + 1))))),1,(F + 1)) is Element of the carrier of V1
1 + (F + 1) is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() set
(power V1) . ((- (1_ V1)),(1 + (F + 1))) is Element of the carrier of V1
((power V1) . ((- (1_ V1)),(1 + (F + 1)))) * (Minor ((B + (F9 * (1. (V1,(V2 + 1))))),1,(F + 1))) is Element of the carrier of V1
((B + (F9 * (1. (V1,(V2 + 1))))) * (1,(F + 1))) * (Cofactor ((B + (F9 * (1. (V1,(V2 + 1))))),1,(F + 1))) is Element of the carrier of V1
Sum ((LaplaceExpL ((B + (F9 * (1. (V1,(V2 + 1))))),1)) | F) is Element of the carrier of V1
K132( the carrier of V1,((LaplaceExpL ((B + (F9 * (1. (V1,(V2 + 1))))),1)) | F), the addF of V1) is Element of the carrier of V1
(Sum ((LaplaceExpL ((B + (F9 * (1. (V1,(V2 + 1))))),1)) | F)) + (eval ((((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))) * FA),F9)) is Element of the carrier of V1
eval (FB,F9) is Element of the carrier of V1
(eval (FB,F9)) + (eval ((((B * (1,(F + 1))) * ((power V1) . ((- (1_ V1)),((F + 1) + 1)))) * FA),F9)) is Element of the carrier of V1
F is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) Element of bool [:NAT, the carrier of V1:]
len F is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
f is Element of the carrier of V1
eval (F,f) is Element of the carrier of V1
f * (1. (V1,(V2 + 1))) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of V2 + 1,V2 + 1, the carrier of V1
B + (f * (1. (V1,(V2 + 1)))) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of V2 + 1,V2 + 1, the carrier of V1
Det (B + (f * (1. (V1,(V2 + 1))))) is Element of the carrier of V1
LaplaceExpL ((B + (f * (1. (V1,(V2 + 1))))),1) is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
len (LaplaceExpL ((B + (f * (1. (V1,(V2 + 1))))),1)) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
(LaplaceExpL ((B + (f * (1. (V1,(V2 + 1))))),1)) | (len (LaplaceExpL ((B + (f * (1. (V1,(V2 + 1))))),1))) is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
Seg (len (LaplaceExpL ((B + (f * (1. (V1,(V2 + 1))))),1))) is finite len (LaplaceExpL ((B + (f * (1. (V1,(V2 + 1))))),1)) -element without_zero Element of bool NAT
{ b₁ where b₁ is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT : ( 1 <= b₁ & b₁ <= len (LaplaceExpL ((B + (f * (1. (V1,(V2 + 1))))),1)) ) } is set
(LaplaceExpL ((B + (f * (1. (V1,(V2 + 1))))),1)) | (Seg (len (LaplaceExpL ((B + (f * (1. (V1,(V2 + 1))))),1)))) is Relation-like NAT -defined Function-like finite FinSubsequence-like set
Sum ((LaplaceExpL ((B + (f * (1. (V1,(V2 + 1))))),1)) | (len (LaplaceExpL ((B + (f * (1. (V1,(V2 + 1))))),1)))) is Element of the carrier of V1
the addF of V1 is Relation-like [: the carrier of V1, the carrier of V1:] -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [:[: the carrier of V1, the carrier of V1:], the carrier of V1:]
[: the carrier of V1, the carrier of V1:] is set
[:[: the carrier of V1, the carrier of V1:], the carrier of V1:] is set
bool [:[: the carrier of V1, the carrier of V1:], the carrier of V1:] is set
K132( the carrier of V1,((LaplaceExpL ((B + (f * (1. (V1,(V2 + 1))))),1)) | (len (LaplaceExpL ((B + (f * (1. (V1,(V2 + 1))))),1)))), the addF of V1) is Element of the carrier of V1
Sum (LaplaceExpL ((B + (f * (1. (V1,(V2 + 1))))),1)) is Element of the carrier of V1
K132( the carrier of V1,(LaplaceExpL ((B + (f * (1. (V1,(V2 + 1))))),1)), the addF of V1) is Element of the carrier of V1
{} + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
1. (V1,{}) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of {} , {} , the carrier of V1
V2 is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of {} , {} , the carrier of V1
1_. V1 is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) Element of bool [:NAT, the carrier of V1:]
A is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total V234(V1) Element of bool [:NAT, the carrier of V1:]
len A is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
B is Element of the carrier of V1
eval (A,B) is Element of the carrier of V1
B * (1. (V1,{})) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of {} , {} , the carrier of V1
V2 + (B * (1. (V1,{}))) is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of {} , {} , the carrier of V1
Det (V2 + (B * (1. (V1,{})))) is Element of the carrier of V1
1_ V1 is Element of the carrier of V1
1. V1 is V65(V1) Element of the carrier of V1
the OneF of V1 is Element of the carrier of V1
V2 is Relation-like NAT -defined the carrier of V1 * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of K,K, the carrier of V1
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
V2 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V2 is non empty set
[: the carrier of V1, the carrier of V2:] is set
bool [: the carrier of V1, the carrier of V2:] is set
A is Relation-like the carrier of V1 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V2:]
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V1
the carrier of B is non empty set
A | B is Relation-like the carrier of B -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of B, the carrier of V2:]
[: the carrier of B, the carrier of V2:] is set
bool [: the carrier of B, the carrier of V2:] is set
A | the carrier of B is Relation-like Function-like set
L is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V2
the carrier of L is non empty set
[: the carrier of B, the carrier of L:] is set
bool [: the carrier of B, the carrier of L:] is set
F is Relation-like the carrier of B -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [: the carrier of B, the carrier of L:]
the carrier of K is non empty non trivial set
f is Element of the carrier of K
D is Element of the carrier of B
f * D is Element of the carrier of B
F . (f * D) is Element of the carrier of L
(A | B) . D is Element of the carrier of V2
f * ((A | B) . D) is Element of the carrier of V2
F . D is Element of the carrier of L
f * (F . D) is Element of the carrier of L
f is Element of the carrier of B
D is Element of the carrier of B
f + D is Element of the carrier of B
F . (f + D) is Element of the carrier of L
(A | B) . f is Element of the carrier of V2
(A | B) . D is Element of the carrier of V2
((A | B) . f) + ((A | B) . D) is Element of the carrier of V2
F . f is Element of the carrier of L
F . D is Element of the carrier of L
(F . f) + (F . D) is Element of the carrier of L
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
1 -VectSp_over K is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional VectSpStr over K
V1 is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional VectSpStr over K
dim V1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
the carrier of V1 is non empty set
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
(Omega). V1 is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of V1
the addF of V1 is Relation-like [: the carrier of V1, the carrier of V1:] -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [:[: the carrier of V1, the carrier of V1:], the carrier of V1:]
[: the carrier of V1, the carrier of V1:] is set
[:[: the carrier of V1, the carrier of V1:], the carrier of V1:] is set
bool [:[: the carrier of V1, the carrier of V1:], the carrier of V1:] is set
the lmult of V1 is Relation-like [: the carrier of K, the carrier of V1:] -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [:[: the carrier of K, the carrier of V1:], the carrier of V1:]
the carrier of K is non empty non trivial set
[: the carrier of K, the carrier of V1:] is set
[:[: the carrier of K, the carrier of V1:], the carrier of V1:] is set
bool [:[: the carrier of K, the carrier of V1:], the carrier of V1:] is set
VectSpStr(# the carrier of V1, the addF of V1, the ZeroF of V1, the lmult of V1 #) is non empty strict VectSpStr over K
V2 is Element of the carrier of V1
{V2} is non empty trivial finite 1 -element Element of bool the carrier of V1
bool the carrier of V1 is set
Lin {V2} is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of V1
K is non empty doubleLoopStr
V1 is non empty VectSpStr over K
the carrier of V1 is non empty set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
1_ K is Element of the carrier of K
the carrier of K is non empty non trivial set
1. K is V65(K) Element of the carrier of K
the OneF of K is Element of the carrier of K
V1 is non empty non trivial right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
id V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
the carrier of V1 is non empty non trivial set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
id the carrier of V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
V2 is Element of the carrier of V1
(id V1) . V2 is Element of the carrier of V1
(1_ K) * V2 is Element of the carrier of V1
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V1 is non empty non trivial right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty non trivial set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
id V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
id the carrier of V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
K is non empty doubleLoopStr
V1 is non empty VectSpStr over K
the carrier of V1 is non empty set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
the carrier of K is non empty set
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
A is Element of the carrier of V1
V2 . A is Element of the carrier of V1
B is Element of the carrier of K
B * A is Element of the carrier of V1
K is non empty doubleLoopStr
V1 is non empty VectSpStr over K
the carrier of V1 is non empty set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
the carrier of K is non empty set
V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
A is Element of the carrier of K
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
B is Element of the carrier of V1
V2 . B is Element of the carrier of V1
A * B is Element of the carrier of V1
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of K is non empty non trivial set
0. K is V65(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
V1 is non empty non trivial right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty non trivial set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
V2 is Element of the carrier of V1
A is Element of the carrier of K
B is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total (K,V1) Element of bool [: the carrier of V1, the carrier of V1:]
A * B is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
L is (K,V1,B)
A * L is Element of the carrier of K
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
F is Element of the carrier of V1
B . F is Element of the carrier of V1
L * F is Element of the carrier of V1
(A * B) . F is Element of the carrier of V1
A * (L * F) is Element of the carrier of V1
(A * L) * F is Element of the carrier of V1
(A * B) . V2 is Element of the carrier of V1
B . V2 is Element of the carrier of V1
A * (B . V2) is Element of the carrier of V1
L * V2 is Element of the carrier of V1
A * (L * V2) is Element of the carrier of V1
(A * L) * V2 is Element of the carrier of V1
- (A * (L * V2)) is Element of the carrier of V1
(A * (B . V2)) + (- (A * (L * V2))) is Element of the carrier of V1
- (L * V2) is Element of the carrier of V1
A * (- (L * V2)) is Element of the carrier of V1
(A * (B . V2)) + (A * (- (L * V2))) is Element of the carrier of V1
(B . V2) - (L * V2) is Element of the carrier of V1
(B . V2) + (- (L * V2)) is Element of the carrier of V1
A * ((B . V2) - (L * V2)) is Element of the carrier of V1
- (B . V2) is Element of the carrier of V1
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of K is non empty non trivial set
V1 is non empty non trivial right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty non trivial set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total (K,V1) Element of bool [: the carrier of V1, the carrier of V1:]
A is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total (K,V1) Element of bool [: the carrier of V1, the carrier of V1:]
V2 + A is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
B is Element of the carrier of K
L is Element of the carrier of K
B + L is Element of the carrier of K
f is Element of the carrier of V1
(V2 + A) . f is Element of the carrier of V1
V2 . f is Element of the carrier of V1
A . f is Element of the carrier of V1
(V2 . f) + (A . f) is Element of the carrier of V1
B * f is Element of the carrier of V1
(B * f) + (A . f) is Element of the carrier of V1
L * f is Element of the carrier of V1
(B * f) + (L * f) is Element of the carrier of V1
(B + L) * f is Element of the carrier of V1
D is Element of the carrier of V1
(V2 + A) . D is Element of the carrier of V1
V2 . D is Element of the carrier of V1
A . D is Element of the carrier of V1
(V2 . D) + (A . D) is Element of the carrier of V1
B * D is Element of the carrier of V1
(B * D) + (A . D) is Element of the carrier of V1
L * D is Element of the carrier of V1
(B * D) + (L * D) is Element of the carrier of V1
(B + L) * D is Element of the carrier of V1
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
1_ K is Element of the carrier of K
the carrier of K is non empty non trivial set
1. K is V65(K) Element of the carrier of K
the OneF of K is Element of the carrier of K
V1 is non empty non trivial right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
id V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
the carrier of V1 is non empty non trivial set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
id the carrier of V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
V2 is Element of the carrier of V1
(id V1) . V2 is Element of the carrier of V1
(1_ K) * V2 is Element of the carrier of V1
V2 is Element of the carrier of V1
(id V1) . V2 is Element of the carrier of V1
(1_ K) * V2 is Element of the carrier of V1
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
1_ K is Element of the carrier of K
the carrier of K is non empty non trivial set
1. K is V65(K) Element of the carrier of K
the OneF of K is Element of the carrier of K
V1 is non empty non trivial right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
id V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
the carrier of V1 is non empty non trivial set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
id the carrier of V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
V2 is (K,V1, id V1)
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
A is Element of the carrier of V1
(id V1) . A is Element of the carrier of V1
V2 * A is Element of the carrier of V1
(1_ K) * A is Element of the carrier of V1
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
0. K is V65(K) Element of the carrier of K
the carrier of K is non empty non trivial set
the ZeroF of K is Element of the carrier of K
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
ker V2 is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V1
the carrier of (ker V2) is non empty set
0. (ker V2) is V65( ker V2) Element of the carrier of (ker V2)
the ZeroF of (ker V2) is Element of the carrier of (ker V2)
A is Element of the carrier of (ker V2)
B is Element of the carrier of V1
V2 . B is Element of the carrier of V1
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
(0. K) * B is Element of the carrier of V1
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of K is non empty non trivial set
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
id V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
id the carrier of V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
A is Element of the carrier of K
- A is Element of the carrier of K
(- A) * (id V1) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
V2 + ((- A) * (id V1)) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
ker (V2 + ((- A) * (id V1))) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V1
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
B is Element of the carrier of V1
V2 . B is Element of the carrier of V1
A * B is Element of the carrier of V1
(V2 + ((- A) * (id V1))) . B is Element of the carrier of V1
((- A) * (id V1)) . B is Element of the carrier of V1
(V2 . B) + (((- A) * (id V1)) . B) is Element of the carrier of V1
(id V1) . B is Element of the carrier of V1
(- A) * ((id V1) . B) is Element of the carrier of V1
(V2 . B) + ((- A) * ((id V1) . B)) is Element of the carrier of V1
(- A) * B is Element of the carrier of V1
(V2 . B) + ((- A) * B) is Element of the carrier of V1
A + (- A) is Element of the carrier of K
(A + (- A)) * B is Element of the carrier of V1
0. K is V65(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
(0. K) * B is Element of the carrier of V1
the carrier of (ker (V2 + ((- A) * (id V1)))) is non empty set
0. (ker (V2 + ((- A) * (id V1)))) is V65( ker (V2 + ((- A) * (id V1)))) Element of the carrier of (ker (V2 + ((- A) * (id V1))))
the ZeroF of (ker (V2 + ((- A) * (id V1)))) is Element of the carrier of (ker (V2 + ((- A) * (id V1))))
B is Element of the carrier of (ker (V2 + ((- A) * (id V1))))
L is Element of the carrier of V1
(V2 + ((- A) * (id V1))) . L is Element of the carrier of V1
V2 . L is Element of the carrier of V1
((- A) * (id V1)) . L is Element of the carrier of V1
(V2 . L) + (((- A) * (id V1)) . L) is Element of the carrier of V1
(id V1) . L is Element of the carrier of V1
(- A) * ((id V1) . L) is Element of the carrier of V1
(V2 . L) + ((- A) * ((id V1) . L)) is Element of the carrier of V1
(- A) * L is Element of the carrier of V1
(V2 . L) + ((- A) * L) is Element of the carrier of V1
- ((- A) * L) is Element of the carrier of V1
- (- A) is Element of the carrier of K
(- (- A)) * L is Element of the carrier of V1
A * L is Element of the carrier of V1
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of K is non empty non trivial set
0. K is V65(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
V1 is Element of the carrier of K
- V1 is Element of the carrier of K
V2 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional VectSpStr over K
the carrier of V2 is non empty set
[: the carrier of V2, the carrier of V2:] is set
bool [: the carrier of V2, the carrier of V2:] is set
id V2 is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
id the carrier of V2 is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of V2, the carrier of V2:]
(- V1) * (id V2) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
A is Relation-like NAT -defined the carrier of V2 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V2
len A is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
B is Relation-like NAT -defined the carrier of V2 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V2
L is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
L + ((- V1) * (id V2)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
AutEqMt ((L + ((- V1) * (id V2))),A,B) is Relation-like NAT -defined the carrier of K * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len A, len A, the carrier of K
the carrier of K * is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
Det (AutEqMt ((L + ((- V1) * (id V2))),A,B)) is Element of the carrier of K
dim V2 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
ker (L + ((- V1) * (id V2))) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of V2
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed algebraic-closed doubleLoopStr
V1 is non empty non trivial right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional VectSpStr over K
the carrier of V1 is non empty non trivial set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1 is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1
AutMt (V2, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1) is Relation-like NAT -defined the carrier of K * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, 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
len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
[:NAT, the carrier of K:] is non trivial non finite set
bool [:NAT, the carrier of K:] is non trivial non finite set
(len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1) + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
1. (K,(len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1)) is Relation-like NAT -defined the carrier of K * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the carrier of K
L is Relation-like NAT -defined the carrier of K -valued Function-like non empty total quasi_total V234(K) Element of bool [:NAT, the carrier of K:]
len L is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
dim V1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
1 + {} is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
F is Element of the carrier of K
id V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
id the carrier of V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
AutMt ((id V1), the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1) is Relation-like NAT -defined the carrier of K * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the carrier of K
F * (AutMt ((id V1), the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1)) is Relation-like NAT -defined the carrier of K * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the carrier of K
Mx2Tran ((F * (AutMt ((id V1), the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1))), the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
Mx2Tran ((AutMt ((id V1), the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1)), the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
F * (Mx2Tran ((AutMt ((id V1), the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1)), the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1)) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
F * (id V1) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
AutMt ((F * (id V1)), the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1) is Relation-like NAT -defined the carrier of K * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the carrier of K
Mx2Tran ((AutMt ((F * (id V1)), the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1)), the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
0. K is V65(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
eval (L,F) is Element of the carrier of K
F * (1. (K,(len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1))) is Relation-like NAT -defined the carrier of K * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the carrier of K
(AutMt (V2, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1)) + (F * (1. (K,(len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1)))) is Relation-like NAT -defined the carrier of K * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the carrier of K
Det ((AutMt (V2, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1)) + (F * (1. (K,(len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1))))) is Element of the carrier of K
(AutMt (V2, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1)) + (F * (AutMt ((id V1), the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1))) is Relation-like NAT -defined the carrier of K * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the carrier of K
Det ((AutMt (V2, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1)) + (F * (AutMt ((id V1), the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1)))) is Element of the carrier of K
(AutMt (V2, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1)) + (AutMt ((F * (id V1)), the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1)) is Relation-like NAT -defined the carrier of K * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the carrier of K
Det ((AutMt (V2, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1)) + (AutMt ((F * (id V1)), the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1))) is Element of the carrier of K
V2 + (F * (id V1)) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
AutMt ((V2 + (F * (id V1))), the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1) is Relation-like NAT -defined the carrier of K * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the carrier of K
Det (AutMt ((V2 + (F * (id V1))), the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1)) is Element of the carrier of K
- F is Element of the carrier of K
- (- F) is Element of the carrier of K
(- (- F)) * (id V1) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
V2 + ((- (- F)) * (id V1)) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
AutMt ((V2 + ((- (- F)) * (id V1))), the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1) is Relation-like NAT -defined the carrier of K * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the carrier of K
Det (AutMt ((V2 + ((- (- F)) * (id V1))), the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1)) is Element of the carrier of K
AutEqMt ((V2 + ((- (- F)) * (id V1))), the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1) is Relation-like NAT -defined the carrier of K * -valued Function-like finite FinSequence-like FinSubsequence-like tabular Matrix of len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, len the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the carrier of K
Det (AutEqMt ((V2 + ((- (- F)) * (id V1))), the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1, the Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like OrdBasis of V1)) is Element of the carrier of K
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of K is non empty non trivial set
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
id V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
id the carrier of V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
V2 is Element of the carrier of V1
A is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
B is Element of the carrier of K
- B is Element of the carrier of K
(- B) * (id V1) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
A + ((- B) * (id V1)) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
ker (A + ((- B) * (id V1))) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V1
A . V2 is Element of the carrier of V1
B * V2 is Element of the carrier of V1
(A + ((- B) * (id V1))) . V2 is Element of the carrier of V1
((- B) * (id V1)) . V2 is Element of the carrier of V1
(A . V2) + (((- B) * (id V1)) . V2) is Element of the carrier of V1
(id V1) . V2 is Element of the carrier of V1
(- B) * ((id V1) . V2) is Element of the carrier of V1
(A . V2) + ((- B) * ((id V1) . V2)) is Element of the carrier of V1
(- B) * V2 is Element of the carrier of V1
(A . V2) + ((- B) * V2) is Element of the carrier of V1
B + (- B) is Element of the carrier of K
(B + (- B)) * V2 is Element of the carrier of V1
0. K is V65(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
(0. K) * V2 is Element of the carrier of V1
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
- ((- B) * V2) is Element of the carrier of V1
- (- B) is Element of the carrier of K
(- (- B)) * V2 is Element of the carrier of V1
K is 1-sorted
the carrier of K is set
[: the carrier of K, the carrier of K:] is set
bool [: the carrier of K, the carrier of K:] is set
GFuncs the carrier of K is non empty strict unital associative constituted-Functions SubStr of GPFuncs the carrier of K
GPFuncs the carrier of K is non empty strict unital associative constituted-Functions multMagma
the carrier of (GFuncs the carrier of K) is non empty set
V1 is Relation-like the carrier of K -defined the carrier of K -valued Function-like total quasi_total Element of bool [: the carrier of K, the carrier of K:]
V2 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
A is Relation-like Function-like Element of the carrier of (GFuncs the carrier of K)
V2 |-> A is Relation-like NAT -defined the carrier of (GFuncs the carrier of K) -valued Function-like finite V2 -element FinSequence-like FinSubsequence-like Element of V2 -tuples_on the carrier of (GFuncs the carrier of K)
V2 -tuples_on the carrier of (GFuncs the carrier of K) is functional non empty FinSequence-membered FinSequenceSet of the carrier of (GFuncs the carrier of K)
Product (V2 |-> A) is Relation-like Function-like Element of the carrier of (GFuncs the carrier of K)
B is Relation-like the carrier of K -defined the carrier of K -valued Function-like total quasi_total Element of bool [: the carrier of K, the carrier of K:]
L is Relation-like Function-like Element of the carrier of (GFuncs the carrier of K)
V2 |-> L is Relation-like NAT -defined the carrier of (GFuncs the carrier of K) -valued Function-like finite V2 -element FinSequence-like FinSubsequence-like Element of V2 -tuples_on the carrier of (GFuncs the carrier of K)
Product (V2 |-> L) is Relation-like Function-like Element of the carrier of (GFuncs the carrier of K)
B is Relation-like the carrier of K -defined the carrier of K -valued Function-like total quasi_total Element of bool [: the carrier of K, the carrier of K:]
L is Relation-like the carrier of K -defined the carrier of K -valued Function-like total quasi_total Element of bool [: the carrier of K, the carrier of K:]
A is Relation-like Function-like Element of the carrier of (GFuncs the carrier of K)
V2 |-> A is Relation-like NAT -defined the carrier of (GFuncs the carrier of K) -valued Function-like finite V2 -element FinSequence-like FinSubsequence-like Element of V2 -tuples_on the carrier of (GFuncs the carrier of K)
V2 -tuples_on the carrier of (GFuncs the carrier of K) is functional non empty FinSequence-membered FinSequenceSet of the carrier of (GFuncs the carrier of K)
Product (V2 |-> A) is Relation-like Function-like Element of the carrier of (GFuncs the carrier of K)
K is 1-sorted
the carrier of K is set
[: the carrier of K, the carrier of K:] is set
bool [: the carrier of K, the carrier of K:] is set
id K is Relation-like the carrier of K -defined the carrier of K -valued Function-like total quasi_total Element of bool [: the carrier of K, the carrier of K:]
id the carrier of K is Relation-like the carrier of K -defined the carrier of K -valued Function-like one-to-one total quasi_total Element of bool [: the carrier of K, the carrier of K:]
V1 is Relation-like the carrier of K -defined the carrier of K -valued Function-like total quasi_total Element of bool [: the carrier of K, the carrier of K:]
(K,V1,{}) is Relation-like the carrier of K -defined the carrier of K -valued Function-like total quasi_total Element of bool [: the carrier of K, the carrier of K:]
GFuncs the carrier of K is non empty strict unital associative constituted-Functions SubStr of GPFuncs the carrier of K
GPFuncs the carrier of K is non empty strict unital associative constituted-Functions multMagma
the carrier of (GFuncs the carrier of K) is non empty set
A is Relation-like Function-like Element of the carrier of (GFuncs the carrier of K)
{} |-> A is Relation-like NAT -defined the carrier of (GFuncs the carrier of K) -valued Function-like one-to-one constant functional empty V25() V26() V27() V29() V30() V31() finite finite-yielding V36() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V46() ext-real non positive non negative V165() Element of {} -tuples_on the carrier of (GFuncs the carrier of K)
{} -tuples_on the carrier of (GFuncs the carrier of K) is functional non empty FinSequence-membered FinSequenceSet of the carrier of (GFuncs the carrier of K)
<*> the carrier of (GFuncs the carrier of K) is Relation-like NAT -defined the carrier of (GFuncs the carrier of K) -valued Function-like one-to-one constant functional empty V25() V26() V27() V29() V30() V31() finite finite-yielding V36() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V46() ext-real non positive non negative V165() FinSequence of the carrier of (GFuncs the carrier of K)
Product ({} |-> A) is Relation-like Function-like Element of the carrier of (GFuncs the carrier of K)
1_ (GFuncs the carrier of K) is Relation-like Function-like Element of the carrier of (GFuncs the carrier of K)
the multF of (GFuncs the carrier of K) is Relation-like [: the carrier of (GFuncs the carrier of K), the carrier of (GFuncs the carrier of K):] -defined the carrier of (GFuncs the carrier of K) -valued Function-like total quasi_total Element of bool [:[: the carrier of (GFuncs the carrier of K), the carrier of (GFuncs the carrier of K):], the carrier of (GFuncs the carrier of K):]
[: the carrier of (GFuncs the carrier of K), the carrier of (GFuncs the carrier of K):] is set
[:[: the carrier of (GFuncs the carrier of K), the carrier of (GFuncs the carrier of K):], the carrier of (GFuncs the carrier of K):] is set
bool [:[: the carrier of (GFuncs the carrier of K), the carrier of (GFuncs the carrier of K):], the carrier of (GFuncs the carrier of K):] is set
the_unity_wrt the multF of (GFuncs the carrier of K) is Relation-like Function-like Element of the carrier of (GFuncs the carrier of K)
K is 1-sorted
the carrier of K is set
[: the carrier of K, the carrier of K:] is set
bool [: the carrier of K, the carrier of K:] is set
V1 is Relation-like the carrier of K -defined the carrier of K -valued Function-like total quasi_total Element of bool [: the carrier of K, the carrier of K:]
(K,V1,1) is Relation-like the carrier of K -defined the carrier of K -valued Function-like total quasi_total Element of bool [: the carrier of K, the carrier of K:]
GFuncs the carrier of K is non empty strict unital associative constituted-Functions SubStr of GPFuncs the carrier of K
GPFuncs the carrier of K is non empty strict unital associative constituted-Functions multMagma
the carrier of (GFuncs the carrier of K) is non empty set
A is Relation-like Function-like Element of the carrier of (GFuncs the carrier of K)
1 |-> A is Relation-like NAT -defined the carrier of (GFuncs the carrier of K) -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of (GFuncs the carrier of K)
1 -tuples_on the carrier of (GFuncs the carrier of K) is functional non empty FinSequence-membered FinSequenceSet of the carrier of (GFuncs the carrier of K)
Product (1 |-> A) is Relation-like Function-like Element of the carrier of (GFuncs the carrier of K)
<*A*> is Relation-like NAT -defined the carrier of (GFuncs the carrier of K) -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Element of 1 -tuples_on the carrier of (GFuncs the carrier of K)
[1,A] is set
{1,A} is non empty finite set
{1} is non empty trivial finite V36() 1 -element set
{{1,A},{1}} is non empty finite V36() set
{[1,A]} is Function-like non empty trivial finite 1 -element set
Product <*A*> is Relation-like Function-like Element of the carrier of (GFuncs the carrier of K)
K is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
V1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
K + V1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
V2 is 1-sorted
the carrier of V2 is set
[: the carrier of V2, the carrier of V2:] is set
bool [: the carrier of V2, the carrier of V2:] is set
A is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like total quasi_total Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,(K + V1)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like total quasi_total Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,K) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like total quasi_total Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,V1) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like total quasi_total Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,V1) * (V2,A,K) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like total quasi_total Element of bool [: the carrier of V2, the carrier of V2:]
GFuncs the carrier of V2 is non empty strict unital associative constituted-Functions SubStr of GPFuncs the carrier of V2
GPFuncs the carrier of V2 is non empty strict unital associative constituted-Functions multMagma
the carrier of (GFuncs the carrier of V2) is non empty set
F is non empty unital associative multMagma
the carrier of F is non empty set
f is Element of the carrier of F
(K + V1) |-> f is Relation-like NAT -defined the carrier of F -valued Function-like finite K + V1 -element FinSequence-like FinSubsequence-like Element of (K + V1) -tuples_on the carrier of F
(K + V1) -tuples_on the carrier of F is functional non empty FinSequence-membered FinSequenceSet of the carrier of F
Product ((K + V1) |-> f) is Element of the carrier of F
K |-> f is Relation-like NAT -defined the carrier of F -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of F
K -tuples_on the carrier of F is functional non empty FinSequence-membered FinSequenceSet of the carrier of F
V1 |-> f is Relation-like NAT -defined the carrier of F -valued Function-like finite V1 -element FinSequence-like FinSubsequence-like Element of V1 -tuples_on the carrier of F
V1 -tuples_on the carrier of F is functional non empty FinSequence-membered FinSequenceSet of the carrier of F
(K |-> f) ^ (V1 |-> f) is Relation-like NAT -defined the carrier of F -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of F *
the carrier of F * is functional non empty FinSequence-membered FinSequenceSet of the carrier of F
Product ((K |-> f) ^ (V1 |-> f)) is Element of the carrier of F
Product (K |-> f) is Element of the carrier of F
Product (V1 |-> f) is Element of the carrier of F
(Product (K |-> f)) * (Product (V1 |-> f)) is Element of the carrier of F
L is Relation-like Function-like Element of the carrier of (GFuncs the carrier of V2)
K |-> L is Relation-like NAT -defined the carrier of (GFuncs the carrier of V2) -valued Function-like finite K -element FinSequence-like FinSubsequence-like Element of K -tuples_on the carrier of (GFuncs the carrier of V2)
K -tuples_on the carrier of (GFuncs the carrier of V2) is functional non empty FinSequence-membered FinSequenceSet of the carrier of (GFuncs the carrier of V2)
Product (K |-> L) is Relation-like Function-like Element of the carrier of (GFuncs the carrier of V2)
V1 |-> L is Relation-like NAT -defined the carrier of (GFuncs the carrier of V2) -valued Function-like finite V1 -element FinSequence-like FinSubsequence-like Element of V1 -tuples_on the carrier of (GFuncs the carrier of V2)
V1 -tuples_on the carrier of (GFuncs the carrier of V2) is functional non empty FinSequence-membered FinSequenceSet of the carrier of (GFuncs the carrier of V2)
Product (V1 |-> L) is Relation-like Function-like Element of the carrier of (GFuncs the carrier of V2)
(Product (K |-> L)) (#) (Product (V1 |-> L)) is Relation-like Function-like set
(Product (K |-> L)) (#) (V2,A,V1) is Relation-like Function-like set
(V2,A,K) (#) (V2,A,V1) is Relation-like Function-like set
K is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
V1 is 1-sorted
the carrier of V1 is set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
A is Element of the carrier of V1
B is Element of the carrier of V1
L is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,L) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,L) . B is set
K * L is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
F is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,F) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,F) . A is set
F + (K * L) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,(F + (K * L))) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,(F + (K * L))) . A is set
f is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
f * L is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
F + (f * L) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,(F + (f * L))) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,(F + (f * L))) . A is set
f + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
(f + 1) * L is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
F + ((f + 1) * L) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,(F + ((f + 1) * L))) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,(F + ((f + 1) * L))) . A is set
dom (V1,V2,(F + (f * L))) is set
(f + 1) * L is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
F + ((f + 1) * L) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
(V1,V2,(F + ((f + 1) * L))) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,(F + ((f + 1) * L))) . A is set
L + (F + (f * L)) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,(L + (F + (f * L)))) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,(L + (F + (f * L)))) . A is set
(V1,V2,L) * (V1,V2,(F + (f * L))) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
((V1,V2,L) * (V1,V2,(F + (f * L)))) . A is set
(f + 1) * L is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
F + ((f + 1) * L) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
(V1,V2,(F + ((f + 1) * L))) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
dom (V1,V2,(F + ((f + 1) * L))) is set
(V1,V2,(F + ((f + 1) * L))) . A is set
{} * L is Function-like functional empty V25() V26() V27() V29() V30() V31() finite V36() cardinal {} -element FinSequence-membered V46() ext-real non positive non negative V165() set
F + ({} * L) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,(F + ({} * L))) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,(F + ({} * L))) . A is set
K is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
V1 is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V2 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over V1
the carrier of V2 is non empty set
[: the carrier of V2, the carrier of V2:] is set
bool [: the carrier of V2, the carrier of V2:] is set
A is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V2
the carrier of A is non empty set
[: the carrier of A, the carrier of A:] is set
bool [: the carrier of A, the carrier of A:] is set
B is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V2, the carrier of V2:]
B | A is Relation-like the carrier of A -defined the carrier of V2 -valued Function-like non empty total quasi_total Element of bool [: the carrier of A, the carrier of V2:]
[: the carrier of A, the carrier of V2:] is set
bool [: the carrier of A, the carrier of V2:] is set
B | the carrier of A is Relation-like Function-like set
(V2,B,K) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V2, the carrier of V2:]
(V2,B,K) | A is Relation-like the carrier of A -defined the carrier of V2 -valued Function-like non empty total quasi_total Element of bool [: the carrier of A, the carrier of V2:]
(V2,B,K) | the carrier of A is Relation-like Function-like set
L is Relation-like the carrier of A -defined the carrier of A -valued Function-like non empty total quasi_total Element of bool [: the carrier of A, the carrier of A:]
(A,L,K) is Relation-like the carrier of A -defined the carrier of A -valued Function-like non empty total quasi_total Element of bool [: the carrier of A, the carrier of A:]
F is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V2,B,F) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V2, the carrier of V2:]
(V2,B,F) | A is Relation-like the carrier of A -defined the carrier of V2 -valued Function-like non empty total quasi_total Element of bool [: the carrier of A, the carrier of V2:]
(V2,B,F) | the carrier of A is Relation-like Function-like set
(A,L,F) is Relation-like the carrier of A -defined the carrier of A -valued Function-like non empty total quasi_total Element of bool [: the carrier of A, the carrier of A:]
F + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
(V2,B,(F + 1)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V2, the carrier of V2:]
(V2,B,(F + 1)) | A is Relation-like the carrier of A -defined the carrier of V2 -valued Function-like non empty total quasi_total Element of bool [: the carrier of A, the carrier of V2:]
(V2,B,(F + 1)) | the carrier of A is Relation-like Function-like set
(A,L,(F + 1)) is Relation-like the carrier of A -defined the carrier of A -valued Function-like non empty total quasi_total Element of bool [: the carrier of A, the carrier of A:]
rng (A,L,F) is set
[#] A is non empty non proper Element of bool the carrier of A
bool the carrier of A is set
(V2,B,1) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V2, the carrier of V2:]
(V2,B,1) * (V2,B,F) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V2, the carrier of V2:]
((V2,B,1) * (V2,B,F)) | A is Relation-like the carrier of A -defined the carrier of V2 -valued Function-like non empty total quasi_total Element of bool [: the carrier of A, the carrier of V2:]
((V2,B,1) * (V2,B,F)) | the carrier of A is Relation-like Function-like set
(V2,B,1) * ((V2,B,F) | A) is Relation-like the carrier of A -defined the carrier of V2 -valued Function-like non empty total quasi_total Element of bool [: the carrier of A, the carrier of V2:]
id A is Relation-like the carrier of A -defined the carrier of A -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of A, the carrier of A:]
id the carrier of A is Relation-like the carrier of A -defined the carrier of A -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of A, the carrier of A:]
(id A) * (A,L,F) is Relation-like the carrier of A -defined the carrier of A -valued Function-like non empty total quasi_total Element of bool [: the carrier of A, the carrier of A:]
(V2,B,1) * ((id A) * (A,L,F)) is Relation-like the carrier of A -defined the carrier of V2 -valued Function-like Element of bool [: the carrier of A, the carrier of V2:]
(V2,B,1) * (id A) is Relation-like the carrier of A -defined the carrier of V2 -valued Function-like Element of bool [: the carrier of A, the carrier of V2:]
((V2,B,1) * (id A)) * (A,L,F) is Relation-like the carrier of A -defined the carrier of V2 -valued Function-like Element of bool [: the carrier of A, the carrier of V2:]
B * (id A) is Relation-like the carrier of A -defined the carrier of V2 -valued Function-like Element of bool [: the carrier of A, the carrier of V2:]
(B * (id A)) * (A,L,F) is Relation-like the carrier of A -defined the carrier of V2 -valued Function-like Element of bool [: the carrier of A, the carrier of V2:]
L * (A,L,F) is Relation-like the carrier of A -defined the carrier of A -valued Function-like non empty total quasi_total Element of bool [: the carrier of A, the carrier of A:]
(A,L,1) is Relation-like the carrier of A -defined the carrier of A -valued Function-like non empty total quasi_total Element of bool [: the carrier of A, the carrier of A:]
(A,L,1) * (A,L,F) is Relation-like the carrier of A -defined the carrier of A -valued Function-like non empty total quasi_total Element of bool [: the carrier of A, the carrier of A:]
[#] A is non empty non proper Element of bool the carrier of A
bool the carrier of A is set
[#] V2 is non empty non proper Element of bool the carrier of V2
bool the carrier of V2 is set
([#] V2) /\ ([#] A) is Element of bool the carrier of A
(V2,B,{}) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V2, the carrier of V2:]
(V2,B,{}) | A is Relation-like the carrier of A -defined the carrier of V2 -valued Function-like non empty total quasi_total Element of bool [: the carrier of A, the carrier of V2:]
(V2,B,{}) | the carrier of A is Relation-like Function-like set
id V2 is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
id the carrier of V2 is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of V2, the carrier of V2:]
(id V2) | A is Relation-like the carrier of A -defined the carrier of V2 -valued Function-like non empty total quasi_total Element of bool [: the carrier of A, the carrier of V2:]
(id V2) | the carrier of A is Relation-like Function-like set
id A is Relation-like the carrier of A -defined the carrier of A -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of A, the carrier of A:]
id the carrier of A is Relation-like the carrier of A -defined the carrier of A -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of A, the carrier of A:]
(id V2) * (id A) is Relation-like the carrier of A -defined the carrier of V2 -valued Function-like Element of bool [: the carrier of A, the carrier of V2:]
(A,L,{}) is Relation-like the carrier of A -defined the carrier of A -valued Function-like non empty total quasi_total Element of bool [: the carrier of A, the carrier of A:]
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
A is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,A) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
B is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,B) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
B + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
(V1,V2,(B + 1)) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,1) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
L is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
L * (V1,V2,1) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
L * V2 is Relation-like the carrier of V1 -defined the carrier of V1 -defined the carrier of V1 -valued the carrier of V1 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,{}) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
id V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
id the carrier of V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
K is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
V1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
K + V1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
V2 is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
A is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over V2
the carrier of A is non empty set
[: the carrier of A, the carrier of A:] is set
bool [: the carrier of A, the carrier of A:] is set
0. A is V65(A) Element of the carrier of A
the ZeroF of A is Element of the carrier of A
B is Relation-like the carrier of A -defined the carrier of A -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of A, the carrier of A:]
(A,B,K) is Relation-like the carrier of A -defined the carrier of A -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of A, the carrier of A:]
(A,B,(K + V1)) is Relation-like the carrier of A -defined the carrier of A -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of A, the carrier of A:]
L is Element of the carrier of A
(A,B,K) . L is Element of the carrier of A
(A,B,(K + V1)) . L is Element of the carrier of A
dom (A,B,K) is set
(A,B,V1) is Relation-like the carrier of A -defined the carrier of A -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of A, the carrier of A:]
(A,B,V1) * (A,B,K) is Relation-like the carrier of A -defined the carrier of A -defined the carrier of A -valued the carrier of A -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of A, the carrier of A:]
((A,B,V1) * (A,B,K)) . L is Element of the carrier of A
(A,B,V1) . (0. A) is Element of the carrier of A
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
{ b₁ where b₁ is Element of the carrier of V1 : ex b₂ being V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set st (V1,V2,b₂) . b₁ = 0. V1 } is set
B is set
L is Element of the carrier of V1
F is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,F) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,F) . L is Element of the carrier of V1
bool the carrier of V1 is set
(V1,V2,{}) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,{}) . (0. V1) is Element of the carrier of V1
id V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
id the carrier of V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
(id V1) . (0. V1) is Element of the carrier of V1
B is Element of bool the carrier of V1
L is Element of the carrier of V1
F is Element of the carrier of V1
f is Element of the carrier of V1
D is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,D) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,D) . f is Element of the carrier of V1
f is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,f) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,f) . L is Element of the carrier of V1
D is Element of the carrier of V1
C is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,C) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,C) . D is Element of the carrier of V1
D is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,D) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,D) . F is Element of the carrier of V1
f - D is V46() ext-real V165() set
L + F is Element of the carrier of V1
(V1,V2,f) . (L + F) is Element of the carrier of V1
C is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
D + C is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,(D + C)) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,(D + C)) . F is Element of the carrier of V1
((V1,V2,f) . L) + ((V1,V2,(D + C)) . F) is Element of the carrier of V1
(0. V1) + (0. V1) is Element of the carrier of V1
D - f is V46() ext-real V165() set
L + F is Element of the carrier of V1
(V1,V2,D) . (L + F) is Element of the carrier of V1
(V1,V2,D) . L is Element of the carrier of V1
C is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
f + C is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,(f + C)) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,(f + C)) . F is Element of the carrier of V1
((V1,V2,D) . L) + ((V1,V2,(f + C)) . F) is Element of the carrier of V1
(0. V1) + (0. V1) is Element of the carrier of V1
L + F is Element of the carrier of V1
L + F is Element of the carrier of V1
the carrier of K is non empty non trivial set
F is Element of the carrier of V1
f is Element of the carrier of V1
D is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,D) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,D) . f is Element of the carrier of V1
f is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,f) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,f) . F is Element of the carrier of V1
L is Element of the carrier of K
L * F is Element of the carrier of V1
(V1,V2,f) . (L * F) is Element of the carrier of V1
L * (0. V1) is Element of the carrier of V1
A is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V1
the carrier of A is non empty set
B is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V1
the carrier of B is non empty set
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(K,V1,V2) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V1
A is Element of the carrier of V1
the carrier of (K,V1,V2) is non empty set
{ b₁ where b₁ is Element of the carrier of V1 : ex b₂ being V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set st (V1,V2,b₂) . b₁ = 0. V1 } is set
B is Element of the carrier of V1
L is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,L) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,L) . B is Element of the carrier of V1
B is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,B) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,B) . A is Element of the carrier of V1
K is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
V1 is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V2 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over V1
the carrier of V2 is non empty set
[: the carrier of V2, the carrier of V2:] is set
bool [: the carrier of V2, the carrier of V2:] is set
A is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,K) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
ker (V2,A,K) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V2
(V1,V2,A) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V2
the carrier of (ker (V2,A,K)) is non empty set
the carrier of (V1,V2,A) is non empty set
B is set
L is Element of the carrier of (ker (V2,A,K))
(V2,A,K) . L is set
0. V2 is V65(V2) Element of the carrier of V2
the ZeroF of V2 is Element of the carrier of V2
K is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
V1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
K + V1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
V2 is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
A is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over V2
the carrier of A is non empty set
[: the carrier of A, the carrier of A:] is set
bool [: the carrier of A, the carrier of A:] is set
B is Relation-like the carrier of A -defined the carrier of A -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of A, the carrier of A:]
(A,B,K) is Relation-like the carrier of A -defined the carrier of A -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of A, the carrier of A:]
ker (A,B,K) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of A
(A,B,(K + V1)) is Relation-like the carrier of A -defined the carrier of A -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of A, the carrier of A:]
ker (A,B,(K + V1)) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of A
the carrier of (ker (A,B,K)) is non empty set
the carrier of (ker (A,B,(K + V1))) is non empty set
L is set
F is Element of the carrier of A
(A,B,K) . F is Element of the carrier of A
0. A is V65(A) Element of the carrier of A
the ZeroF of A is Element of the carrier of A
(A,B,(K + V1)) . F is Element of the carrier of A
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional VectSpStr over K
the carrier of V1 is non empty set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(K,V1,V2) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of V1
dim (K,V1,V2) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
A is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,A) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
ker (V1,V2,A) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of V1
dim (ker (V1,V2,A)) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
A is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
A is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,{}) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
ker (V1,V2,{}) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of V1
dim (ker (V1,V2,{})) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
A - 1 is V46() ext-real V165() set
L is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,L) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
ker (V1,V2,L) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of V1
dim (ker (V1,V2,L)) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
B is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
B + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
B is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,B) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
ker (V1,V2,B) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of V1
dim (ker (V1,V2,B)) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
B is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,B) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
ker (V1,V2,B) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of V1
dim (ker (V1,V2,B)) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
the carrier of (K,V1,V2) is non empty set
L is Element of the carrier of (K,V1,V2)
F is Element of the carrier of V1
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
f is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,f) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,f) . F is Element of the carrier of V1
B - f is V46() ext-real V165() set
D is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
D + f is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
(V1,V2,(D + f)) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,(D + f)) . F is Element of the carrier of V1
f - B is V46() ext-real V165() set
D is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
B + D is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
(V1,V2,(B + D)) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
ker (V1,V2,(B + D)) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of V1
ker (V1,V2,f) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of V1
dim (ker (V1,V2,f)) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(Omega). (ker (V1,V2,B)) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of ker (V1,V2,B)
the carrier of (ker (V1,V2,B)) is non empty set
the addF of (ker (V1,V2,B)) is Relation-like [: the carrier of (ker (V1,V2,B)), the carrier of (ker (V1,V2,B)):] -defined the carrier of (ker (V1,V2,B)) -valued Function-like total quasi_total Element of bool [:[: the carrier of (ker (V1,V2,B)), the carrier of (ker (V1,V2,B)):], the carrier of (ker (V1,V2,B)):]
[: the carrier of (ker (V1,V2,B)), the carrier of (ker (V1,V2,B)):] is set
[:[: the carrier of (ker (V1,V2,B)), the carrier of (ker (V1,V2,B)):], the carrier of (ker (V1,V2,B)):] is set
bool [:[: the carrier of (ker (V1,V2,B)), the carrier of (ker (V1,V2,B)):], the carrier of (ker (V1,V2,B)):] is set
the ZeroF of (ker (V1,V2,B)) is Element of the carrier of (ker (V1,V2,B))
the lmult of (ker (V1,V2,B)) is Relation-like [: the carrier of K, the carrier of (ker (V1,V2,B)):] -defined the carrier of (ker (V1,V2,B)) -valued Function-like total quasi_total Element of bool [:[: the carrier of K, the carrier of (ker (V1,V2,B)):], the carrier of (ker (V1,V2,B)):]
the carrier of K is non empty non trivial set
[: the carrier of K, the carrier of (ker (V1,V2,B)):] is set
[:[: the carrier of K, the carrier of (ker (V1,V2,B)):], the carrier of (ker (V1,V2,B)):] is set
bool [:[: the carrier of K, the carrier of (ker (V1,V2,B)):], the carrier of (ker (V1,V2,B)):] is set
VectSpStr(# the carrier of (ker (V1,V2,B)), the addF of (ker (V1,V2,B)), the ZeroF of (ker (V1,V2,B)), the lmult of (ker (V1,V2,B)) #) is non empty strict VectSpStr over K
(Omega). (ker (V1,V2,f)) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of ker (V1,V2,f)
the carrier of (ker (V1,V2,f)) is non empty set
the addF of (ker (V1,V2,f)) is Relation-like [: the carrier of (ker (V1,V2,f)), the carrier of (ker (V1,V2,f)):] -defined the carrier of (ker (V1,V2,f)) -valued Function-like total quasi_total Element of bool [:[: the carrier of (ker (V1,V2,f)), the carrier of (ker (V1,V2,f)):], the carrier of (ker (V1,V2,f)):]
[: the carrier of (ker (V1,V2,f)), the carrier of (ker (V1,V2,f)):] is set
[:[: the carrier of (ker (V1,V2,f)), the carrier of (ker (V1,V2,f)):], the carrier of (ker (V1,V2,f)):] is set
bool [:[: the carrier of (ker (V1,V2,f)), the carrier of (ker (V1,V2,f)):], the carrier of (ker (V1,V2,f)):] is set
the ZeroF of (ker (V1,V2,f)) is Element of the carrier of (ker (V1,V2,f))
the lmult of (ker (V1,V2,f)) is Relation-like [: the carrier of K, the carrier of (ker (V1,V2,f)):] -defined the carrier of (ker (V1,V2,f)) -valued Function-like total quasi_total Element of bool [:[: the carrier of K, the carrier of (ker (V1,V2,f)):], the carrier of (ker (V1,V2,f)):]
[: the carrier of K, the carrier of (ker (V1,V2,f)):] is set
[:[: the carrier of K, the carrier of (ker (V1,V2,f)):], the carrier of (ker (V1,V2,f)):] is set
bool [:[: the carrier of K, the carrier of (ker (V1,V2,f)):], the carrier of (ker (V1,V2,f)):] is set
VectSpStr(# the carrier of (ker (V1,V2,f)), the addF of (ker (V1,V2,f)), the ZeroF of (ker (V1,V2,f)), the lmult of (ker (V1,V2,f)) #) is non empty strict VectSpStr over K
K is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
V1 is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V2 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over V1
the carrier of V2 is non empty set
[: the carrier of V2, the carrier of V2:] is set
bool [: the carrier of V2, the carrier of V2:] is set
A is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,K) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
ker (V2,A,K) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V2
A | (ker (V2,A,K)) is Relation-like the carrier of (ker (V2,A,K)) -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of (ker (V2,A,K)), the carrier of V2:]
the carrier of (ker (V2,A,K)) is non empty set
[: the carrier of (ker (V2,A,K)), the carrier of V2:] is set
bool [: the carrier of (ker (V2,A,K)), the carrier of V2:] is set
A | the carrier of (ker (V2,A,K)) is Relation-like Function-like set
[: the carrier of (ker (V2,A,K)), the carrier of (ker (V2,A,K)):] is set
bool [: the carrier of (ker (V2,A,K)), the carrier of (ker (V2,A,K)):] is set
rng (A | (ker (V2,A,K))) is set
L is set
dom (A | (ker (V2,A,K))) is set
F is set
(A | (ker (V2,A,K))) . F is set
dom A is set
f is Element of the carrier of V2
(V2,A,K) . f is Element of the carrier of V2
0. V2 is V65(V2) Element of the carrier of V2
the ZeroF of V2 is Element of the carrier of V2
K + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
(V2,A,(K + 1)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,(K + 1)) . f is Element of the carrier of V2
(V2,A,1) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,K) * (V2,A,1) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((V2,A,K) * (V2,A,1)) . f is Element of the carrier of V2
(V2,A,K) * A is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((V2,A,K) * A) . f is Element of the carrier of V2
A . f is Element of the carrier of V2
(V2,A,K) . (A . f) is Element of the carrier of V2
K is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
V1 is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of V1 is non empty non trivial set
V2 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over V1
the carrier of V2 is non empty set
[: the carrier of V2, the carrier of V2:] is set
bool [: the carrier of V2, the carrier of V2:] is set
id V2 is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
id the carrier of V2 is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of V2, the carrier of V2:]
A is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
B is Element of the carrier of V1
B * (id V2) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
A + (B * (id V2)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,(A + (B * (id V2))),K) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
ker (V2,(A + (B * (id V2))),K) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V2
A | (ker (V2,(A + (B * (id V2))),K)) is Relation-like the carrier of (ker (V2,(A + (B * (id V2))),K)) -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of (ker (V2,(A + (B * (id V2))),K)), the carrier of V2:]
the carrier of (ker (V2,(A + (B * (id V2))),K)) is non empty set
[: the carrier of (ker (V2,(A + (B * (id V2))),K)), the carrier of V2:] is set
bool [: the carrier of (ker (V2,(A + (B * (id V2))),K)), the carrier of V2:] is set
A | the carrier of (ker (V2,(A + (B * (id V2))),K)) is Relation-like Function-like set
[: the carrier of (ker (V2,(A + (B * (id V2))),K)), the carrier of (ker (V2,(A + (B * (id V2))),K)):] is set
bool [: the carrier of (ker (V2,(A + (B * (id V2))),K)), the carrier of (ker (V2,(A + (B * (id V2))),K)):] is set
(A + (B * (id V2))) | (ker (V2,(A + (B * (id V2))),K)) is Relation-like the carrier of (ker (V2,(A + (B * (id V2))),K)) -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of (ker (V2,(A + (B * (id V2))),K)), the carrier of V2:]
(A + (B * (id V2))) | the carrier of (ker (V2,(A + (B * (id V2))),K)) is Relation-like Function-like set
rng (A | (ker (V2,(A + (B * (id V2))),K))) is set
D is set
dom (A | (ker (V2,(A + (B * (id V2))),K))) is set
C is set
(A | (ker (V2,(A + (B * (id V2))),K))) . C is set
FA is Element of the carrier of V2
(A | (ker (V2,(A + (B * (id V2))),K))) . FA is set
A . FA is Element of the carrier of V2
f is Relation-like the carrier of (ker (V2,(A + (B * (id V2))),K)) -defined the carrier of (ker (V2,(A + (B * (id V2))),K)) -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of (ker (V2,(A + (B * (id V2))),K)), the carrier of (ker (V2,(A + (B * (id V2))),K)):]
dom f is set
f . FA is set
(A + (B * (id V2))) . FA is Element of the carrier of V2
f /. FA is Element of the carrier of (ker (V2,(A + (B * (id V2))),K))
(B * (id V2)) . FA is Element of the carrier of V2
(A . FA) + ((B * (id V2)) . FA) is Element of the carrier of V2
(id V2) . FA is Element of the carrier of V2
B * ((id V2) . FA) is Element of the carrier of V2
(A . FA) + (B * ((id V2) . FA)) is Element of the carrier of V2
B * FA is Element of the carrier of V2
(A . FA) + (B * FA) is Element of the carrier of V2
- B is Element of the carrier of V1
(- B) * FA is Element of the carrier of V2
((A + (B * (id V2))) . FA) + ((- B) * FA) is Element of the carrier of V2
(B * FA) + ((- B) * FA) is Element of the carrier of V2
(A . FA) + ((B * FA) + ((- B) * FA)) is Element of the carrier of V2
B + (- B) is Element of the carrier of V1
(B + (- B)) * FA is Element of the carrier of V2
(A . FA) + ((B + (- B)) * FA) is Element of the carrier of V2
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
(0. V1) * FA is Element of the carrier of V2
(A . FA) + ((0. V1) * FA) is Element of the carrier of V2
0. V2 is V65(V2) Element of the carrier of V2
the ZeroF of V2 is Element of the carrier of V2
(A . FA) + (0. V2) is Element of the carrier of V2
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(K,V1,V2) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V1
V2 | (K,V1,V2) is Relation-like the carrier of (K,V1,V2) -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of (K,V1,V2), the carrier of V1:]
the carrier of (K,V1,V2) is non empty set
[: the carrier of (K,V1,V2), the carrier of V1:] is set
bool [: the carrier of (K,V1,V2), the carrier of V1:] is set
V2 | the carrier of (K,V1,V2) is Relation-like Function-like set
[: the carrier of (K,V1,V2), the carrier of (K,V1,V2):] is set
bool [: the carrier of (K,V1,V2), the carrier of (K,V1,V2):] is set
rng (V2 | (K,V1,V2)) is set
B is set
dom (V2 | (K,V1,V2)) is set
L is set
(V2 | (K,V1,V2)) . L is set
F is Element of the carrier of V1
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
f is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,f) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,f) . F is Element of the carrier of V1
dom V2 is set
[#] V1 is non empty non proper Element of bool the carrier of V1
bool the carrier of V1 is set
f + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
(V1,V2,(f + 1)) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,(f + 1)) . F is Element of the carrier of V1
(V1,V2,1) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,V2,f) * (V1,V2,1) is Relation-like the carrier of V1 -defined the carrier of V1 -defined the carrier of V1 -valued the carrier of V1 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
((V1,V2,f) * (V1,V2,1)) . F is Element of the carrier of V1
(V1,V2,f) * V2 is Relation-like the carrier of V1 -defined the carrier of V1 -defined the carrier of V1 -valued the carrier of V1 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
((V1,V2,f) * V2) . F is Element of the carrier of V1
V2 . F is Element of the carrier of V1
(V1,V2,f) . (V2 . F) is Element of the carrier of V1
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of K is non empty non trivial set
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
id V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
id the carrier of V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
A is Element of the carrier of K
A * (id V1) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
V2 + (A * (id V1)) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(K,V1,(V2 + (A * (id V1)))) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V1
V2 | (K,V1,(V2 + (A * (id V1)))) is Relation-like the carrier of (K,V1,(V2 + (A * (id V1)))) -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of (K,V1,(V2 + (A * (id V1)))), the carrier of V1:]
the carrier of (K,V1,(V2 + (A * (id V1)))) is non empty set
[: the carrier of (K,V1,(V2 + (A * (id V1)))), the carrier of V1:] is set
bool [: the carrier of (K,V1,(V2 + (A * (id V1)))), the carrier of V1:] is set
V2 | the carrier of (K,V1,(V2 + (A * (id V1)))) is Relation-like Function-like set
[: the carrier of (K,V1,(V2 + (A * (id V1)))), the carrier of (K,V1,(V2 + (A * (id V1)))):] is set
bool [: the carrier of (K,V1,(V2 + (A * (id V1)))), the carrier of (K,V1,(V2 + (A * (id V1)))):] is set
(V2 + (A * (id V1))) | (K,V1,(V2 + (A * (id V1)))) is Relation-like the carrier of (K,V1,(V2 + (A * (id V1)))) -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of (K,V1,(V2 + (A * (id V1)))), the carrier of V1:]
(V2 + (A * (id V1))) | the carrier of (K,V1,(V2 + (A * (id V1)))) is Relation-like Function-like set
rng (V2 | (K,V1,(V2 + (A * (id V1))))) is set
f is set
dom (V2 | (K,V1,(V2 + (A * (id V1))))) is set
D is set
(V2 | (K,V1,(V2 + (A * (id V1))))) . D is set
C is Element of the carrier of V1
(V2 | (K,V1,(V2 + (A * (id V1))))) . C is set
V2 . C is Element of the carrier of V1
F is Relation-like the carrier of (K,V1,(V2 + (A * (id V1)))) -defined the carrier of (K,V1,(V2 + (A * (id V1)))) -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of (K,V1,(V2 + (A * (id V1)))), the carrier of (K,V1,(V2 + (A * (id V1)))):]
dom F is set
F . C is set
(V2 + (A * (id V1))) . C is Element of the carrier of V1
F /. C is Element of the carrier of (K,V1,(V2 + (A * (id V1))))
(A * (id V1)) . C is Element of the carrier of V1
(V2 . C) + ((A * (id V1)) . C) is Element of the carrier of V1
(id V1) . C is Element of the carrier of V1
A * ((id V1) . C) is Element of the carrier of V1
(V2 . C) + (A * ((id V1) . C)) is Element of the carrier of V1
A * C is Element of the carrier of V1
(V2 . C) + (A * C) is Element of the carrier of V1
- A is Element of the carrier of K
(- A) * C is Element of the carrier of V1
((V2 + (A * (id V1))) . C) + ((- A) * C) is Element of the carrier of V1
(A * C) + ((- A) * C) is Element of the carrier of V1
(V2 . C) + ((A * C) + ((- A) * C)) is Element of the carrier of V1
A + (- A) is Element of the carrier of K
(A + (- A)) * C is Element of the carrier of V1
(V2 . C) + ((A + (- A)) * C) is Element of the carrier of V1
0. K is V65(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
(0. K) * C is Element of the carrier of V1
(V2 . C) + ((0. K) * C) is Element of the carrier of V1
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
(V2 . C) + (0. V1) is Element of the carrier of V1
K is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
V1 is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V2 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over V1
the carrier of V2 is non empty set
[: the carrier of V2, the carrier of V2:] is set
bool [: the carrier of V2, the carrier of V2:] is set
A is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,K) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
im (V2,A,K) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V2
A | (im (V2,A,K)) is Relation-like the carrier of (im (V2,A,K)) -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of (im (V2,A,K)), the carrier of V2:]
the carrier of (im (V2,A,K)) is non empty set
[: the carrier of (im (V2,A,K)), the carrier of V2:] is set
bool [: the carrier of (im (V2,A,K)), the carrier of V2:] is set
A | the carrier of (im (V2,A,K)) is Relation-like Function-like set
[: the carrier of (im (V2,A,K)), the carrier of (im (V2,A,K)):] is set
bool [: the carrier of (im (V2,A,K)), the carrier of (im (V2,A,K)):] is set
rng (A | (im (V2,A,K))) is set
L is set
dom (A | (im (V2,A,K))) is set
F is set
(A | (im (V2,A,K))) . F is set
f is Element of the carrier of V2
D is Element of the carrier of V2
(V2,A,K) . D is Element of the carrier of V2
(V2,A,1) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
dom (V2,A,1) is set
dom (V2,A,K) is set
A . F is set
A * (V2,A,K) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(A * (V2,A,K)) . D is Element of the carrier of V2
(V2,A,1) * (V2,A,K) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((V2,A,1) * (V2,A,K)) . D is Element of the carrier of V2
1 + K is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
(V2,A,(1 + K)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,(1 + K)) . D is Element of the carrier of V2
(V2,A,K) * (V2,A,1) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((V2,A,K) * (V2,A,1)) . D is Element of the carrier of V2
(V2,A,1) . D is Element of the carrier of V2
(V2,A,K) . ((V2,A,1) . D) is Element of the carrier of V2
K is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
V1 is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of V1 is non empty non trivial set
V2 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over V1
the carrier of V2 is non empty set
[: the carrier of V2, the carrier of V2:] is set
bool [: the carrier of V2, the carrier of V2:] is set
id V2 is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
id the carrier of V2 is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of V2, the carrier of V2:]
A is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
B is Element of the carrier of V1
B * (id V2) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
A + (B * (id V2)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,(A + (B * (id V2))),K) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
im (V2,(A + (B * (id V2))),K) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V2
A | (im (V2,(A + (B * (id V2))),K)) is Relation-like the carrier of (im (V2,(A + (B * (id V2))),K)) -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of (im (V2,(A + (B * (id V2))),K)), the carrier of V2:]
the carrier of (im (V2,(A + (B * (id V2))),K)) is non empty set
[: the carrier of (im (V2,(A + (B * (id V2))),K)), the carrier of V2:] is set
bool [: the carrier of (im (V2,(A + (B * (id V2))),K)), the carrier of V2:] is set
A | the carrier of (im (V2,(A + (B * (id V2))),K)) is Relation-like Function-like set
[: the carrier of (im (V2,(A + (B * (id V2))),K)), the carrier of (im (V2,(A + (B * (id V2))),K)):] is set
bool [: the carrier of (im (V2,(A + (B * (id V2))),K)), the carrier of (im (V2,(A + (B * (id V2))),K)):] is set
(A + (B * (id V2))) | (im (V2,(A + (B * (id V2))),K)) is Relation-like the carrier of (im (V2,(A + (B * (id V2))),K)) -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of (im (V2,(A + (B * (id V2))),K)), the carrier of V2:]
(A + (B * (id V2))) | the carrier of (im (V2,(A + (B * (id V2))),K)) is Relation-like Function-like set
rng (A | (im (V2,(A + (B * (id V2))),K))) is set
D is set
dom (A | (im (V2,(A + (B * (id V2))),K))) is set
C is set
(A | (im (V2,(A + (B * (id V2))),K))) . C is set
FA is Element of the carrier of V2
(A | (im (V2,(A + (B * (id V2))),K))) . FA is set
A . FA is Element of the carrier of V2
f is Relation-like the carrier of (im (V2,(A + (B * (id V2))),K)) -defined the carrier of (im (V2,(A + (B * (id V2))),K)) -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of (im (V2,(A + (B * (id V2))),K)), the carrier of (im (V2,(A + (B * (id V2))),K)):]
dom f is set
f . FA is set
(A + (B * (id V2))) . FA is Element of the carrier of V2
f /. FA is Element of the carrier of (im (V2,(A + (B * (id V2))),K))
(B * (id V2)) . FA is Element of the carrier of V2
(A . FA) + ((B * (id V2)) . FA) is Element of the carrier of V2
(id V2) . FA is Element of the carrier of V2
B * ((id V2) . FA) is Element of the carrier of V2
(A . FA) + (B * ((id V2) . FA)) is Element of the carrier of V2
B * FA is Element of the carrier of V2
(A . FA) + (B * FA) is Element of the carrier of V2
- B is Element of the carrier of V1
(- B) * FA is Element of the carrier of V2
((A + (B * (id V2))) . FA) + ((- B) * FA) is Element of the carrier of V2
(B * FA) + ((- B) * FA) is Element of the carrier of V2
(A . FA) + ((B * FA) + ((- B) * FA)) is Element of the carrier of V2
B + (- B) is Element of the carrier of V1
(B + (- B)) * FA is Element of the carrier of V2
(A . FA) + ((B + (- B)) * FA) is Element of the carrier of V2
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
(0. V1) * FA is Element of the carrier of V2
(A . FA) + ((0. V1) * FA) is Element of the carrier of V2
0. V2 is V65(V2) Element of the carrier of V2
the ZeroF of V2 is Element of the carrier of V2
(A . FA) + (0. V2) is Element of the carrier of V2
K is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
V1 is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V2 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over V1
the carrier of V2 is non empty set
[: the carrier of V2, the carrier of V2:] is set
bool [: the carrier of V2, the carrier of V2:] is set
(0). V2 is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V2
A is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V1,V2,A) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V2
(V2,A,K) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
ker (V2,A,K) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V2
im (V2,A,K) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V2
(ker (V2,A,K)) /\ (im (V2,A,K)) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V2
the carrier of ((ker (V2,A,K)) /\ (im (V2,A,K))) is non empty set
0. V2 is V65(V2) Element of the carrier of V2
the ZeroF of V2 is Element of the carrier of V2
{(0. V2)} is non empty trivial finite 1 -element Element of bool the carrier of V2
bool the carrier of V2 is set
F is set
f is Element of the carrier of V2
D is Element of the carrier of V2
(V2,A,K) . D is Element of the carrier of V2
dom (V2,A,K) is set
(V2,A,K) . ((V2,A,K) . D) is Element of the carrier of V2
(V2,A,K) * (V2,A,K) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((V2,A,K) * (V2,A,K)) . D is Element of the carrier of V2
K + K is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V2,A,(K + K)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,(K + K)) . D is Element of the carrier of V2
the carrier of ((0). V2) is non empty set
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional VectSpStr over K
the carrier of V1 is non empty set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(K,V1,V2) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of V1
A is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,V2,A) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
ker (V1,V2,A) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of V1
im (V1,V2,A) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of V1
dim V1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
rank (V1,V2,A) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
dim (im (V1,V2,A)) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
nullity (V1,V2,A) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
dim (ker (V1,V2,A)) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(rank (V1,V2,A)) + (nullity (V1,V2,A)) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(im (V1,V2,A)) + (ker (V1,V2,A)) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of V1
dim ((im (V1,V2,A)) + (ker (V1,V2,A))) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(im (V1,V2,A)) /\ (ker (V1,V2,A)) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of V1
dim ((im (V1,V2,A)) /\ (ker (V1,V2,A))) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(dim ((im (V1,V2,A)) + (ker (V1,V2,A)))) + (dim ((im (V1,V2,A)) /\ (ker (V1,V2,A)))) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(Omega). ((im (V1,V2,A)) /\ (ker (V1,V2,A))) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of (im (V1,V2,A)) /\ (ker (V1,V2,A))
the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))) is non empty set
the addF of ((im (V1,V2,A)) /\ (ker (V1,V2,A))) is Relation-like [: the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))), the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))):] -defined the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))) -valued Function-like total quasi_total Element of bool [:[: the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))), the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))):], the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))):]
[: the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))), the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))):] is set
[:[: the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))), the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))):], the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))):] is set
bool [:[: the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))), the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))):], the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))):] is set
the ZeroF of ((im (V1,V2,A)) /\ (ker (V1,V2,A))) is Element of the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A)))
the lmult of ((im (V1,V2,A)) /\ (ker (V1,V2,A))) is Relation-like [: the carrier of K, the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))):] -defined the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))) -valued Function-like total quasi_total Element of bool [:[: the carrier of K, the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))):], the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))):]
the carrier of K is non empty non trivial set
[: the carrier of K, the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))):] is set
[:[: the carrier of K, the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))):], the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))):] is set
bool [:[: the carrier of K, the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))):], the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))):] is set
VectSpStr(# the carrier of ((im (V1,V2,A)) /\ (ker (V1,V2,A))), the addF of ((im (V1,V2,A)) /\ (ker (V1,V2,A))), the ZeroF of ((im (V1,V2,A)) /\ (ker (V1,V2,A))), the lmult of ((im (V1,V2,A)) /\ (ker (V1,V2,A))) #) is non empty strict VectSpStr over K
(0). V1 is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of V1
(0). ((im (V1,V2,A)) /\ (ker (V1,V2,A))) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of (im (V1,V2,A)) /\ (ker (V1,V2,A))
(Omega). V1 is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of V1
the addF of V1 is Relation-like [: the carrier of V1, the carrier of V1:] -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [:[: the carrier of V1, the carrier of V1:], the carrier of V1:]
[:[: the carrier of V1, the carrier of V1:], the carrier of V1:] is set
bool [:[: the carrier of V1, the carrier of V1:], the carrier of V1:] is set
the ZeroF of V1 is Element of the carrier of V1
the lmult of V1 is Relation-like [: the carrier of K, the carrier of V1:] -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [:[: the carrier of K, the carrier of V1:], the carrier of V1:]
[: the carrier of K, the carrier of V1:] is set
[:[: the carrier of K, the carrier of V1:], the carrier of V1:] is set
bool [:[: the carrier of K, the carrier of V1:], the carrier of V1:] is set
VectSpStr(# the carrier of V1, the addF of V1, the ZeroF of V1, the lmult of V1 #) is non empty strict VectSpStr over K
(Omega). ((im (V1,V2,A)) + (ker (V1,V2,A))) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of (im (V1,V2,A)) + (ker (V1,V2,A))
the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))) is non empty set
the addF of ((im (V1,V2,A)) + (ker (V1,V2,A))) is Relation-like [: the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))), the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))):] -defined the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))) -valued Function-like total quasi_total Element of bool [:[: the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))), the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))):], the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))):]
[: the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))), the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))):] is set
[:[: the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))), the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))):], the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))):] is set
bool [:[: the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))), the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))):], the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))):] is set
the ZeroF of ((im (V1,V2,A)) + (ker (V1,V2,A))) is Element of the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A)))
the lmult of ((im (V1,V2,A)) + (ker (V1,V2,A))) is Relation-like [: the carrier of K, the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))):] -defined the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))) -valued Function-like total quasi_total Element of bool [:[: the carrier of K, the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))):], the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))):]
[: the carrier of K, the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))):] is set
[:[: the carrier of K, the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))):], the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))):] is set
bool [:[: the carrier of K, the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))):], the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))):] is set
VectSpStr(# the carrier of ((im (V1,V2,A)) + (ker (V1,V2,A))), the addF of ((im (V1,V2,A)) + (ker (V1,V2,A))), the ZeroF of ((im (V1,V2,A)) + (ker (V1,V2,A))), the lmult of ((im (V1,V2,A)) + (ker (V1,V2,A))) #) is non empty strict VectSpStr over K
(ker (V1,V2,A)) + (im (V1,V2,A)) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of V1
(ker (V1,V2,A)) /\ (im (V1,V2,A)) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed finite-dimensional Subspace of V1
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(K,V1,V2) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V1
A is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Linear_Compl of (K,V1,V2)
V2 | A is Relation-like the carrier of A -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of A, the carrier of V1:]
the carrier of A is non empty set
[: the carrier of A, the carrier of V1:] is set
bool [: the carrier of A, the carrier of V1:] is set
V2 | the carrier of A is Relation-like Function-like set
ker (V2 | A) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of A
the carrier of (ker (V2 | A)) is non empty set
0. A is V65(A) Element of the carrier of A
the ZeroF of A is Element of the carrier of A
{(0. A)} is non empty trivial finite 1 -element Element of bool the carrier of A
bool the carrier of A is set
F is set
f is Element of the carrier of A
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
(V2 | A) . f is Element of the carrier of V1
V2 . f is set
(V1,V2,1) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
D is Element of the carrier of V1
(V1,V2,1) . D is Element of the carrier of V1
(K,V1,V2) /\ A is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V1
(0). V1 is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V1
the carrier of ((0). V1) is non empty set
{(0. V1)} is non empty trivial finite 1 -element Element of bool the carrier of V1
bool the carrier of V1 is set
(0). A is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of A
the carrier of ((0). A) is non empty set
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of K is non empty non trivial set
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
id V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
id the carrier of V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
A is Element of the carrier of K
- A is Element of the carrier of K
(- A) * (id V1) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
V2 + ((- A) * (id V1)) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(K,V1,(V2 + ((- A) * (id V1)))) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V1
F is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Linear_Compl of (K,V1,(V2 + ((- A) * (id V1))))
the carrier of F is non empty set
[: the carrier of F, the carrier of F:] is set
bool [: the carrier of F, the carrier of F:] is set
V2 | F is Relation-like the carrier of F -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of F, the carrier of V1:]
[: the carrier of F, the carrier of V1:] is set
bool [: the carrier of F, the carrier of V1:] is set
V2 | the carrier of F is Relation-like Function-like set
f is Relation-like the carrier of F -defined the carrier of F -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of F, the carrier of F:]
D is Element of the carrier of F
f . D is Element of the carrier of F
A * D is Element of the carrier of F
V2 . D is set
C is Element of the carrier of V1
A * C is Element of the carrier of V1
(V2 + ((- A) * (id V1))) | F is Relation-like the carrier of F -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of F, the carrier of V1:]
(V2 + ((- A) * (id V1))) | the carrier of F is Relation-like Function-like set
((V2 + ((- A) * (id V1))) | F) . C is set
(V2 + ((- A) * (id V1))) . C is Element of the carrier of V1
V2 . C is Element of the carrier of V1
((- A) * (id V1)) . C is Element of the carrier of V1
(V2 . C) + (((- A) * (id V1)) . C) is Element of the carrier of V1
(id V1) . C is Element of the carrier of V1
(- A) * ((id V1) . C) is Element of the carrier of V1
(V2 . C) + ((- A) * ((id V1) . C)) is Element of the carrier of V1
(- A) * C is Element of the carrier of V1
(A * C) + ((- A) * C) is Element of the carrier of V1
A + (- A) is Element of the carrier of K
(A + (- A)) * C is Element of the carrier of V1
0. K is V65(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
(0. K) * C is Element of the carrier of V1
ker ((V2 + ((- A) * (id V1))) | F) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of F
(0). F is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of F
0. F is V65(F) Element of the carrier of F
the ZeroF of F is Element of the carrier of F
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of K is non empty non trivial set
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
A is Element of the carrier of K
B is Element of the carrier of K
A * B is Element of the carrier of K
(A * B) * V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
B * V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
A * (B * V2) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
L is set
dom ((A * B) * V2) is set
((A * B) * V2) . L is set
F is Element of the carrier of V1
V2 . F is Element of the carrier of V1
(A * B) * (V2 . F) is Element of the carrier of V1
B * (V2 . F) is Element of the carrier of V1
A * (B * (V2 . F)) is Element of the carrier of V1
(B * V2) . F is Element of the carrier of V1
A * ((B * V2) . F) is Element of the carrier of V1
(A * (B * V2)) . L is set
[#] V1 is non empty non proper Element of bool the carrier of V1
bool the carrier of V1 is set
dom (A * (B * V2)) is set
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of K is non empty non trivial set
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
V2 is Element of the carrier of K
B is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
A is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
A * B is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
V2 * (A * B) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
V2 * A is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
(V2 * A) * B is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
dom ((V2 * A) * B) is set
[#] V1 is non empty non proper Element of bool the carrier of V1
bool the carrier of V1 is set
dom B is set
L is set
dom (V2 * (A * B)) is set
(V2 * (A * B)) . L is set
F is Element of the carrier of V1
(A * B) . F is Element of the carrier of V1
V2 * ((A * B) . F) is Element of the carrier of V1
B . F is Element of the carrier of V1
A . (B . F) is Element of the carrier of V1
V2 * (A . (B . F)) is Element of the carrier of V1
(V2 * A) . (B . F) is Element of the carrier of V1
((V2 * A) * B) . L is set
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of K is non empty non trivial set
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
V2 is Element of the carrier of K
A is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
B is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
A * B is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
V2 * (A * B) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
V2 * B is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
A * (V2 * B) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
dom (A * (V2 * B)) is set
[#] V1 is non empty non proper Element of bool the carrier of V1
bool the carrier of V1 is set
dom B is set
L is set
dom (V2 * (A * B)) is set
(V2 * (A * B)) . L is set
F is Element of the carrier of V1
(A * B) . F is Element of the carrier of V1
V2 * ((A * B) . F) is Element of the carrier of V1
B . F is Element of the carrier of V1
A . (B . F) is Element of the carrier of V1
V2 * (A . (B . F)) is Element of the carrier of V1
V2 * (B . F) is Element of the carrier of V1
A . (V2 * (B . F)) is Element of the carrier of V1
(V2 * B) . F is Element of the carrier of V1
A . ((V2 * B) . F) is Element of the carrier of V1
(A * (V2 * B)) . L is set
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
B is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
A is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
V2 + A is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
(V2 + A) * B is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
V2 * B is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
A * B is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
(V2 * B) + (A * B) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
dom B is set
[#] V1 is non empty non proper Element of bool the carrier of V1
bool the carrier of V1 is set
dom ((V2 + A) * B) is set
L is set
((V2 + A) * B) . L is set
F is Element of the carrier of V1
B . F is Element of the carrier of V1
(V2 + A) . (B . F) is Element of the carrier of V1
V2 . (B . F) is Element of the carrier of V1
A . (B . F) is Element of the carrier of V1
(V2 . (B . F)) + (A . (B . F)) is Element of the carrier of V1
(V2 * B) . F is Element of the carrier of V1
((V2 * B) . F) + (A . (B . F)) is Element of the carrier of V1
(A * B) . F is Element of the carrier of V1
((V2 * B) . F) + ((A * B) . F) is Element of the carrier of V1
((V2 * B) + (A * B)) . L is set
dom ((V2 * B) + (A * B)) is set
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
B is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
A is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
V2 + A is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
B * (V2 + A) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
B * V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
B * A is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
(B * V2) + (B * A) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
dom (B * (V2 + A)) is set
[#] V1 is non empty non proper Element of bool the carrier of V1
bool the carrier of V1 is set
dom A is set
dom V2 is set
L is set
(B * (V2 + A)) . L is set
F is Element of the carrier of V1
(V2 + A) . F is Element of the carrier of V1
B . ((V2 + A) . F) is Element of the carrier of V1
V2 . F is Element of the carrier of V1
A . F is Element of the carrier of V1
(V2 . F) + (A . F) is Element of the carrier of V1
B . ((V2 . F) + (A . F)) is Element of the carrier of V1
B . (V2 . F) is Element of the carrier of V1
B . (A . F) is Element of the carrier of V1
(B . (V2 . F)) + (B . (A . F)) is Element of the carrier of V1
(B * V2) . F is Element of the carrier of V1
((B * V2) . F) + (B . (A . F)) is Element of the carrier of V1
(B * A) . F is Element of the carrier of V1
((B * V2) . F) + ((B * A) . F) is Element of the carrier of V1
((B * V2) + (B * A)) . L is set
dom ((B * V2) + (B * A)) is set
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
A is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
V2 + A is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
B is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
(V2 + A) + B is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
A + B is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
V2 + (A + B) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
L is set
dom ((V2 + A) + B) is set
((V2 + A) + B) . L is set
F is Element of the carrier of V1
(V2 + A) . F is Element of the carrier of V1
B . F is Element of the carrier of V1
((V2 + A) . F) + (B . F) is Element of the carrier of V1
V2 . F is Element of the carrier of V1
A . F is Element of the carrier of V1
(V2 . F) + (A . F) is Element of the carrier of V1
((V2 . F) + (A . F)) + (B . F) is Element of the carrier of V1
(A . F) + (B . F) is Element of the carrier of V1
(V2 . F) + ((A . F) + (B . F)) is Element of the carrier of V1
(A + B) . F is Element of the carrier of V1
(V2 . F) + ((A + B) . F) is Element of the carrier of V1
(V2 + (A + B)) . L is set
[#] V1 is non empty non proper Element of bool the carrier of V1
bool the carrier of V1 is set
dom (V2 + (A + B)) is set
K is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
V1 is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of V1 is non empty non trivial set
power V1 is Relation-like [: the carrier of V1,NAT:] -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [:[: the carrier of V1,NAT:], the carrier of V1:]
[: the carrier of V1,NAT:] is non trivial non finite set
[:[: the carrier of V1,NAT:], the carrier of V1:] is non trivial non finite set
bool [:[: the carrier of V1,NAT:], the carrier of V1:] is non trivial non finite set
V2 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over V1
the carrier of V2 is non empty set
id V2 is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
[: the carrier of V2, the carrier of V2:] is set
bool [: the carrier of V2, the carrier of V2:] is set
id the carrier of V2 is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of V2, the carrier of V2:]
A is Element of the carrier of V1
A * (id V2) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,(A * (id V2)),K) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(power V1) . (A,K) is Element of the carrier of V1
((power V1) . (A,K)) * (id V2) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
dom (id V2) is set
[#] V2 is non empty non proper Element of bool the carrier of V2
bool the carrier of V2 is set
1_ V1 is Element of the carrier of V1
1. V1 is V65(V1) Element of the carrier of V1
the OneF of V1 is Element of the carrier of V1
(1_ V1) * (id V2) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
dom ((1_ V1) * (id V2)) is set
B is set
(id V2) . B is set
L is Element of the carrier of V2
(1_ V1) * L is Element of the carrier of V2
((1_ V1) * (id V2)) . B is set
B is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V2,(A * (id V2)),B) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(power V1) . (A,B) is Element of the carrier of V1
((power V1) . (A,B)) * (id V2) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
B + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
(V2,(A * (id V2)),(B + 1)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(power V1) . (A,(B + 1)) is Element of the carrier of V1
((power V1) . (A,(B + 1))) * (id V2) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,(A * (id V2)),1) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,(A * (id V2)),1) * (((power V1) . (A,B)) * (id V2)) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(A * (id V2)) * (((power V1) . (A,B)) * (id V2)) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(A * (id V2)) * (id V2) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((power V1) . (A,B)) * ((A * (id V2)) * (id V2)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(id V2) * (id V2) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
A * ((id V2) * (id V2)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((power V1) . (A,B)) * (A * ((id V2) * (id V2))) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((power V1) . (A,B)) * (A * (id V2)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((power V1) . (A,B)) * A is Element of the carrier of V1
(((power V1) . (A,B)) * A) * (id V2) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,(A * (id V2)),{}) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(power V1) . (A,{}) is Element of the carrier of V1
((power V1) . (A,{})) * (id V2) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of K is non empty non trivial set
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
A is Element of the carrier of K
B is Element of the carrier of K
A + B is Element of the carrier of K
(A + B) * V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
A * V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
B * V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(A * V2) + (B * V2) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
L is set
dom ((A + B) * V2) is set
((A + B) * V2) . L is set
F is Element of the carrier of V1
V2 . F is Element of the carrier of V1
(A + B) * (V2 . F) is Element of the carrier of V1
A * (V2 . F) is Element of the carrier of V1
B * (V2 . F) is Element of the carrier of V1
(A * (V2 . F)) + (B * (V2 . F)) is Element of the carrier of V1
(A * V2) . F is Element of the carrier of V1
((A * V2) . F) + (B * (V2 . F)) is Element of the carrier of V1
(B * V2) . F is Element of the carrier of V1
((A * V2) . F) + ((B * V2) . F) is Element of the carrier of V1
((A * V2) + (B * V2)) . L is set
[#] V1 is non empty non proper Element of bool the carrier of V1
bool the carrier of V1 is set
dom ((A * V2) + (B * V2)) is set
K is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
V1 is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of V1 is non empty non trivial set
V2 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over V1
the carrier of V2 is non empty set
[: the carrier of V2, the carrier of V2:] is set
bool [: the carrier of V2, the carrier of V2:] is set
id V2 is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
id the carrier of V2 is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of V2, the carrier of V2:]
A is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
B is Element of the carrier of V1
B * (id V2) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
A + (B * (id V2)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,(A + (B * (id V2))),K) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,(B * (id V2)),K) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
F is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V2,(A + (B * (id V2))),F) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,(B * (id V2)),F) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
F + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
(V2,(A + (B * (id V2))),(F + 1)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,(B * (id V2)),(F + 1)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
f is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
A * f is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(A * f) + (V2,(B * (id V2)),F) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
f is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
A * f is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(A * f) + (V2,(B * (id V2)),F) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
B * f is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((A * f) + (V2,(B * (id V2)),F)) + (B * f) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
D is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
A * D is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(A * D) + (V2,(B * (id V2)),(F + 1)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
rng (A * f) is set
[#] V2 is non empty non proper Element of bool the carrier of V2
bool the carrier of V2 is set
(V2,(A + (B * (id V2))),1) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,(A + (B * (id V2))),1) * (V2,(A + (B * (id V2))),F) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(A + (B * (id V2))) * ((A * f) + (V2,(B * (id V2)),F)) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
A * ((A * f) + (V2,(B * (id V2)),F)) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(B * (id V2)) * ((A * f) + (V2,(B * (id V2)),F)) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(A * ((A * f) + (V2,(B * (id V2)),F))) + ((B * (id V2)) * ((A * f) + (V2,(B * (id V2)),F))) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(B * (id V2)) * (A * f) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(B * (id V2)) * (V2,(B * (id V2)),F) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((B * (id V2)) * (A * f)) + ((B * (id V2)) * (V2,(B * (id V2)),F)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(A * ((A * f) + (V2,(B * (id V2)),F))) + (((B * (id V2)) * (A * f)) + ((B * (id V2)) * (V2,(B * (id V2)),F))) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(A * ((A * f) + (V2,(B * (id V2)),F))) + ((B * (id V2)) * (A * f)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((A * ((A * f) + (V2,(B * (id V2)),F))) + ((B * (id V2)) * (A * f))) + ((B * (id V2)) * (V2,(B * (id V2)),F)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(id V2) * (A * f) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
B * ((id V2) * (A * f)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(A * ((A * f) + (V2,(B * (id V2)),F))) + (B * ((id V2) * (A * f))) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((A * ((A * f) + (V2,(B * (id V2)),F))) + (B * ((id V2) * (A * f)))) + ((B * (id V2)) * (V2,(B * (id V2)),F)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
B * (A * f) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(A * ((A * f) + (V2,(B * (id V2)),F))) + (B * (A * f)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((A * ((A * f) + (V2,(B * (id V2)),F))) + (B * (A * f))) + ((B * (id V2)) * (V2,(B * (id V2)),F)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
A * (B * f) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(A * ((A * f) + (V2,(B * (id V2)),F))) + (A * (B * f)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((A * ((A * f) + (V2,(B * (id V2)),F))) + (A * (B * f))) + ((B * (id V2)) * (V2,(B * (id V2)),F)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(A * D) + ((B * (id V2)) * (V2,(B * (id V2)),F)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,(B * (id V2)),1) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,(B * (id V2)),1) * (V2,(B * (id V2)),F) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(A * D) + ((V2,(B * (id V2)),1) * (V2,(B * (id V2)),F)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
C is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V2,A,C) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,C) * D is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
D * (V2,A,C) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,C) * (A * f) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,C) * A is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((V2,A,C) * A) * f is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,1) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,C) * (V2,A,1) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((V2,A,C) * (V2,A,1)) * f is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
C + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
(V2,A,(C + 1)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,(C + 1)) * f is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
f * (V2,A,(C + 1)) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,1) * (V2,A,C) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
f * ((V2,A,1) * (V2,A,C)) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
f * (V2,A,1) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(f * (V2,A,1)) * (V2,A,C) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,1) * f is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((V2,A,1) * f) * (V2,A,C) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(A * f) * (V2,A,C) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,C) * (V2,(B * (id V2)),F) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
power V1 is Relation-like [: the carrier of V1,NAT:] -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [:[: the carrier of V1,NAT:], the carrier of V1:]
[: the carrier of V1,NAT:] is non trivial non finite set
[:[: the carrier of V1,NAT:], the carrier of V1:] is non trivial non finite set
bool [:[: the carrier of V1,NAT:], the carrier of V1:] is non trivial non finite set
(power V1) . (B,F) is Element of the carrier of V1
((power V1) . (B,F)) * (id V2) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,C) * (((power V1) . (B,F)) * (id V2)) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,C) * (id V2) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((power V1) . (B,F)) * ((V2,A,C) * (id V2)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,{}) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,C) * (V2,A,{}) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((power V1) . (B,F)) * ((V2,A,C) * (V2,A,{})) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
C + {} is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V2,A,(C + {})) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((power V1) . (B,F)) * (V2,A,(C + {})) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,{}) * (V2,A,C) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((power V1) . (B,F)) * ((V2,A,{}) * (V2,A,C)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(id V2) * (V2,A,C) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((power V1) . (B,F)) * ((id V2) * (V2,A,C)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(((power V1) . (B,F)) * (id V2)) * (V2,A,C) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,(B * (id V2)),F) * (V2,A,C) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,C) * (B * f) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,C) * f is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
B * ((V2,A,C) * f) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
f * (V2,A,C) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
B * (f * (V2,A,C)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(B * f) * (V2,A,C) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,C) * ((A * f) + (V2,(B * (id V2)),F)) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((V2,A,C) * ((A * f) + (V2,(B * (id V2)),F))) + ((B * f) * (V2,A,C)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((A * f) * (V2,A,C)) + ((V2,(B * (id V2)),F) * (V2,A,C)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(((A * f) * (V2,A,C)) + ((V2,(B * (id V2)),F) * (V2,A,C))) + ((B * f) * (V2,A,C)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((A * f) + (V2,(B * (id V2)),F)) * (V2,A,C) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(((A * f) + (V2,(B * (id V2)),F)) * (V2,A,C)) + ((B * f) * (V2,A,C)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,(A + (B * (id V2))),1) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,(B * (id V2)),1) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
F is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
A * F is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(A * F) + (V2,(B * (id V2)),1) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
1 + {} is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
(V2,A,(1 + {})) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,(1 + {})) + (B * (id V2)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,{}) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,1) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,1) * (V2,A,{}) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((V2,A,1) * (V2,A,{})) + (B * (id V2)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,1) * F is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
((V2,A,1) * F) + (B * (id V2)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(A * F) + (B * (id V2)) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
f is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V2,A,f) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,f) * F is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
F * (V2,A,f) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,f) * (V2,A,{}) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
f + {} is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V2,A,(f + {})) is Relation-like the carrier of V2 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
(V2,A,{}) * (V2,A,f) is Relation-like the carrier of V2 -defined the carrier of V2 -defined the carrier of V2 -valued the carrier of V2 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V2, the carrier of V2:]
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of K is non empty non trivial set
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
[: the carrier of V1, the carrier of V1:] is set
bool [: the carrier of V1, the carrier of V1:] is set
id V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
id the carrier of V1 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of V1, the carrier of V1:]
V2 is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
A is Element of the carrier of K
B is Element of the carrier of K
- A is Element of the carrier of K
(- A) * (id V1) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
V2 + ((- A) * (id V1)) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(K,V1,(V2 + ((- A) * (id V1)))) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V1
- B is Element of the carrier of K
(- B) * (id V1) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
V2 + ((- B) * (id V1)) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(K,V1,(V2 + ((- B) * (id V1)))) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V1
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
F is Element of the carrier of V1
V2 . F is Element of the carrier of V1
B * F is Element of the carrier of V1
the carrier of (K,V1,(V2 + ((- A) * (id V1)))) is non empty set
[: the carrier of (K,V1,(V2 + ((- A) * (id V1)))), the carrier of (K,V1,(V2 + ((- A) * (id V1)))):] is set
bool [: the carrier of (K,V1,(V2 + ((- A) * (id V1)))), the carrier of (K,V1,(V2 + ((- A) * (id V1)))):] is set
V2 | (K,V1,(V2 + ((- A) * (id V1)))) is Relation-like the carrier of (K,V1,(V2 + ((- A) * (id V1)))) -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of (K,V1,(V2 + ((- A) * (id V1)))), the carrier of V1:]
[: the carrier of (K,V1,(V2 + ((- A) * (id V1)))), the carrier of V1:] is set
bool [: the carrier of (K,V1,(V2 + ((- A) * (id V1)))), the carrier of V1:] is set
V2 | the carrier of (K,V1,(V2 + ((- A) * (id V1)))) is Relation-like Function-like set
FB is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Linear_Compl of (K,V1,(V2 + ((- A) * (id V1))))
the carrier of FB is non empty set
[: the carrier of FB, the carrier of FB:] is set
bool [: the carrier of FB, the carrier of FB:] is set
V2 | FB is Relation-like the carrier of FB -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of FB, the carrier of V1:]
[: the carrier of FB, the carrier of V1:] is set
bool [: the carrier of FB, the carrier of V1:] is set
V2 | the carrier of FB is Relation-like Function-like set
SS is Relation-like the carrier of FB -defined the carrier of FB -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of FB, the carrier of FB:]
F9 is Element of the carrier of V1
SA is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,(V2 + ((- B) * (id V1))),SA) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,(V2 + ((- B) * (id V1))),SA) . F9 is Element of the carrier of V1
F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1))))) is Element of [: the carrier of V1, the carrier of V1:]
(F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `1 is Element of the carrier of V1
(F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2 is Element of the carrier of V1
((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `1) + ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2) is Element of the carrier of V1
B - A is Element of the carrier of K
B + (- A) is Element of the carrier of K
(B - A) * (id V1) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V2 + ((- B) * (id V1))) + ((B - A) * (id V1)) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
FSB is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,(V2 + ((- B) * (id V1))),FSB) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
FSB + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
(V1,(V2 + ((- B) * (id V1))),(FSB + 1)) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
Lf is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V1
x is Element of the carrier of V1
(V1,(V2 + ((- B) * (id V1))),(FSB + 1)) . x is Element of the carrier of V1
(V1,(V2 + ((- B) * (id V1))),FSB) . x is Element of the carrier of V1
V2 . ((V1,(V2 + ((- B) * (id V1))),FSB) . x) is Element of the carrier of V1
F is Element of the carrier of FB
SS . F is Element of the carrier of FB
V2 . ((V1,(V2 + ((- B) * (id V1))),FSB) . x) is Element of the carrier of V1
C is Relation-like the carrier of (K,V1,(V2 + ((- A) * (id V1)))) -defined the carrier of (K,V1,(V2 + ((- A) * (id V1)))) -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of (K,V1,(V2 + ((- A) * (id V1)))), the carrier of (K,V1,(V2 + ((- A) * (id V1)))):]
F is Element of the carrier of (K,V1,(V2 + ((- A) * (id V1))))
C . F is Element of the carrier of (K,V1,(V2 + ((- A) * (id V1))))
V2 . ((V1,(V2 + ((- B) * (id V1))),FSB) . x) is Element of the carrier of V1
V2 . ((V1,(V2 + ((- B) * (id V1))),FSB) . x) is Element of the carrier of V1
((- B) * (id V1)) . ((V1,(V2 + ((- B) * (id V1))),FSB) . x) is Element of the carrier of V1
(id V1) . ((V1,(V2 + ((- B) * (id V1))),FSB) . x) is Element of the carrier of V1
(- B) * ((id V1) . ((V1,(V2 + ((- B) * (id V1))),FSB) . x)) is Element of the carrier of V1
(- B) * ((V1,(V2 + ((- B) * (id V1))),FSB) . x) is Element of the carrier of V1
dom (V1,(V2 + ((- B) * (id V1))),FSB) is set
[#] V1 is non empty non proper Element of bool the carrier of V1
bool the carrier of V1 is set
(V1,(V2 + ((- B) * (id V1))),1) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,(V2 + ((- B) * (id V1))),1) * (V1,(V2 + ((- B) * (id V1))),FSB) is Relation-like the carrier of V1 -defined the carrier of V1 -defined the carrier of V1 -valued the carrier of V1 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
((V1,(V2 + ((- B) * (id V1))),1) * (V1,(V2 + ((- B) * (id V1))),FSB)) . x is Element of the carrier of V1
(V1,(V2 + ((- B) * (id V1))),1) . ((V1,(V2 + ((- B) * (id V1))),FSB) . x) is Element of the carrier of V1
(V2 + ((- B) * (id V1))) . ((V1,(V2 + ((- B) * (id V1))),FSB) . x) is Element of the carrier of V1
(V2 . ((V1,(V2 + ((- B) * (id V1))),FSB) . x)) + (((- B) * (id V1)) . ((V1,(V2 + ((- B) * (id V1))),FSB) . x)) is Element of the carrier of V1
(0. V1) + (0. V1) is Element of the carrier of V1
(V1,(V2 + ((- B) * (id V1))),SA) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `1) is Element of the carrier of V1
(V1,(V2 + ((- B) * (id V1))),SA) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2) is Element of the carrier of V1
((V1,(V2 + ((- B) * (id V1))),SA) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `1)) + ((V1,(V2 + ((- B) * (id V1))),SA) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2)) is Element of the carrier of V1
FSB is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,(V2 + ((- A) * (id V1))),FSB) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,(V2 + ((- A) * (id V1))),FSB) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2) is Element of the carrier of V1
(V1,(V2 + ((- B) * (id V1))),{}) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
Lf is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V1
x is Element of the carrier of V1
(V1,(V2 + ((- B) * (id V1))),{}) . x is Element of the carrier of V1
(id V1) . x is Element of the carrier of V1
Lf is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(V1,(V2 + ((- B) * (id V1))),Lf) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,(V2 + ((- B) * (id V1))),Lf) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2) is Element of the carrier of V1
(id V1) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2) is Element of the carrier of V1
(V1,((V2 + ((- B) * (id V1))) + ((B - A) * (id V1))),FSB) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,((B - A) * (id V1)),FSB) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
x is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V2 + ((- B) * (id V1))) * x is Relation-like the carrier of V1 -defined the carrier of V1 -defined the carrier of V1 -valued the carrier of V1 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
((V2 + ((- B) * (id V1))) * x) + (V1,((B - A) * (id V1)),FSB) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
dom (V1,((V2 + ((- B) * (id V1))) + ((B - A) * (id V1))),FSB) is set
[#] V1 is non empty non proper Element of bool the carrier of V1
bool the carrier of V1 is set
(id V1) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2) is Element of the carrier of V1
Lf - 1 is V46() ext-real V165() set
v1 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
(V1,(V2 + ((- B) * (id V1))),v1) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,(V2 + ((- B) * (id V1))),v1) * ((V2 + ((- B) * (id V1))) * x) is Relation-like the carrier of V1 -defined the carrier of V1 -defined the carrier of V1 -valued the carrier of V1 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,(V2 + ((- B) * (id V1))),v1) * (V2 + ((- B) * (id V1))) is Relation-like the carrier of V1 -defined the carrier of V1 -defined the carrier of V1 -valued the carrier of V1 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
((V1,(V2 + ((- B) * (id V1))),v1) * (V2 + ((- B) * (id V1)))) * x is Relation-like the carrier of V1 -defined the carrier of V1 -defined the carrier of V1 -valued the carrier of V1 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,(V2 + ((- B) * (id V1))),1) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,(V2 + ((- B) * (id V1))),v1) * (V1,(V2 + ((- B) * (id V1))),1) is Relation-like the carrier of V1 -defined the carrier of V1 -defined the carrier of V1 -valued the carrier of V1 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
((V1,(V2 + ((- B) * (id V1))),v1) * (V1,(V2 + ((- B) * (id V1))),1)) * x is Relation-like the carrier of V1 -defined the carrier of V1 -defined the carrier of V1 -valued the carrier of V1 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
v1 + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
(V1,(V2 + ((- B) * (id V1))),(v1 + 1)) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,(V2 + ((- B) * (id V1))),(v1 + 1)) * x is Relation-like the carrier of V1 -defined the carrier of V1 -defined the carrier of V1 -valued the carrier of V1 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
x * (V1,(V2 + ((- B) * (id V1))),Lf) is Relation-like the carrier of V1 -defined the carrier of V1 -defined the carrier of V1 -valued the carrier of V1 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
dom (V1,((B - A) * (id V1)),FSB) is set
(V1,(V2 + ((- B) * (id V1))),v1) * (V1,((B - A) * (id V1)),FSB) is Relation-like the carrier of V1 -defined the carrier of V1 -defined the carrier of V1 -valued the carrier of V1 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
((V1,(V2 + ((- B) * (id V1))),v1) * (V1,((B - A) * (id V1)),FSB)) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2) is Element of the carrier of V1
(V1,((B - A) * (id V1)),FSB) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2) is Element of the carrier of V1
(V1,(V2 + ((- B) * (id V1))),v1) . ((V1,((B - A) * (id V1)),FSB) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2)) is Element of the carrier of V1
power K is Relation-like [: the carrier of K,NAT:] -defined the carrier of K -valued Function-like total quasi_total Element of bool [:[: the carrier of K,NAT:], the carrier of K:]
[: the carrier of K,NAT:] is non trivial non finite set
[:[: the carrier of K,NAT:], the carrier of K:] is non trivial non finite set
bool [:[: the carrier of K,NAT:], the carrier of K:] is non trivial non finite set
(power K) . ((B - A),FSB) is Element of the carrier of K
((power K) . ((B - A),FSB)) * (id V1) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(((power K) . ((B - A),FSB)) * (id V1)) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2) is Element of the carrier of V1
(V1,(V2 + ((- B) * (id V1))),v1) . ((((power K) . ((B - A),FSB)) * (id V1)) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2)) is Element of the carrier of V1
(id V1) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2) is Element of the carrier of V1
((power K) . ((B - A),FSB)) * ((id V1) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2)) is Element of the carrier of V1
(V1,(V2 + ((- B) * (id V1))),v1) . (((power K) . ((B - A),FSB)) * ((id V1) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2))) is Element of the carrier of V1
((power K) . ((B - A),FSB)) * ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2) is Element of the carrier of V1
(V1,(V2 + ((- B) * (id V1))),v1) . (((power K) . ((B - A),FSB)) * ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2)) is Element of the carrier of V1
(V1,(V2 + ((- B) * (id V1))),v1) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2) is Element of the carrier of V1
((power K) . ((B - A),FSB)) * ((V1,(V2 + ((- B) * (id V1))),v1) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2)) is Element of the carrier of V1
0. K is V65(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
FSB |-> (B - A) is Relation-like NAT -defined the carrier of K -valued Function-like finite FSB -element FinSequence-like FinSubsequence-like Element of FSB -tuples_on the carrier of K
FSB -tuples_on the carrier of K is functional non empty FinSequence-membered FinSequenceSet of the carrier of K
Product (FSB |-> (B - A)) is Element of the carrier of K
dom (FSB |-> (B - A)) is finite FSB -element Element of bool NAT
Seg FSB is finite FSB -element without_zero Element of bool NAT
{ b₁ where b₁ is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT : ( 1 <= b₁ & b₁ <= FSB ) } is set
F is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
(FSB |-> (B - A)) . F is set
dom (V1,(V2 + ((- B) * (id V1))),Lf) is set
(x * (V1,(V2 + ((- B) * (id V1))),Lf)) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2) is Element of the carrier of V1
x . ((V1,(V2 + ((- B) * (id V1))),Lf) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2)) is Element of the carrier of V1
((- B) * (id V1)) + ((B - A) * (id V1)) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
V2 + (((- B) * (id V1)) + ((B - A) * (id V1))) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(- B) + (B - A) is Element of the carrier of K
((- B) + (B - A)) * (id V1) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
V2 + (((- B) + (B - A)) * (id V1)) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(- B) + B is Element of the carrier of K
((- B) + B) - A is Element of the carrier of K
((- B) + B) + (- A) is Element of the carrier of K
(((- B) + B) - A) * (id V1) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
V2 + ((((- B) + B) - A) * (id V1)) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(0. K) + (- A) is Element of the carrier of K
((0. K) + (- A)) * (id V1) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
V2 + (((0. K) + (- A)) * (id V1)) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
(V1,((V2 + ((- B) * (id V1))) + ((B - A) * (id V1))),FSB) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2) is Element of the carrier of V1
(V1,(V2 + ((- B) * (id V1))),v1) . ((V1,((V2 + ((- B) * (id V1))) + ((B - A) * (id V1))),FSB) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2)) is Element of the carrier of V1
(V1,(V2 + ((- B) * (id V1))),v1) * (((V2 + ((- B) * (id V1))) * x) + (V1,((B - A) * (id V1)),FSB)) is Relation-like the carrier of V1 -defined the carrier of V1 -defined the carrier of V1 -valued the carrier of V1 -valued Function-like non empty total quasi_total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
((V1,(V2 + ((- B) * (id V1))),v1) * (((V2 + ((- B) * (id V1))) * x) + (V1,((B - A) * (id V1)),FSB))) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2) is Element of the carrier of V1
(x * (V1,(V2 + ((- B) * (id V1))),Lf)) + ((V1,(V2 + ((- B) * (id V1))),v1) * (V1,((B - A) * (id V1)),FSB)) is Relation-like the carrier of V1 -defined the carrier of V1 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V1:]
((x * (V1,(V2 + ((- B) * (id V1))),Lf)) + ((V1,(V2 + ((- B) * (id V1))),v1) * (V1,((B - A) * (id V1)),FSB))) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2) is Element of the carrier of V1
(0. V1) + (((power K) . ((B - A),FSB)) * ((V1,(V2 + ((- B) * (id V1))),v1) . ((F9 |-- (FB,(K,V1,(V2 + ((- A) * (id V1)))))) `2))) is Element of the carrier of V1
ker (V2 + ((- B) * (id V1))) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V1
(V2 + ((- B) * (id V1))) . F is Element of the carrier of V1
(V1,(V2 + ((- B) * (id V1))),1) . F is Element of the carrier of V1
0. FB is V65(FB) Element of the carrier of FB
the ZeroF of FB is Element of the carrier of FB
F9 is Element of the carrier of FB
B * F9 is Element of the carrier of FB
SS . F9 is Element of the carrier of FB
SA is Element of the carrier of FB
SS . SA is Element of the carrier of FB
A * SA is Element of the carrier of FB
the carrier of (K,V1,(V2 + ((- B) * (id V1)))) is non empty set
SA is set
SB is Element of the carrier of V1
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of K is non empty non trivial set
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
bool the carrier of V1 is set
A is finite Element of bool the carrier of V1
card A is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
B is Element of the carrier of V1
{B} is non empty trivial finite 1 -element Element of bool the carrier of V1
A \ {B} is finite Element of bool the carrier of V1
(card A) - 1 is V46() ext-real V165() set
F is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
F + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
D is Relation-like the carrier of V1 -defined the carrier of K -valued Function-like total quasi_total Linear_Combination of A \ {B}
Carrier D is finite Element of bool the carrier of V1
0. K is V65(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V1 : not D . b₁ = 0. K } is set
card (Carrier D) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
Sum D is Element of the carrier of V1
B + (Sum D) is Element of the carrier of V1
{(B + (Sum D))} is non empty trivial finite 1 -element Element of bool the carrier of V1
(A \ {B}) \/ {(B + (Sum D))} is non empty finite Element of bool the carrier of V1
card ((A \ {B}) \/ {(B + (Sum D))}) is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
C is set
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
FA is Element of the carrier of V1
{FA} is non empty trivial finite 1 -element Element of bool the carrier of V1
Lin {FA} is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V1
FB is Relation-like the carrier of V1 -defined the carrier of K -valued Function-like total quasi_total Linear_Combination of {FA}
Sum FB is Element of the carrier of V1
D . FA is Element of the carrier of K
(D . FA) * FB is Relation-like the carrier of V1 -defined the carrier of K -valued Function-like total quasi_total Linear_Combination of V1
Carrier ((D . FA) * FB) is finite Element of bool the carrier of V1
{ b₁ where b₁ is Element of the carrier of V1 : not ((D . FA) * FB) . b₁ = 0. K } is set
Carrier FB is finite Element of bool the carrier of V1
{ b₁ where b₁ is Element of the carrier of V1 : not FB . b₁ = 0. K } is set
D - ((D . FA) * FB) is Relation-like the carrier of V1 -defined the carrier of K -valued Function-like total quasi_total Linear_Combination of V1
- ((D . FA) * FB) is Relation-like the carrier of V1 -defined the carrier of K -valued Function-like total quasi_total Linear_Combination of V1
1. K is V65(K) Element of the carrier of K
the OneF of K is Element of the carrier of K
- (1. K) is Element of the carrier of K
(- (1. K)) * ((D . FA) * FB) is Relation-like the carrier of V1 -defined the carrier of K -valued Function-like total quasi_total Linear_Combination of V1
D + (- ((D . FA) * FB)) is Relation-like the carrier of V1 -defined the carrier of K -valued Function-like total quasi_total Linear_Combination of V1
Carrier (D - ((D . FA) * FB)) is finite Element of bool the carrier of V1
{ b₁ where b₁ is Element of the carrier of V1 : not (D - ((D . FA) * FB)) . b₁ = 0. K } is set
(Carrier D) \/ (Carrier ((D . FA) * FB)) is finite Element of bool the carrier of V1
(Carrier D) \/ {FA} is non empty finite Element of bool the carrier of V1
SA is Relation-like the carrier of V1 -defined the carrier of K -valued Function-like total quasi_total Linear_Combination of A \ {B}
Sum SA is Element of the carrier of V1
B + (Sum SA) is Element of the carrier of V1
{(B + (Sum SA))} is non empty trivial finite 1 -element Element of bool the carrier of V1
(A \ {B}) \/ {(B + (Sum SA))} is non empty finite Element of bool the carrier of V1
(Carrier D) \ {FA} is finite Element of bool the carrier of V1
SB is set
SS is Element of the carrier of V1
D . SS is Element of the carrier of K
((D . FA) * FB) . SS is Element of the carrier of K
(D - ((D . FA) * FB)) . SS is Element of the carrier of K
(D . SS) - (0. K) is Element of the carrier of K
- (0. K) is Element of the carrier of K
(D . SS) + (- (0. K)) is Element of the carrier of K
FB . FA is Element of the carrier of K
(FB . FA) * FA is Element of the carrier of V1
1_ K is Element of the carrier of K
(1_ K) * FA is Element of the carrier of V1
(D - ((D . FA) * FB)) . FA is Element of the carrier of K
((D . FA) * FB) . FA is Element of the carrier of K
(D . FA) - (((D . FA) * FB) . FA) is Element of the carrier of K
- (((D . FA) * FB) . FA) is Element of the carrier of K
(D . FA) + (- (((D . FA) * FB) . FA)) is Element of the carrier of K
(D . FA) * (1_ K) is Element of the carrier of K
(D . FA) - ((D . FA) * (1_ K)) is Element of the carrier of K
- ((D . FA) * (1_ K)) is Element of the carrier of K
(D . FA) + (- ((D . FA) * (1_ K))) is Element of the carrier of K
(D . FA) - (D . FA) is Element of the carrier of K
- (D . FA) is Element of the carrier of K
(D . FA) + (- (D . FA)) is Element of the carrier of K
card (Carrier (D - ((D . FA) * FB))) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
card {FA} is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
(F + 1) - (card {FA}) is V46() ext-real V165() set
(F + 1) - 1 is V46() ext-real V165() set
Lin (A \ {B}) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V1
(B + (Sum D)) - (Sum D) is Element of the carrier of V1
- (Sum D) is Element of the carrier of V1
(B + (Sum D)) + (- (Sum D)) is Element of the carrier of V1
(Sum D) - (Sum D) is Element of the carrier of V1
(Sum D) + (- (Sum D)) is Element of the carrier of V1
B + ((Sum D) - (Sum D)) is Element of the carrier of V1
B + (0. V1) is Element of the carrier of V1
L is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
L + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
card (A \ {B}) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
(0. V1) + (Sum D) is Element of the carrier of V1
Sum ((D . FA) * FB) is Element of the carrier of V1
- (Sum ((D . FA) * FB)) is Element of the carrier of V1
(Sum ((D . FA) * FB)) + (- (Sum ((D . FA) * FB))) is Element of the carrier of V1
((Sum ((D . FA) * FB)) + (- (Sum ((D . FA) * FB)))) + (Sum D) is Element of the carrier of V1
(Sum D) - (Sum ((D . FA) * FB)) is Element of the carrier of V1
(Sum D) + (- (Sum ((D . FA) * FB))) is Element of the carrier of V1
(Sum ((D . FA) * FB)) + ((Sum D) - (Sum ((D . FA) * FB))) is Element of the carrier of V1
(Sum ((D . FA) * FB)) + (Sum SA) is Element of the carrier of V1
(D . FA) * FA is Element of the carrier of V1
((D . FA) * FA) + (Sum SA) is Element of the carrier of V1
(B + (Sum SA)) + ((D . FA) * FA) is Element of the carrier of V1
Lin (A \ {B}) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V1
(B + (Sum SA)) - (Sum SA) is Element of the carrier of V1
- (Sum SA) is Element of the carrier of V1
(B + (Sum SA)) + (- (Sum SA)) is Element of the carrier of V1
(Sum SA) - (Sum SA) is Element of the carrier of V1
(Sum SA) + (- (Sum SA)) is Element of the carrier of V1
B + ((Sum SA) - (Sum SA)) is Element of the carrier of V1
B + (0. V1) is Element of the carrier of V1
((A \ {B}) \/ {(B + (Sum SA))}) \ {(B + (Sum SA))} is finite Element of bool the carrier of V1
L is Relation-like the carrier of V1 -defined the carrier of K -valued Function-like total quasi_total Linear_Combination of A \ {B}
Sum L is Element of the carrier of V1
B + (Sum L) is Element of the carrier of V1
{(B + (Sum L))} is non empty trivial finite 1 -element Element of bool the carrier of V1
(A \ {B}) \/ {(B + (Sum L))} is non empty finite Element of bool the carrier of V1
card ((A \ {B}) \/ {(B + (Sum L))}) is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
F is Relation-like the carrier of V1 -defined the carrier of K -valued Function-like total quasi_total Linear_Combination of A \ {B}
Carrier F is finite Element of bool the carrier of V1
0. K is V65(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V1 : not F . b₁ = 0. K } is set
card (Carrier F) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
Sum F is Element of the carrier of V1
B + (Sum F) is Element of the carrier of V1
{(B + (Sum F))} is non empty trivial finite 1 -element Element of bool the carrier of V1
(A \ {B}) \/ {(B + (Sum F))} is non empty finite Element of bool the carrier of V1
card ((A \ {B}) \/ {(B + (Sum F))}) is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
B + (0. V1) is Element of the carrier of V1
Carrier L is finite Element of bool the carrier of V1
0. K is V65(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V1 : not L . b₁ = 0. K } is set
card (Carrier L) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
F is Relation-like the carrier of V1 -defined the carrier of K -valued Function-like total quasi_total Linear_Combination of A \ {B}
Carrier F is finite Element of bool the carrier of V1
{ b₁ where b₁ is Element of the carrier of V1 : not F . b₁ = 0. K } is set
card (Carrier F) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
Sum F is Element of the carrier of V1
B + (Sum F) is Element of the carrier of V1
{(B + (Sum F))} is non empty trivial finite 1 -element Element of bool the carrier of V1
(A \ {B}) \/ {(B + (Sum F))} is non empty finite Element of bool the carrier of V1
card ((A \ {B}) \/ {(B + (Sum F))}) is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of K is non empty non trivial set
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
bool the carrier of V1 is set
V2 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V2 is non empty set
[: the carrier of V1, the carrier of V2:] is set
bool [: the carrier of V1, the carrier of V2:] is set
A is Element of bool the carrier of V1
B is Relation-like the carrier of V2 -defined the carrier of K -valued Function-like total quasi_total Linear_Combination of V2
Carrier B is finite Element of bool the carrier of V2
bool the carrier of V2 is set
0. K is V65(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V2 : not B . b₁ = 0. K } is set
Sum B is Element of the carrier of V2
L is Relation-like the carrier of V1 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V2:]
L .: A is Element of bool the carrier of V2
f is Relation-like NAT -defined the carrier of V2 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V2
rng f is finite set
B (#) f is Relation-like NAT -defined the carrier of V2 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V2
Sum (B (#) f) is Element of the carrier of V2
the addF of V2 is Relation-like [: the carrier of V2, the carrier of V2:] -defined the carrier of V2 -valued Function-like total quasi_total Element of bool [:[: the carrier of V2, the carrier of V2:], the carrier of V2:]
[: the carrier of V2, the carrier of V2:] is set
[:[: the carrier of V2, the carrier of V2:], the carrier of V2:] is set
bool [:[: the carrier of V2, the carrier of V2:], the carrier of V2:] is set
K132( the carrier of V2,(B (#) f), the addF of V2) is Element of the carrier of V2
dom f is finite Element of bool NAT
C is set
f . C is set
dom L is set
FA is set
L . FA is set
[:(dom f), the carrier of V1:] is set
bool [:(dom f), the carrier of V1:] is set
C is Relation-like dom f -defined the carrier of V1 -valued Function-like total quasi_total finite Element of bool [:(dom f), the carrier of V1:]
rng C is finite set
dom C is finite set
len f is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
Seg (len f) is finite len f -element without_zero Element of bool NAT
{ b₁ where b₁ is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT : ( 1 <= b₁ & b₁ <= len f ) } is set
FA is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
SS is set
FB is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
dom FB is finite Element of bool NAT
F9 is set
FB . SS is set
FB . F9 is set
L . (FB . SS) is set
f . SS is set
L . (FB . F9) is set
f . F9 is set
rng FB is finite set
F9 is set
SA is Element of the carrier of V1
SB is set
FB . SB is set
f . SB is set
B . (f . SB) is set
SA is Element of the carrier of V1
SB is set
FB . SB is set
f . SB is set
B . (f . SB) is set
f /. SB is Element of the carrier of V2
B . (f /. SB) is Element of the carrier of K
SS is set
FB . SS is set
f . SS is set
B . (f . SS) is set
SA is Element of the carrier of V1
[: the carrier of V1, the carrier of K:] is set
bool [: the carrier of V1, the carrier of K:] is set
F9 is Relation-like the carrier of V1 -defined the carrier of K -valued Function-like non empty total quasi_total Element of bool [: the carrier of V1, the carrier of K:]
Funcs ( the carrier of V1, the carrier of K) is functional non empty FUNCTION_DOMAIN of the carrier of V1, the carrier of K
SS is finite Element of bool the carrier of V1
SA is Relation-like the carrier of V1 -defined the carrier of K -valued Function-like total quasi_total Element of Funcs ( the carrier of V1, the carrier of K)
SB is Element of the carrier of V1
SA . SB is Element of the carrier of K
SB is Relation-like the carrier of V1 -defined the carrier of K -valued Function-like total quasi_total Linear_Combination of V1
Carrier SB is finite Element of bool the carrier of V1
{ b₁ where b₁ is Element of the carrier of V1 : not SB . b₁ = 0. K } is set
SS is set
SS is Element of the carrier of V1
SB . SS is Element of the carrier of K
SS is set
SS is Element of the carrier of V1
FS is set
FB . FS is set
f . FS is set
B . (f . FS) is set
SB . SS is Element of the carrier of K
SS is set
SS is set
FB . SS is set
SS is Relation-like the carrier of V1 -defined the carrier of K -valued Function-like total quasi_total Linear_Combination of A
SS (#) FB is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
len (SS (#) FB) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
len FB is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
dom (SS (#) FB) is finite Element of bool NAT
len (B (#) f) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
dom (B (#) f) is finite Element of bool NAT
SS is set
FS is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
f . FS is set
f /. FS is Element of the carrier of V2
FB . FS is set
SS . (FB . FS) is set
B . (f . FS) is set
FB /. FS is Element of the carrier of V1
L . (FB . FS) is set
L * (SS (#) FB) is Relation-like NAT -defined the carrier of V2 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V2
(L * (SS (#) FB)) . SS is set
(SS (#) FB) . FS is set
L . ((SS (#) FB) . FS) is set
SS . (FB /. FS) is Element of the carrier of K
(SS . (FB /. FS)) * (FB /. FS) is Element of the carrier of V1
L . ((SS . (FB /. FS)) * (FB /. FS)) is Element of the carrier of V2
B . (f /. FS) is Element of the carrier of K
(B . (f /. FS)) * (f /. FS) is Element of the carrier of V2
(B (#) f) . SS is set
Sum SS is Element of the carrier of V1
L . (Sum SS) is Element of the carrier of V2
dom L is set
[#] V1 is non empty non proper Element of bool the carrier of V1
rng (SS (#) FB) is finite set
dom (L * (SS (#) FB)) is finite Element of bool NAT
Sum (SS (#) FB) is Element of the carrier of V1
the addF of V1 is Relation-like [: the carrier of V1, the carrier of V1:] -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [:[: the carrier of V1, the carrier of V1:], the carrier of V1:]
[: the carrier of V1, the carrier of V1:] is set
[:[: the carrier of V1, the carrier of V1:], the carrier of V1:] is set
bool [:[: the carrier of V1, the carrier of V1:], the carrier of V1:] is set
K132( the carrier of V1,(SS (#) FB), the addF of V1) is Element of the carrier of V1
L . (Sum (SS (#) FB)) is Element of the carrier of V2
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
bool the carrier of V1 is set
V2 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V2 is non empty set
[: the carrier of V1, the carrier of V2:] is set
bool [: the carrier of V1, the carrier of V2:] is set
bool the carrier of V2 is set
A is Relation-like the carrier of V1 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V2:]
dom A is set
[#] V1 is non empty non proper Element of bool the carrier of V1
B is Element of bool the carrier of V1
A .: B is Element of bool the carrier of V2
Lin B is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V1
the carrier of (Lin B) is non empty set
A .: the carrier of (Lin B) is set
L is Element of bool the carrier of V2
Lin L is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed Subspace of V2
the carrier of (Lin L) is non empty set
F is set
f is set
A . f is set
the carrier of K is non empty non trivial set
D is Relation-like the carrier of V1 -defined the carrier of K -valued Function-like total quasi_total Linear_Combination of B
Sum D is Element of the carrier of V1
Carrier D is finite Element of bool the carrier of V1
0. K is V65(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V1 : not D . b₁ = 0. K } is set
C is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
rng C is finite set
D (#) C is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
Sum (D (#) C) is Element of the carrier of V1
the addF of V1 is Relation-like [: the carrier of V1, the carrier of V1:] -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [:[: the carrier of V1, the carrier of V1:], the carrier of V1:]
[: the carrier of V1, the carrier of V1:] is set
[:[: the carrier of V1, the carrier of V1:], the carrier of V1:] is set
bool [:[: the carrier of V1, the carrier of V1:], the carrier of V1:] is set
K132( the carrier of V1,(D (#) C), the addF of V1) is Element of the carrier of V1
[:NAT, the carrier of V1:] is non trivial non finite set
bool [:NAT, the carrier of V1:] is non trivial non finite set
len (D (#) C) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
FB is Relation-like NAT -defined the carrier of V1 -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of V1:]
FB . (len (D (#) C)) is Element of the carrier of V1
FB . {} is set
len C is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
dom (D (#) C) is finite Element of bool NAT
dom C is finite Element of bool NAT
SS is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
FB . SS is set
A . (FB . SS) is set
SS + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
FB . (SS + 1) is set
A . (FB . (SS + 1)) is set
F9 is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
FB . F9 is Element of the carrier of V1
F9 + 1 is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
C /. (F9 + 1) is Element of the carrier of V1
C . (F9 + 1) is set
A . (C /. (F9 + 1)) is Element of the carrier of V2
D . (C /. (F9 + 1)) is Element of the carrier of K
(D . (C /. (F9 + 1))) * (A . (C /. (F9 + 1))) is Element of the carrier of V2
(D (#) C) . (F9 + 1) is set
(D . (C /. (F9 + 1))) * (C /. (F9 + 1)) is Element of the carrier of V1
FB . (F9 + 1) is Element of the carrier of V1
SA is Element of the carrier of V1
SA + ((D . (C /. (F9 + 1))) * (C /. (F9 + 1))) is Element of the carrier of V1
FB . (SS + 1) is Element of the carrier of V1
A . (FB . (SS + 1)) is Element of the carrier of V2
A . SA is Element of the carrier of V2
A . ((D . (C /. (F9 + 1))) * (C /. (F9 + 1))) is Element of the carrier of V2
(A . SA) + (A . ((D . (C /. (F9 + 1))) * (C /. (F9 + 1)))) is Element of the carrier of V2
(A . SA) + ((D . (C /. (F9 + 1))) * (A . (C /. (F9 + 1)))) is Element of the carrier of V2
A . (0. V1) is Element of the carrier of V2
0. V2 is V65(V2) Element of the carrier of V2
the ZeroF of V2 is Element of the carrier of V2
A . (FB . {}) is set
FB . (len C) is set
A . (FB . (len C)) is set
F is set
the carrier of K is non empty non trivial set
f is Relation-like the carrier of V2 -defined the carrier of K -valued Function-like total quasi_total Linear_Combination of L
Sum f is Element of the carrier of V2
Carrier f is finite Element of bool the carrier of V2
0. K is V65(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V2 : not f . b₁ = 0. K } is set
D is Relation-like the carrier of V1 -defined the carrier of K -valued Function-like total quasi_total Linear_Combination of B
Sum D is Element of the carrier of V1
A . (Sum D) is Element of the carrier of V2
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of K is non empty non trivial set
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
V2 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V2 is non empty set
[: the carrier of V1, the carrier of V2:] is set
bool [: the carrier of V1, the carrier of V2:] is set
A is Relation-like the carrier of V1 -defined the carrier of K -valued Function-like total quasi_total Linear_Combination of V1
Carrier A is finite Element of bool the carrier of V1
bool the carrier of V1 is set
0. K is V65(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V1 : not A . b₁ = 0. K } is set
B is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
rng B is finite set
(Carrier A) /\ (rng B) is finite Element of bool the carrier of V1
A (#) B is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
L is Relation-like the carrier of V1 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V2:]
L | ((Carrier A) /\ (rng B)) is Relation-like the carrier of V1 -defined the carrier of V2 -valued Function-like finite Element of bool [: the carrier of V1, the carrier of V2:]
L .: ((Carrier A) /\ (rng B)) is finite Element of bool the carrier of V2
bool the carrier of V2 is set
L * (A (#) B) is Relation-like NAT -defined the carrier of V2 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V2
L * B is Relation-like NAT -defined the carrier of V2 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V2
D is set
C is Element of the carrier of V1
L . C is Element of the carrier of V2
A . C is Element of the carrier of K
dom L is set
C is set
L . C is set
FA is Element of the carrier of V1
A . FA is Element of the carrier of K
[#] V1 is non empty non proper Element of bool the carrier of V1
dom (L | ((Carrier A) /\ (rng B))) is finite set
(L | ((Carrier A) /\ (rng B))) . FA is set
FB is Element of the carrier of V1
L . FB is Element of the carrier of V2
(L | ((Carrier A) /\ (rng B))) . FB is set
A . FB is Element of the carrier of K
FB is Element of the carrier of V1
L . FB is Element of the carrier of V2
A . FB is Element of the carrier of K
[: the carrier of V2, the carrier of K:] is set
bool [: the carrier of V2, the carrier of K:] is set
D is Relation-like the carrier of V2 -defined the carrier of K -valued Function-like non empty total quasi_total Element of bool [: the carrier of V2, the carrier of K:]
Funcs ( the carrier of V2, the carrier of K) is functional non empty FUNCTION_DOMAIN of the carrier of V2, the carrier of K
C is Relation-like the carrier of V2 -defined the carrier of K -valued Function-like total quasi_total Element of Funcs ( the carrier of V2, the carrier of K)
FA is Element of the carrier of V2
C . FA is Element of the carrier of K
dom L is set
[#] V1 is non empty non proper Element of bool the carrier of V1
FA is Relation-like the carrier of V2 -defined the carrier of K -valued Function-like total quasi_total Linear_Combination of V2
Carrier FA is finite Element of bool the carrier of V2
{ b₁ where b₁ is Element of the carrier of V2 : not FA . b₁ = 0. K } is set
FA (#) (L * B) is Relation-like NAT -defined the carrier of V2 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V2
FB is set
SS is set
L . SS is set
F9 is Element of the carrier of V1
A . F9 is Element of the carrier of K
SA is Element of the carrier of V2
FA . SA is Element of the carrier of K
FB is set
SS is Element of the carrier of V2
FA . SS is Element of the carrier of K
len (A (#) B) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
len B is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
dom (A (#) B) is finite Element of bool NAT
dom B is finite Element of bool NAT
dom (L * B) is finite Element of bool NAT
len (FA (#) (L * B)) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
len (L * B) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
dom (FA (#) (L * B)) is finite Element of bool NAT
FB is set
SS is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() set
(L * B) . SS is set
(L * B) /. SS is Element of the carrier of V2
B /. SS is Element of the carrier of V1
B . SS is set
L . (B /. SS) is Element of the carrier of V2
A . (B /. SS) is Element of the carrier of K
FA . ((L * B) /. SS) is Element of the carrier of K
(L * (A (#) B)) . FB is set
(A (#) B) . SS is set
L . ((A (#) B) . SS) is set
(A . (B /. SS)) * (B /. SS) is Element of the carrier of V1
L . ((A . (B /. SS)) * (B /. SS)) is Element of the carrier of V2
(FA . ((L * B) /. SS)) * ((L * B) /. SS) is Element of the carrier of V2
(FA (#) (L * B)) . FB is set
rng (A (#) B) is finite set
dom (L * (A (#) B)) is finite Element of bool NAT
FB is Element of the carrier of V1
A . FB is Element of the carrier of K
L . FB is Element of the carrier of V2
FA . (L . FB) is Element of the carrier of K
K is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of K is non empty non trivial set
V1 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V1 is non empty set
bool the carrier of V1 is set
0. V1 is V65(V1) Element of the carrier of V1
the ZeroF of V1 is Element of the carrier of V1
V2 is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over K
the carrier of V2 is non empty set
[: the carrier of V1, the carrier of V2:] is set
bool [: the carrier of V1, the carrier of V2:] is set
bool the carrier of V2 is set
0. V2 is V65(V2) Element of the carrier of V2
the ZeroF of V2 is Element of the carrier of V2
{(0. V2)} is non empty trivial finite 1 -element Element of bool the carrier of V2
A is Element of bool the carrier of V1
B is Element of bool the carrier of V1
A \/ B is Element of bool the carrier of V1
L is Relation-like the carrier of V1 -defined the carrier of K -valued Function-like total quasi_total Linear_Combination of V1
Carrier L is finite Element of bool the carrier of V1
0. K is V65(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V1 : not L . b₁ = 0. K } is set
Sum L is Element of the carrier of V1
F is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
rng F is finite set
L (#) F is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
Sum (L (#) F) is Element of the carrier of V1
the addF of V1 is Relation-like [: the carrier of V1, the carrier of V1:] -defined the carrier of V1 -valued Function-like total quasi_total Element of bool [:[: the carrier of V1, the carrier of V1:], the carrier of V1:]
[: the carrier of V1, the carrier of V1:] is set
[:[: the carrier of V1, the carrier of V1:], the carrier of V1:] is set
bool [:[: the carrier of V1, the carrier of V1:], the carrier of V1:] is set
K132( the carrier of V1,(L (#) F), the addF of V1) is Element of the carrier of V1
f is Relation-like the carrier of V1 -defined the carrier of V2 -valued Function-like non empty total quasi_total additive homogeneous Element of bool [: the carrier of V1, the carrier of V2:]
f | B is Relation-like the carrier of V1 -defined the carrier of V2 -valued Function-like Element of bool [: the carrier of V1, the carrier of V2:]
f .: B is Element of bool the carrier of V2
f .: A is Element of bool the carrier of V2
dom F is finite Element of bool NAT
dom F is finite Element of bool NAT
(Carrier L) /\ A is finite Element of bool the carrier of V1
F " ((Carrier L) /\ A) is finite set
(Carrier L) /\ B is finite Element of bool the carrier of V1
F " ((Carrier L) /\ B) is finite set
Sgm (F " ((Carrier L) /\ B)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V177() FinSequence of NAT
Sgm (F " ((Carrier L) /\ A)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V177() FinSequence of NAT
(Sgm (F " ((Carrier L) /\ B))) ^ (Sgm (F " ((Carrier L) /\ A))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V177() Element of NAT *
NAT * is functional non empty FinSequence-membered FinSequenceSet of NAT
(Carrier L) /\ ((Carrier L) /\ B) is finite Element of bool the carrier of V1
D is non empty finite set
[:D, the carrier of V1:] is set
bool [:D, the carrier of V1:] is set
len F is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
Seg (len F) is finite len F -element without_zero Element of bool NAT
{ b₁ where b₁ is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT : ( 1 <= b₁ & b₁ <= len F ) } is set
len (Sgm (F " ((Carrier L) /\ A))) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
card (F " ((Carrier L) /\ A)) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
len (Sgm (F " ((Carrier L) /\ B))) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
card (F " ((Carrier L) /\ B)) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
rng (Sgm (F " ((Carrier L) /\ B))) is finite set
rng (Sgm (F " ((Carrier L) /\ A))) is finite set
SS is set
dom f is set
SS is Element of the carrier of V1
f . SS is Element of the carrier of V2
((Carrier L) /\ A) \/ ((Carrier L) /\ B) is finite Element of bool the carrier of V1
(Carrier L) /\ (A \/ B) is finite Element of bool the carrier of V1
(F " ((Carrier L) /\ A)) \/ (F " ((Carrier L) /\ B)) is finite set
F " (Carrier L) is finite set
(card (F " ((Carrier L) /\ A))) + (card (F " ((Carrier L) /\ B))) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
card (Seg (len F)) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
len ((Sgm (F " ((Carrier L) /\ B))) ^ (Sgm (F " ((Carrier L) /\ A)))) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
dom ((Sgm (F " ((Carrier L) /\ B))) ^ (Sgm (F " ((Carrier L) /\ A)))) is finite Element of bool NAT
rng ((Sgm (F " ((Carrier L) /\ B))) ^ (Sgm (F " ((Carrier L) /\ A)))) is finite set
[:D,D:] is finite set
bool [:D,D:] is finite V36() set
card D is non empty V25() V26() V27() V31() finite cardinal V46() ext-real positive non negative V165() Element of NAT
SS is Relation-like D -defined D -valued Function-like non empty total quasi_total finite Element of bool [:D,D:]
SS is Relation-like D -defined D -valued Function-like one-to-one non empty total quasi_total onto bijective finite Element of bool [:D,D:]
F9 is Relation-like D -defined the carrier of V1 -valued Function-like non empty total quasi_total finite Element of bool [:D, the carrier of V1:]
F9 * SS is Relation-like D -defined the carrier of V1 -valued Function-like non empty total quasi_total finite Element of bool [:D, the carrier of V1:]
SA is Relation-like NAT -defined D -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of D
F9 * SA is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
SB is Relation-like NAT -defined D -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of D
F9 * SB is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
FSB is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
rng FSB is finite set
Lf is set
x is set
F . x is set
dom SB is finite Element of bool NAT
v1 is set
SB . v1 is set
FSB . v1 is set
dom FSB is finite Element of bool NAT
Lf is set
dom FSB is finite Element of bool NAT
x is set
FSB . x is set
dom SB is finite Element of bool NAT
SB . x is set
F . (SB . x) is set
FSA is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
L (#) FSA is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
len (L (#) FSA) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
len FSA is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
dom (L (#) FSA) is finite Element of bool NAT
dom FSA is finite Element of bool NAT
dom f is set
[#] V1 is non empty non proper Element of bool the carrier of V1
rng (L (#) FSA) is finite set
f * (L (#) FSA) is Relation-like NAT -defined the carrier of V2 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V2
dom (f * (L (#) FSA)) is finite Element of bool NAT
Lf is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
x is Element of the carrier of V2
(f * (L (#) FSA)) . Lf is set
dom SA is finite Element of bool NAT
SA . Lf is set
F . (SA . Lf) is set
FSA /. Lf is Element of the carrier of V1
FSA . Lf is set
f . (FSA /. Lf) is Element of the carrier of V2
(L (#) FSA) . Lf is set
f . ((L (#) FSA) . Lf) is set
L . (FSA /. Lf) is Element of the carrier of K
(L . (FSA /. Lf)) * (FSA /. Lf) is Element of the carrier of V1
f . ((L . (FSA /. Lf)) * (FSA /. Lf)) is Element of the carrier of V2
(L . (FSA /. Lf)) * (0. V2) is Element of the carrier of V2
(0. K) * x is Element of the carrier of V2
len (f * (L (#) FSA)) is V25() V26() V27() V31() finite cardinal V46() ext-real non negative V165() Element of NAT
Sum (f * (L (#) FSA)) is Element of the carrier of V2
the addF of V2 is Relation-like [: the carrier of V2, the carrier of V2:] -defined the carrier of V2 -valued Function-like total quasi_total Element of bool [:[: the carrier of V2, the carrier of V2:], the carrier of V2:]
[: the carrier of V2, the carrier of V2:] is set
[:[: the carrier of V2, the carrier of V2:], the carrier of V2:] is set
bool [:[: the carrier of V2, the carrier of V2:], the carrier of V2:] is set
K132( the carrier of V2,(f * (L (#) FSA)), the addF of V2) is Element of the carrier of V2
(0. K) * (Sum (f * (L (#) FSA))) is Element of the carrier of V2
FS is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
FSB ^ FSA is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of V1 *
the carrier of V1 * is functional non empty FinSequence-membered FinSequenceSet of the carrier of V1
L (#) FS is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
L (#) FSB is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V1
(L (#) FSB) ^ (L (#) FSA) is Relation-like NAT -defined the carrier of V1 -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of V1 *
f * (L (#) FS) is Relation-like NAT -defined the carrier of V2 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V2
f * (L (#) FSB) is Relation-like NAT -defined the carrier of V2 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V2
(f * (L (#) FSB)) ^ (f * (L (#) FSA)) is Relation-like NAT -defined the carrier of V2 -valued Function-like finite FinSequence-like FinSubsequence-like Element of the carrier of V2 *
the carrier of V2 * is functional non empty FinSequence-membered FinSequenceSet of the carrier of V2
(f | B) | ((Carrier L) /\ B) is Relation-like the carrier of V1 -defined the carrier of V2 -valued Function-like finite Element of bool [: the carrier of V1, the carrier of V2:]
f | ((Carrier L) /\ B) is Relation-like the carrier of V1 -defined the carrier of V2 -valued Function-like finite Element of bool [: the carrier of V1, the carrier of V2:]
(Carrier L) /\ (rng FSB) is finite Element of bool the carrier of V1
f .: ((Carrier L) /\ (rng FSB)) is finite Element of bool the carrier of V2
f * FSB is Relation-like NAT -defined the carrier of V2 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V2
Lf is Relation-like the carrier of V2 -defined the carrier of K -valued Function-like total quasi_total Linear_Combination of V2
Carrier Lf is finite Element of bool the carrier of V2
{ b₁ where b₁ is Element of the carrier of V2 : not Lf . b₁ = 0. K } is set
Lf (#) (f * FSB) is Relation-like NAT -defined the carrier of V2 -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of V2
rng (f * FSB) is finite set
id (rng FSB) is Relation-like rng FSB -defined rng FSB -valued Function-like one-to-one total quasi_total finite Element of bool [:(rng FSB),(rng FSB):]
[:(rng FSB),(rng FSB):] is finite set
bool [:(rng FSB),(rng FSB):] is finite V36() set
(id (rng FSB)) * FSB is Relation-like NAT -defined rng FSB -valued Function-like finite Element of bool [:NAT,(rng FSB):]
[:NAT,(rng FSB):] is set
bool [:NAT,(rng FSB):] is set
f * ((id (rng FSB)) * FSB) is Relation-like NAT -defined the carrier of V2 -valued Function-like finite Element of bool [:NAT, the carrier of V2:]
[:NAT, the carrier of V2:] is non trivial non finite set
bool [:NAT, the carrier of V2:] is non trivial non finite set
f * (id (rng FSB)) is Relation-like rng FSB -defined the carrier of V2 -valued Function-like finite Element of bool [:(rng FSB), the carrier of V2:]
[:(rng FSB), the carrier of V2:] is set
bool [:(rng FSB), the carrier of V2:] is set
(f * (id (rng FSB))) * FSB is Relation-like NAT -defined the carrier of V2 -valued Function-like finite Element of bool [:NAT, the carrier of V2:]
(f | ((Carrier L) /\ B)) * FSB is Relation-like NAT -defined the carrier of V2 -valued Function-like finite Element of bool [:NAT, the carrier of V2:]
f . (0. V1) is Element of the carrier of V2
Sum (L (#) FS) is Element of the carrier of V1
K132( the carrier of V1,(L (#) FS), the addF of V1) is Element of the carrier of V1
f . (Sum (L (#) FS)) is Element of the carrier of V2
Sum (f * (L (#) FS)) is Element of the carrier of V2
K132( the carrier of V2,(f * (L (#) FS)), the addF of V2) is Element of the carrier of V2
Sum (f * (L (#) FSB)) is Element of the carrier of V2
K132( the carrier of V2,(f * (L (#) FSB)), the addF of V2) is Element of the carrier of V2
(Sum (f * (L (#) FSB))) + (Sum (f * (L (#) FSA))) is Element of the carrier of V2
(Sum (f * (L (#) FSB))) + (0. V2) is Element of the carrier of V2
Sum (Lf (#) (f * FSB)) is Element of the carrier of V2
K132( the carrier of V2,(Lf (#) (f * FSB)), the addF of V2) is Element of the carrier of V2
Sum Lf is Element of the carrier of V2
x is set
v1 is Element of the carrier of V1
L . v1 is Element of the carrier of K
f . v1 is Element of the carrier of V2
Lf . (f . v1) is Element of the carrier of K
dom F is finite Element of bool NAT