:: CONVEX4 semantic presentation

REAL is non empty non trivial non finite V68() V69() V70() V74() set
NAT is non trivial ordinal non finite cardinal limit_cardinal V68() V69() V70() V71() V72() V73() V74() Element of bool REAL
bool REAL is non empty non trivial non finite set
omega is non trivial ordinal non finite cardinal limit_cardinal V68() V69() V70() V71() V72() V73() V74() set
bool omega is non empty non trivial non finite set
bool NAT is non empty non trivial non finite set
COMPLEX is non empty non trivial non finite V68() V74() set
RAT is non empty non trivial non finite V68() V69() V70() V71() V74() set
INT is non empty non trivial non finite V68() V69() V70() V71() V72() V74() set
[:COMPLEX,COMPLEX:] is non empty non trivial non finite V58() set
bool [:COMPLEX,COMPLEX:] is non empty non trivial non finite set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is non empty non trivial non finite V58() set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is non empty non trivial non finite set
[:REAL,REAL:] is non empty non trivial non finite V58() V59() V60() set
bool [:REAL,REAL:] is non empty non trivial non finite set
[:[:REAL,REAL:],REAL:] is non empty non trivial non finite V58() V59() V60() set
bool [:[:REAL,REAL:],REAL:] is non empty non trivial non finite set
[:RAT,RAT:] is non empty non trivial RAT -valued non finite V58() V59() V60() set
bool [:RAT,RAT:] is non empty non trivial non finite set
[:[:RAT,RAT:],RAT:] is non empty non trivial RAT -valued non finite V58() V59() V60() set
bool [:[:RAT,RAT:],RAT:] is non empty non trivial non finite set
[:INT,INT:] is non empty non trivial RAT -valued INT -valued non finite V58() V59() V60() set
bool [:INT,INT:] is non empty non trivial non finite set
[:[:INT,INT:],INT:] is non empty non trivial RAT -valued INT -valued non finite V58() V59() V60() set
bool [:[:INT,INT:],INT:] is non empty non trivial non finite set
[:NAT,NAT:] is RAT -valued INT -valued V58() V59() V60() V61() set
[:[:NAT,NAT:],NAT:] is RAT -valued INT -valued V58() V59() V60() V61() set
bool [:[:NAT,NAT:],NAT:] is non empty set
K294(NAT) is V54() set
{} is empty ordinal natural complex real finite V42() cardinal {} -element ext-real non positive non negative V68() V69() V70() V71() V72() V73() V74() set
the empty ordinal natural complex real finite V42() cardinal {} -element ext-real non positive non negative V68() V69() V70() V71() V72() V73() V74() set is empty ordinal natural complex real finite V42() cardinal {} -element ext-real non positive non negative V68() V69() V70() V71() V72() V73() V74() set
2 is non empty ordinal natural complex real finite cardinal V49() V50() ext-real positive non negative V68() V69() V70() V71() V72() V73() Element of NAT
[:NAT,REAL:] is non trivial non finite V58() V59() V60() set
bool [:NAT,REAL:] is non empty non trivial non finite set
[:NAT,COMPLEX:] is non trivial non finite V58() set
bool [:NAT,COMPLEX:] is non empty non trivial non finite set
the_set_of_ComplexSequences is non empty set
[:the_set_of_ComplexSequences,the_set_of_ComplexSequences:] is non empty set
[:[:the_set_of_ComplexSequences,the_set_of_ComplexSequences:],the_set_of_ComplexSequences:] is non empty set
bool [:[:the_set_of_ComplexSequences,the_set_of_ComplexSequences:],the_set_of_ComplexSequences:] is non empty set
[:COMPLEX,the_set_of_ComplexSequences:] is non empty non trivial non finite set
[:[:COMPLEX,the_set_of_ComplexSequences:],the_set_of_ComplexSequences:] is non empty non trivial non finite set
bool [:[:COMPLEX,the_set_of_ComplexSequences:],the_set_of_ComplexSequences:] is non empty non trivial non finite set
Linear_Space_of_ComplexSequences is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of Linear_Space_of_ComplexSequences is non empty set
bool the carrier of Linear_Space_of_ComplexSequences is non empty set
the_set_of_l2ComplexSequences is Element of bool the carrier of Linear_Space_of_ComplexSequences
[:the_set_of_l2ComplexSequences,the_set_of_l2ComplexSequences:] is set
[:[:the_set_of_l2ComplexSequences,the_set_of_l2ComplexSequences:],COMPLEX:] is V58() set
bool [:[:the_set_of_l2ComplexSequences,the_set_of_l2ComplexSequences:],COMPLEX:] is non empty set
1 is non empty ordinal natural complex real finite cardinal V49() V50() ext-real positive non negative V68() V69() V70() V71() V72() V73() Element of NAT
<*> REAL is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V58() V59() V60() FinSequence of REAL
Sum (<*> REAL) is complex real ext-real Element of REAL
K267() is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total quasi_total V58() V59() V60() Element of bool [:[:REAL,REAL:],REAL:]
K295(REAL,(<*> REAL),K267()) is complex real ext-real Element of REAL
0 is empty ordinal natural complex real finite V42() cardinal {} -element V49() V50() ext-real non positive non negative V68() V69() V70() V71() V72() V73() V74() Element of NAT
len {} is empty ordinal natural complex real finite V42() cardinal {} -element ext-real non positive non negative V68() V69() V70() V71() V72() V73() V74() set
3 is non empty ordinal natural complex real finite cardinal V49() V50() ext-real positive non negative V68() V69() V70() V71() V72() V73() Element of NAT
Seg 1 is V68() V69() V70() V71() V72() V73() Element of bool NAT
{ b₁ where b₁ is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT : ( 1 <= b₁ & b₁ <= 1 ) } is set
{1} is non empty trivial finite V42() 1 -element V68() V69() V70() V71() V72() V73() set
Seg 2 is V68() V69() V70() V71() V72() V73() Element of bool NAT
{ b₁ where b₁ is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT : ( 1 <= b₁ & b₁ <= 2 ) } is set
{1,2} is non empty finite V42() V68() V69() V70() V71() V72() V73() set
Seg 3 is V68() V69() V70() V71() V72() V73() Element of bool NAT
{ b₁ where b₁ is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT : ( 1 <= b₁ & b₁ <= 3 ) } is set
K198(1,2,3) is non empty finite V68() V69() V70() V71() V72() V73() set
[:2,REAL:] is non empty non trivial non finite V58() V59() V60() set
bool [:2,REAL:] is non empty non trivial non finite set
1r is complex Element of COMPLEX
- 1r is complex Element of COMPLEX
V is non empty 1-sorted
the carrier of V is non empty set
Funcs ( the carrier of V,COMPLEX) is non empty functional FUNCTION_DOMAIN of the carrier of V, COMPLEX
bool the carrier of V is non empty set
0c is empty ordinal natural complex real finite V42() cardinal {} -element ext-real non positive non negative V68() V69() V70() V71() V72() V73() V74() Element of COMPLEX
the carrier of V --> 0c is non empty Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() V59() V60() V61() Element of bool [: the carrier of V,COMPLEX:]
[: the carrier of V,COMPLEX:] is non empty non trivial non finite V58() set
bool [: the carrier of V,COMPLEX:] is non empty non trivial non finite set
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() Element of Funcs ( the carrier of V,COMPLEX)
{} V is empty proper ordinal natural complex real finite V42() cardinal {} -element ext-real non positive non negative V68() V69() V70() V71() V72() V73() V74() Element of bool the carrier of V
N is Element of the carrier of V
M . N is complex Element of COMPLEX
V is non empty addLoopStr
the carrier of V is non empty set
Funcs ( the carrier of V,COMPLEX) is non empty functional FUNCTION_DOMAIN of the carrier of V, COMPLEX
V is non empty addLoopStr
the carrier of V is non empty set
Funcs ( the carrier of V,COMPLEX) is non empty functional FUNCTION_DOMAIN of the carrier of V, COMPLEX
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() Element of Funcs ( the carrier of V,COMPLEX)
support M is set
dom M is Element of bool the carrier of V
bool the carrier of V is non empty set
N is set
V is non empty addLoopStr
the carrier of V is non empty set
Funcs ( the carrier of V,COMPLEX) is non empty functional FUNCTION_DOMAIN of the carrier of V, COMPLEX
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() Element of Funcs ( the carrier of V,COMPLEX)
support M is set
bool the carrier of V is non empty set
0c is empty ordinal natural complex real finite V42() cardinal {} -element ext-real non positive non negative V68() V69() V70() V71() V72() V73() V74() Element of COMPLEX
{ b₁ where b₁ is Element of the carrier of V : not M . b₁ = 0c } is set
N is Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not M . b₁ = {} } is set
r2 is set
M . r2 is complex set
r2 is set
r1 is Element of the carrier of V
M . r1 is complex Element of COMPLEX
r2 is set
r1 is Element of the carrier of V
M . r1 is complex Element of COMPLEX
r2 is set
M . r2 is complex set
V is non empty addLoopStr
the carrier of V is non empty set
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ b₁ where b₁ is Element of the carrier of V : not M . b₁ = 0c } is set
SG is finite Element of bool the carrier of V
Y is set
r2 is Element of the carrier of V
M . r2 is complex Element of COMPLEX
V is non empty addLoopStr
the carrier of V is non empty set
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M) is finite Element of bool the carrier of V
bool the carrier of V is non empty set
{ b₁ where b₁ is Element of the carrier of V : not M . b₁ = 0c } is set
N is Element of the carrier of V
M . N is complex Element of COMPLEX
SG is Element of the carrier of V
M . SG is complex Element of COMPLEX
V is non empty addLoopStr
the carrier of V is non empty set
Funcs ( the carrier of V,COMPLEX) is non empty functional FUNCTION_DOMAIN of the carrier of V, COMPLEX
the carrier of V --> 0c is non empty Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() V59() V60() V61() Element of bool [: the carrier of V,COMPLEX:]
[: the carrier of V,COMPLEX:] is non empty non trivial non finite V58() set
bool [: the carrier of V,COMPLEX:] is non empty non trivial non finite set
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() Element of Funcs ( the carrier of V,COMPLEX)
{} V is empty proper ordinal natural complex real finite V42() cardinal {} -element ext-real non positive non negative V68() V69() V70() V71() V72() V73() V74() Element of bool the carrier of V
bool the carrier of V is non empty set
N is Element of the carrier of V
M . N is complex Element of COMPLEX
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,N) is finite Element of bool the carrier of V
bool the carrier of V is non empty set
{ b₁ where b₁ is Element of the carrier of V : not N . b₁ = 0c } is set
the Element of { b₁ where b₁ is Element of the carrier of V : not N . b₁ = 0c } is Element of { b₁ where b₁ is Element of the carrier of V : not N . b₁ = 0c }
r2 is Element of the carrier of V
N . r2 is complex Element of COMPLEX
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M) is finite Element of bool the carrier of V
bool the carrier of V is non empty set
{ b₁ where b₁ is Element of the carrier of V : not M . b₁ = 0c } is set
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,N) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not N . b₁ = 0c } is set
SG is set
Y is Element of the carrier of V
N . Y is complex Element of COMPLEX
M . Y is complex Element of COMPLEX
M . SG is complex set
N . SG is complex set
V is non empty addLoopStr
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
the carrier of V is non empty set
(V,(V)) is finite Element of bool the carrier of V
bool the carrier of V is non empty set
{ b₁ where b₁ is Element of the carrier of V : not (V) . b₁ = 0c } is set
V is non empty addLoopStr
the carrier of V is non empty set
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
M is Element of the carrier of V
(V) . M is complex Element of COMPLEX
(V,(V)) is empty proper ordinal natural complex real finite V42() cardinal {} -element ext-real non positive non negative V68() V69() V70() V71() V72() V73() V74() Element of bool the carrier of V
bool the carrier of V is non empty set
{ b₁ where b₁ is Element of the carrier of V : not (V) . b₁ = 0c } is set
V is non empty addLoopStr
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,N) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not N . b₁ = 0c } is set
V is non empty addLoopStr
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Element of bool the carrier of V
SG is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,M)
(V,SG) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not SG . b₁ = 0c } is set
V is non empty addLoopStr
the carrier of V is non empty set
bool the carrier of V is non empty set
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
M is Element of bool the carrier of V
(V,(V)) is empty proper ordinal natural complex real finite V42() cardinal {} -element ext-real non positive non negative V68() V69() V70() V71() V72() V73() V74() Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not (V) . b₁ = 0c } is set
V is non empty addLoopStr
the carrier of V is non empty set
{} the carrier of V is empty proper ordinal natural complex real finite V42() cardinal {} -element ext-real non positive non negative V68() V69() V70() V71() V72() V73() V74() Element of bool the carrier of V
bool the carrier of V is non empty set
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V, {} the carrier of V)
(V,M) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not M . b₁ = 0c } is set
V is non empty CLSStruct
the carrier of V is non empty set
[: the carrier of V,COMPLEX:] is non empty non trivial non finite V58() set
bool [: the carrier of V,COMPLEX:] is non empty non trivial non finite set
M is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
len M is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
N is non empty Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() Element of bool [: the carrier of V,COMPLEX:]
SG is Relation-like Function-like FinSequence-like set
len SG is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
dom SG is V68() V69() V70() V71() V72() V73() Element of bool NAT
rng SG is set
Y is set
r2 is set
SG . r2 is set
r1 is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
SG . r1 is set
M /. r1 is Element of the carrier of V
N . (M /. r1) is complex Element of COMPLEX
(N . (M /. r1)) * (M /. r1) is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(N . (M /. r1)),(M /. r1)] is set
{(N . (M /. r1)),(M /. r1)} is non empty finite set
{(N . (M /. r1))} is non empty trivial finite 1 -element V68() set
{{(N . (M /. r1)),(M /. r1)},{(N . (M /. r1))}} is non empty finite V42() set
the Mult of V . [(N . (M /. r1)),(M /. r1)] is set
Y is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
len Y is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
dom Y is V68() V69() V70() V71() V72() V73() Element of bool NAT
r2 is ordinal natural complex real finite cardinal ext-real non negative set
Y . r2 is set
M /. r2 is Element of the carrier of V
N . (M /. r2) is complex Element of COMPLEX
(N . (M /. r2)) * (M /. r2) is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(N . (M /. r2)),(M /. r2)] is set
{(N . (M /. r2)),(M /. r2)} is non empty finite set
{(N . (M /. r2))} is non empty trivial finite 1 -element V68() set
{{(N . (M /. r2)),(M /. r2)},{(N . (M /. r2))}} is non empty finite V42() set
the Mult of V . [(N . (M /. r2)),(M /. r2)] is set
SG is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
len SG is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
dom SG is V68() V69() V70() V71() V72() V73() Element of bool NAT
Y is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
len Y is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
dom Y is V68() V69() V70() V71() V72() V73() Element of bool NAT
r2 is ordinal natural complex real finite cardinal ext-real non negative set
Seg (len SG) is V68() V69() V70() V71() V72() V73() Element of bool NAT
{ b₁ where b₁ is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT : ( 1 <= b₁ & b₁ <= len SG ) } is set
SG . r2 is set
M /. r2 is Element of the carrier of V
N . (M /. r2) is complex Element of COMPLEX
(N . (M /. r2)) * (M /. r2) is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(N . (M /. r2)),(M /. r2)] is set
{(N . (M /. r2)),(M /. r2)} is non empty finite set
{(N . (M /. r2))} is non empty trivial finite 1 -element V68() set
{{(N . (M /. r2)),(M /. r2)},{(N . (M /. r2))}} is non empty finite V42() set
the Mult of V . [(N . (M /. r2)),(M /. r2)] is set
Y . r2 is set
V is non empty CLSStruct
the carrier of V is non empty set
[: the carrier of V,COMPLEX:] is non empty non trivial non finite V58() set
bool [: the carrier of V,COMPLEX:] is non empty non trivial non finite set
M is Element of the carrier of V
N is set
SG is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
dom SG is V68() V69() V70() V71() V72() V73() Element of bool NAT
SG . N is set
Y is non empty Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() Element of bool [: the carrier of V,COMPLEX:]
(V,SG,Y) is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
(V,SG,Y) . N is set
Y . M is complex Element of COMPLEX
(Y . M) * M is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(Y . M),M] is set
{(Y . M),M} is non empty finite set
{(Y . M)} is non empty trivial finite 1 -element V68() set
{{(Y . M),M},{(Y . M)}} is non empty finite V42() set
the Mult of V . [(Y . M),M] is set
SG /. N is Element of the carrier of V
len (V,SG,Y) is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
len SG is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
dom (V,SG,Y) is V68() V69() V70() V71() V72() V73() Element of bool NAT
V is non empty CLSStruct
the carrier of V is non empty set
[: the carrier of V,COMPLEX:] is non empty non trivial non finite V58() set
bool [: the carrier of V,COMPLEX:] is non empty non trivial non finite set
<*> the carrier of V is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
M is non empty Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() Element of bool [: the carrier of V,COMPLEX:]
(V,(<*> the carrier of V),M) is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
len (V,(<*> the carrier of V),M) is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
len (<*> the carrier of V) is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
V is non empty CLSStruct
the carrier of V is non empty set
[: the carrier of V,COMPLEX:] is non empty non trivial non finite V58() set
bool [: the carrier of V,COMPLEX:] is non empty non trivial non finite set
M is Element of the carrier of V
<*M*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
[1,M] is set
{1,M} is non empty finite set
{{1,M},{1}} is non empty finite V42() set
{[1,M]} is non empty trivial finite 1 -element set
N is non empty Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() Element of bool [: the carrier of V,COMPLEX:]
(V,<*M*>,N) is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
N . M is complex Element of COMPLEX
(N . M) * M is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(N . M),M] is set
{(N . M),M} is non empty finite set
{(N . M)} is non empty trivial finite 1 -element V68() set
{{(N . M),M},{(N . M)}} is non empty finite V42() set
the Mult of V . [(N . M),M] is set
<*((N . M) * M)*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
[1,((N . M) * M)] is set
{1,((N . M) * M)} is non empty finite set
{{1,((N . M) * M)},{1}} is non empty finite V42() set
{[1,((N . M) * M)]} is non empty trivial finite 1 -element set
{1} is non empty trivial finite V42() 1 -element V68() V69() V70() V71() V72() V73() Element of bool REAL
len (V,<*M*>,N) is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
len <*M*> is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
dom (V,<*M*>,N) is V68() V69() V70() V71() V72() V73() Element of bool NAT
(V,<*M*>,N) . 1 is set
<*M*> /. 1 is Element of the carrier of V
N . (<*M*> /. 1) is complex Element of COMPLEX
(N . (<*M*> /. 1)) * (<*M*> /. 1) is Element of the carrier of V
[(N . (<*M*> /. 1)),(<*M*> /. 1)] is set
{(N . (<*M*> /. 1)),(<*M*> /. 1)} is non empty finite set
{(N . (<*M*> /. 1))} is non empty trivial finite 1 -element V68() set
{{(N . (<*M*> /. 1)),(<*M*> /. 1)},{(N . (<*M*> /. 1))}} is non empty finite V42() set
the Mult of V . [(N . (<*M*> /. 1)),(<*M*> /. 1)] is set
(N . (<*M*> /. 1)) * M is Element of the carrier of V
[(N . (<*M*> /. 1)),M] is set
{(N . (<*M*> /. 1)),M} is non empty finite set
{{(N . (<*M*> /. 1)),M},{(N . (<*M*> /. 1))}} is non empty finite V42() set
the Mult of V . [(N . (<*M*> /. 1)),M] is set
V is non empty CLSStruct
the carrier of V is non empty set
[: the carrier of V,COMPLEX:] is non empty non trivial non finite V58() set
bool [: the carrier of V,COMPLEX:] is non empty non trivial non finite set
M is Element of the carrier of V
N is Element of the carrier of V
<*M,N*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
<*M*> is Relation-like Function-like set
[1,M] is set
{1,M} is non empty finite set
{{1,M},{1}} is non empty finite V42() set
{[1,M]} is non empty trivial finite 1 -element set
<*N*> is Relation-like Function-like set
[1,N] is set
{1,N} is non empty finite set
{{1,N},{1}} is non empty finite V42() set
{[1,N]} is non empty trivial finite 1 -element set
K158(<*M*>,<*N*>) is Relation-like Function-like FinSequence-like set
SG is non empty Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() Element of bool [: the carrier of V,COMPLEX:]
(V,<*M,N*>,SG) is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
SG . M is complex Element of COMPLEX
(SG . M) * M is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(SG . M),M] is set
{(SG . M),M} is non empty finite set
{(SG . M)} is non empty trivial finite 1 -element V68() set
{{(SG . M),M},{(SG . M)}} is non empty finite V42() set
the Mult of V . [(SG . M),M] is set
SG . N is complex Element of COMPLEX
(SG . N) * N is Element of the carrier of V
[(SG . N),N] is set
{(SG . N),N} is non empty finite set
{(SG . N)} is non empty trivial finite 1 -element V68() set
{{(SG . N),N},{(SG . N)}} is non empty finite V42() set
the Mult of V . [(SG . N),N] is set
<*((SG . M) * M),((SG . N) * N)*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
<*((SG . M) * M)*> is Relation-like Function-like set
[1,((SG . M) * M)] is set
{1,((SG . M) * M)} is non empty finite set
{{1,((SG . M) * M)},{1}} is non empty finite V42() set
{[1,((SG . M) * M)]} is non empty trivial finite 1 -element set
<*((SG . N) * N)*> is Relation-like Function-like set
[1,((SG . N) * N)] is set
{1,((SG . N) * N)} is non empty finite set
{{1,((SG . N) * N)},{1}} is non empty finite V42() set
{[1,((SG . N) * N)]} is non empty trivial finite 1 -element set
K158(<*((SG . M) * M)*>,<*((SG . N) * N)*>) is Relation-like Function-like FinSequence-like set
len (V,<*M,N*>,SG) is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
len <*M,N*> is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
dom (V,<*M,N*>,SG) is V68() V69() V70() V71() V72() V73() Element of bool NAT
{1,2} is non empty finite V42() V68() V69() V70() V71() V72() V73() Element of bool REAL
(V,<*M,N*>,SG) . 2 is set
<*M,N*> /. 2 is Element of the carrier of V
SG . (<*M,N*> /. 2) is complex Element of COMPLEX
(SG . (<*M,N*> /. 2)) * (<*M,N*> /. 2) is Element of the carrier of V
[(SG . (<*M,N*> /. 2)),(<*M,N*> /. 2)] is set
{(SG . (<*M,N*> /. 2)),(<*M,N*> /. 2)} is non empty finite set
{(SG . (<*M,N*> /. 2))} is non empty trivial finite 1 -element V68() set
{{(SG . (<*M,N*> /. 2)),(<*M,N*> /. 2)},{(SG . (<*M,N*> /. 2))}} is non empty finite V42() set
the Mult of V . [(SG . (<*M,N*> /. 2)),(<*M,N*> /. 2)] is set
(SG . (<*M,N*> /. 2)) * N is Element of the carrier of V
[(SG . (<*M,N*> /. 2)),N] is set
{(SG . (<*M,N*> /. 2)),N} is non empty finite set
{{(SG . (<*M,N*> /. 2)),N},{(SG . (<*M,N*> /. 2))}} is non empty finite V42() set
the Mult of V . [(SG . (<*M,N*> /. 2)),N] is set
(V,<*M,N*>,SG) . 1 is set
<*M,N*> /. 1 is Element of the carrier of V
SG . (<*M,N*> /. 1) is complex Element of COMPLEX
(SG . (<*M,N*> /. 1)) * (<*M,N*> /. 1) is Element of the carrier of V
[(SG . (<*M,N*> /. 1)),(<*M,N*> /. 1)] is set
{(SG . (<*M,N*> /. 1)),(<*M,N*> /. 1)} is non empty finite set
{(SG . (<*M,N*> /. 1))} is non empty trivial finite 1 -element V68() set
{{(SG . (<*M,N*> /. 1)),(<*M,N*> /. 1)},{(SG . (<*M,N*> /. 1))}} is non empty finite V42() set
the Mult of V . [(SG . (<*M,N*> /. 1)),(<*M,N*> /. 1)] is set
(SG . (<*M,N*> /. 1)) * M is Element of the carrier of V
[(SG . (<*M,N*> /. 1)),M] is set
{(SG . (<*M,N*> /. 1)),M} is non empty finite set
{{(SG . (<*M,N*> /. 1)),M},{(SG . (<*M,N*> /. 1))}} is non empty finite V42() set
the Mult of V . [(SG . (<*M,N*> /. 1)),M] is set
V is non empty CLSStruct
the carrier of V is non empty set
[: the carrier of V,COMPLEX:] is non empty non trivial non finite V58() set
bool [: the carrier of V,COMPLEX:] is non empty non trivial non finite set
M is Element of the carrier of V
N is Element of the carrier of V
SG is Element of the carrier of V
<*M,N,SG*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
<*M*> is Relation-like Function-like set
[1,M] is set
{1,M} is non empty finite set
{{1,M},{1}} is non empty finite V42() set
{[1,M]} is non empty trivial finite 1 -element set
<*N*> is Relation-like Function-like set
[1,N] is set
{1,N} is non empty finite set
{{1,N},{1}} is non empty finite V42() set
{[1,N]} is non empty trivial finite 1 -element set
K158(<*M*>,<*N*>) is Relation-like Function-like FinSequence-like set
<*SG*> is Relation-like Function-like set
[1,SG] is set
{1,SG} is non empty finite set
{{1,SG},{1}} is non empty finite V42() set
{[1,SG]} is non empty trivial finite 1 -element set
K158(K158(<*M*>,<*N*>),<*SG*>) is Relation-like Function-like FinSequence-like set
Y is non empty Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() Element of bool [: the carrier of V,COMPLEX:]
(V,<*M,N,SG*>,Y) is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
Y . M is complex Element of COMPLEX
(Y . M) * M is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(Y . M),M] is set
{(Y . M),M} is non empty finite set
{(Y . M)} is non empty trivial finite 1 -element V68() set
{{(Y . M),M},{(Y . M)}} is non empty finite V42() set
the Mult of V . [(Y . M),M] is set
Y . N is complex Element of COMPLEX
(Y . N) * N is Element of the carrier of V
[(Y . N),N] is set
{(Y . N),N} is non empty finite set
{(Y . N)} is non empty trivial finite 1 -element V68() set
{{(Y . N),N},{(Y . N)}} is non empty finite V42() set
the Mult of V . [(Y . N),N] is set
Y . SG is complex Element of COMPLEX
(Y . SG) * SG is Element of the carrier of V
[(Y . SG),SG] is set
{(Y . SG),SG} is non empty finite set
{(Y . SG)} is non empty trivial finite 1 -element V68() set
{{(Y . SG),SG},{(Y . SG)}} is non empty finite V42() set
the Mult of V . [(Y . SG),SG] is set
<*((Y . M) * M),((Y . N) * N),((Y . SG) * SG)*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
<*((Y . M) * M)*> is Relation-like Function-like set
[1,((Y . M) * M)] is set
{1,((Y . M) * M)} is non empty finite set
{{1,((Y . M) * M)},{1}} is non empty finite V42() set
{[1,((Y . M) * M)]} is non empty trivial finite 1 -element set
<*((Y . N) * N)*> is Relation-like Function-like set
[1,((Y . N) * N)] is set
{1,((Y . N) * N)} is non empty finite set
{{1,((Y . N) * N)},{1}} is non empty finite V42() set
{[1,((Y . N) * N)]} is non empty trivial finite 1 -element set
K158(<*((Y . M) * M)*>,<*((Y . N) * N)*>) is Relation-like Function-like FinSequence-like set
<*((Y . SG) * SG)*> is Relation-like Function-like set
[1,((Y . SG) * SG)] is set
{1,((Y . SG) * SG)} is non empty finite set
{{1,((Y . SG) * SG)},{1}} is non empty finite V42() set
{[1,((Y . SG) * SG)]} is non empty trivial finite 1 -element set
K158(K158(<*((Y . M) * M)*>,<*((Y . N) * N)*>),<*((Y . SG) * SG)*>) is Relation-like Function-like FinSequence-like set
len (V,<*M,N,SG*>,Y) is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
len <*M,N,SG*> is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
dom (V,<*M,N,SG*>,Y) is V68() V69() V70() V71() V72() V73() Element of bool NAT
{1,2,3} is non empty finite V68() V69() V70() V71() V72() V73() Element of bool REAL
(V,<*M,N,SG*>,Y) . 3 is set
<*M,N,SG*> /. 3 is Element of the carrier of V
Y . (<*M,N,SG*> /. 3) is complex Element of COMPLEX
(Y . (<*M,N,SG*> /. 3)) * (<*M,N,SG*> /. 3) is Element of the carrier of V
[(Y . (<*M,N,SG*> /. 3)),(<*M,N,SG*> /. 3)] is set
{(Y . (<*M,N,SG*> /. 3)),(<*M,N,SG*> /. 3)} is non empty finite set
{(Y . (<*M,N,SG*> /. 3))} is non empty trivial finite 1 -element V68() set
{{(Y . (<*M,N,SG*> /. 3)),(<*M,N,SG*> /. 3)},{(Y . (<*M,N,SG*> /. 3))}} is non empty finite V42() set
the Mult of V . [(Y . (<*M,N,SG*> /. 3)),(<*M,N,SG*> /. 3)] is set
(Y . (<*M,N,SG*> /. 3)) * SG is Element of the carrier of V
[(Y . (<*M,N,SG*> /. 3)),SG] is set
{(Y . (<*M,N,SG*> /. 3)),SG} is non empty finite set
{{(Y . (<*M,N,SG*> /. 3)),SG},{(Y . (<*M,N,SG*> /. 3))}} is non empty finite V42() set
the Mult of V . [(Y . (<*M,N,SG*> /. 3)),SG] is set
(V,<*M,N,SG*>,Y) . 2 is set
<*M,N,SG*> /. 2 is Element of the carrier of V
Y . (<*M,N,SG*> /. 2) is complex Element of COMPLEX
(Y . (<*M,N,SG*> /. 2)) * (<*M,N,SG*> /. 2) is Element of the carrier of V
[(Y . (<*M,N,SG*> /. 2)),(<*M,N,SG*> /. 2)] is set
{(Y . (<*M,N,SG*> /. 2)),(<*M,N,SG*> /. 2)} is non empty finite set
{(Y . (<*M,N,SG*> /. 2))} is non empty trivial finite 1 -element V68() set
{{(Y . (<*M,N,SG*> /. 2)),(<*M,N,SG*> /. 2)},{(Y . (<*M,N,SG*> /. 2))}} is non empty finite V42() set
the Mult of V . [(Y . (<*M,N,SG*> /. 2)),(<*M,N,SG*> /. 2)] is set
(Y . (<*M,N,SG*> /. 2)) * N is Element of the carrier of V
[(Y . (<*M,N,SG*> /. 2)),N] is set
{(Y . (<*M,N,SG*> /. 2)),N} is non empty finite set
{{(Y . (<*M,N,SG*> /. 2)),N},{(Y . (<*M,N,SG*> /. 2))}} is non empty finite V42() set
the Mult of V . [(Y . (<*M,N,SG*> /. 2)),N] is set
(V,<*M,N,SG*>,Y) . 1 is set
<*M,N,SG*> /. 1 is Element of the carrier of V
Y . (<*M,N,SG*> /. 1) is complex Element of COMPLEX
(Y . (<*M,N,SG*> /. 1)) * (<*M,N,SG*> /. 1) is Element of the carrier of V
[(Y . (<*M,N,SG*> /. 1)),(<*M,N,SG*> /. 1)] is set
{(Y . (<*M,N,SG*> /. 1)),(<*M,N,SG*> /. 1)} is non empty finite set
{(Y . (<*M,N,SG*> /. 1))} is non empty trivial finite 1 -element V68() set
{{(Y . (<*M,N,SG*> /. 1)),(<*M,N,SG*> /. 1)},{(Y . (<*M,N,SG*> /. 1))}} is non empty finite V42() set
the Mult of V . [(Y . (<*M,N,SG*> /. 1)),(<*M,N,SG*> /. 1)] is set
(Y . (<*M,N,SG*> /. 1)) * M is Element of the carrier of V
[(Y . (<*M,N,SG*> /. 1)),M] is set
{(Y . (<*M,N,SG*> /. 1)),M} is non empty finite set
{{(Y . (<*M,N,SG*> /. 1)),M},{(Y . (<*M,N,SG*> /. 1))}} is non empty finite V42() set
the Mult of V . [(Y . (<*M,N,SG*> /. 1)),M] is set
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() CLSStruct
the carrier of V is non empty set
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M) is finite Element of bool the carrier of V
bool the carrier of V is non empty set
{ b₁ where b₁ is Element of the carrier of V : not M . b₁ = 0c } is set
N is Relation-like Function-like FinSequence-like set
rng N is set
SG is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
(V,SG,M) is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
Sum (V,SG,M) is Element of the carrier of V
rng SG is Element of bool the carrier of V
N is Element of the carrier of V
SG is Element of the carrier of V
Y is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
rng Y is Element of bool the carrier of V
(V,Y,M) is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
Sum (V,Y,M) is Element of the carrier of V
r2 is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
rng r2 is Element of bool the carrier of V
(V,r2,M) is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
Sum (V,r2,M) is Element of the carrier of V
len Y is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
len r2 is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
dom Y is V68() V69() V70() V71() V72() V73() Element of bool NAT
Seg (len Y) is V68() V69() V70() V71() V72() V73() Element of bool NAT
{ b₁ where b₁ is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT : ( 1 <= b₁ & b₁ <= len Y ) } is set
dom r2 is V68() V69() V70() V71() V72() V73() Element of bool NAT
Seg (len r2) is V68() V69() V70() V71() V72() V73() Element of bool NAT
{ b₁ where b₁ is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT : ( 1 <= b₁ & b₁ <= len r2 ) } is set
r1 is set
r2 . r1 is set
{(r2 . r1)} is non empty trivial finite 1 -element set
Y " {(r2 . r1)} is V68() V69() V70() V71() V72() V73() Element of bool NAT
r3 is set
{r3} is non empty trivial finite 1 -element set
[:(dom Y),(dom Y):] is RAT -valued INT -valued V58() V59() V60() V61() set
bool [:(dom Y),(dom Y):] is non empty set
r1 is Relation-like dom Y -defined dom Y -valued Function-like total quasi_total V58() V59() V60() V61() Element of bool [:(dom Y),(dom Y):]
rng r1 is V68() V69() V70() V71() V72() V73() Element of bool REAL
r3 is set
Y . r3 is set
r2 is set
r2 . r2 is set
{(r2 . r2)} is non empty trivial finite 1 -element set
Y " {(r2 . r2)} is V68() V69() V70() V71() V72() V73() Element of bool NAT
Im (Y,r3) is set
{r3} is non empty trivial finite 1 -element set
Y .: {r3} is finite set
Y " (Im (Y,r3)) is V68() V69() V70() V71() V72() V73() Element of bool NAT
r1 . r2 is ordinal natural complex real finite cardinal ext-real non negative set
{(r1 . r2)} is non empty trivial finite V42() 1 -element V68() V69() V70() V71() V72() V73() set
dom r1 is V68() V69() V70() V71() V72() V73() Element of bool (dom Y)
bool (dom Y) is non empty set
len (V,Y,M) is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
r2 is set
dom r1 is set
r1 . r2 is ordinal natural complex real finite cardinal ext-real non negative set
r3 is set
r1 . r3 is ordinal natural complex real finite cardinal ext-real non negative set
dom r1 is V68() V69() V70() V71() V72() V73() Element of bool (dom Y)
bool (dom Y) is non empty set
r2 . r2 is set
{(r2 . r2)} is non empty trivial finite 1 -element set
r2 . r3 is set
{(r2 . r3)} is non empty trivial finite 1 -element set
Y " {(r2 . r2)} is V68() V69() V70() V71() V72() V73() Element of bool NAT
{(r1 . r2)} is non empty trivial finite V42() 1 -element V68() V69() V70() V71() V72() V73() set
Y " {(r2 . r3)} is V68() V69() V70() V71() V72() V73() Element of bool NAT
{(r1 . r3)} is non empty trivial finite V42() 1 -element V68() V69() V70() V71() V72() V73() set
dom (V,r2,M) is V68() V69() V70() V71() V72() V73() Element of bool NAT
len (V,r2,M) is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
Seg (len (V,r2,M)) is V68() V69() V70() V71() V72() V73() Element of bool NAT
{ b₁ where b₁ is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT : ( 1 <= b₁ & b₁ <= len (V,r2,M) ) } is set
dom (V,Y,M) is V68() V69() V70() V71() V72() V73() Element of bool NAT
Seg (len (V,Y,M)) is V68() V69() V70() V71() V72() V73() Element of bool NAT
{ b₁ where b₁ is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT : ( 1 <= b₁ & b₁ <= len (V,Y,M) ) } is set
[:(dom (V,Y,M)),(dom (V,Y,M)):] is RAT -valued INT -valued V58() V59() V60() V61() set
bool [:(dom (V,Y,M)),(dom (V,Y,M)):] is non empty set
r3 is Relation-like dom Y -defined dom Y -valued Function-like one-to-one total quasi_total onto bijective V58() V59() V60() V61() Element of bool [:(dom Y),(dom Y):]
u2 is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
(V,r2,M) . u2 is set
r2 /. u2 is Element of the carrier of V
M . (r2 /. u2) is complex Element of COMPLEX
(M . (r2 /. u2)) * (r2 /. u2) is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(M . (r2 /. u2)),(r2 /. u2)] is set
{(M . (r2 /. u2)),(r2 /. u2)} is non empty finite set
{(M . (r2 /. u2))} is non empty trivial finite 1 -element V68() set
{{(M . (r2 /. u2)),(r2 /. u2)},{(M . (r2 /. u2))}} is non empty finite V42() set
the Mult of V . [(M . (r2 /. u2)),(r2 /. u2)] is set
r2 . u2 is set
r1 is Relation-like dom (V,Y,M) -defined dom (V,Y,M) -valued Function-like one-to-one total quasi_total onto bijective V58() V59() V60() V61() Element of bool [:(dom (V,Y,M)),(dom (V,Y,M)):]
dom r1 is V68() V69() V70() V71() V72() V73() Element of bool (dom (V,Y,M))
bool (dom (V,Y,M)) is non empty set
r1 . u2 is ordinal natural complex real finite cardinal ext-real non negative set
Y . (r1 . u2) is set
{(Y . (r1 . u2))} is non empty trivial finite 1 -element set
Im (Y,(r1 . u2)) is set
{(r1 . u2)} is non empty trivial finite V42() 1 -element V68() V69() V70() V71() V72() V73() set
Y .: {(r1 . u2)} is finite set
{(r2 . u2)} is non empty trivial finite 1 -element set
Y " {(r2 . u2)} is V68() V69() V70() V71() V72() V73() Element of bool NAT
Y .: (Y " {(r2 . u2)}) is Element of bool the carrier of V
y1 is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
Y . y1 is set
Y /. y1 is Element of the carrier of V
(V,Y,M) . (r1 . u2) is set
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() CLSStruct
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
the carrier of V is non empty set
(V,(V)) is Element of the carrier of V
0. V is zero Element of the carrier of V
the ZeroF of V is Element of the carrier of V
(V,(V)) is empty proper ordinal natural complex real finite V42() cardinal {} -element ext-real non positive non negative V68() V69() V70() V71() V72() V73() V74() Element of bool the carrier of V
bool the carrier of V is non empty set
{ b₁ where b₁ is Element of the carrier of V : not (V) . b₁ = 0c } is set
M is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
rng M is Element of bool the carrier of V
(V,M,(V)) is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
Sum (V,M,(V)) is Element of the carrier of V
len (V,M,(V)) is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
N + 1 is non empty ordinal natural complex real finite cardinal ext-real positive non negative Element of REAL
SG is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,M)
(V,SG) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not SG . b₁ = 0c } is set
(V,SG) is Element of the carrier of V
Y is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
rng Y is Element of bool the carrier of V
(V,Y,SG) is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
Sum (V,Y,SG) is Element of the carrier of V
Seg N is V68() V69() V70() V71() V72() V73() Element of bool NAT
{ b₁ where b₁ is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT : ( 1 <= b₁ & b₁ <= N ) } is set
Y | (Seg N) is Relation-like NAT -defined the carrier of V -valued Function-like Element of bool [:NAT, the carrier of V:]
[:NAT, the carrier of V:] is non trivial non finite set
bool [:NAT, the carrier of V:] is non empty non trivial non finite set
card (V,SG) is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of omega
len Y is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
len (V,Y,SG) is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
Seg (N + 1) is V68() V69() V70() V71() V72() V73() Element of bool NAT
{ b₁ where b₁ is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT : ( 1 <= b₁ & b₁ <= N + 1 ) } is set
dom Y is V68() V69() V70() V71() V72() V73() Element of bool NAT
Y . (N + 1) is set
[: the carrier of V,COMPLEX:] is non empty non trivial non finite V58() set
bool [: the carrier of V,COMPLEX:] is non empty non trivial non finite set
r1 is Element of the carrier of V
r3 is non empty Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() Element of bool [: the carrier of V,COMPLEX:]
r3 . r1 is complex Element of COMPLEX
Funcs ( the carrier of V,COMPLEX) is non empty functional FUNCTION_DOMAIN of the carrier of V, COMPLEX
r3 is Element of the carrier of V
SG . r3 is complex Element of COMPLEX
r2 is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() Element of Funcs ( the carrier of V,COMPLEX)
r2 . r3 is complex Element of COMPLEX
r3 is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,r3) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not r3 . b₁ = 0c } is set
{r1} is non empty trivial finite 1 -element Element of bool the carrier of V
(V,SG) \ {r1} is finite Element of bool the carrier of V
r1 is set
r3 . r1 is complex set
SG . r1 is complex set
u2 is Element of the carrier of V
r3 . u2 is complex Element of COMPLEX
u2 is Element of the carrier of V
r3 . u2 is complex Element of COMPLEX
u2 is Element of the carrier of V
r3 . u2 is complex Element of COMPLEX
r1 is set
SG . r1 is complex set
r3 . r1 is complex set
u2 is Element of the carrier of V
SG . u2 is complex Element of COMPLEX
M \ {r1} is Element of bool the carrier of V
r2 is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
len r2 is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
r1 is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,M)
(V,r2,r1) is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
len (V,r2,r1) is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
rng r2 is Element of bool the carrier of V
(V,r1) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not r1 . b₁ = 0c } is set
u2 is set
dom r2 is V68() V69() V70() V71() V72() V73() Element of bool NAT
y1 is set
r2 . y1 is set
x1 is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
r2 . x1 is set
Y . x1 is set
u2 is set
y1 is set
Y . y1 is set
(dom Y) \ (Seg N) is V68() V69() V70() V71() V72() V73() Element of bool NAT
(Seg (N + 1)) \ (Seg N) is V68() V69() V70() V71() V72() V73() Element of bool NAT
{(N + 1)} is non empty trivial finite V42() 1 -element V68() V69() V70() V71() V72() V73() Element of bool REAL
(dom Y) /\ (Seg N) is V68() V69() V70() V71() V72() V73() Element of bool NAT
dom r2 is V68() V69() V70() V71() V72() V73() Element of bool NAT
r2 . y1 is set
(Seg (N + 1)) /\ (Seg N) is V68() V69() V70() V71() V72() V73() Element of bool NAT
dom (V,r2,r1) is V68() V69() V70() V71() V72() V73() Element of bool NAT
dom (V,Y,SG) is V68() V69() V70() V71() V72() V73() Element of bool NAT
(dom (V,Y,SG)) /\ (Seg N) is V68() V69() V70() V71() V72() V73() Element of bool NAT
u2 is set
dom r2 is V68() V69() V70() V71() V72() V73() Element of bool NAT
r2 . u2 is set
Y . u2 is set
y1 is Element of the carrier of V
(V,r2,r1) . u2 is set
r1 . y1 is complex Element of COMPLEX
(r1 . y1) * y1 is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(r1 . y1),y1] is set
{(r1 . y1),y1} is non empty finite set
{(r1 . y1)} is non empty trivial finite 1 -element V68() set
{{(r1 . y1),y1},{(r1 . y1)}} is non empty finite V42() set
the Mult of V . [(r1 . y1),y1] is set
SG . y1 is complex Element of COMPLEX
(SG . y1) * y1 is Element of the carrier of V
[(SG . y1),y1] is set
{(SG . y1),y1} is non empty finite set
{(SG . y1)} is non empty trivial finite 1 -element V68() set
{{(SG . y1),y1},{(SG . y1)}} is non empty finite V42() set
the Mult of V . [(SG . y1),y1] is set
(V,Y,SG) . u2 is set
(V,Y,SG) | (Seg N) is Relation-like NAT -defined the carrier of V -valued Function-like Element of bool [:NAT, the carrier of V:]
card (V,r1) is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of omega
card {r1} is non empty ordinal natural complex real finite cardinal V49() V50() ext-real positive non negative V68() V69() V70() V71() V72() V73() Element of omega
(N + 1) - (card {r1}) is complex real ext-real Element of REAL
- (card {r1}) is non empty complex real ext-real non positive negative set
(N + 1) + (- (card {r1})) is complex real ext-real set
(N + 1) - 1 is complex real ext-real Element of REAL
- 1 is non empty complex real ext-real non positive negative set
(N + 1) + (- 1) is complex real ext-real set
(V,r1) is Element of the carrier of V
SG . r1 is complex Element of COMPLEX
(SG . r1) * r1 is Element of the carrier of V
[(SG . r1),r1] is set
{(SG . r1),r1} is non empty finite set
{(SG . r1)} is non empty trivial finite 1 -element V68() set
{{(SG . r1),r1},{(SG . r1)}} is non empty finite V42() set
the Mult of V . [(SG . r1),r1] is set
Sum (V,r2,r1) is Element of the carrier of V
Seg (len (V,r2,r1)) is V68() V69() V70() V71() V72() V73() Element of bool NAT
{ b₁ where b₁ is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT : ( 1 <= b₁ & b₁ <= len (V,r2,r1) ) } is set
(V,Y,SG) . (len Y) is set
(Sum (V,r2,r1)) + ((SG . r1) * r1) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((Sum (V,r2,r1)),((SG . r1) * r1)) is Element of the carrier of V
[(Sum (V,r2,r1)),((SG . r1) * r1)] is set
{(Sum (V,r2,r1)),((SG . r1) * r1)} is non empty finite set
{(Sum (V,r2,r1))} is non empty trivial finite 1 -element set
{{(Sum (V,r2,r1)),((SG . r1) * r1)},{(Sum (V,r2,r1))}} is non empty finite V42() set
the addF of V . [(Sum (V,r2,r1)),((SG . r1) * r1)] is set
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,M)
(V,N) is Element of the carrier of V
(V,N) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not N . b₁ = 0c } is set
card (V,N) is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of omega
SG is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,M)
(V,SG) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not SG . b₁ = 0c } is set
card (V,SG) is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of omega
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,SG) is Element of the carrier of V
0. V is zero Element of the carrier of V
the ZeroF of V is Element of the carrier of V
SG is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,M)
(V,SG) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not SG . b₁ = 0c } is set
card (V,SG) is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of omega
(V,SG) is Element of the carrier of V
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(V)) is Element of the carrier of V
0. V is zero Element of the carrier of V
the ZeroF of V is Element of the carrier of V
N is complex set
SG is Element of the carrier of V
N * SG is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[N,SG] is set
{N,SG} is non empty finite set
{N} is non empty trivial finite 1 -element V68() set
{{N,SG},{N}} is non empty finite V42() set
the Mult of V . [N,SG] is set
[: the carrier of V,COMPLEX:] is non empty non trivial non finite V58() set
bool [: the carrier of V,COMPLEX:] is non empty non trivial non finite set
Y is complex Element of COMPLEX
r2 is non empty Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() Element of bool [: the carrier of V,COMPLEX:]
r2 . SG is complex Element of COMPLEX
Funcs ( the carrier of V,COMPLEX) is non empty functional FUNCTION_DOMAIN of the carrier of V, COMPLEX
r3 is Element of the carrier of V
{SG} is non empty trivial finite 1 -element Element of bool the carrier of V
r1 is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() Element of Funcs ( the carrier of V,COMPLEX)
r1 . r3 is complex Element of COMPLEX
r3 is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,r3) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not r3 . b₁ = 0c } is set
r2 is set
r3 is Element of the carrier of V
r3 . r3 is complex Element of COMPLEX
r2 is set
r2 is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,M)
(V,r2) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not r2 . b₁ = 0c } is set
(V,r2) is Element of the carrier of V
r3 is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
rng r3 is Element of bool the carrier of V
(V,r3,r2) is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
Sum (V,r3,r2) is Element of the carrier of V
<*SG*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
[1,SG] is set
{1,SG} is non empty finite set
{{1,SG},{1}} is non empty finite V42() set
{[1,SG]} is non empty trivial finite 1 -element set
r2 . SG is complex Element of COMPLEX
(r2 . SG) * SG is Element of the carrier of V
[(r2 . SG),SG] is set
{(r2 . SG),SG} is non empty finite set
{(r2 . SG)} is non empty trivial finite 1 -element V68() set
{{(r2 . SG),SG},{(r2 . SG)}} is non empty finite V42() set
the Mult of V . [(r2 . SG),SG] is set
<*((r2 . SG) * SG)*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
[1,((r2 . SG) * SG)] is set
{1,((r2 . SG) * SG)} is non empty finite set
{{1,((r2 . SG) * SG)},{1}} is non empty finite V42() set
{[1,((r2 . SG) * SG)]} is non empty trivial finite 1 -element set
N is Element of the carrier of V
SG is Element of the carrier of V
N + SG is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (N,SG) is Element of the carrier of V
[N,SG] is set
{N,SG} is non empty finite set
{N} is non empty trivial finite 1 -element set
{{N,SG},{N}} is non empty finite V42() set
the addF of V . [N,SG] is set
1r * N is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[1r,N] is set
{1r,N} is non empty finite set
{1r} is non empty trivial finite 1 -element V68() set
{{1r,N},{1r}} is non empty finite V42() set
the Mult of V . [1r,N] is set
1r * SG is Element of the carrier of V
[1r,SG] is set
{1r,SG} is non empty finite set
{{1r,SG},{1r}} is non empty finite V42() set
the Mult of V . [1r,SG] is set
[: the carrier of V,COMPLEX:] is non empty non trivial non finite V58() set
bool [: the carrier of V,COMPLEX:] is non empty non trivial non finite set
Y is non empty Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() Element of bool [: the carrier of V,COMPLEX:]
Y . N is complex Element of COMPLEX
Y . SG is complex Element of COMPLEX
Funcs ( the carrier of V,COMPLEX) is non empty functional FUNCTION_DOMAIN of the carrier of V, COMPLEX
r1 is Element of the carrier of V
{N,SG} is non empty finite Element of bool the carrier of V
r2 is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() Element of Funcs ( the carrier of V,COMPLEX)
r2 . r1 is complex Element of COMPLEX
r1 is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,r1) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not r1 . b₁ = 0c } is set
r3 is set
r2 is Element of the carrier of V
r1 . r2 is complex Element of COMPLEX
r3 is set
r3 is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,M)
(V,r3) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not r3 . b₁ = 0c } is set
(V,r3) is Element of the carrier of V
r2 is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
rng r2 is Element of bool the carrier of V
(V,r2,r3) is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
Sum (V,r2,r3) is Element of the carrier of V
<*N,SG*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
<*N*> is Relation-like Function-like set
[1,N] is set
{1,N} is non empty finite set
{{1,N},{1}} is non empty finite V42() set
{[1,N]} is non empty trivial finite 1 -element set
<*SG*> is Relation-like Function-like set
[1,SG] is set
{1,SG} is non empty finite set
{{1,SG},{1}} is non empty finite V42() set
{[1,SG]} is non empty trivial finite 1 -element set
K158(<*N*>,<*SG*>) is Relation-like Function-like FinSequence-like set
<*SG,N*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
K158(<*SG*>,<*N*>) is Relation-like Function-like FinSequence-like set
<*(1r * N),(1r * SG)*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
<*(1r * N)*> is Relation-like Function-like set
[1,(1r * N)] is set
{1,(1r * N)} is non empty finite set
{{1,(1r * N)},{1}} is non empty finite V42() set
{[1,(1r * N)]} is non empty trivial finite 1 -element set
<*(1r * SG)*> is Relation-like Function-like set
[1,(1r * SG)] is set
{1,(1r * SG)} is non empty finite set
{{1,(1r * SG)},{1}} is non empty finite V42() set
{[1,(1r * SG)]} is non empty trivial finite 1 -element set
K158(<*(1r * N)*>,<*(1r * SG)*>) is Relation-like Function-like FinSequence-like set
<*(1r * SG),(1r * N)*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
K158(<*(1r * SG)*>,<*(1r * N)*>) is Relation-like Function-like FinSequence-like set
N + N is Element of the carrier of V
the addF of V . (N,N) is Element of the carrier of V
[N,N] is set
{N,N} is non empty finite set
{{N,N},{N}} is non empty finite V42() set
the addF of V . [N,N] is set
1r + 1r is complex Element of COMPLEX
(1r + 1r) * N is Element of the carrier of V
[(1r + 1r),N] is set
{(1r + 1r),N} is non empty finite set
{(1r + 1r)} is non empty trivial finite 1 -element V68() set
{{(1r + 1r),N},{(1r + 1r)}} is non empty finite V42() set
the Mult of V . [(1r + 1r),N] is set
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() CLSStruct
the carrier of V is non empty set
{} the carrier of V is empty proper ordinal natural complex real finite V42() cardinal {} -element ext-real non positive non negative V68() V69() V70() V71() V72() V73() V74() Element of bool the carrier of V
bool the carrier of V is non empty set
0. V is zero Element of the carrier of V
the ZeroF of V is Element of the carrier of V
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V, {} the carrier of V)
(V,M) is Element of the carrier of V
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
M is Element of the carrier of V
{M} is non empty trivial finite 1 -element Element of bool the carrier of V
bool the carrier of V is non empty set
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,{M})
(V,N) is Element of the carrier of V
N . M is complex Element of COMPLEX
(N . M) * M is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(N . M),M] is set
{(N . M),M} is non empty finite set
{(N . M)} is non empty trivial finite 1 -element V68() set
{{(N . M),M},{(N . M)}} is non empty finite V42() set
the Mult of V . [(N . M),M] is set
(V,N) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not N . b₁ = 0c } is set
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
0. V is zero Element of the carrier of V
the ZeroF of V is Element of the carrier of V
0c * M is Element of the carrier of V
[0c,M] is set
{0c,M} is non empty finite set
{0c} is non empty trivial finite V42() 1 -element V68() V69() V70() V71() V72() V73() set
{{0c,M},{0c}} is non empty finite V42() set
the Mult of V . [0c,M] is set
SG is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
rng SG is Element of bool the carrier of V
(V,SG,N) is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
Sum (V,SG,N) is Element of the carrier of V
<*M*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
[1,M] is set
{1,M} is non empty finite set
{{1,M},{1}} is non empty finite V42() set
{[1,M]} is non empty trivial finite 1 -element set
<*((N . M) * M)*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
[1,((N . M) * M)] is set
{1,((N . M) * M)} is non empty finite set
{{1,((N . M) * M)},{1}} is non empty finite V42() set
{[1,((N . M) * M)]} is non empty trivial finite 1 -element set
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
M is Element of the carrier of V
N is Element of the carrier of V
{M,N} is non empty finite Element of bool the carrier of V
bool the carrier of V is non empty set
SG is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,{M,N})
(V,SG) is Element of the carrier of V
SG . M is complex Element of COMPLEX
(SG . M) * M is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(SG . M),M] is set
{(SG . M),M} is non empty finite set
{(SG . M)} is non empty trivial finite 1 -element V68() set
{{(SG . M),M},{(SG . M)}} is non empty finite V42() set
the Mult of V . [(SG . M),M] is set
SG . N is complex Element of COMPLEX
(SG . N) * N is Element of the carrier of V
[(SG . N),N] is set
{(SG . N),N} is non empty finite set
{(SG . N)} is non empty trivial finite 1 -element V68() set
{{(SG . N),N},{(SG . N)}} is non empty finite V42() set
the Mult of V . [(SG . N),N] is set
((SG . M) * M) + ((SG . N) * N) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (((SG . M) * M),((SG . N) * N)) is Element of the carrier of V
[((SG . M) * M),((SG . N) * N)] is set
{((SG . M) * M),((SG . N) * N)} is non empty finite set
{((SG . M) * M)} is non empty trivial finite 1 -element set
{{((SG . M) * M),((SG . N) * N)},{((SG . M) * M)}} is non empty finite V42() set
the addF of V . [((SG . M) * M),((SG . N) * N)] is set
0. V is zero Element of the carrier of V
the ZeroF of V is Element of the carrier of V
0c * M is Element of the carrier of V
[0c,M] is set
{0c,M} is non empty finite set
{0c} is non empty trivial finite V42() 1 -element V68() V69() V70() V71() V72() V73() set
{{0c,M},{0c}} is non empty finite V42() set
the Mult of V . [0c,M] is set
(V,SG) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not SG . b₁ = 0c } is set
0c * N is Element of the carrier of V
[0c,N] is set
{0c,N} is non empty finite set
{{0c,N},{0c}} is non empty finite V42() set
the Mult of V . [0c,N] is set
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(0. V) + (0. V) is Element of the carrier of V
the addF of V . ((0. V),(0. V)) is Element of the carrier of V
[(0. V),(0. V)] is set
{(0. V),(0. V)} is non empty finite set
{(0. V)} is non empty trivial finite 1 -element set
{{(0. V),(0. V)},{(0. V)}} is non empty finite V42() set
the addF of V . [(0. V),(0. V)] is set
((SG . M) * M) + (0c * N) is Element of the carrier of V
the addF of V . (((SG . M) * M),(0c * N)) is Element of the carrier of V
[((SG . M) * M),(0c * N)] is set
{((SG . M) * M),(0c * N)} is non empty finite set
{{((SG . M) * M),(0c * N)},{((SG . M) * M)}} is non empty finite V42() set
the addF of V . [((SG . M) * M),(0c * N)] is set
{M} is non empty trivial finite 1 -element Element of bool the carrier of V
Y is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,{M})
(V,Y) is Element of the carrier of V
((SG . M) * M) + (0. V) is Element of the carrier of V
the addF of V . (((SG . M) * M),(0. V)) is Element of the carrier of V
[((SG . M) * M),(0. V)] is set
{((SG . M) * M),(0. V)} is non empty finite set
{{((SG . M) * M),(0. V)},{((SG . M) * M)}} is non empty finite V42() set
the addF of V . [((SG . M) * M),(0. V)] is set
{N} is non empty trivial finite 1 -element Element of bool the carrier of V
Y is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,{N})
(V,Y) is Element of the carrier of V
(0. V) + ((SG . N) * N) is Element of the carrier of V
the addF of V . ((0. V),((SG . N) * N)) is Element of the carrier of V
[(0. V),((SG . N) * N)] is set
{(0. V),((SG . N) * N)} is non empty finite set
{(0. V)} is non empty trivial finite 1 -element set
{{(0. V),((SG . N) * N)},{(0. V)}} is non empty finite V42() set
the addF of V . [(0. V),((SG . N) * N)] is set
Y is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
rng Y is Element of bool the carrier of V
(V,Y,SG) is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
Sum (V,Y,SG) is Element of the carrier of V
<*M,N*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
<*M*> is Relation-like Function-like set
[1,M] is set
{1,M} is non empty finite set
{{1,M},{1}} is non empty finite V42() set
{[1,M]} is non empty trivial finite 1 -element set
<*N*> is Relation-like Function-like set
[1,N] is set
{1,N} is non empty finite set
{{1,N},{1}} is non empty finite V42() set
{[1,N]} is non empty trivial finite 1 -element set
K158(<*M*>,<*N*>) is Relation-like Function-like FinSequence-like set
<*N,M*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
K158(<*N*>,<*M*>) is Relation-like Function-like FinSequence-like set
<*((SG . M) * M),((SG . N) * N)*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
<*((SG . M) * M)*> is Relation-like Function-like set
[1,((SG . M) * M)] is set
{1,((SG . M) * M)} is non empty finite set
{{1,((SG . M) * M)},{1}} is non empty finite V42() set
{[1,((SG . M) * M)]} is non empty trivial finite 1 -element set
<*((SG . N) * N)*> is Relation-like Function-like set
[1,((SG . N) * N)] is set
{1,((SG . N) * N)} is non empty finite set
{{1,((SG . N) * N)},{1}} is non empty finite V42() set
{[1,((SG . N) * N)]} is non empty trivial finite 1 -element set
K158(<*((SG . M) * M)*>,<*((SG . N) * N)*>) is Relation-like Function-like FinSequence-like set
<*((SG . N) * N),((SG . M) * M)*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
K158(<*((SG . N) * N)*>,<*((SG . M) * M)*>) is Relation-like Function-like FinSequence-like set
{M} is non empty trivial finite 1 -element Element of bool the carrier of V
{N} is non empty trivial finite 1 -element Element of bool the carrier of V
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() CLSStruct
the carrier of V is non empty set
0. V is zero Element of the carrier of V
the ZeroF of V is Element of the carrier of V
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M) is finite Element of bool the carrier of V
bool the carrier of V is non empty set
{ b₁ where b₁ is Element of the carrier of V : not M . b₁ = 0c } is set
(V,M) is Element of the carrier of V
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M) is finite Element of bool the carrier of V
bool the carrier of V is non empty set
{ b₁ where b₁ is Element of the carrier of V : not M . b₁ = 0c } is set
(V,M) is Element of the carrier of V
N is Element of the carrier of V
{N} is non empty trivial finite 1 -element Element of bool the carrier of V
M . N is complex Element of COMPLEX
(M . N) * N is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(M . N),N] is set
{(M . N),N} is non empty finite set
{(M . N)} is non empty trivial finite 1 -element V68() set
{{(M . N),N},{(M . N)}} is non empty finite V42() set
the Mult of V . [(M . N),N] is set
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M) is finite Element of bool the carrier of V
bool the carrier of V is non empty set
{ b₁ where b₁ is Element of the carrier of V : not M . b₁ = 0c } is set
(V,M) is Element of the carrier of V
N is Element of the carrier of V
SG is Element of the carrier of V
{N,SG} is non empty finite Element of bool the carrier of V
M . N is complex Element of COMPLEX
(M . N) * N is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(M . N),N] is set
{(M . N),N} is non empty finite set
{(M . N)} is non empty trivial finite 1 -element V68() set
{{(M . N),N},{(M . N)}} is non empty finite V42() set
the Mult of V . [(M . N),N] is set
M . SG is complex Element of COMPLEX
(M . SG) * SG is Element of the carrier of V
[(M . SG),SG] is set
{(M . SG),SG} is non empty finite set
{(M . SG)} is non empty trivial finite 1 -element V68() set
{{(M . SG),SG},{(M . SG)}} is non empty finite V42() set
the Mult of V . [(M . SG),SG] is set
((M . N) * N) + ((M . SG) * SG) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (((M . N) * N),((M . SG) * SG)) is Element of the carrier of V
[((M . N) * N),((M . SG) * SG)] is set
{((M . N) * N),((M . SG) * SG)} is non empty finite set
{((M . N) * N)} is non empty trivial finite 1 -element set
{{((M . N) * N),((M . SG) * SG)},{((M . N) * N)}} is non empty finite V42() set
the addF of V . [((M . N) * N),((M . SG) * SG)] is set
V is non empty addLoopStr
the carrier of V is non empty set
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
SG is Element of the carrier of V
M . SG is complex Element of COMPLEX
N . SG is complex Element of COMPLEX
V is non empty addLoopStr
the carrier of V is non empty set
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
M + N is Relation-like the carrier of V -defined Function-like total V58() set
Funcs ( the carrier of V,COMPLEX) is non empty functional FUNCTION_DOMAIN of the carrier of V, COMPLEX
M + N is non empty Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() Element of bool [: the carrier of V,COMPLEX:]
[: the carrier of V,COMPLEX:] is non empty non trivial non finite V58() set
bool [: the carrier of V,COMPLEX:] is non empty non trivial non finite set
Y is Element of the carrier of V
(V,M) is finite Element of bool the carrier of V
bool the carrier of V is non empty set
{ b₁ where b₁ is Element of the carrier of V : not M . b₁ = 0c } is set
(V,N) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not N . b₁ = 0c } is set
(V,M) \/ (V,N) is finite Element of bool the carrier of V
N . Y is complex Element of COMPLEX
M . Y is complex Element of COMPLEX
SG is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() Element of Funcs ( the carrier of V,COMPLEX)
SG . Y is complex Element of COMPLEX
{} + {} is empty ordinal natural complex real finite V42() cardinal {} -element ext-real non positive non negative V68() V69() V70() V71() V72() V73() V74() set
SG is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
M + N is non empty Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() Element of bool [: the carrier of V,COMPLEX:]
[: the carrier of V,COMPLEX:] is non empty non trivial non finite V58() set
bool [: the carrier of V,COMPLEX:] is non empty non trivial non finite set
Y is Element of the carrier of V
SG . Y is complex Element of COMPLEX
M . Y is complex Element of COMPLEX
N . Y is complex Element of COMPLEX
(M . Y) + (N . Y) is complex Element of COMPLEX
dom SG is Element of bool the carrier of V
bool the carrier of V is non empty set
Y is set
SG . Y is complex set
M . Y is complex set
N . Y is complex set
(M . Y) + (N . Y) is complex set
dom M is Element of bool the carrier of V
dom N is Element of bool the carrier of V
(dom M) /\ (dom N) is Element of bool the carrier of V
V is non empty CLSStruct
the carrier of V is non empty set
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M) is finite Element of bool the carrier of V
bool the carrier of V is non empty set
{ b₁ where b₁ is Element of the carrier of V : not M . b₁ = 0c } is set
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M,N) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
(V,(V,M,N)) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not (V,M,N) . b₁ = 0c } is set
(V,N) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not N . b₁ = 0c } is set
(V,M) \/ (V,N) is finite Element of bool the carrier of V
SG is set
Y is Element of the carrier of V
(V,M,N) . Y is complex Element of COMPLEX
M . Y is complex Element of COMPLEX
N . Y is complex Element of COMPLEX
(M . Y) + (N . Y) is complex Element of COMPLEX
V is non empty CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
SG is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,N,SG) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
(V,N) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not N . b₁ = 0c } is set
(V,SG) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not SG . b₁ = 0c } is set
(V,N) \/ (V,SG) is finite Element of bool the carrier of V
(V,(V,N,SG)) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not (V,N,SG) . b₁ = 0c } is set
V is non empty CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,M)
SG is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,M)
N + SG is Relation-like the carrier of V -defined Function-like total V58() set
V is non empty addLoopStr
the carrier of V is non empty set
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M,N) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
(V,N,M) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
V is non empty CLSStruct
the carrier of V is non empty set
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M,N) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
SG is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,N,SG) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
(V,M,(V,N,SG)) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
(V,(V,M,N),SG) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
Y is Element of the carrier of V
(V,M,(V,N,SG)) . Y is complex Element of COMPLEX
(V,(V,M,N),SG) . Y is complex Element of COMPLEX
M . Y is complex Element of COMPLEX
(V,N,SG) . Y is complex Element of COMPLEX
(M . Y) + ((V,N,SG) . Y) is complex Element of COMPLEX
N . Y is complex Element of COMPLEX
SG . Y is complex Element of COMPLEX
(N . Y) + (SG . Y) is complex Element of COMPLEX
(M . Y) + ((N . Y) + (SG . Y)) is complex Element of COMPLEX
(M . Y) + (N . Y) is complex Element of COMPLEX
((M . Y) + (N . Y)) + (SG . Y) is complex Element of COMPLEX
(V,M,N) . Y is complex Element of COMPLEX
((V,M,N) . Y) + (SG . Y) is complex Element of COMPLEX
V is non empty CLSStruct
the carrier of V is non empty set
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M,(V)) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
N is Element of the carrier of V
(V,M,(V)) . N is complex Element of COMPLEX
M . N is complex Element of COMPLEX
(V) . N is complex Element of COMPLEX
(M . N) + ((V) . N) is complex Element of COMPLEX
(M . N) + 0c is complex Element of COMPLEX
V is non empty CLSStruct
the carrier of V is non empty set
M is complex set
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
SG is complex Element of COMPLEX
[: the carrier of V,COMPLEX:] is non empty non trivial non finite V58() set
bool [: the carrier of V,COMPLEX:] is non empty non trivial non finite set
Y is non empty Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() Element of bool [: the carrier of V,COMPLEX:]
Funcs ( the carrier of V,COMPLEX) is non empty functional FUNCTION_DOMAIN of the carrier of V, COMPLEX
r1 is Element of the carrier of V
(V,N) is finite Element of bool the carrier of V
bool the carrier of V is non empty set
{ b₁ where b₁ is Element of the carrier of V : not N . b₁ = 0c } is set
N . r1 is complex Element of COMPLEX
r2 is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() Element of Funcs ( the carrier of V,COMPLEX)
r2 . r1 is complex Element of COMPLEX
SG * 0c is complex Element of COMPLEX
r1 is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
r3 is Element of the carrier of V
r1 . r3 is complex Element of COMPLEX
N . r3 is complex Element of COMPLEX
M * (N . r3) is complex set
SG is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
Y is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
r2 is Element of the carrier of V
SG . r2 is complex Element of COMPLEX
Y . r2 is complex Element of COMPLEX
N . r2 is complex Element of COMPLEX
M * (N . r2) is complex set
V is non empty CLSStruct
the carrier of V is non empty set
M is complex set
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M,N) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(V,M,N)) is finite Element of bool the carrier of V
bool the carrier of V is non empty set
{ b₁ where b₁ is Element of the carrier of V : not (V,M,N) . b₁ = 0c } is set
(V,N) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not N . b₁ = 0c } is set
r2 is set
r1 is Element of the carrier of V
(V,M,N) . r1 is complex Element of COMPLEX
N . r1 is complex Element of COMPLEX
M * (N . r1) is complex set
r2 is set
r1 is Element of the carrier of V
N . r1 is complex Element of COMPLEX
(V,M,N) . r1 is complex Element of COMPLEX
M * (N . r1) is complex set
V is non empty CLSStruct
the carrier of V is non empty set
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,0c,M) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
N is Element of the carrier of V
(V,0c,M) . N is complex Element of COMPLEX
(V) . N is complex Element of COMPLEX
M . N is complex Element of COMPLEX
0c * (M . N) is complex Element of COMPLEX
V is non empty CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is complex set
SG is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,N,SG) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(V,N,SG)) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not (V,N,SG) . b₁ = 0c } is set
(V,SG) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not SG . b₁ = 0c } is set
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
V is non empty CLSStruct
the carrier of V is non empty set
M is complex set
N is complex set
M + N is complex set
SG is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(M + N),SG) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M,SG) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,N,SG) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(V,M,SG),(V,N,SG)) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
Y is Element of the carrier of V
(V,(M + N),SG) . Y is complex Element of COMPLEX
(V,(V,M,SG),(V,N,SG)) . Y is complex Element of COMPLEX
SG . Y is complex Element of COMPLEX
(M + N) * (SG . Y) is complex set
M * (SG . Y) is complex set
N * (SG . Y) is complex set
(M * (SG . Y)) + (N * (SG . Y)) is complex set
(V,M,SG) . Y is complex Element of COMPLEX
((V,M,SG) . Y) + (N * (SG . Y)) is complex set
(V,N,SG) . Y is complex Element of COMPLEX
((V,M,SG) . Y) + ((V,N,SG) . Y) is complex Element of COMPLEX
V is non empty CLSStruct
the carrier of V is non empty set
M is complex set
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M,N) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
SG is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,N,SG) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
(V,M,(V,N,SG)) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M,SG) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(V,M,N),(V,M,SG)) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
Y is Element of the carrier of V
(V,M,(V,N,SG)) . Y is complex Element of COMPLEX
(V,(V,M,N),(V,M,SG)) . Y is complex Element of COMPLEX
(V,N,SG) . Y is complex Element of COMPLEX
M * ((V,N,SG) . Y) is complex set
N . Y is complex Element of COMPLEX
SG . Y is complex Element of COMPLEX
(N . Y) + (SG . Y) is complex Element of COMPLEX
M * ((N . Y) + (SG . Y)) is complex set
M * (N . Y) is complex set
M * (SG . Y) is complex set
(M * (N . Y)) + (M * (SG . Y)) is complex set
(V,M,N) . Y is complex Element of COMPLEX
((V,M,N) . Y) + (M * (SG . Y)) is complex set
(V,M,SG) . Y is complex Element of COMPLEX
((V,M,N) . Y) + ((V,M,SG) . Y) is complex Element of COMPLEX
V is non empty CLSStruct
the carrier of V is non empty set
M is complex set
N is complex set
M * N is complex set
SG is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,N,SG) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M,(V,N,SG)) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(M * N),SG) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
Y is Element of the carrier of V
(V,M,(V,N,SG)) . Y is complex Element of COMPLEX
(V,(M * N),SG) . Y is complex Element of COMPLEX
(V,N,SG) . Y is complex Element of COMPLEX
M * ((V,N,SG) . Y) is complex set
SG . Y is complex Element of COMPLEX
N * (SG . Y) is complex set
M * (N * (SG . Y)) is complex set
(M * N) * (SG . Y) is complex set
V is non empty CLSStruct
the carrier of V is non empty set
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,1r,M) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
N is Element of the carrier of V
(V,1r,M) . N is complex Element of COMPLEX
M . N is complex Element of COMPLEX
1r * (M . N) is complex Element of COMPLEX
V is non empty CLSStruct
the carrier of V is non empty set
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(- 1r),M) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
V is non empty CLSStruct
the carrier of V is non empty set
M is Element of the carrier of V
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,N) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(- 1r),N) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,N) . M is complex Element of COMPLEX
N . M is complex Element of COMPLEX
- (N . M) is complex Element of COMPLEX
(- 1r) * (N . M) is complex Element of COMPLEX
V is non empty CLSStruct
the carrier of V is non empty set
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(- 1r),M) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M,N) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
SG is Element of the carrier of V
N . SG is complex Element of COMPLEX
(V,M) . SG is complex Element of COMPLEX
M . SG is complex Element of COMPLEX
(M . SG) + (N . SG) is complex Element of COMPLEX
(V) . SG is complex Element of COMPLEX
- (M . SG) is complex Element of COMPLEX
V is non empty CLSStruct
the carrier of V is non empty set
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(- 1r),M) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(V,M)) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(- 1r),(V,M)) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
N is Element of the carrier of V
(V,(V,M)) . N is complex Element of COMPLEX
M . N is complex Element of COMPLEX
(- 1r) * (- 1r) is complex Element of COMPLEX
(V,((- 1r) * (- 1r)),M) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,((- 1r) * (- 1r)),M) . N is complex Element of COMPLEX
1r * (M . N) is complex Element of COMPLEX
V is non empty CLSStruct
the carrier of V is non empty set
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,N) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(- 1r),N) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M,(V,N)) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
V is non empty CLSStruct
the carrier of V is non empty set
M is Element of the carrier of V
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
N . M is complex Element of COMPLEX
SG is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,N,SG) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,SG) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(- 1r),SG) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,N,(V,SG)) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
(V,N,SG) . M is complex Element of COMPLEX
SG . M is complex Element of COMPLEX
(N . M) - (SG . M) is complex Element of COMPLEX
- (SG . M) is complex set
(N . M) + (- (SG . M)) is complex set
(V,SG) . M is complex Element of COMPLEX
(N . M) + ((V,SG) . M) is complex Element of COMPLEX
V is non empty CLSStruct
the carrier of V is non empty set
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M) is finite Element of bool the carrier of V
bool the carrier of V is non empty set
{ b₁ where b₁ is Element of the carrier of V : not M . b₁ = 0c } is set
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M,N) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,N) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(- 1r),N) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M,(V,N)) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
(V,(V,M,N)) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not (V,M,N) . b₁ = 0c } is set
(V,N) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not N . b₁ = 0c } is set
(V,M) \/ (V,N) is finite Element of bool the carrier of V
(V,(V,N)) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not (V,N) . b₁ = 0c } is set
(V,M) \/ (V,(V,N)) is finite Element of bool the carrier of V
V is non empty CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
SG is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,N,SG) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,SG) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(- 1r),SG) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,N,(V,SG)) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
V is non empty CLSStruct
the carrier of V is non empty set
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M,M) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(- 1r),M) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M,(V,M)) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
N is Element of the carrier of V
(V,M,M) . N is complex Element of COMPLEX
(V) . N is complex Element of COMPLEX
M . N is complex Element of COMPLEX
(M . N) - (M . N) is complex Element of COMPLEX
- (M . N) is complex set
(M . N) + (- (M . N)) is complex set
V is non empty CLSStruct
the carrier of V is non empty set
Funcs ( the carrier of V,COMPLEX) is non empty functional FUNCTION_DOMAIN of the carrier of V, COMPLEX
M is set
N is set
M is set
N is set
SG is set
SG is set
V is non empty CLSStruct
(V) is set
the carrier of V is non empty set
the Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
V is non empty CLSStruct
(V) is non empty set
M is Element of (V)
the carrier of V is non empty set
V is non empty CLSStruct
the carrier of V is non empty set
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V) is non empty set
V is non empty CLSStruct
(V) is non empty set
[:(V),(V):] is non empty set
[:[:(V),(V):],(V):] is non empty set
bool [:[:(V),(V):],(V):] is non empty set
M is non empty Relation-like [:(V),(V):] -defined (V) -valued Function-like total quasi_total Element of bool [:[:(V),(V):],(V):]
N is Element of (V)
(V,N) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
the carrier of V is non empty set
SG is Element of (V)
M . (N,SG) is Element of (V)
[N,SG] is set
{N,SG} is non empty finite set
{N} is non empty trivial finite 1 -element set
{{N,SG},{N}} is non empty finite V42() set
M . [N,SG] is set
(V,SG) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(V,N),(V,SG)) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
(V,(V,(V,N),(V,SG))) is Element of (V)
M is non empty Relation-like [:(V),(V):] -defined (V) -valued Function-like total quasi_total Element of bool [:[:(V),(V):],(V):]
N is non empty Relation-like [:(V),(V):] -defined (V) -valued Function-like total quasi_total Element of bool [:[:(V),(V):],(V):]
SG is Element of (V)
Y is Element of (V)
M . (SG,Y) is Element of (V)
[SG,Y] is set
{SG,Y} is non empty finite set
{SG} is non empty trivial finite 1 -element set
{{SG,Y},{SG}} is non empty finite V42() set
M . [SG,Y] is set
(V,SG) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
the carrier of V is non empty set
(V,Y) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(V,SG),(V,Y)) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
N . (SG,Y) is Element of (V)
N . [SG,Y] is set
V is non empty CLSStruct
(V) is non empty set
[:COMPLEX,(V):] is non empty non trivial non finite set
[:[:COMPLEX,(V):],(V):] is non empty non trivial non finite set
bool [:[:COMPLEX,(V):],(V):] is non empty non trivial non finite set
M is complex Element of COMPLEX
N is Element of (V)
(V,N) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
the carrier of V is non empty set
(V,M,(V,N)) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(V,M,(V,N))) is Element of (V)
M is non empty Relation-like [:COMPLEX,(V):] -defined (V) -valued Function-like total quasi_total Element of bool [:[:COMPLEX,(V):],(V):]
N is complex set
SG is Element of (V)
[N,SG] is set
{N,SG} is non empty finite set
{N} is non empty trivial finite 1 -element V68() set
{{N,SG},{N}} is non empty finite V42() set
M . [N,SG] is set
(V,SG) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
the carrier of V is non empty set
(V,N,(V,SG)) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
M . (N,SG) is set
Y is complex set
(V,Y,(V,SG)) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
M is non empty Relation-like [:COMPLEX,(V):] -defined (V) -valued Function-like total quasi_total Element of bool [:[:COMPLEX,(V):],(V):]
N is non empty Relation-like [:COMPLEX,(V):] -defined (V) -valued Function-like total quasi_total Element of bool [:[:COMPLEX,(V):],(V):]
SG is complex Element of COMPLEX
Y is Element of (V)
M . (SG,Y) is Element of (V)
[SG,Y] is set
{SG,Y} is non empty finite set
{SG} is non empty trivial finite 1 -element V68() set
{{SG,Y},{SG}} is non empty finite V42() set
M . [SG,Y] is set
(V,Y) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
the carrier of V is non empty set
(V,SG,(V,Y)) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
N . (SG,Y) is Element of (V)
N . [SG,Y] is set
V is non empty CLSStruct
(V) is non empty set
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
the carrier of V is non empty set
(V,(V)) is Element of (V)
(V) is non empty Relation-like [:(V),(V):] -defined (V) -valued Function-like total quasi_total Element of bool [:[:(V),(V):],(V):]
[:(V),(V):] is non empty set
[:[:(V),(V):],(V):] is non empty set
bool [:[:(V),(V):],(V):] is non empty set
(V) is non empty Relation-like [:COMPLEX,(V):] -defined (V) -valued Function-like total quasi_total Element of bool [:[:COMPLEX,(V):],(V):]
[:COMPLEX,(V):] is non empty non trivial non finite set
[:[:COMPLEX,(V):],(V):] is non empty non trivial non finite set
bool [:[:COMPLEX,(V):],(V):] is non empty non trivial non finite set
CLSStruct(# (V),(V,(V)),(V),(V) #) is non empty strict CLSStruct
the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #) is non empty set
N is complex set
SG is complex set
Y is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
r2 is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
r1 is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
r2 + Y is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) is non empty Relation-like [: the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #), the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #):] -defined the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #) -valued Function-like total quasi_total Element of bool [:[: the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #), the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #):], the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #):]
[: the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #), the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #):] is non empty set
[:[: the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #), the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #):], the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #):] is non empty set
bool [:[: the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #), the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #):], the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #):] is non empty set
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . (r2,Y) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[r2,Y] is set
{r2,Y} is non empty finite set
{r2} is non empty trivial finite 1 -element set
{{r2,Y},{r2}} is non empty finite V42() set
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . [r2,Y] is set
Y + r1 is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . (Y,r1) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[Y,r1] is set
{Y,r1} is non empty finite set
{Y} is non empty trivial finite 1 -element set
{{Y,r1},{Y}} is non empty finite V42() set
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . [Y,r1] is set
r3 is complex Element of COMPLEX
r3 * Y is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
the Mult of CLSStruct(# (V),(V,(V)),(V),(V) #) is non empty Relation-like [:COMPLEX, the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #):] -defined the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #) -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #):], the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #):]
[:COMPLEX, the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #):] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #):], the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #):] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #):], the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #):] is non empty non trivial non finite set
[r3,Y] is set
{r3,Y} is non empty finite set
{r3} is non empty trivial finite 1 -element V68() set
{{r3,Y},{r3}} is non empty finite V42() set
the Mult of CLSStruct(# (V),(V,(V)),(V),(V) #) . [r3,Y] is set
r3 * r1 is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[r3,r1] is set
{r3,r1} is non empty finite set
{{r3,r1},{r3}} is non empty finite V42() set
the Mult of CLSStruct(# (V),(V,(V)),(V),(V) #) . [r3,r1] is set
r2 is complex Element of COMPLEX
r2 * Y is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[r2,Y] is set
{r2,Y} is non empty finite set
{r2} is non empty trivial finite 1 -element V68() set
{{r2,Y},{r2}} is non empty finite V42() set
the Mult of CLSStruct(# (V),(V,(V)),(V),(V) #) . [r2,Y] is set
u2 is Element of (V)
(V,u2) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
y1 is Element of (V)
(V,y1) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
x1 is Element of (V)
(V,x1) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
y2 is Element of (V)
(V,y2) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
N * Y is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[N,Y] is set
{N,Y} is non empty finite set
{N} is non empty trivial finite 1 -element V68() set
{{N,Y},{N}} is non empty finite V42() set
the Mult of CLSStruct(# (V),(V,(V)),(V),(V) #) . [N,Y] is set
x2 is Element of (V)
(V,x2) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
N * r1 is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[N,r1] is set
{N,r1} is non empty finite set
{{N,r1},{N}} is non empty finite V42() set
the Mult of CLSStruct(# (V),(V,(V)),(V),(V) #) . [N,r1] is set
bx is Element of (V)
(V,bx) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
SG * Y is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[SG,Y] is set
{SG,Y} is non empty finite set
{SG} is non empty trivial finite 1 -element V68() set
{{SG,Y},{SG}} is non empty finite V42() set
the Mult of CLSStruct(# (V),(V,(V)),(V),(V) #) . [SG,Y] is set
r3 is Element of (V)
(V,r3) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
r1 is Element of (V)
(V,r1) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
a is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,a) is Element of (V)
(V,(V,a)) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
L is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,L) is Element of (V)
(V,(V,L)) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
v is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
L is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
v + L is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . (v,L) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[v,L] is set
{v,L} is non empty finite set
{v} is non empty trivial finite 1 -element set
{{v,L},{v}} is non empty finite V42() set
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . [v,L] is set
(V,a,L) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
K is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,K,M) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
r1 + Y is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . (r1,Y) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[r1,Y] is set
{r1,Y} is non empty finite set
{r1} is non empty trivial finite 1 -element set
{{r1,Y},{r1}} is non empty finite V42() set
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . [r1,Y] is set
(r2 + Y) + r1 is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . ((r2 + Y),r1) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[(r2 + Y),r1] is set
{(r2 + Y),r1} is non empty finite set
{(r2 + Y)} is non empty trivial finite 1 -element set
{{(r2 + Y),r1},{(r2 + Y)}} is non empty finite V42() set
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . [(r2 + Y),r1] is set
LK is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,LK,M) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
L is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,L,K) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
(V,(V,L,K),M) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
(V,L,(V,K,M)) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
KM is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,L,KM) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
r2 + (Y + r1) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . (r2,(Y + r1)) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[r2,(Y + r1)] is set
{r2,(Y + r1)} is non empty finite set
{{r2,(Y + r1)},{r2}} is non empty finite V42() set
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . [r2,(Y + r1)] is set
0. CLSStruct(# (V),(V,(V)),(V),(V) #) is zero Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
the ZeroF of CLSStruct(# (V),(V,(V)),(V),(V) #) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
Y + (0. CLSStruct(# (V),(V,(V)),(V),(V) #)) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . (Y,(0. CLSStruct(# (V),(V,(V)),(V),(V) #))) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[Y,(0. CLSStruct(# (V),(V,(V)),(V),(V) #))] is set
{Y,(0. CLSStruct(# (V),(V,(V)),(V),(V) #))} is non empty finite set
{{Y,(0. CLSStruct(# (V),(V,(V)),(V),(V) #))},{Y}} is non empty finite V42() set
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . [Y,(0. CLSStruct(# (V),(V,(V)),(V),(V) #))] is set
(V,K,(V)) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
(V,K) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(- 1r),K) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
vector (CLSStruct(# (V),(V,(V)),(V),(V) #),(V,K)) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
Y + (vector (CLSStruct(# (V),(V,(V)),(V),(V) #),(V,K))) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . (Y,(vector (CLSStruct(# (V),(V,(V)),(V),(V) #),(V,K)))) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[Y,(vector (CLSStruct(# (V),(V,(V)),(V),(V) #),(V,K)))] is set
{Y,(vector (CLSStruct(# (V),(V,(V)),(V),(V) #),(V,K)))} is non empty finite set
{{Y,(vector (CLSStruct(# (V),(V,(V)),(V),(V) #),(V,K)))},{Y}} is non empty finite V42() set
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . [Y,(vector (CLSStruct(# (V),(V,(V)),(V),(V) #),(V,K)))] is set
(V,K,K) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,K,(V,K)) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
v is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
L is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
a is complex set
[a,v] is set
{a,v} is non empty finite set
{a} is non empty trivial finite 1 -element V68() set
{{a,v},{a}} is non empty finite V42() set
(V) . [a,v] is set
(V,L) is Element of (V)
(V,(V,L)) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,a,(V,(V,L))) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
a * v is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
the Mult of CLSStruct(# (V),(V,(V)),(V),(V) #) . [a,v] is set
(V,a,L) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
N * (Y + r1) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[N,(Y + r1)] is set
{N,(Y + r1)} is non empty finite set
{{N,(Y + r1)},{N}} is non empty finite V42() set
the Mult of CLSStruct(# (V),(V,(V)),(V),(V) #) . [N,(Y + r1)] is set
(V,r3,KM) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,r3,(V,K,M)) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,r3,K) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,r3,M) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(V,r3,K),(V,r3,M)) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
aK is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,aK,(V,r3,M)) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
aM is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,aK,aM) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
(N * Y) + (N * r1) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . ((N * Y),(N * r1)) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[(N * Y),(N * r1)] is set
{(N * Y),(N * r1)} is non empty finite set
{(N * Y)} is non empty trivial finite 1 -element set
{{(N * Y),(N * r1)},{(N * Y)}} is non empty finite V42() set
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . [(N * Y),(N * r1)] is set
N + SG is complex set
(N + SG) * Y is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[(N + SG),Y] is set
{(N + SG),Y} is non empty finite set
{(N + SG)} is non empty trivial finite 1 -element V68() set
{{(N + SG),Y},{(N + SG)}} is non empty finite V42() set
the Mult of CLSStruct(# (V),(V,(V)),(V),(V) #) . [(N + SG),Y] is set
r3 + r2 is complex Element of COMPLEX
(V,(r3 + r2),K) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,r2,K) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(V,r3,K),(V,r2,K)) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
(V,SG,K) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,aK,(V,SG,K)) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
bK is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,aK,bK) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
(N * Y) + (SG * Y) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . ((N * Y),(SG * Y)) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[(N * Y),(SG * Y)] is set
{(N * Y),(SG * Y)} is non empty finite set
{{(N * Y),(SG * Y)},{(N * Y)}} is non empty finite V42() set
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . [(N * Y),(SG * Y)] is set
N * SG is complex set
(N * SG) * Y is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[(N * SG),Y] is set
{(N * SG),Y} is non empty finite set
{(N * SG)} is non empty trivial finite 1 -element V68() set
{{(N * SG),Y},{(N * SG)}} is non empty finite V42() set
the Mult of CLSStruct(# (V),(V,(V)),(V),(V) #) . [(N * SG),Y] is set
(V,(N * SG),K) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,r3,(V,r2,K)) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,N,bK) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
N * (SG * Y) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[N,(SG * Y)] is set
{N,(SG * Y)} is non empty finite set
{{N,(SG * Y)},{N}} is non empty finite V42() set
the Mult of CLSStruct(# (V),(V,(V)),(V),(V) #) . [N,(SG * Y)] is set
1r * Y is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[1r,Y] is set
{1r,Y} is non empty finite set
{1r} is non empty trivial finite 1 -element V68() set
{{1r,Y},{1r}} is non empty finite V42() set
the Mult of CLSStruct(# (V),(V,(V)),(V),(V) #) . [1r,Y] is set
(V,1r,K) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
N is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
SG is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
N + SG is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . (N,SG) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[N,SG] is set
{N,SG} is non empty finite set
{N} is non empty trivial finite 1 -element set
{{N,SG},{N}} is non empty finite V42() set
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . [N,SG] is set
N is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
SG is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
N + SG is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . (N,SG) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[N,SG] is set
{N,SG} is non empty finite set
{N} is non empty trivial finite 1 -element set
{{N,SG},{N}} is non empty finite V42() set
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . [N,SG] is set
Y is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
(N + SG) + Y is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . ((N + SG),Y) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[(N + SG),Y] is set
{(N + SG),Y} is non empty finite set
{(N + SG)} is non empty trivial finite 1 -element set
{{(N + SG),Y},{(N + SG)}} is non empty finite V42() set
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . [(N + SG),Y] is set
SG + Y is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . (SG,Y) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[SG,Y] is set
{SG,Y} is non empty finite set
{SG} is non empty trivial finite 1 -element set
{{SG,Y},{SG}} is non empty finite V42() set
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . [SG,Y] is set
N + (SG + Y) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . (N,(SG + Y)) is Element of the carrier of CLSStruct(# (V),(V,(V)),(V),(V) #)
[N,(SG + Y)] is set
{N,(SG + Y)} is non empty finite set
{{N,(SG + Y)},{N}} is non empty finite V42() set
the addF of CLSStruct(# (V),(V,(V)),(V),(V) #) . [N,(SG + Y)] is set
V is non empty CLSStruct
(V) is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
(V) is non empty set
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
the carrier of V is non empty set
(V,(V)) is Element of (V)
(V) is non empty Relation-like [:(V),(V):] -defined (V) -valued Function-like total quasi_total Element of bool [:[:(V),(V):],(V):]
[:(V),(V):] is non empty set
[:[:(V),(V):],(V):] is non empty set
bool [:[:(V),(V):],(V):] is non empty set
(V) is non empty Relation-like [:COMPLEX,(V):] -defined (V) -valued Function-like total quasi_total Element of bool [:[:COMPLEX,(V):],(V):]
[:COMPLEX,(V):] is non empty non trivial non finite set
[:[:COMPLEX,(V):],(V):] is non empty non trivial non finite set
bool [:[:COMPLEX,(V):],(V):] is non empty non trivial non finite set
CLSStruct(# (V),(V,(V)),(V),(V) #) is non empty strict CLSStruct
V is non empty CLSStruct
the carrier of V is non empty set
(V) is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
(V) is non empty set
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(V)) is Element of (V)
(V) is non empty Relation-like [:(V),(V):] -defined (V) -valued Function-like total quasi_total Element of bool [:[:(V),(V):],(V):]
[:(V),(V):] is non empty set
[:[:(V),(V):],(V):] is non empty set
bool [:[:(V),(V):],(V):] is non empty set
(V) is non empty Relation-like [:COMPLEX,(V):] -defined (V) -valued Function-like total quasi_total Element of bool [:[:COMPLEX,(V):],(V):]
[:COMPLEX,(V):] is non empty non trivial non finite set
[:[:COMPLEX,(V):],(V):] is non empty non trivial non finite set
bool [:[:COMPLEX,(V):],(V):] is non empty non trivial non finite set
CLSStruct(# (V),(V,(V)),(V),(V) #) is non empty strict CLSStruct
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
vector ((V),M) is Element of the carrier of (V)
the carrier of (V) is non empty set
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
vector ((V),N) is Element of the carrier of (V)
(vector ((V),M)) + (vector ((V),N)) is Element of the carrier of (V)
the addF of (V) is non empty Relation-like [: the carrier of (V), the carrier of (V):] -defined the carrier of (V) -valued Function-like total quasi_total Element of bool [:[: the carrier of (V), the carrier of (V):], the carrier of (V):]
[: the carrier of (V), the carrier of (V):] is non empty set
[:[: the carrier of (V), the carrier of (V):], the carrier of (V):] is non empty set
bool [:[: the carrier of (V), the carrier of (V):], the carrier of (V):] is non empty set
the addF of (V) . ((vector ((V),M)),(vector ((V),N))) is Element of the carrier of (V)
[(vector ((V),M)),(vector ((V),N))] is set
{(vector ((V),M)),(vector ((V),N))} is non empty finite set
{(vector ((V),M))} is non empty trivial finite 1 -element set
{{(vector ((V),M)),(vector ((V),N))},{(vector ((V),M))}} is non empty finite V42() set
the addF of (V) . [(vector ((V),M)),(vector ((V),N))] is set
(V,M,N) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
(V,M) is Element of (V)
(V,(V,M)) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,N) is Element of (V)
(V,(V,N)) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
Funcs ( the carrier of V,COMPLEX) is non empty functional FUNCTION_DOMAIN of the carrier of V, COMPLEX
[M,(vector ((V),N))] is Element of [:(Funcs ( the carrier of V,COMPLEX)), the carrier of (V):]
[:(Funcs ( the carrier of V,COMPLEX)), the carrier of (V):] is non empty set
{M,(vector ((V),N))} is non empty finite set
{M} is non empty trivial finite 1 -element set
{{M,(vector ((V),N))},{M}} is non empty finite V42() set
(V) . [M,(vector ((V),N))] is set
(V) . ((V,M),(V,N)) is Element of (V)
[(V,M),(V,N)] is set
{(V,M),(V,N)} is non empty finite set
{(V,M)} is non empty trivial finite 1 -element set
{{(V,M),(V,N)},{(V,M)}} is non empty finite V42() set
(V) . [(V,M),(V,N)] is set
V is non empty CLSStruct
the carrier of V is non empty set
(V) is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
(V) is non empty set
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(V)) is Element of (V)
(V) is non empty Relation-like [:(V),(V):] -defined (V) -valued Function-like total quasi_total Element of bool [:[:(V),(V):],(V):]
[:(V),(V):] is non empty set
[:[:(V),(V):],(V):] is non empty set
bool [:[:(V),(V):],(V):] is non empty set
(V) is non empty Relation-like [:COMPLEX,(V):] -defined (V) -valued Function-like total quasi_total Element of bool [:[:COMPLEX,(V):],(V):]
[:COMPLEX,(V):] is non empty non trivial non finite set
[:[:COMPLEX,(V):],(V):] is non empty non trivial non finite set
bool [:[:COMPLEX,(V):],(V):] is non empty non trivial non finite set
CLSStruct(# (V),(V,(V)),(V),(V) #) is non empty strict CLSStruct
M is complex set
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
vector ((V),N) is Element of the carrier of (V)
the carrier of (V) is non empty set
M * (vector ((V),N)) is Element of the carrier of (V)
the Mult of (V) is non empty Relation-like [:COMPLEX, the carrier of (V):] -defined the carrier of (V) -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of (V):], the carrier of (V):]
[:COMPLEX, the carrier of (V):] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of (V):], the carrier of (V):] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of (V):], the carrier of (V):] is non empty non trivial non finite set
[M,(vector ((V),N))] is set
{M,(vector ((V),N))} is non empty finite set
{M} is non empty trivial finite 1 -element V68() set
{{M,(vector ((V),N))},{M}} is non empty finite V42() set
the Mult of (V) . [M,(vector ((V),N))] is set
(V,M,N) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V) . [M,(vector ((V),N))] is set
(V,N) is Element of (V)
[M,(V,N)] is set
{M,(V,N)} is non empty finite set
{{M,(V,N)},{M}} is non empty finite V42() set
(V) . [M,(V,N)] is set
(V,(V,N)) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
V is non empty CLSStruct
the carrier of V is non empty set
(V) is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
(V) is non empty set
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(V)) is Element of (V)
(V) is non empty Relation-like [:(V),(V):] -defined (V) -valued Function-like total quasi_total Element of bool [:[:(V),(V):],(V):]
[:(V),(V):] is non empty set
[:[:(V),(V):],(V):] is non empty set
bool [:[:(V),(V):],(V):] is non empty set
(V) is non empty Relation-like [:COMPLEX,(V):] -defined (V) -valued Function-like total quasi_total Element of bool [:[:COMPLEX,(V):],(V):]
[:COMPLEX,(V):] is non empty non trivial non finite set
[:[:COMPLEX,(V):],(V):] is non empty non trivial non finite set
bool [:[:COMPLEX,(V):],(V):] is non empty non trivial non finite set
CLSStruct(# (V),(V,(V)),(V),(V) #) is non empty strict CLSStruct
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
vector ((V),M) is Element of the carrier of (V)
the carrier of (V) is non empty set
- (vector ((V),M)) is Element of the carrier of (V)
(V,M) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(- 1r),M) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(- 1r) * (vector ((V),M)) is Element of the carrier of (V)
the Mult of (V) is non empty Relation-like [:COMPLEX, the carrier of (V):] -defined the carrier of (V) -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of (V):], the carrier of (V):]
[:COMPLEX, the carrier of (V):] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of (V):], the carrier of (V):] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of (V):], the carrier of (V):] is non empty non trivial non finite set
[(- 1r),(vector ((V),M))] is set
{(- 1r),(vector ((V),M))} is non empty finite set
{(- 1r)} is non empty trivial finite 1 -element V68() set
{{(- 1r),(vector ((V),M))},{(- 1r)}} is non empty finite V42() set
the Mult of (V) . [(- 1r),(vector ((V),M))] is set
V is non empty CLSStruct
the carrier of V is non empty set
(V) is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
(V) is non empty set
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(V)) is Element of (V)
(V) is non empty Relation-like [:(V),(V):] -defined (V) -valued Function-like total quasi_total Element of bool [:[:(V),(V):],(V):]
[:(V),(V):] is non empty set
[:[:(V),(V):],(V):] is non empty set
bool [:[:(V),(V):],(V):] is non empty set
(V) is non empty Relation-like [:COMPLEX,(V):] -defined (V) -valued Function-like total quasi_total Element of bool [:[:COMPLEX,(V):],(V):]
[:COMPLEX,(V):] is non empty non trivial non finite set
[:[:COMPLEX,(V):],(V):] is non empty non trivial non finite set
bool [:[:COMPLEX,(V):],(V):] is non empty non trivial non finite set
CLSStruct(# (V),(V,(V)),(V),(V) #) is non empty strict CLSStruct
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
vector ((V),M) is Element of the carrier of (V)
the carrier of (V) is non empty set
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
vector ((V),N) is Element of the carrier of (V)
(vector ((V),M)) - (vector ((V),N)) is Element of the carrier of (V)
- (vector ((V),N)) is Element of the carrier of (V)
(vector ((V),M)) + (- (vector ((V),N))) is Element of the carrier of (V)
the addF of (V) is non empty Relation-like [: the carrier of (V), the carrier of (V):] -defined the carrier of (V) -valued Function-like total quasi_total Element of bool [:[: the carrier of (V), the carrier of (V):], the carrier of (V):]
[: the carrier of (V), the carrier of (V):] is non empty set
[:[: the carrier of (V), the carrier of (V):], the carrier of (V):] is non empty set
bool [:[: the carrier of (V), the carrier of (V):], the carrier of (V):] is non empty set
the addF of (V) . ((vector ((V),M)),(- (vector ((V),N)))) is Element of the carrier of (V)
[(vector ((V),M)),(- (vector ((V),N)))] is set
{(vector ((V),M)),(- (vector ((V),N)))} is non empty finite set
{(vector ((V),M))} is non empty trivial finite 1 -element set
{{(vector ((V),M)),(- (vector ((V),N)))},{(vector ((V),M))}} is non empty finite V42() set
the addF of (V) . [(vector ((V),M)),(- (vector ((V),N)))] is set
(V,M,N) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,N) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(- 1r),N) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M,(V,N)) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V)
vector ((V),(V,N)) is Element of the carrier of (V)
V is non empty CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
(V) is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
(V) is non empty set
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,(V)) is Element of (V)
(V) is non empty Relation-like [:(V),(V):] -defined (V) -valued Function-like total quasi_total Element of bool [:[:(V),(V):],(V):]
[:(V),(V):] is non empty set
[:[:(V),(V):],(V):] is non empty set
bool [:[:(V),(V):],(V):] is non empty set
(V) is non empty Relation-like [:COMPLEX,(V):] -defined (V) -valued Function-like total quasi_total Element of bool [:[:COMPLEX,(V):],(V):]
[:COMPLEX,(V):] is non empty non trivial non finite set
[:[:COMPLEX,(V):],(V):] is non empty non trivial non finite set
bool [:[:COMPLEX,(V):],(V):] is non empty non trivial non finite set
CLSStruct(# (V),(V,(V)),(V),(V) #) is non empty strict CLSStruct
M is Element of bool the carrier of V
{ b₁ where b₁ is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,M) : verum } is set
the carrier of (V) is non empty set
SG is set
Y is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,M)
bool the carrier of (V) is non empty set
SG is Element of bool the carrier of (V)
Y is Element of the carrier of (V)
r2 is Element of the carrier of (V)
Y + r2 is Element of the carrier of (V)
the addF of (V) is non empty Relation-like [: the carrier of (V), the carrier of (V):] -defined the carrier of (V) -valued Function-like total quasi_total Element of bool [:[: the carrier of (V), the carrier of (V):], the carrier of (V):]
[: the carrier of (V), the carrier of (V):] is non empty set
[:[: the carrier of (V), the carrier of (V):], the carrier of (V):] is non empty set
bool [:[: the carrier of (V), the carrier of (V):], the carrier of (V):] is non empty set
the addF of (V) . (Y,r2) is Element of the carrier of (V)
[Y,r2] is set
{Y,r2} is non empty finite set
{Y} is non empty trivial finite 1 -element set
{{Y,r2},{Y}} is non empty finite V42() set
the addF of (V) . [Y,r2] is set
r1 is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,M)
r3 is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,M)
vector ((V),r3) is Element of the carrier of (V)
vector ((V),r1) is Element of the carrier of (V)
(V,M,r1,r3) is Relation-like the carrier of V -defined the carrier of V -defined COMPLEX -valued Function-like total total quasi_total V58() (V,M)
Y is complex set
r2 is Element of the carrier of (V)
Y * r2 is Element of the carrier of (V)
the Mult of (V) is non empty Relation-like [:COMPLEX, the carrier of (V):] -defined the carrier of (V) -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of (V):], the carrier of (V):]
[:COMPLEX, the carrier of (V):] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of (V):], the carrier of (V):] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of (V):], the carrier of (V):] is non empty non trivial non finite set
[Y,r2] is set
{Y,r2} is non empty finite set
{Y} is non empty trivial finite 1 -element V68() set
{{Y,r2},{Y}} is non empty finite V42() set
the Mult of (V) . [Y,r2] is set
r1 is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,M)
vector ((V),r1) is Element of the carrier of (V)
Y * (vector ((V),r1)) is Element of the carrier of (V)
[Y,(vector ((V),r1))] is set
{Y,(vector ((V),r1))} is non empty finite set
{{Y,(vector ((V),r1))},{Y}} is non empty finite V42() set
the Mult of (V) . [Y,(vector ((V),r1))] is set
(V,Y,r1) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
N is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of (V)
the carrier of N is non empty set
SG is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of (V)
the carrier of SG is non empty set
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
M is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
the carrier of M is non empty set
the carrier of V is non empty set
bool the carrier of V is non empty set
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
M is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
(V,M) is Element of bool the carrier of V
the carrier of V is non empty set
bool the carrier of V is non empty set
the carrier of M is non empty set
V is non empty CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
the ZeroF of V is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is non empty strict CLSStruct
the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is non empty set
N is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
SG is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
N + SG is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is non empty Relation-like [: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] -defined the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) -valued Function-like total quasi_total Element of bool [:[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):]
[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
[:[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
bool [:[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (N,SG) is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
[N,SG] is set
{N,SG} is non empty finite set
{N} is non empty trivial finite 1 -element set
{{N,SG},{N}} is non empty finite V42() set
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [N,SG] is set
SG + N is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (SG,N) is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
[SG,N] is set
{SG,N} is non empty finite set
{SG} is non empty trivial finite 1 -element set
{{SG,N},{SG}} is non empty finite V42() set
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [SG,N] is set
Y is Element of the carrier of V
r2 is Element of the carrier of V
Y + r2 is Element of the carrier of V
the addF of V . (Y,r2) is Element of the carrier of V
[Y,r2] is set
{Y,r2} is non empty finite set
{Y} is non empty trivial finite 1 -element set
{{Y,r2},{Y}} is non empty finite V42() set
the addF of V . [Y,r2] is set
r2 + Y is Element of the carrier of V
the addF of V . (r2,Y) is Element of the carrier of V
[r2,Y] is set
{r2,Y} is non empty finite set
{r2} is non empty trivial finite 1 -element set
{{r2,Y},{r2}} is non empty finite V42() set
the addF of V . [r2,Y] is set
N is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
SG is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
N + SG is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is non empty Relation-like [: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] -defined the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) -valued Function-like total quasi_total Element of bool [:[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):]
[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
[:[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
bool [:[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (N,SG) is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
[N,SG] is set
{N,SG} is non empty finite set
{N} is non empty trivial finite 1 -element set
{{N,SG},{N}} is non empty finite V42() set
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [N,SG] is set
Y is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
(N + SG) + Y is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . ((N + SG),Y) is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
[(N + SG),Y] is set
{(N + SG),Y} is non empty finite set
{(N + SG)} is non empty trivial finite 1 -element set
{{(N + SG),Y},{(N + SG)}} is non empty finite V42() set
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [(N + SG),Y] is set
SG + Y is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (SG,Y) is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
[SG,Y] is set
{SG,Y} is non empty finite set
{SG} is non empty trivial finite 1 -element set
{{SG,Y},{SG}} is non empty finite V42() set
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [SG,Y] is set
N + (SG + Y) is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (N,(SG + Y)) is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
[N,(SG + Y)] is set
{N,(SG + Y)} is non empty finite set
{{N,(SG + Y)},{N}} is non empty finite V42() set
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [N,(SG + Y)] is set
r2 is Element of the carrier of V
r1 is Element of the carrier of V
r2 + r1 is Element of the carrier of V
the addF of V . (r2,r1) is Element of the carrier of V
[r2,r1] is set
{r2,r1} is non empty finite set
{r2} is non empty trivial finite 1 -element set
{{r2,r1},{r2}} is non empty finite V42() set
the addF of V . [r2,r1] is set
r3 is Element of the carrier of V
(r2 + r1) + r3 is Element of the carrier of V
the addF of V . ((r2 + r1),r3) is Element of the carrier of V
[(r2 + r1),r3] is set
{(r2 + r1),r3} is non empty finite set
{(r2 + r1)} is non empty trivial finite 1 -element set
{{(r2 + r1),r3},{(r2 + r1)}} is non empty finite V42() set
the addF of V . [(r2 + r1),r3] is set
r1 + r3 is Element of the carrier of V
the addF of V . (r1,r3) is Element of the carrier of V
[r1,r3] is set
{r1,r3} is non empty finite set
{r1} is non empty trivial finite 1 -element set
{{r1,r3},{r1}} is non empty finite V42() set
the addF of V . [r1,r3] is set
r2 + (r1 + r3) is Element of the carrier of V
the addF of V . (r2,(r1 + r3)) is Element of the carrier of V
[r2,(r1 + r3)] is set
{r2,(r1 + r3)} is non empty finite set
{{r2,(r1 + r3)},{r2}} is non empty finite V42() set
the addF of V . [r2,(r1 + r3)] is set
N is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
SG is Element of the carrier of V
0. V is zero Element of the carrier of V
Y is Element of the carrier of V
SG + Y is Element of the carrier of V
the addF of V . (SG,Y) is Element of the carrier of V
[SG,Y] is set
{SG,Y} is non empty finite set
{SG} is non empty trivial finite 1 -element set
{{SG,Y},{SG}} is non empty finite V42() set
the addF of V . [SG,Y] is set
r2 is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
N + r2 is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is non empty Relation-like [: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] -defined the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) -valued Function-like total quasi_total Element of bool [:[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):]
[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
[:[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
bool [:[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (N,r2) is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
[N,r2] is set
{N,r2} is non empty finite set
{N} is non empty trivial finite 1 -element set
{{N,r2},{N}} is non empty finite V42() set
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [N,r2] is set
0. CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is zero Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the ZeroF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
0. CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is zero Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the ZeroF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
N is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
N + (0. CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)) is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is non empty Relation-like [: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] -defined the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) -valued Function-like total quasi_total Element of bool [:[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):]
[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
[:[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
bool [:[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (N,(0. CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #))) is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
[N,(0. CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #))] is set
{N,(0. CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #))} is non empty finite set
{N} is non empty trivial finite 1 -element set
{{N,(0. CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #))},{N}} is non empty finite V42() set
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [N,(0. CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #))] is set
SG is Element of the carrier of V
0. V is zero Element of the carrier of V
SG + (0. V) is Element of the carrier of V
the addF of V . (SG,(0. V)) is Element of the carrier of V
[SG,(0. V)] is set
{SG,(0. V)} is non empty finite set
{SG} is non empty trivial finite 1 -element set
{{SG,(0. V)},{SG}} is non empty finite V42() set
the addF of V . [SG,(0. V)] is set
N is complex set
SG is complex set
N * SG is complex set
Y is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
(N * SG) * Y is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the Mult of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is non empty Relation-like [:COMPLEX, the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] -defined the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):]
[:COMPLEX, the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty non trivial non finite set
[(N * SG),Y] is set
{(N * SG),Y} is non empty finite set
{(N * SG)} is non empty trivial finite 1 -element V68() set
{{(N * SG),Y},{(N * SG)}} is non empty finite V42() set
the Mult of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [(N * SG),Y] is set
SG * Y is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
[SG,Y] is set
{SG,Y} is non empty finite set
{SG} is non empty trivial finite 1 -element V68() set
{{SG,Y},{SG}} is non empty finite V42() set
the Mult of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [SG,Y] is set
N * (SG * Y) is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
[N,(SG * Y)] is set
{N,(SG * Y)} is non empty finite set
{N} is non empty trivial finite 1 -element V68() set
{{N,(SG * Y)},{N}} is non empty finite V42() set
the Mult of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [N,(SG * Y)] is set
r2 is Element of the carrier of V
(N * SG) * r2 is Element of the carrier of V
[(N * SG),r2] is set
{(N * SG),r2} is non empty finite set
{{(N * SG),r2},{(N * SG)}} is non empty finite V42() set
the Mult of V . [(N * SG),r2] is set
SG * r2 is Element of the carrier of V
[SG,r2] is set
{SG,r2} is non empty finite set
{{SG,r2},{SG}} is non empty finite V42() set
the Mult of V . [SG,r2] is set
N * (SG * r2) is Element of the carrier of V
[N,(SG * r2)] is set
{N,(SG * r2)} is non empty finite set
{{N,(SG * r2)},{N}} is non empty finite V42() set
the Mult of V . [N,(SG * r2)] is set
N is complex set
SG is complex set
N + SG is complex set
Y is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
(N + SG) * Y is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the Mult of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is non empty Relation-like [:COMPLEX, the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] -defined the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):]
[:COMPLEX, the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty non trivial non finite set
[(N + SG),Y] is set
{(N + SG),Y} is non empty finite set
{(N + SG)} is non empty trivial finite 1 -element V68() set
{{(N + SG),Y},{(N + SG)}} is non empty finite V42() set
the Mult of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [(N + SG),Y] is set
N * Y is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
[N,Y] is set
{N,Y} is non empty finite set
{N} is non empty trivial finite 1 -element V68() set
{{N,Y},{N}} is non empty finite V42() set
the Mult of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [N,Y] is set
SG * Y is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
[SG,Y] is set
{SG,Y} is non empty finite set
{SG} is non empty trivial finite 1 -element V68() set
{{SG,Y},{SG}} is non empty finite V42() set
the Mult of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [SG,Y] is set
(N * Y) + (SG * Y) is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is non empty Relation-like [: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] -defined the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) -valued Function-like total quasi_total Element of bool [:[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):]
[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
[:[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
bool [:[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . ((N * Y),(SG * Y)) is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
[(N * Y),(SG * Y)] is set
{(N * Y),(SG * Y)} is non empty finite set
{(N * Y)} is non empty trivial finite 1 -element set
{{(N * Y),(SG * Y)},{(N * Y)}} is non empty finite V42() set
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [(N * Y),(SG * Y)] is set
r2 is Element of the carrier of V
(N + SG) * r2 is Element of the carrier of V
[(N + SG),r2] is set
{(N + SG),r2} is non empty finite set
{{(N + SG),r2},{(N + SG)}} is non empty finite V42() set
the Mult of V . [(N + SG),r2] is set
N * r2 is Element of the carrier of V
[N,r2] is set
{N,r2} is non empty finite set
{{N,r2},{N}} is non empty finite V42() set
the Mult of V . [N,r2] is set
SG * r2 is Element of the carrier of V
[SG,r2] is set
{SG,r2} is non empty finite set
{{SG,r2},{SG}} is non empty finite V42() set
the Mult of V . [SG,r2] is set
(N * r2) + (SG * r2) is Element of the carrier of V
the addF of V . ((N * r2),(SG * r2)) is Element of the carrier of V
[(N * r2),(SG * r2)] is set
{(N * r2),(SG * r2)} is non empty finite set
{(N * r2)} is non empty trivial finite 1 -element set
{{(N * r2),(SG * r2)},{(N * r2)}} is non empty finite V42() set
the addF of V . [(N * r2),(SG * r2)] is set
N is complex set
SG is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
Y is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
SG + Y is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is non empty Relation-like [: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] -defined the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) -valued Function-like total quasi_total Element of bool [:[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):]
[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
[:[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
bool [:[: the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (SG,Y) is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
[SG,Y] is set
{SG,Y} is non empty finite set
{SG} is non empty trivial finite 1 -element set
{{SG,Y},{SG}} is non empty finite V42() set
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [SG,Y] is set
N * (SG + Y) is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the Mult of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is non empty Relation-like [:COMPLEX, the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] -defined the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):]
[:COMPLEX, the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty non trivial non finite set
[N,(SG + Y)] is set
{N,(SG + Y)} is non empty finite set
{N} is non empty trivial finite 1 -element V68() set
{{N,(SG + Y)},{N}} is non empty finite V42() set
the Mult of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [N,(SG + Y)] is set
N * SG is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
[N,SG] is set
{N,SG} is non empty finite set
{{N,SG},{N}} is non empty finite V42() set
the Mult of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [N,SG] is set
N * Y is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
[N,Y] is set
{N,Y} is non empty finite set
{{N,Y},{N}} is non empty finite V42() set
the Mult of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [N,Y] is set
(N * SG) + (N * Y) is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . ((N * SG),(N * Y)) is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
[(N * SG),(N * Y)] is set
{(N * SG),(N * Y)} is non empty finite set
{(N * SG)} is non empty trivial finite 1 -element set
{{(N * SG),(N * Y)},{(N * SG)}} is non empty finite V42() set
the addF of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [(N * SG),(N * Y)] is set
r2 is Element of the carrier of V
r1 is Element of the carrier of V
r2 + r1 is Element of the carrier of V
the addF of V . (r2,r1) is Element of the carrier of V
[r2,r1] is set
{r2,r1} is non empty finite set
{r2} is non empty trivial finite 1 -element set
{{r2,r1},{r2}} is non empty finite V42() set
the addF of V . [r2,r1] is set
N * (r2 + r1) is Element of the carrier of V
[N,(r2 + r1)] is set
{N,(r2 + r1)} is non empty finite set
{{N,(r2 + r1)},{N}} is non empty finite V42() set
the Mult of V . [N,(r2 + r1)] is set
N * r2 is Element of the carrier of V
[N,r2] is set
{N,r2} is non empty finite set
{{N,r2},{N}} is non empty finite V42() set
the Mult of V . [N,r2] is set
N * r1 is Element of the carrier of V
[N,r1] is set
{N,r1} is non empty finite set
{{N,r1},{N}} is non empty finite V42() set
the Mult of V . [N,r1] is set
(N * r2) + (N * r1) is Element of the carrier of V
the addF of V . ((N * r2),(N * r1)) is Element of the carrier of V
[(N * r2),(N * r1)] is set
{(N * r2),(N * r1)} is non empty finite set
{(N * r2)} is non empty trivial finite 1 -element set
{{(N * r2),(N * r1)},{(N * r2)}} is non empty finite V42() set
the addF of V . [(N * r2),(N * r1)] is set
N is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
1r * N is Element of the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the Mult of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is non empty Relation-like [:COMPLEX, the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] -defined the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):]
[:COMPLEX, the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty non trivial non finite set
[1r,N] is set
{1r,N} is non empty finite set
{1r} is non empty trivial finite 1 -element V68() set
{{1r,N},{1r}} is non empty finite V42() set
the Mult of CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [1r,N] is set
SG is Element of the carrier of V
1r * SG is Element of the carrier of V
[1r,SG] is set
{1r,SG} is non empty finite set
{{1r,SG},{1r}} is non empty finite V42() set
the Mult of V . [1r,SG] is set
N is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the Mult of N is non empty Relation-like [:COMPLEX, the carrier of N:] -defined the carrier of N -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of N:], the carrier of N:]
the carrier of N is non empty set
[:COMPLEX, the carrier of N:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of N:], the carrier of N:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of N:], the carrier of N:] is non empty non trivial non finite set
the Mult of V | [:COMPLEX, the carrier of N:] is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
0. N is zero Element of the carrier of N
the ZeroF of N is Element of the carrier of N
0. V is zero Element of the carrier of V
the addF of N is non empty Relation-like [: the carrier of N, the carrier of N:] -defined the carrier of N -valued Function-like total quasi_total Element of bool [:[: the carrier of N, the carrier of N:], the carrier of N:]
[: the carrier of N, the carrier of N:] is non empty set
[:[: the carrier of N, the carrier of N:], the carrier of N:] is non empty set
bool [:[: the carrier of N, the carrier of N:], the carrier of N:] is non empty set
the addF of V || the carrier of N is set
the addF of V | [: the carrier of N, the carrier of N:] is Relation-like set
V is non empty CLSStruct
[#] V is non empty non proper Element of bool the carrier of V
the carrier of V is non empty set
bool the carrier of V is non empty set
SG is complex set
M is Element of the carrier of V
N is Element of the carrier of V
1r - SG is complex set
- SG is complex set
1r + (- SG) is complex set
(1r - SG) * M is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(1r - SG),M] is set
{(1r - SG),M} is non empty finite set
{(1r - SG)} is non empty trivial finite 1 -element V68() set
{{(1r - SG),M},{(1r - SG)}} is non empty finite V42() set
the Mult of V . [(1r - SG),M] is set
SG * N is Element of the carrier of V
[SG,N] is set
{SG,N} is non empty finite set
{SG} is non empty trivial finite 1 -element V68() set
{{SG,N},{SG}} is non empty finite V42() set
the Mult of V . [SG,N] is set
((1r - SG) * M) + (SG * N) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (((1r - SG) * M),(SG * N)) is Element of the carrier of V
[((1r - SG) * M),(SG * N)] is set
{((1r - SG) * M),(SG * N)} is non empty finite set
{((1r - SG) * M)} is non empty trivial finite 1 -element set
{{((1r - SG) * M),(SG * N)},{((1r - SG) * M)}} is non empty finite V42() set
the addF of V . [((1r - SG) * M),(SG * N)] is set
M is Element of bool the carrier of V
Y is complex set
N is Element of the carrier of V
SG is Element of the carrier of V
1r - Y is complex set
- Y is complex set
1r + (- Y) is complex set
(1r - Y) * N is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(1r - Y),N] is set
{(1r - Y),N} is non empty finite set
{(1r - Y)} is non empty trivial finite 1 -element V68() set
{{(1r - Y),N},{(1r - Y)}} is non empty finite V42() set
the Mult of V . [(1r - Y),N] is set
Y * SG is Element of the carrier of V
[Y,SG] is set
{Y,SG} is non empty finite set
{Y} is non empty trivial finite 1 -element V68() set
{{Y,SG},{Y}} is non empty finite V42() set
the Mult of V . [Y,SG] is set
((1r - Y) * N) + (Y * SG) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (((1r - Y) * N),(Y * SG)) is Element of the carrier of V
[((1r - Y) * N),(Y * SG)] is set
{((1r - Y) * N),(Y * SG)} is non empty finite set
{((1r - Y) * N)} is non empty trivial finite 1 -element set
{{((1r - Y) * N),(Y * SG)},{((1r - Y) * N)}} is non empty finite V42() set
the addF of V . [((1r - Y) * N),(Y * SG)] is set
V is non empty CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
[#] V is non empty non proper (V) Element of bool the carrier of V
{} V is empty proper ordinal natural complex real finite V42() cardinal {} -element ext-real non positive non negative V68() V69() V70() V71() V72() V73() V74() (V) Element of bool the carrier of V
V is complex real ext-real set
M is complex set
V * M is complex set
Re (V * M) is complex real ext-real Element of REAL
Re M is complex real ext-real Element of REAL
V * (Re M) is complex real ext-real Element of REAL
Re V is complex real ext-real Element of REAL
(Re V) * (Re M) is complex real ext-real Element of REAL
Im V is complex real ext-real Element of REAL
Im M is complex real ext-real Element of REAL
(Im V) * (Im M) is complex real ext-real Element of REAL
((Re V) * (Re M)) - ((Im V) * (Im M)) is complex real ext-real Element of REAL
- ((Im V) * (Im M)) is complex real ext-real set
((Re V) * (Re M)) + (- ((Im V) * (Im M))) is complex real ext-real set
{} * (Im M) is complex real ext-real Element of REAL
((Re V) * (Re M)) - ({} * (Im M)) is complex real ext-real Element of REAL
- ({} * (Im M)) is complex real ext-real set
((Re V) * (Re M)) + (- ({} * (Im M))) is complex real ext-real set
V is complex real ext-real set
M is complex set
V * M is complex set
Im (V * M) is complex real ext-real Element of REAL
Im M is complex real ext-real Element of REAL
V * (Im M) is complex real ext-real Element of REAL
Re V is complex real ext-real Element of REAL
(Re V) * (Im M) is complex real ext-real Element of REAL
Re M is complex real ext-real Element of REAL
Im V is complex real ext-real Element of REAL
(Re M) * (Im V) is complex real ext-real Element of REAL
((Re V) * (Im M)) + ((Re M) * (Im V)) is complex real ext-real Element of REAL
(Re M) * {} is complex real ext-real Element of REAL
((Re V) * (Im M)) + ((Re M) * {}) is complex real ext-real Element of REAL
V is complex real ext-real set
1r - V is complex set
- V is complex real ext-real set
1r + (- V) is complex set
M is complex set
V * M is complex set
|.(V * M).| is complex real ext-real Element of REAL
|.M.| is complex real ext-real Element of REAL
V * |.M.| is complex real ext-real Element of REAL
(1r - V) * M is complex set
|.((1r - V) * M).| is complex real ext-real Element of REAL
(1r - V) * |.M.| is complex set
|.(1r - V).| is complex real ext-real Element of REAL
|.(1r - V).| * |.M.| is complex real ext-real Element of REAL
|.V.| is complex real ext-real Element of REAL
|.V.| * |.M.| is complex real ext-real Element of REAL
V is non empty CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
N is complex set
M is Element of bool the carrier of V
{ (N * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
{ H₁(b₁) where b₁ is Element of the carrier of V : S₁[b₁] } is set
V is non empty CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
V is non empty vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is complex set
(V,M,N) is Element of bool the carrier of V
{ (N * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
SG is Element of the carrier of V
Y is Element of the carrier of V
r2 is complex set
r2 * SG is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[r2,SG] is set
{r2,SG} is non empty finite set
{r2} is non empty trivial finite 1 -element V68() set
{{r2,SG},{r2}} is non empty finite V42() set
the Mult of V . [r2,SG] is set
1r - r2 is complex set
- r2 is complex set
1r + (- r2) is complex set
(1r - r2) * Y is Element of the carrier of V
[(1r - r2),Y] is set
{(1r - r2),Y} is non empty finite set
{(1r - r2)} is non empty trivial finite 1 -element V68() set
{{(1r - r2),Y},{(1r - r2)}} is non empty finite V42() set
the Mult of V . [(1r - r2),Y] is set
(r2 * SG) + ((1r - r2) * Y) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((r2 * SG),((1r - r2) * Y)) is Element of the carrier of V
[(r2 * SG),((1r - r2) * Y)] is set
{(r2 * SG),((1r - r2) * Y)} is non empty finite set
{(r2 * SG)} is non empty trivial finite 1 -element set
{{(r2 * SG),((1r - r2) * Y)},{(r2 * SG)}} is non empty finite V42() set
the addF of V . [(r2 * SG),((1r - r2) * Y)] is set
r1 is Element of the carrier of V
N * r1 is Element of the carrier of V
[N,r1] is set
{N,r1} is non empty finite set
{N} is non empty trivial finite 1 -element V68() set
{{N,r1},{N}} is non empty finite V42() set
the Mult of V . [N,r1] is set
r3 is Element of the carrier of V
N * r3 is Element of the carrier of V
[N,r3] is set
{N,r3} is non empty finite set
{{N,r3},{N}} is non empty finite V42() set
the Mult of V . [N,r3] is set
r2 * N is complex set
(r2 * N) * r3 is Element of the carrier of V
[(r2 * N),r3] is set
{(r2 * N),r3} is non empty finite set
{(r2 * N)} is non empty trivial finite 1 -element V68() set
{{(r2 * N),r3},{(r2 * N)}} is non empty finite V42() set
the Mult of V . [(r2 * N),r3] is set
(1r - r2) * (N * r1) is Element of the carrier of V
[(1r - r2),(N * r1)] is set
{(1r - r2),(N * r1)} is non empty finite set
{{(1r - r2),(N * r1)},{(1r - r2)}} is non empty finite V42() set
the Mult of V . [(1r - r2),(N * r1)] is set
((r2 * N) * r3) + ((1r - r2) * (N * r1)) is Element of the carrier of V
the addF of V . (((r2 * N) * r3),((1r - r2) * (N * r1))) is Element of the carrier of V
[((r2 * N) * r3),((1r - r2) * (N * r1))] is set
{((r2 * N) * r3),((1r - r2) * (N * r1))} is non empty finite set
{((r2 * N) * r3)} is non empty trivial finite 1 -element set
{{((r2 * N) * r3),((1r - r2) * (N * r1))},{((r2 * N) * r3)}} is non empty finite V42() set
the addF of V . [((r2 * N) * r3),((1r - r2) * (N * r1))] is set
N * r2 is complex set
(N * r2) * r3 is Element of the carrier of V
[(N * r2),r3] is set
{(N * r2),r3} is non empty finite set
{(N * r2)} is non empty trivial finite 1 -element V68() set
{{(N * r2),r3},{(N * r2)}} is non empty finite V42() set
the Mult of V . [(N * r2),r3] is set
N * (1r - r2) is complex set
(N * (1r - r2)) * r1 is Element of the carrier of V
[(N * (1r - r2)),r1] is set
{(N * (1r - r2)),r1} is non empty finite set
{(N * (1r - r2))} is non empty trivial finite 1 -element V68() set
{{(N * (1r - r2)),r1},{(N * (1r - r2))}} is non empty finite V42() set
the Mult of V . [(N * (1r - r2)),r1] is set
((N * r2) * r3) + ((N * (1r - r2)) * r1) is Element of the carrier of V
the addF of V . (((N * r2) * r3),((N * (1r - r2)) * r1)) is Element of the carrier of V
[((N * r2) * r3),((N * (1r - r2)) * r1)] is set
{((N * r2) * r3),((N * (1r - r2)) * r1)} is non empty finite set
{((N * r2) * r3)} is non empty trivial finite 1 -element set
{{((N * r2) * r3),((N * (1r - r2)) * r1)},{((N * r2) * r3)}} is non empty finite V42() set
the addF of V . [((N * r2) * r3),((N * (1r - r2)) * r1)] is set
r2 * r3 is Element of the carrier of V
[r2,r3] is set
{r2,r3} is non empty finite set
{{r2,r3},{r2}} is non empty finite V42() set
the Mult of V . [r2,r3] is set
N * (r2 * r3) is Element of the carrier of V
[N,(r2 * r3)] is set
{N,(r2 * r3)} is non empty finite set
{{N,(r2 * r3)},{N}} is non empty finite V42() set
the Mult of V . [N,(r2 * r3)] is set
(N * (r2 * r3)) + ((N * (1r - r2)) * r1) is Element of the carrier of V
the addF of V . ((N * (r2 * r3)),((N * (1r - r2)) * r1)) is Element of the carrier of V
[(N * (r2 * r3)),((N * (1r - r2)) * r1)] is set
{(N * (r2 * r3)),((N * (1r - r2)) * r1)} is non empty finite set
{(N * (r2 * r3))} is non empty trivial finite 1 -element set
{{(N * (r2 * r3)),((N * (1r - r2)) * r1)},{(N * (r2 * r3))}} is non empty finite V42() set
the addF of V . [(N * (r2 * r3)),((N * (1r - r2)) * r1)] is set
(1r - r2) * r1 is Element of the carrier of V
[(1r - r2),r1] is set
{(1r - r2),r1} is non empty finite set
{{(1r - r2),r1},{(1r - r2)}} is non empty finite V42() set
the Mult of V . [(1r - r2),r1] is set
N * ((1r - r2) * r1) is Element of the carrier of V
[N,((1r - r2) * r1)] is set
{N,((1r - r2) * r1)} is non empty finite set
{{N,((1r - r2) * r1)},{N}} is non empty finite V42() set
the Mult of V . [N,((1r - r2) * r1)] is set
(N * (r2 * r3)) + (N * ((1r - r2) * r1)) is Element of the carrier of V
the addF of V . ((N * (r2 * r3)),(N * ((1r - r2) * r1))) is Element of the carrier of V
[(N * (r2 * r3)),(N * ((1r - r2) * r1))] is set
{(N * (r2 * r3)),(N * ((1r - r2) * r1))} is non empty finite set
{{(N * (r2 * r3)),(N * ((1r - r2) * r1))},{(N * (r2 * r3))}} is non empty finite V42() set
the addF of V . [(N * (r2 * r3)),(N * ((1r - r2) * r1))] is set
(r2 * r3) + ((1r - r2) * r1) is Element of the carrier of V
the addF of V . ((r2 * r3),((1r - r2) * r1)) is Element of the carrier of V
[(r2 * r3),((1r - r2) * r1)] is set
{(r2 * r3),((1r - r2) * r1)} is non empty finite set
{(r2 * r3)} is non empty trivial finite 1 -element set
{{(r2 * r3),((1r - r2) * r1)},{(r2 * r3)}} is non empty finite V42() set
the addF of V . [(r2 * r3),((1r - r2) * r1)] is set
N * ((r2 * r3) + ((1r - r2) * r1)) is Element of the carrier of V
[N,((r2 * r3) + ((1r - r2) * r1))] is set
{N,((r2 * r3) + ((1r - r2) * r1))} is non empty finite set
{{N,((r2 * r3) + ((1r - r2) * r1))},{N}} is non empty finite V42() set
the Mult of V . [N,((r2 * r3) + ((1r - r2) * r1))] is set
r2 is complex real ext-real Element of REAL
V is non empty Abelian add-associative vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Element of bool the carrier of V
M + N is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in M & b₂ in N ) } is set
SG is Element of the carrier of V
Y is Element of the carrier of V
r2 is complex set
r2 * SG is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[r2,SG] is set
{r2,SG} is non empty finite set
{r2} is non empty trivial finite 1 -element V68() set
{{r2,SG},{r2}} is non empty finite V42() set
the Mult of V . [r2,SG] is set
1r - r2 is complex set
- r2 is complex set
1r + (- r2) is complex set
(1r - r2) * Y is Element of the carrier of V
[(1r - r2),Y] is set
{(1r - r2),Y} is non empty finite set
{(1r - r2)} is non empty trivial finite 1 -element V68() set
{{(1r - r2),Y},{(1r - r2)}} is non empty finite V42() set
the Mult of V . [(1r - r2),Y] is set
(r2 * SG) + ((1r - r2) * Y) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((r2 * SG),((1r - r2) * Y)) is Element of the carrier of V
[(r2 * SG),((1r - r2) * Y)] is set
{(r2 * SG),((1r - r2) * Y)} is non empty finite set
{(r2 * SG)} is non empty trivial finite 1 -element set
{{(r2 * SG),((1r - r2) * Y)},{(r2 * SG)}} is non empty finite V42() set
the addF of V . [(r2 * SG),((1r - r2) * Y)] is set
r1 is Element of the carrier of V
r3 is Element of the carrier of V
r1 + r3 is Element of the carrier of V
the addF of V . (r1,r3) is Element of the carrier of V
[r1,r3] is set
{r1,r3} is non empty finite set
{r1} is non empty trivial finite 1 -element set
{{r1,r3},{r1}} is non empty finite V42() set
the addF of V . [r1,r3] is set
r2 is Element of the carrier of V
r3 is Element of the carrier of V
r2 + r3 is Element of the carrier of V
the addF of V . (r2,r3) is Element of the carrier of V
[r2,r3] is set
{r2,r3} is non empty finite set
{r2} is non empty trivial finite 1 -element set
{{r2,r3},{r2}} is non empty finite V42() set
the addF of V . [r2,r3] is set
r2 * r2 is Element of the carrier of V
[r2,r2] is set
{r2,r2} is non empty finite set
{{r2,r2},{r2}} is non empty finite V42() set
the Mult of V . [r2,r2] is set
r2 * r3 is Element of the carrier of V
[r2,r3] is set
{r2,r3} is non empty finite set
{{r2,r3},{r2}} is non empty finite V42() set
the Mult of V . [r2,r3] is set
(r2 * r2) + (r2 * r3) is Element of the carrier of V
the addF of V . ((r2 * r2),(r2 * r3)) is Element of the carrier of V
[(r2 * r2),(r2 * r3)] is set
{(r2 * r2),(r2 * r3)} is non empty finite set
{(r2 * r2)} is non empty trivial finite 1 -element set
{{(r2 * r2),(r2 * r3)},{(r2 * r2)}} is non empty finite V42() set
the addF of V . [(r2 * r2),(r2 * r3)] is set
(1r - r2) * (r1 + r3) is Element of the carrier of V
[(1r - r2),(r1 + r3)] is set
{(1r - r2),(r1 + r3)} is non empty finite set
{{(1r - r2),(r1 + r3)},{(1r - r2)}} is non empty finite V42() set
the Mult of V . [(1r - r2),(r1 + r3)] is set
((r2 * r2) + (r2 * r3)) + ((1r - r2) * (r1 + r3)) is Element of the carrier of V
the addF of V . (((r2 * r2) + (r2 * r3)),((1r - r2) * (r1 + r3))) is Element of the carrier of V
[((r2 * r2) + (r2 * r3)),((1r - r2) * (r1 + r3))] is set
{((r2 * r2) + (r2 * r3)),((1r - r2) * (r1 + r3))} is non empty finite set
{((r2 * r2) + (r2 * r3))} is non empty trivial finite 1 -element set
{{((r2 * r2) + (r2 * r3)),((1r - r2) * (r1 + r3))},{((r2 * r2) + (r2 * r3))}} is non empty finite V42() set
the addF of V . [((r2 * r2) + (r2 * r3)),((1r - r2) * (r1 + r3))] is set
(1r - r2) * r1 is Element of the carrier of V
[(1r - r2),r1] is set
{(1r - r2),r1} is non empty finite set
{{(1r - r2),r1},{(1r - r2)}} is non empty finite V42() set
the Mult of V . [(1r - r2),r1] is set
(1r - r2) * r3 is Element of the carrier of V
[(1r - r2),r3] is set
{(1r - r2),r3} is non empty finite set
{{(1r - r2),r3},{(1r - r2)}} is non empty finite V42() set
the Mult of V . [(1r - r2),r3] is set
((1r - r2) * r1) + ((1r - r2) * r3) is Element of the carrier of V
the addF of V . (((1r - r2) * r1),((1r - r2) * r3)) is Element of the carrier of V
[((1r - r2) * r1),((1r - r2) * r3)] is set
{((1r - r2) * r1),((1r - r2) * r3)} is non empty finite set
{((1r - r2) * r1)} is non empty trivial finite 1 -element set
{{((1r - r2) * r1),((1r - r2) * r3)},{((1r - r2) * r1)}} is non empty finite V42() set
the addF of V . [((1r - r2) * r1),((1r - r2) * r3)] is set
((r2 * r2) + (r2 * r3)) + (((1r - r2) * r1) + ((1r - r2) * r3)) is Element of the carrier of V
the addF of V . (((r2 * r2) + (r2 * r3)),(((1r - r2) * r1) + ((1r - r2) * r3))) is Element of the carrier of V
[((r2 * r2) + (r2 * r3)),(((1r - r2) * r1) + ((1r - r2) * r3))] is set
{((r2 * r2) + (r2 * r3)),(((1r - r2) * r1) + ((1r - r2) * r3))} is non empty finite set
{{((r2 * r2) + (r2 * r3)),(((1r - r2) * r1) + ((1r - r2) * r3))},{((r2 * r2) + (r2 * r3))}} is non empty finite V42() set
the addF of V . [((r2 * r2) + (r2 * r3)),(((1r - r2) * r1) + ((1r - r2) * r3))] is set
((r2 * r2) + (r2 * r3)) + ((1r - r2) * r1) is Element of the carrier of V
the addF of V . (((r2 * r2) + (r2 * r3)),((1r - r2) * r1)) is Element of the carrier of V
[((r2 * r2) + (r2 * r3)),((1r - r2) * r1)] is set
{((r2 * r2) + (r2 * r3)),((1r - r2) * r1)} is non empty finite set
{{((r2 * r2) + (r2 * r3)),((1r - r2) * r1)},{((r2 * r2) + (r2 * r3))}} is non empty finite V42() set
the addF of V . [((r2 * r2) + (r2 * r3)),((1r - r2) * r1)] is set
(((r2 * r2) + (r2 * r3)) + ((1r - r2) * r1)) + ((1r - r2) * r3) is Element of the carrier of V
the addF of V . ((((r2 * r2) + (r2 * r3)) + ((1r - r2) * r1)),((1r - r2) * r3)) is Element of the carrier of V
[(((r2 * r2) + (r2 * r3)) + ((1r - r2) * r1)),((1r - r2) * r3)] is set
{(((r2 * r2) + (r2 * r3)) + ((1r - r2) * r1)),((1r - r2) * r3)} is non empty finite set
{(((r2 * r2) + (r2 * r3)) + ((1r - r2) * r1))} is non empty trivial finite 1 -element set
{{(((r2 * r2) + (r2 * r3)) + ((1r - r2) * r1)),((1r - r2) * r3)},{(((r2 * r2) + (r2 * r3)) + ((1r - r2) * r1))}} is non empty finite V42() set
the addF of V . [(((r2 * r2) + (r2 * r3)) + ((1r - r2) * r1)),((1r - r2) * r3)] is set
(r2 * r2) + ((1r - r2) * r1) is Element of the carrier of V
the addF of V . ((r2 * r2),((1r - r2) * r1)) is Element of the carrier of V
[(r2 * r2),((1r - r2) * r1)] is set
{(r2 * r2),((1r - r2) * r1)} is non empty finite set
{{(r2 * r2),((1r - r2) * r1)},{(r2 * r2)}} is non empty finite V42() set
the addF of V . [(r2 * r2),((1r - r2) * r1)] is set
((r2 * r2) + ((1r - r2) * r1)) + (r2 * r3) is Element of the carrier of V
the addF of V . (((r2 * r2) + ((1r - r2) * r1)),(r2 * r3)) is Element of the carrier of V
[((r2 * r2) + ((1r - r2) * r1)),(r2 * r3)] is set
{((r2 * r2) + ((1r - r2) * r1)),(r2 * r3)} is non empty finite set
{((r2 * r2) + ((1r - r2) * r1))} is non empty trivial finite 1 -element set
{{((r2 * r2) + ((1r - r2) * r1)),(r2 * r3)},{((r2 * r2) + ((1r - r2) * r1))}} is non empty finite V42() set
the addF of V . [((r2 * r2) + ((1r - r2) * r1)),(r2 * r3)] is set
(((r2 * r2) + ((1r - r2) * r1)) + (r2 * r3)) + ((1r - r2) * r3) is Element of the carrier of V
the addF of V . ((((r2 * r2) + ((1r - r2) * r1)) + (r2 * r3)),((1r - r2) * r3)) is Element of the carrier of V
[(((r2 * r2) + ((1r - r2) * r1)) + (r2 * r3)),((1r - r2) * r3)] is set
{(((r2 * r2) + ((1r - r2) * r1)) + (r2 * r3)),((1r - r2) * r3)} is non empty finite set
{(((r2 * r2) + ((1r - r2) * r1)) + (r2 * r3))} is non empty trivial finite 1 -element set
{{(((r2 * r2) + ((1r - r2) * r1)) + (r2 * r3)),((1r - r2) * r3)},{(((r2 * r2) + ((1r - r2) * r1)) + (r2 * r3))}} is non empty finite V42() set
the addF of V . [(((r2 * r2) + ((1r - r2) * r1)) + (r2 * r3)),((1r - r2) * r3)] is set
(r2 * r3) + ((1r - r2) * r3) is Element of the carrier of V
the addF of V . ((r2 * r3),((1r - r2) * r3)) is Element of the carrier of V
[(r2 * r3),((1r - r2) * r3)] is set
{(r2 * r3),((1r - r2) * r3)} is non empty finite set
{(r2 * r3)} is non empty trivial finite 1 -element set
{{(r2 * r3),((1r - r2) * r3)},{(r2 * r3)}} is non empty finite V42() set
the addF of V . [(r2 * r3),((1r - r2) * r3)] is set
((r2 * r2) + ((1r - r2) * r1)) + ((r2 * r3) + ((1r - r2) * r3)) is Element of the carrier of V
the addF of V . (((r2 * r2) + ((1r - r2) * r1)),((r2 * r3) + ((1r - r2) * r3))) is Element of the carrier of V
[((r2 * r2) + ((1r - r2) * r1)),((r2 * r3) + ((1r - r2) * r3))] is set
{((r2 * r2) + ((1r - r2) * r1)),((r2 * r3) + ((1r - r2) * r3))} is non empty finite set
{{((r2 * r2) + ((1r - r2) * r1)),((r2 * r3) + ((1r - r2) * r3))},{((r2 * r2) + ((1r - r2) * r1))}} is non empty finite V42() set
the addF of V . [((r2 * r2) + ((1r - r2) * r1)),((r2 * r3) + ((1r - r2) * r3))] is set
r1 is complex real ext-real Element of REAL
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Element of bool the carrier of V
M - N is Element of bool the carrier of V
{ (b₁ - b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in M & b₂ in N ) } is set
SG is Element of the carrier of V
Y is Element of the carrier of V
r2 is complex set
r2 * SG is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[r2,SG] is set
{r2,SG} is non empty finite set
{r2} is non empty trivial finite 1 -element V68() set
{{r2,SG},{r2}} is non empty finite V42() set
the Mult of V . [r2,SG] is set
1r - r2 is complex set
- r2 is complex set
1r + (- r2) is complex set
(1r - r2) * Y is Element of the carrier of V
[(1r - r2),Y] is set
{(1r - r2),Y} is non empty finite set
{(1r - r2)} is non empty trivial finite 1 -element V68() set
{{(1r - r2),Y},{(1r - r2)}} is non empty finite V42() set
the Mult of V . [(1r - r2),Y] is set
(r2 * SG) + ((1r - r2) * Y) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((r2 * SG),((1r - r2) * Y)) is Element of the carrier of V
[(r2 * SG),((1r - r2) * Y)] is set
{(r2 * SG),((1r - r2) * Y)} is non empty finite set
{(r2 * SG)} is non empty trivial finite 1 -element set
{{(r2 * SG),((1r - r2) * Y)},{(r2 * SG)}} is non empty finite V42() set
the addF of V . [(r2 * SG),((1r - r2) * Y)] is set
r1 is Element of the carrier of V
r3 is Element of the carrier of V
r1 - r3 is Element of the carrier of V
- r3 is Element of the carrier of V
r1 + (- r3) is Element of the carrier of V
the addF of V . (r1,(- r3)) is Element of the carrier of V
[r1,(- r3)] is set
{r1,(- r3)} is non empty finite set
{r1} is non empty trivial finite 1 -element set
{{r1,(- r3)},{r1}} is non empty finite V42() set
the addF of V . [r1,(- r3)] is set
r2 is Element of the carrier of V
r3 is Element of the carrier of V
r2 - r3 is Element of the carrier of V
- r3 is Element of the carrier of V
r2 + (- r3) is Element of the carrier of V
the addF of V . (r2,(- r3)) is Element of the carrier of V
[r2,(- r3)] is set
{r2,(- r3)} is non empty finite set
{r2} is non empty trivial finite 1 -element set
{{r2,(- r3)},{r2}} is non empty finite V42() set
the addF of V . [r2,(- r3)] is set
r2 * r2 is Element of the carrier of V
[r2,r2] is set
{r2,r2} is non empty finite set
{{r2,r2},{r2}} is non empty finite V42() set
the Mult of V . [r2,r2] is set
r2 * r3 is Element of the carrier of V
[r2,r3] is set
{r2,r3} is non empty finite set
{{r2,r3},{r2}} is non empty finite V42() set
the Mult of V . [r2,r3] is set
(r2 * r2) - (r2 * r3) is Element of the carrier of V
- (r2 * r3) is Element of the carrier of V
(r2 * r2) + (- (r2 * r3)) is Element of the carrier of V
the addF of V . ((r2 * r2),(- (r2 * r3))) is Element of the carrier of V
[(r2 * r2),(- (r2 * r3))] is set
{(r2 * r2),(- (r2 * r3))} is non empty finite set
{(r2 * r2)} is non empty trivial finite 1 -element set
{{(r2 * r2),(- (r2 * r3))},{(r2 * r2)}} is non empty finite V42() set
the addF of V . [(r2 * r2),(- (r2 * r3))] is set
(1r - r2) * (r1 - r3) is Element of the carrier of V
[(1r - r2),(r1 - r3)] is set
{(1r - r2),(r1 - r3)} is non empty finite set
{{(1r - r2),(r1 - r3)},{(1r - r2)}} is non empty finite V42() set
the Mult of V . [(1r - r2),(r1 - r3)] is set
((r2 * r2) - (r2 * r3)) + ((1r - r2) * (r1 - r3)) is Element of the carrier of V
the addF of V . (((r2 * r2) - (r2 * r3)),((1r - r2) * (r1 - r3))) is Element of the carrier of V
[((r2 * r2) - (r2 * r3)),((1r - r2) * (r1 - r3))] is set
{((r2 * r2) - (r2 * r3)),((1r - r2) * (r1 - r3))} is non empty finite set
{((r2 * r2) - (r2 * r3))} is non empty trivial finite 1 -element set
{{((r2 * r2) - (r2 * r3)),((1r - r2) * (r1 - r3))},{((r2 * r2) - (r2 * r3))}} is non empty finite V42() set
the addF of V . [((r2 * r2) - (r2 * r3)),((1r - r2) * (r1 - r3))] is set
(1r - r2) * r1 is Element of the carrier of V
[(1r - r2),r1] is set
{(1r - r2),r1} is non empty finite set
{{(1r - r2),r1},{(1r - r2)}} is non empty finite V42() set
the Mult of V . [(1r - r2),r1] is set
(1r - r2) * r3 is Element of the carrier of V
[(1r - r2),r3] is set
{(1r - r2),r3} is non empty finite set
{{(1r - r2),r3},{(1r - r2)}} is non empty finite V42() set
the Mult of V . [(1r - r2),r3] is set
((1r - r2) * r1) - ((1r - r2) * r3) is Element of the carrier of V
- ((1r - r2) * r3) is Element of the carrier of V
((1r - r2) * r1) + (- ((1r - r2) * r3)) is Element of the carrier of V
the addF of V . (((1r - r2) * r1),(- ((1r - r2) * r3))) is Element of the carrier of V
[((1r - r2) * r1),(- ((1r - r2) * r3))] is set
{((1r - r2) * r1),(- ((1r - r2) * r3))} is non empty finite set
{((1r - r2) * r1)} is non empty trivial finite 1 -element set
{{((1r - r2) * r1),(- ((1r - r2) * r3))},{((1r - r2) * r1)}} is non empty finite V42() set
the addF of V . [((1r - r2) * r1),(- ((1r - r2) * r3))] is set
((r2 * r2) - (r2 * r3)) + (((1r - r2) * r1) - ((1r - r2) * r3)) is Element of the carrier of V
the addF of V . (((r2 * r2) - (r2 * r3)),(((1r - r2) * r1) - ((1r - r2) * r3))) is Element of the carrier of V
[((r2 * r2) - (r2 * r3)),(((1r - r2) * r1) - ((1r - r2) * r3))] is set
{((r2 * r2) - (r2 * r3)),(((1r - r2) * r1) - ((1r - r2) * r3))} is non empty finite set
{{((r2 * r2) - (r2 * r3)),(((1r - r2) * r1) - ((1r - r2) * r3))},{((r2 * r2) - (r2 * r3))}} is non empty finite V42() set
the addF of V . [((r2 * r2) - (r2 * r3)),(((1r - r2) * r1) - ((1r - r2) * r3))] is set
((r2 * r2) - (r2 * r3)) + ((1r - r2) * r1) is Element of the carrier of V
the addF of V . (((r2 * r2) - (r2 * r3)),((1r - r2) * r1)) is Element of the carrier of V
[((r2 * r2) - (r2 * r3)),((1r - r2) * r1)] is set
{((r2 * r2) - (r2 * r3)),((1r - r2) * r1)} is non empty finite set
{{((r2 * r2) - (r2 * r3)),((1r - r2) * r1)},{((r2 * r2) - (r2 * r3))}} is non empty finite V42() set
the addF of V . [((r2 * r2) - (r2 * r3)),((1r - r2) * r1)] is set
(((r2 * r2) - (r2 * r3)) + ((1r - r2) * r1)) - ((1r - r2) * r3) is Element of the carrier of V
(((r2 * r2) - (r2 * r3)) + ((1r - r2) * r1)) + (- ((1r - r2) * r3)) is Element of the carrier of V
the addF of V . ((((r2 * r2) - (r2 * r3)) + ((1r - r2) * r1)),(- ((1r - r2) * r3))) is Element of the carrier of V
[(((r2 * r2) - (r2 * r3)) + ((1r - r2) * r1)),(- ((1r - r2) * r3))] is set
{(((r2 * r2) - (r2 * r3)) + ((1r - r2) * r1)),(- ((1r - r2) * r3))} is non empty finite set
{(((r2 * r2) - (r2 * r3)) + ((1r - r2) * r1))} is non empty trivial finite 1 -element set
{{(((r2 * r2) - (r2 * r3)) + ((1r - r2) * r1)),(- ((1r - r2) * r3))},{(((r2 * r2) - (r2 * r3)) + ((1r - r2) * r1))}} is non empty finite V42() set
the addF of V . [(((r2 * r2) - (r2 * r3)) + ((1r - r2) * r1)),(- ((1r - r2) * r3))] is set
(r2 * r3) - ((1r - r2) * r1) is Element of the carrier of V
- ((1r - r2) * r1) is Element of the carrier of V
(r2 * r3) + (- ((1r - r2) * r1)) is Element of the carrier of V
the addF of V . ((r2 * r3),(- ((1r - r2) * r1))) is Element of the carrier of V
[(r2 * r3),(- ((1r - r2) * r1))] is set
{(r2 * r3),(- ((1r - r2) * r1))} is non empty finite set
{(r2 * r3)} is non empty trivial finite 1 -element set
{{(r2 * r3),(- ((1r - r2) * r1))},{(r2 * r3)}} is non empty finite V42() set
the addF of V . [(r2 * r3),(- ((1r - r2) * r1))] is set
(r2 * r2) - ((r2 * r3) - ((1r - r2) * r1)) is Element of the carrier of V
- ((r2 * r3) - ((1r - r2) * r1)) is Element of the carrier of V
(r2 * r2) + (- ((r2 * r3) - ((1r - r2) * r1))) is Element of the carrier of V
the addF of V . ((r2 * r2),(- ((r2 * r3) - ((1r - r2) * r1)))) is Element of the carrier of V
[(r2 * r2),(- ((r2 * r3) - ((1r - r2) * r1)))] is set
{(r2 * r2),(- ((r2 * r3) - ((1r - r2) * r1)))} is non empty finite set
{{(r2 * r2),(- ((r2 * r3) - ((1r - r2) * r1)))},{(r2 * r2)}} is non empty finite V42() set
the addF of V . [(r2 * r2),(- ((r2 * r3) - ((1r - r2) * r1)))] is set
((r2 * r2) - ((r2 * r3) - ((1r - r2) * r1))) - ((1r - r2) * r3) is Element of the carrier of V
((r2 * r2) - ((r2 * r3) - ((1r - r2) * r1))) + (- ((1r - r2) * r3)) is Element of the carrier of V
the addF of V . (((r2 * r2) - ((r2 * r3) - ((1r - r2) * r1))),(- ((1r - r2) * r3))) is Element of the carrier of V
[((r2 * r2) - ((r2 * r3) - ((1r - r2) * r1))),(- ((1r - r2) * r3))] is set
{((r2 * r2) - ((r2 * r3) - ((1r - r2) * r1))),(- ((1r - r2) * r3))} is non empty finite set
{((r2 * r2) - ((r2 * r3) - ((1r - r2) * r1)))} is non empty trivial finite 1 -element set
{{((r2 * r2) - ((r2 * r3) - ((1r - r2) * r1))),(- ((1r - r2) * r3))},{((r2 * r2) - ((r2 * r3) - ((1r - r2) * r1)))}} is non empty finite V42() set
the addF of V . [((r2 * r2) - ((r2 * r3) - ((1r - r2) * r1))),(- ((1r - r2) * r3))] is set
((1r - r2) * r1) + (- (r2 * r3)) is Element of the carrier of V
the addF of V . (((1r - r2) * r1),(- (r2 * r3))) is Element of the carrier of V
[((1r - r2) * r1),(- (r2 * r3))] is set
{((1r - r2) * r1),(- (r2 * r3))} is non empty finite set
{{((1r - r2) * r1),(- (r2 * r3))},{((1r - r2) * r1)}} is non empty finite V42() set
the addF of V . [((1r - r2) * r1),(- (r2 * r3))] is set
(r2 * r2) + (((1r - r2) * r1) + (- (r2 * r3))) is Element of the carrier of V
the addF of V . ((r2 * r2),(((1r - r2) * r1) + (- (r2 * r3)))) is Element of the carrier of V
[(r2 * r2),(((1r - r2) * r1) + (- (r2 * r3)))] is set
{(r2 * r2),(((1r - r2) * r1) + (- (r2 * r3)))} is non empty finite set
{{(r2 * r2),(((1r - r2) * r1) + (- (r2 * r3)))},{(r2 * r2)}} is non empty finite V42() set
the addF of V . [(r2 * r2),(((1r - r2) * r1) + (- (r2 * r3)))] is set
((r2 * r2) + (((1r - r2) * r1) + (- (r2 * r3)))) - ((1r - r2) * r3) is Element of the carrier of V
((r2 * r2) + (((1r - r2) * r1) + (- (r2 * r3)))) + (- ((1r - r2) * r3)) is Element of the carrier of V
the addF of V . (((r2 * r2) + (((1r - r2) * r1) + (- (r2 * r3)))),(- ((1r - r2) * r3))) is Element of the carrier of V
[((r2 * r2) + (((1r - r2) * r1) + (- (r2 * r3)))),(- ((1r - r2) * r3))] is set
{((r2 * r2) + (((1r - r2) * r1) + (- (r2 * r3)))),(- ((1r - r2) * r3))} is non empty finite set
{((r2 * r2) + (((1r - r2) * r1) + (- (r2 * r3))))} is non empty trivial finite 1 -element set
{{((r2 * r2) + (((1r - r2) * r1) + (- (r2 * r3)))),(- ((1r - r2) * r3))},{((r2 * r2) + (((1r - r2) * r1) + (- (r2 * r3))))}} is non empty finite V42() set
the addF of V . [((r2 * r2) + (((1r - r2) * r1) + (- (r2 * r3)))),(- ((1r - r2) * r3))] is set
(r2 * r2) + ((1r - r2) * r1) is Element of the carrier of V
the addF of V . ((r2 * r2),((1r - r2) * r1)) is Element of the carrier of V
[(r2 * r2),((1r - r2) * r1)] is set
{(r2 * r2),((1r - r2) * r1)} is non empty finite set
{{(r2 * r2),((1r - r2) * r1)},{(r2 * r2)}} is non empty finite V42() set
the addF of V . [(r2 * r2),((1r - r2) * r1)] is set
((r2 * r2) + ((1r - r2) * r1)) + (- (r2 * r3)) is Element of the carrier of V
the addF of V . (((r2 * r2) + ((1r - r2) * r1)),(- (r2 * r3))) is Element of the carrier of V
[((r2 * r2) + ((1r - r2) * r1)),(- (r2 * r3))] is set
{((r2 * r2) + ((1r - r2) * r1)),(- (r2 * r3))} is non empty finite set
{((r2 * r2) + ((1r - r2) * r1))} is non empty trivial finite 1 -element set
{{((r2 * r2) + ((1r - r2) * r1)),(- (r2 * r3))},{((r2 * r2) + ((1r - r2) * r1))}} is non empty finite V42() set
the addF of V . [((r2 * r2) + ((1r - r2) * r1)),(- (r2 * r3))] is set
(((r2 * r2) + ((1r - r2) * r1)) + (- (r2 * r3))) - ((1r - r2) * r3) is Element of the carrier of V
(((r2 * r2) + ((1r - r2) * r1)) + (- (r2 * r3))) + (- ((1r - r2) * r3)) is Element of the carrier of V
the addF of V . ((((r2 * r2) + ((1r - r2) * r1)) + (- (r2 * r3))),(- ((1r - r2) * r3))) is Element of the carrier of V
[(((r2 * r2) + ((1r - r2) * r1)) + (- (r2 * r3))),(- ((1r - r2) * r3))] is set
{(((r2 * r2) + ((1r - r2) * r1)) + (- (r2 * r3))),(- ((1r - r2) * r3))} is non empty finite set
{(((r2 * r2) + ((1r - r2) * r1)) + (- (r2 * r3)))} is non empty trivial finite 1 -element set
{{(((r2 * r2) + ((1r - r2) * r1)) + (- (r2 * r3))),(- ((1r - r2) * r3))},{(((r2 * r2) + ((1r - r2) * r1)) + (- (r2 * r3)))}} is non empty finite V42() set
the addF of V . [(((r2 * r2) + ((1r - r2) * r1)) + (- (r2 * r3))),(- ((1r - r2) * r3))] is set
(- (r2 * r3)) - ((1r - r2) * r3) is Element of the carrier of V
(- (r2 * r3)) + (- ((1r - r2) * r3)) is Element of the carrier of V
the addF of V . ((- (r2 * r3)),(- ((1r - r2) * r3))) is Element of the carrier of V
[(- (r2 * r3)),(- ((1r - r2) * r3))] is set
{(- (r2 * r3)),(- ((1r - r2) * r3))} is non empty finite set
{(- (r2 * r3))} is non empty trivial finite 1 -element set
{{(- (r2 * r3)),(- ((1r - r2) * r3))},{(- (r2 * r3))}} is non empty finite V42() set
the addF of V . [(- (r2 * r3)),(- ((1r - r2) * r3))] is set
((r2 * r2) + ((1r - r2) * r1)) + ((- (r2 * r3)) - ((1r - r2) * r3)) is Element of the carrier of V
the addF of V . (((r2 * r2) + ((1r - r2) * r1)),((- (r2 * r3)) - ((1r - r2) * r3))) is Element of the carrier of V
[((r2 * r2) + ((1r - r2) * r1)),((- (r2 * r3)) - ((1r - r2) * r3))] is set
{((r2 * r2) + ((1r - r2) * r1)),((- (r2 * r3)) - ((1r - r2) * r3))} is non empty finite set
{{((r2 * r2) + ((1r - r2) * r1)),((- (r2 * r3)) - ((1r - r2) * r3))},{((r2 * r2) + ((1r - r2) * r1))}} is non empty finite V42() set
the addF of V . [((r2 * r2) + ((1r - r2) * r1)),((- (r2 * r3)) - ((1r - r2) * r3))] is set
(r2 * r3) + ((1r - r2) * r3) is Element of the carrier of V
the addF of V . ((r2 * r3),((1r - r2) * r3)) is Element of the carrier of V
[(r2 * r3),((1r - r2) * r3)] is set
{(r2 * r3),((1r - r2) * r3)} is non empty finite set
{{(r2 * r3),((1r - r2) * r3)},{(r2 * r3)}} is non empty finite V42() set
the addF of V . [(r2 * r3),((1r - r2) * r3)] is set
((r2 * r2) + ((1r - r2) * r1)) - ((r2 * r3) + ((1r - r2) * r3)) is Element of the carrier of V
- ((r2 * r3) + ((1r - r2) * r3)) is Element of the carrier of V
((r2 * r2) + ((1r - r2) * r1)) + (- ((r2 * r3) + ((1r - r2) * r3))) is Element of the carrier of V
the addF of V . (((r2 * r2) + ((1r - r2) * r1)),(- ((r2 * r3) + ((1r - r2) * r3)))) is Element of the carrier of V
[((r2 * r2) + ((1r - r2) * r1)),(- ((r2 * r3) + ((1r - r2) * r3)))] is set
{((r2 * r2) + ((1r - r2) * r1)),(- ((r2 * r3) + ((1r - r2) * r3)))} is non empty finite set
{{((r2 * r2) + ((1r - r2) * r1)),(- ((r2 * r3) + ((1r - r2) * r3)))},{((r2 * r2) + ((1r - r2) * r1))}} is non empty finite V42() set
the addF of V . [((r2 * r2) + ((1r - r2) * r1)),(- ((r2 * r3) + ((1r - r2) * r3)))] is set
r1 is complex real ext-real Element of REAL
V is non empty CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is complex set
(V,M,N) is Element of bool the carrier of V
{ (N * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
1r - N is complex set
- N is complex set
1r + (- N) is complex set
(V,M,(1r - N)) is Element of bool the carrier of V
{ ((1r - N) * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
(V,M,N) + (V,M,(1r - N)) is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in (V,M,N) & b₂ in (V,M,(1r - N)) ) } is set
SG is Element of the carrier of V
Y is Element of the carrier of V
r2 is Element of the carrier of V
Y + r2 is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (Y,r2) is Element of the carrier of V
[Y,r2] is set
{Y,r2} is non empty finite set
{Y} is non empty trivial finite 1 -element set
{{Y,r2},{Y}} is non empty finite V42() set
the addF of V . [Y,r2] is set
r1 is Element of the carrier of V
N * r1 is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[N,r1] is set
{N,r1} is non empty finite set
{N} is non empty trivial finite 1 -element V68() set
{{N,r1},{N}} is non empty finite V42() set
the Mult of V . [N,r1] is set
r3 is Element of the carrier of V
(1r - N) * r3 is Element of the carrier of V
[(1r - N),r3] is set
{(1r - N),r3} is non empty finite set
{(1r - N)} is non empty trivial finite 1 -element V68() set
{{(1r - N),r3},{(1r - N)}} is non empty finite V42() set
the Mult of V . [(1r - N),r3] is set
r2 is complex real ext-real Element of REAL
N is Element of the carrier of V
SG is Element of the carrier of V
Y is complex set
Y * N is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[Y,N] is set
{Y,N} is non empty finite set
{Y} is non empty trivial finite 1 -element V68() set
{{Y,N},{Y}} is non empty finite V42() set
the Mult of V . [Y,N] is set
1r - Y is complex set
- Y is complex set
1r + (- Y) is complex set
(1r - Y) * SG is Element of the carrier of V
[(1r - Y),SG] is set
{(1r - Y),SG} is non empty finite set
{(1r - Y)} is non empty trivial finite 1 -element V68() set
{{(1r - Y),SG},{(1r - Y)}} is non empty finite V42() set
the Mult of V . [(1r - Y),SG] is set
(Y * N) + ((1r - Y) * SG) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((Y * N),((1r - Y) * SG)) is Element of the carrier of V
[(Y * N),((1r - Y) * SG)] is set
{(Y * N),((1r - Y) * SG)} is non empty finite set
{(Y * N)} is non empty trivial finite 1 -element set
{{(Y * N),((1r - Y) * SG)},{(Y * N)}} is non empty finite V42() set
the addF of V . [(Y * N),((1r - Y) * SG)] is set
(V,M,Y) is Element of bool the carrier of V
{ (Y * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
(V,M,(1r - Y)) is Element of bool the carrier of V
{ ((1r - Y) * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
(V,M,Y) + (V,M,(1r - Y)) is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in (V,M,Y) & b₂ in (V,M,(1r - Y)) ) } is set
r2 is complex real ext-real Element of REAL
N is complex set
SG is complex real ext-real Element of REAL
(V,M,N) is Element of bool the carrier of V
{ (N * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
1r - N is complex set
- N is complex set
1r + (- N) is complex set
(V,M,(1r - N)) is Element of bool the carrier of V
{ ((1r - N) * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
(V,M,N) + (V,M,(1r - N)) is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in (V,M,N) & b₂ in (V,M,(1r - N)) ) } is set
Y is complex set
r2 is complex real ext-real Element of REAL
(V,M,Y) is Element of bool the carrier of V
{ (Y * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
1r - Y is complex set
- Y is complex set
1r + (- Y) is complex set
(V,M,(1r - Y)) is Element of bool the carrier of V
{ ((1r - Y) * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
(V,M,Y) + (V,M,(1r - Y)) is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in (V,M,Y) & b₂ in (V,M,(1r - Y)) ) } is set
V is non empty Abelian CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is complex set
1r - N is complex set
- N is complex set
1r + (- N) is complex set
(V,M,(1r - N)) is Element of bool the carrier of V
{ ((1r - N) * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
(V,M,N) is Element of bool the carrier of V
{ (N * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
(V,M,(1r - N)) + (V,M,N) is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in (V,M,(1r - N)) & b₂ in (V,M,N) ) } is set
SG is Element of the carrier of V
Y is Element of the carrier of V
r2 is Element of the carrier of V
Y + r2 is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (Y,r2) is Element of the carrier of V
[Y,r2] is set
{Y,r2} is non empty finite set
{Y} is non empty trivial finite 1 -element set
{{Y,r2},{Y}} is non empty finite V42() set
the addF of V . [Y,r2] is set
r1 is Element of the carrier of V
(1r - N) * r1 is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(1r - N),r1] is set
{(1r - N),r1} is non empty finite set
{(1r - N)} is non empty trivial finite 1 -element V68() set
{{(1r - N),r1},{(1r - N)}} is non empty finite V42() set
the Mult of V . [(1r - N),r1] is set
r3 is Element of the carrier of V
N * r3 is Element of the carrier of V
[N,r3] is set
{N,r3} is non empty finite set
{N} is non empty trivial finite 1 -element V68() set
{{N,r3},{N}} is non empty finite V42() set
the Mult of V . [N,r3] is set
r2 is complex real ext-real Element of REAL
V is non empty Abelian add-associative vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Element of bool the carrier of V
SG is complex set
(V,M,SG) is Element of bool the carrier of V
{ (SG * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
1r - SG is complex set
- SG is complex set
1r + (- SG) is complex set
(V,N,(1r - SG)) is Element of bool the carrier of V
{ ((1r - SG) * b₁) where b₁ is Element of the carrier of V : b₁ in N } is set
(V,M,SG) + (V,N,(1r - SG)) is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in (V,M,SG) & b₂ in (V,N,(1r - SG)) ) } is set
Y is Element of the carrier of V
r2 is Element of the carrier of V
r1 is complex set
r1 * Y is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[r1,Y] is set
{r1,Y} is non empty finite set
{r1} is non empty trivial finite 1 -element V68() set
{{r1,Y},{r1}} is non empty finite V42() set
the Mult of V . [r1,Y] is set
1r - r1 is complex set
- r1 is complex set
1r + (- r1) is complex set
(1r - r1) * r2 is Element of the carrier of V
[(1r - r1),r2] is set
{(1r - r1),r2} is non empty finite set
{(1r - r1)} is non empty trivial finite 1 -element V68() set
{{(1r - r1),r2},{(1r - r1)}} is non empty finite V42() set
the Mult of V . [(1r - r1),r2] is set
(r1 * Y) + ((1r - r1) * r2) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((r1 * Y),((1r - r1) * r2)) is Element of the carrier of V
[(r1 * Y),((1r - r1) * r2)] is set
{(r1 * Y),((1r - r1) * r2)} is non empty finite set
{(r1 * Y)} is non empty trivial finite 1 -element set
{{(r1 * Y),((1r - r1) * r2)},{(r1 * Y)}} is non empty finite V42() set
the addF of V . [(r1 * Y),((1r - r1) * r2)] is set
r3 is Element of the carrier of V
r2 is Element of the carrier of V
r3 + r2 is Element of the carrier of V
the addF of V . (r3,r2) is Element of the carrier of V
[r3,r2] is set
{r3,r2} is non empty finite set
{r3} is non empty trivial finite 1 -element set
{{r3,r2},{r3}} is non empty finite V42() set
the addF of V . [r3,r2] is set
r3 is Element of the carrier of V
r1 is Element of the carrier of V
r3 + r1 is Element of the carrier of V
the addF of V . (r3,r1) is Element of the carrier of V
[r3,r1] is set
{r3,r1} is non empty finite set
{r3} is non empty trivial finite 1 -element set
{{r3,r1},{r3}} is non empty finite V42() set
the addF of V . [r3,r1] is set
u2 is Element of the carrier of V
SG * u2 is Element of the carrier of V
[SG,u2] is set
{SG,u2} is non empty finite set
{SG} is non empty trivial finite 1 -element V68() set
{{SG,u2},{SG}} is non empty finite V42() set
the Mult of V . [SG,u2] is set
y1 is Element of the carrier of V
SG * y1 is Element of the carrier of V
[SG,y1] is set
{SG,y1} is non empty finite set
{{SG,y1},{SG}} is non empty finite V42() set
the Mult of V . [SG,y1] is set
r1 * r3 is Element of the carrier of V
[r1,r3] is set
{r1,r3} is non empty finite set
{{r1,r3},{r1}} is non empty finite V42() set
the Mult of V . [r1,r3] is set
(1r - r1) * r3 is Element of the carrier of V
[(1r - r1),r3] is set
{(1r - r1),r3} is non empty finite set
{{(1r - r1),r3},{(1r - r1)}} is non empty finite V42() set
the Mult of V . [(1r - r1),r3] is set
(r1 * r3) + ((1r - r1) * r3) is Element of the carrier of V
the addF of V . ((r1 * r3),((1r - r1) * r3)) is Element of the carrier of V
[(r1 * r3),((1r - r1) * r3)] is set
{(r1 * r3),((1r - r1) * r3)} is non empty finite set
{(r1 * r3)} is non empty trivial finite 1 -element set
{{(r1 * r3),((1r - r1) * r3)},{(r1 * r3)}} is non empty finite V42() set
the addF of V . [(r1 * r3),((1r - r1) * r3)] is set
r1 * SG is complex set
(r1 * SG) * y1 is Element of the carrier of V
[(r1 * SG),y1] is set
{(r1 * SG),y1} is non empty finite set
{(r1 * SG)} is non empty trivial finite 1 -element V68() set
{{(r1 * SG),y1},{(r1 * SG)}} is non empty finite V42() set
the Mult of V . [(r1 * SG),y1] is set
(1r - r1) * (SG * u2) is Element of the carrier of V
[(1r - r1),(SG * u2)] is set
{(1r - r1),(SG * u2)} is non empty finite set
{{(1r - r1),(SG * u2)},{(1r - r1)}} is non empty finite V42() set
the Mult of V . [(1r - r1),(SG * u2)] is set
((r1 * SG) * y1) + ((1r - r1) * (SG * u2)) is Element of the carrier of V
the addF of V . (((r1 * SG) * y1),((1r - r1) * (SG * u2))) is Element of the carrier of V
[((r1 * SG) * y1),((1r - r1) * (SG * u2))] is set
{((r1 * SG) * y1),((1r - r1) * (SG * u2))} is non empty finite set
{((r1 * SG) * y1)} is non empty trivial finite 1 -element set
{{((r1 * SG) * y1),((1r - r1) * (SG * u2))},{((r1 * SG) * y1)}} is non empty finite V42() set
the addF of V . [((r1 * SG) * y1),((1r - r1) * (SG * u2))] is set
(1r - r1) * SG is complex set
((1r - r1) * SG) * u2 is Element of the carrier of V
[((1r - r1) * SG),u2] is set
{((1r - r1) * SG),u2} is non empty finite set
{((1r - r1) * SG)} is non empty trivial finite 1 -element V68() set
{{((1r - r1) * SG),u2},{((1r - r1) * SG)}} is non empty finite V42() set
the Mult of V . [((1r - r1) * SG),u2] is set
((r1 * SG) * y1) + (((1r - r1) * SG) * u2) is Element of the carrier of V
the addF of V . (((r1 * SG) * y1),(((1r - r1) * SG) * u2)) is Element of the carrier of V
[((r1 * SG) * y1),(((1r - r1) * SG) * u2)] is set
{((r1 * SG) * y1),(((1r - r1) * SG) * u2)} is non empty finite set
{{((r1 * SG) * y1),(((1r - r1) * SG) * u2)},{((r1 * SG) * y1)}} is non empty finite V42() set
the addF of V . [((r1 * SG) * y1),(((1r - r1) * SG) * u2)] is set
r1 * y1 is Element of the carrier of V
[r1,y1] is set
{r1,y1} is non empty finite set
{{r1,y1},{r1}} is non empty finite V42() set
the Mult of V . [r1,y1] is set
SG * (r1 * y1) is Element of the carrier of V
[SG,(r1 * y1)] is set
{SG,(r1 * y1)} is non empty finite set
{{SG,(r1 * y1)},{SG}} is non empty finite V42() set
the Mult of V . [SG,(r1 * y1)] is set
(SG * (r1 * y1)) + (((1r - r1) * SG) * u2) is Element of the carrier of V
the addF of V . ((SG * (r1 * y1)),(((1r - r1) * SG) * u2)) is Element of the carrier of V
[(SG * (r1 * y1)),(((1r - r1) * SG) * u2)] is set
{(SG * (r1 * y1)),(((1r - r1) * SG) * u2)} is non empty finite set
{(SG * (r1 * y1))} is non empty trivial finite 1 -element set
{{(SG * (r1 * y1)),(((1r - r1) * SG) * u2)},{(SG * (r1 * y1))}} is non empty finite V42() set
the addF of V . [(SG * (r1 * y1)),(((1r - r1) * SG) * u2)] is set
(1r - r1) * u2 is Element of the carrier of V
[(1r - r1),u2] is set
{(1r - r1),u2} is non empty finite set
{{(1r - r1),u2},{(1r - r1)}} is non empty finite V42() set
the Mult of V . [(1r - r1),u2] is set
SG * ((1r - r1) * u2) is Element of the carrier of V
[SG,((1r - r1) * u2)] is set
{SG,((1r - r1) * u2)} is non empty finite set
{{SG,((1r - r1) * u2)},{SG}} is non empty finite V42() set
the Mult of V . [SG,((1r - r1) * u2)] is set
(SG * (r1 * y1)) + (SG * ((1r - r1) * u2)) is Element of the carrier of V
the addF of V . ((SG * (r1 * y1)),(SG * ((1r - r1) * u2))) is Element of the carrier of V
[(SG * (r1 * y1)),(SG * ((1r - r1) * u2))] is set
{(SG * (r1 * y1)),(SG * ((1r - r1) * u2))} is non empty finite set
{{(SG * (r1 * y1)),(SG * ((1r - r1) * u2))},{(SG * (r1 * y1))}} is non empty finite V42() set
the addF of V . [(SG * (r1 * y1)),(SG * ((1r - r1) * u2))] is set
(r1 * y1) + ((1r - r1) * u2) is Element of the carrier of V
the addF of V . ((r1 * y1),((1r - r1) * u2)) is Element of the carrier of V
[(r1 * y1),((1r - r1) * u2)] is set
{(r1 * y1),((1r - r1) * u2)} is non empty finite set
{(r1 * y1)} is non empty trivial finite 1 -element set
{{(r1 * y1),((1r - r1) * u2)},{(r1 * y1)}} is non empty finite V42() set
the addF of V . [(r1 * y1),((1r - r1) * u2)] is set
SG * ((r1 * y1) + ((1r - r1) * u2)) is Element of the carrier of V
[SG,((r1 * y1) + ((1r - r1) * u2))] is set
{SG,((r1 * y1) + ((1r - r1) * u2))} is non empty finite set
{{SG,((r1 * y1) + ((1r - r1) * u2))},{SG}} is non empty finite V42() set
the Mult of V . [SG,((r1 * y1) + ((1r - r1) * u2))] is set
x1 is Element of the carrier of V
(1r - SG) * x1 is Element of the carrier of V
[(1r - SG),x1] is set
{(1r - SG),x1} is non empty finite set
{(1r - SG)} is non empty trivial finite 1 -element V68() set
{{(1r - SG),x1},{(1r - SG)}} is non empty finite V42() set
the Mult of V . [(1r - SG),x1] is set
y2 is Element of the carrier of V
(1r - SG) * y2 is Element of the carrier of V
[(1r - SG),y2] is set
{(1r - SG),y2} is non empty finite set
{{(1r - SG),y2},{(1r - SG)}} is non empty finite V42() set
the Mult of V . [(1r - SG),y2] is set
r1 * r1 is Element of the carrier of V
[r1,r1] is set
{r1,r1} is non empty finite set
{{r1,r1},{r1}} is non empty finite V42() set
the Mult of V . [r1,r1] is set
(1r - r1) * r2 is Element of the carrier of V
[(1r - r1),r2] is set
{(1r - r1),r2} is non empty finite set
{{(1r - r1),r2},{(1r - r1)}} is non empty finite V42() set
the Mult of V . [(1r - r1),r2] is set
(r1 * r1) + ((1r - r1) * r2) is Element of the carrier of V
the addF of V . ((r1 * r1),((1r - r1) * r2)) is Element of the carrier of V
[(r1 * r1),((1r - r1) * r2)] is set
{(r1 * r1),((1r - r1) * r2)} is non empty finite set
{(r1 * r1)} is non empty trivial finite 1 -element set
{{(r1 * r1),((1r - r1) * r2)},{(r1 * r1)}} is non empty finite V42() set
the addF of V . [(r1 * r1),((1r - r1) * r2)] is set
r1 * (1r - SG) is complex set
(r1 * (1r - SG)) * y2 is Element of the carrier of V
[(r1 * (1r - SG)),y2] is set
{(r1 * (1r - SG)),y2} is non empty finite set
{(r1 * (1r - SG))} is non empty trivial finite 1 -element V68() set
{{(r1 * (1r - SG)),y2},{(r1 * (1r - SG))}} is non empty finite V42() set
the Mult of V . [(r1 * (1r - SG)),y2] is set
(1r - r1) * ((1r - SG) * x1) is Element of the carrier of V
[(1r - r1),((1r - SG) * x1)] is set
{(1r - r1),((1r - SG) * x1)} is non empty finite set
{{(1r - r1),((1r - SG) * x1)},{(1r - r1)}} is non empty finite V42() set
the Mult of V . [(1r - r1),((1r - SG) * x1)] is set
((r1 * (1r - SG)) * y2) + ((1r - r1) * ((1r - SG) * x1)) is Element of the carrier of V
the addF of V . (((r1 * (1r - SG)) * y2),((1r - r1) * ((1r - SG) * x1))) is Element of the carrier of V
[((r1 * (1r - SG)) * y2),((1r - r1) * ((1r - SG) * x1))] is set
{((r1 * (1r - SG)) * y2),((1r - r1) * ((1r - SG) * x1))} is non empty finite set
{((r1 * (1r - SG)) * y2)} is non empty trivial finite 1 -element set
{{((r1 * (1r - SG)) * y2),((1r - r1) * ((1r - SG) * x1))},{((r1 * (1r - SG)) * y2)}} is non empty finite V42() set
the addF of V . [((r1 * (1r - SG)) * y2),((1r - r1) * ((1r - SG) * x1))] is set
(1r - r1) * (1r - SG) is complex set
((1r - r1) * (1r - SG)) * x1 is Element of the carrier of V
[((1r - r1) * (1r - SG)),x1] is set
{((1r - r1) * (1r - SG)),x1} is non empty finite set
{((1r - r1) * (1r - SG))} is non empty trivial finite 1 -element V68() set
{{((1r - r1) * (1r - SG)),x1},{((1r - r1) * (1r - SG))}} is non empty finite V42() set
the Mult of V . [((1r - r1) * (1r - SG)),x1] is set
((r1 * (1r - SG)) * y2) + (((1r - r1) * (1r - SG)) * x1) is Element of the carrier of V
the addF of V . (((r1 * (1r - SG)) * y2),(((1r - r1) * (1r - SG)) * x1)) is Element of the carrier of V
[((r1 * (1r - SG)) * y2),(((1r - r1) * (1r - SG)) * x1)] is set
{((r1 * (1r - SG)) * y2),(((1r - r1) * (1r - SG)) * x1)} is non empty finite set
{{((r1 * (1r - SG)) * y2),(((1r - r1) * (1r - SG)) * x1)},{((r1 * (1r - SG)) * y2)}} is non empty finite V42() set
the addF of V . [((r1 * (1r - SG)) * y2),(((1r - r1) * (1r - SG)) * x1)] is set
r1 * y2 is Element of the carrier of V
[r1,y2] is set
{r1,y2} is non empty finite set
{{r1,y2},{r1}} is non empty finite V42() set
the Mult of V . [r1,y2] is set
(1r - SG) * (r1 * y2) is Element of the carrier of V
[(1r - SG),(r1 * y2)] is set
{(1r - SG),(r1 * y2)} is non empty finite set
{{(1r - SG),(r1 * y2)},{(1r - SG)}} is non empty finite V42() set
the Mult of V . [(1r - SG),(r1 * y2)] is set
((1r - SG) * (r1 * y2)) + (((1r - r1) * (1r - SG)) * x1) is Element of the carrier of V
the addF of V . (((1r - SG) * (r1 * y2)),(((1r - r1) * (1r - SG)) * x1)) is Element of the carrier of V
[((1r - SG) * (r1 * y2)),(((1r - r1) * (1r - SG)) * x1)] is set
{((1r - SG) * (r1 * y2)),(((1r - r1) * (1r - SG)) * x1)} is non empty finite set
{((1r - SG) * (r1 * y2))} is non empty trivial finite 1 -element set
{{((1r - SG) * (r1 * y2)),(((1r - r1) * (1r - SG)) * x1)},{((1r - SG) * (r1 * y2))}} is non empty finite V42() set
the addF of V . [((1r - SG) * (r1 * y2)),(((1r - r1) * (1r - SG)) * x1)] is set
(1r - r1) * x1 is Element of the carrier of V
[(1r - r1),x1] is set
{(1r - r1),x1} is non empty finite set
{{(1r - r1),x1},{(1r - r1)}} is non empty finite V42() set
the Mult of V . [(1r - r1),x1] is set
(1r - SG) * ((1r - r1) * x1) is Element of the carrier of V
[(1r - SG),((1r - r1) * x1)] is set
{(1r - SG),((1r - r1) * x1)} is non empty finite set
{{(1r - SG),((1r - r1) * x1)},{(1r - SG)}} is non empty finite V42() set
the Mult of V . [(1r - SG),((1r - r1) * x1)] is set
((1r - SG) * (r1 * y2)) + ((1r - SG) * ((1r - r1) * x1)) is Element of the carrier of V
the addF of V . (((1r - SG) * (r1 * y2)),((1r - SG) * ((1r - r1) * x1))) is Element of the carrier of V
[((1r - SG) * (r1 * y2)),((1r - SG) * ((1r - r1) * x1))] is set
{((1r - SG) * (r1 * y2)),((1r - SG) * ((1r - r1) * x1))} is non empty finite set
{{((1r - SG) * (r1 * y2)),((1r - SG) * ((1r - r1) * x1))},{((1r - SG) * (r1 * y2))}} is non empty finite V42() set
the addF of V . [((1r - SG) * (r1 * y2)),((1r - SG) * ((1r - r1) * x1))] is set
(r1 * y2) + ((1r - r1) * x1) is Element of the carrier of V
the addF of V . ((r1 * y2),((1r - r1) * x1)) is Element of the carrier of V
[(r1 * y2),((1r - r1) * x1)] is set
{(r1 * y2),((1r - r1) * x1)} is non empty finite set
{(r1 * y2)} is non empty trivial finite 1 -element set
{{(r1 * y2),((1r - r1) * x1)},{(r1 * y2)}} is non empty finite V42() set
the addF of V . [(r1 * y2),((1r - r1) * x1)] is set
(1r - SG) * ((r1 * y2) + ((1r - r1) * x1)) is Element of the carrier of V
[(1r - SG),((r1 * y2) + ((1r - r1) * x1))] is set
{(1r - SG),((r1 * y2) + ((1r - r1) * x1))} is non empty finite set
{{(1r - SG),((r1 * y2) + ((1r - r1) * x1))},{(1r - SG)}} is non empty finite V42() set
the Mult of V . [(1r - SG),((r1 * y2) + ((1r - r1) * x1))] is set
x2 is complex real ext-real Element of REAL
x2 is complex real ext-real Element of REAL
(r1 * Y) + ((1r - r1) * r2) is Element of the carrier of V
(r1 * r3) + (r1 * r1) is Element of the carrier of V
the addF of V . ((r1 * r3),(r1 * r1)) is Element of the carrier of V
[(r1 * r3),(r1 * r1)] is set
{(r1 * r3),(r1 * r1)} is non empty finite set
{{(r1 * r3),(r1 * r1)},{(r1 * r3)}} is non empty finite V42() set
the addF of V . [(r1 * r3),(r1 * r1)] is set
(1r - r1) * (r3 + r2) is Element of the carrier of V
[(1r - r1),(r3 + r2)] is set
{(1r - r1),(r3 + r2)} is non empty finite set
{{(1r - r1),(r3 + r2)},{(1r - r1)}} is non empty finite V42() set
the Mult of V . [(1r - r1),(r3 + r2)] is set
((r1 * r3) + (r1 * r1)) + ((1r - r1) * (r3 + r2)) is Element of the carrier of V
the addF of V . (((r1 * r3) + (r1 * r1)),((1r - r1) * (r3 + r2))) is Element of the carrier of V
[((r1 * r3) + (r1 * r1)),((1r - r1) * (r3 + r2))] is set
{((r1 * r3) + (r1 * r1)),((1r - r1) * (r3 + r2))} is non empty finite set
{((r1 * r3) + (r1 * r1))} is non empty trivial finite 1 -element set
{{((r1 * r3) + (r1 * r1)),((1r - r1) * (r3 + r2))},{((r1 * r3) + (r1 * r1))}} is non empty finite V42() set
the addF of V . [((r1 * r3) + (r1 * r1)),((1r - r1) * (r3 + r2))] is set
((1r - r1) * r3) + ((1r - r1) * r2) is Element of the carrier of V
the addF of V . (((1r - r1) * r3),((1r - r1) * r2)) is Element of the carrier of V
[((1r - r1) * r3),((1r - r1) * r2)] is set
{((1r - r1) * r3),((1r - r1) * r2)} is non empty finite set
{((1r - r1) * r3)} is non empty trivial finite 1 -element set
{{((1r - r1) * r3),((1r - r1) * r2)},{((1r - r1) * r3)}} is non empty finite V42() set
the addF of V . [((1r - r1) * r3),((1r - r1) * r2)] is set
((r1 * r3) + (r1 * r1)) + (((1r - r1) * r3) + ((1r - r1) * r2)) is Element of the carrier of V
the addF of V . (((r1 * r3) + (r1 * r1)),(((1r - r1) * r3) + ((1r - r1) * r2))) is Element of the carrier of V
[((r1 * r3) + (r1 * r1)),(((1r - r1) * r3) + ((1r - r1) * r2))] is set
{((r1 * r3) + (r1 * r1)),(((1r - r1) * r3) + ((1r - r1) * r2))} is non empty finite set
{{((r1 * r3) + (r1 * r1)),(((1r - r1) * r3) + ((1r - r1) * r2))},{((r1 * r3) + (r1 * r1))}} is non empty finite V42() set
the addF of V . [((r1 * r3) + (r1 * r1)),(((1r - r1) * r3) + ((1r - r1) * r2))] is set
((r1 * r3) + (r1 * r1)) + ((1r - r1) * r3) is Element of the carrier of V
the addF of V . (((r1 * r3) + (r1 * r1)),((1r - r1) * r3)) is Element of the carrier of V
[((r1 * r3) + (r1 * r1)),((1r - r1) * r3)] is set
{((r1 * r3) + (r1 * r1)),((1r - r1) * r3)} is non empty finite set
{{((r1 * r3) + (r1 * r1)),((1r - r1) * r3)},{((r1 * r3) + (r1 * r1))}} is non empty finite V42() set
the addF of V . [((r1 * r3) + (r1 * r1)),((1r - r1) * r3)] is set
(((r1 * r3) + (r1 * r1)) + ((1r - r1) * r3)) + ((1r - r1) * r2) is Element of the carrier of V
the addF of V . ((((r1 * r3) + (r1 * r1)) + ((1r - r1) * r3)),((1r - r1) * r2)) is Element of the carrier of V
[(((r1 * r3) + (r1 * r1)) + ((1r - r1) * r3)),((1r - r1) * r2)] is set
{(((r1 * r3) + (r1 * r1)) + ((1r - r1) * r3)),((1r - r1) * r2)} is non empty finite set
{(((r1 * r3) + (r1 * r1)) + ((1r - r1) * r3))} is non empty trivial finite 1 -element set
{{(((r1 * r3) + (r1 * r1)) + ((1r - r1) * r3)),((1r - r1) * r2)},{(((r1 * r3) + (r1 * r1)) + ((1r - r1) * r3))}} is non empty finite V42() set
the addF of V . [(((r1 * r3) + (r1 * r1)) + ((1r - r1) * r3)),((1r - r1) * r2)] is set
((r1 * r3) + ((1r - r1) * r3)) + (r1 * r1) is Element of the carrier of V
the addF of V . (((r1 * r3) + ((1r - r1) * r3)),(r1 * r1)) is Element of the carrier of V
[((r1 * r3) + ((1r - r1) * r3)),(r1 * r1)] is set
{((r1 * r3) + ((1r - r1) * r3)),(r1 * r1)} is non empty finite set
{((r1 * r3) + ((1r - r1) * r3))} is non empty trivial finite 1 -element set
{{((r1 * r3) + ((1r - r1) * r3)),(r1 * r1)},{((r1 * r3) + ((1r - r1) * r3))}} is non empty finite V42() set
the addF of V . [((r1 * r3) + ((1r - r1) * r3)),(r1 * r1)] is set
(((r1 * r3) + ((1r - r1) * r3)) + (r1 * r1)) + ((1r - r1) * r2) is Element of the carrier of V
the addF of V . ((((r1 * r3) + ((1r - r1) * r3)) + (r1 * r1)),((1r - r1) * r2)) is Element of the carrier of V
[(((r1 * r3) + ((1r - r1) * r3)) + (r1 * r1)),((1r - r1) * r2)] is set
{(((r1 * r3) + ((1r - r1) * r3)) + (r1 * r1)),((1r - r1) * r2)} is non empty finite set
{(((r1 * r3) + ((1r - r1) * r3)) + (r1 * r1))} is non empty trivial finite 1 -element set
{{(((r1 * r3) + ((1r - r1) * r3)) + (r1 * r1)),((1r - r1) * r2)},{(((r1 * r3) + ((1r - r1) * r3)) + (r1 * r1))}} is non empty finite V42() set
the addF of V . [(((r1 * r3) + ((1r - r1) * r3)) + (r1 * r1)),((1r - r1) * r2)] is set
((r1 * r3) + ((1r - r1) * r3)) + ((r1 * r1) + ((1r - r1) * r2)) is Element of the carrier of V
the addF of V . (((r1 * r3) + ((1r - r1) * r3)),((r1 * r1) + ((1r - r1) * r2))) is Element of the carrier of V
[((r1 * r3) + ((1r - r1) * r3)),((r1 * r1) + ((1r - r1) * r2))] is set
{((r1 * r3) + ((1r - r1) * r3)),((r1 * r1) + ((1r - r1) * r2))} is non empty finite set
{{((r1 * r3) + ((1r - r1) * r3)),((r1 * r1) + ((1r - r1) * r2))},{((r1 * r3) + ((1r - r1) * r3))}} is non empty finite V42() set
the addF of V . [((r1 * r3) + ((1r - r1) * r3)),((r1 * r1) + ((1r - r1) * r2))] is set
V is non empty vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
(V,M,1r) is Element of bool the carrier of V
{ (1r * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
N is Element of the carrier of V
1r * N is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[1r,N] is set
{1r,N} is non empty finite set
{1r} is non empty trivial finite 1 -element V68() set
{{1r,N},{1r}} is non empty finite V42() set
the Mult of V . [1r,N] is set
N is Element of the carrier of V
SG is Element of the carrier of V
1r * SG is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[1r,SG] is set
{1r,SG} is non empty finite set
{1r} is non empty trivial finite 1 -element V68() set
{{1r,SG},{1r}} is non empty finite V42() set
the Mult of V . [1r,SG] is set
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
0. V is zero Element of the carrier of V
the ZeroF of V is Element of the carrier of V
{(0. V)} is non empty trivial finite 1 -element Element of bool the carrier of V
M is non empty Element of bool the carrier of V
(V,M,0c) is Element of bool the carrier of V
{ (0c * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
N is Element of the carrier of V
SG is set
Y is Element of the carrier of V
0c * Y is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[0c,Y] is set
{0c,Y} is non empty finite set
{0c} is non empty trivial finite V42() 1 -element V68() V69() V70() V71() V72() V73() set
{{0c,Y},{0c}} is non empty finite V42() set
the Mult of V . [0c,Y] is set
N is Element of the carrier of V
SG is Element of the carrier of V
0c * SG is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[0c,SG] is set
{0c,SG} is non empty finite set
{0c} is non empty trivial finite V42() 1 -element V68() V69() V70() V71() V72() V73() set
{{0c,SG},{0c}} is non empty finite V42() set
the Mult of V . [0c,SG] is set
V is non empty add-associative addLoopStr
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Element of bool the carrier of V
M + N is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in M & b₂ in N ) } is set
SG is Element of bool the carrier of V
(M + N) + SG is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in M + N & b₂ in SG ) } is set
N + SG is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in N & b₂ in SG ) } is set
M + (N + SG) is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in M & b₂ in N + SG ) } is set
Y is Element of the carrier of V
r2 is Element of the carrier of V
r1 is Element of the carrier of V
r2 + r1 is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (r2,r1) is Element of the carrier of V
[r2,r1] is set
{r2,r1} is non empty finite set
{r2} is non empty trivial finite 1 -element set
{{r2,r1},{r2}} is non empty finite V42() set
the addF of V . [r2,r1] is set
r3 is Element of the carrier of V
r2 is Element of the carrier of V
r3 + r2 is Element of the carrier of V
the addF of V . (r3,r2) is Element of the carrier of V
[r3,r2] is set
{r3,r2} is non empty finite set
{r3} is non empty trivial finite 1 -element set
{{r3,r2},{r3}} is non empty finite V42() set
the addF of V . [r3,r2] is set
r2 + r3 is Element of the carrier of V
the addF of V . (r2,r3) is Element of the carrier of V
[r2,r3] is set
{r2,r3} is non empty finite set
{{r2,r3},{r2}} is non empty finite V42() set
the addF of V . [r2,r3] is set
(r2 + r3) + r2 is Element of the carrier of V
the addF of V . ((r2 + r3),r2) is Element of the carrier of V
[(r2 + r3),r2] is set
{(r2 + r3),r2} is non empty finite set
{(r2 + r3)} is non empty trivial finite 1 -element set
{{(r2 + r3),r2},{(r2 + r3)}} is non empty finite V42() set
the addF of V . [(r2 + r3),r2] is set
Y is Element of the carrier of V
r2 is Element of the carrier of V
r1 is Element of the carrier of V
r2 + r1 is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (r2,r1) is Element of the carrier of V
[r2,r1] is set
{r2,r1} is non empty finite set
{r2} is non empty trivial finite 1 -element set
{{r2,r1},{r2}} is non empty finite V42() set
the addF of V . [r2,r1] is set
r3 is Element of the carrier of V
r2 is Element of the carrier of V
r3 + r2 is Element of the carrier of V
the addF of V . (r3,r2) is Element of the carrier of V
[r3,r2] is set
{r3,r2} is non empty finite set
{r3} is non empty trivial finite 1 -element set
{{r3,r2},{r3}} is non empty finite V42() set
the addF of V . [r3,r2] is set
r2 + r1 is Element of the carrier of V
the addF of V . (r2,r1) is Element of the carrier of V
[r2,r1] is set
{r2,r1} is non empty finite set
{r2} is non empty trivial finite 1 -element set
{{r2,r1},{r2}} is non empty finite V42() set
the addF of V . [r2,r1] is set
r3 + (r2 + r1) is Element of the carrier of V
the addF of V . (r3,(r2 + r1)) is Element of the carrier of V
[r3,(r2 + r1)] is set
{r3,(r2 + r1)} is non empty finite set
{{r3,(r2 + r1)},{r3}} is non empty finite V42() set
the addF of V . [r3,(r2 + r1)] is set
V is non empty vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
SG is complex set
(V,M,SG) is Element of bool the carrier of V
{ (SG * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
N is complex set
(V,(V,M,SG),N) is Element of bool the carrier of V
{ (N * b₁) where b₁ is Element of the carrier of V : b₁ in (V,M,SG) } is set
N * SG is complex set
(V,M,(N * SG)) is Element of bool the carrier of V
{ ((N * SG) * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
Y is Element of the carrier of V
r2 is Element of the carrier of V
N * r2 is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[N,r2] is set
{N,r2} is non empty finite set
{N} is non empty trivial finite 1 -element V68() set
{{N,r2},{N}} is non empty finite V42() set
the Mult of V . [N,r2] is set
r1 is Element of the carrier of V
SG * r1 is Element of the carrier of V
[SG,r1] is set
{SG,r1} is non empty finite set
{SG} is non empty trivial finite 1 -element V68() set
{{SG,r1},{SG}} is non empty finite V42() set
the Mult of V . [SG,r1] is set
(N * SG) * r1 is Element of the carrier of V
[(N * SG),r1] is set
{(N * SG),r1} is non empty finite set
{(N * SG)} is non empty trivial finite 1 -element V68() set
{{(N * SG),r1},{(N * SG)}} is non empty finite V42() set
the Mult of V . [(N * SG),r1] is set
Y is Element of the carrier of V
r2 is Element of the carrier of V
(N * SG) * r2 is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(N * SG),r2] is set
{(N * SG),r2} is non empty finite set
{(N * SG)} is non empty trivial finite 1 -element V68() set
{{(N * SG),r2},{(N * SG)}} is non empty finite V42() set
the Mult of V . [(N * SG),r2] is set
SG * r2 is Element of the carrier of V
[SG,r2] is set
{SG,r2} is non empty finite set
{SG} is non empty trivial finite 1 -element V68() set
{{SG,r2},{SG}} is non empty finite V42() set
the Mult of V . [SG,r2] is set
N * (SG * r2) is Element of the carrier of V
[N,(SG * r2)] is set
{N,(SG * r2)} is non empty finite set
{N} is non empty trivial finite 1 -element V68() set
{{N,(SG * r2)},{N}} is non empty finite V42() set
the Mult of V . [N,(SG * r2)] is set
V is non empty vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Element of bool the carrier of V
M + N is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in M & b₂ in N ) } is set
SG is complex set
(V,(M + N),SG) is Element of bool the carrier of V
{ (SG * b₁) where b₁ is Element of the carrier of V : b₁ in M + N } is set
(V,M,SG) is Element of bool the carrier of V
{ (SG * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
(V,N,SG) is Element of bool the carrier of V
{ (SG * b₁) where b₁ is Element of the carrier of V : b₁ in N } is set
(V,M,SG) + (V,N,SG) is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in (V,M,SG) & b₂ in (V,N,SG) ) } is set
Y is Element of the carrier of V
r2 is Element of the carrier of V
r1 is Element of the carrier of V
r2 + r1 is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (r2,r1) is Element of the carrier of V
[r2,r1] is set
{r2,r1} is non empty finite set
{r2} is non empty trivial finite 1 -element set
{{r2,r1},{r2}} is non empty finite V42() set
the addF of V . [r2,r1] is set
r3 is Element of the carrier of V
SG * r3 is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[SG,r3] is set
{SG,r3} is non empty finite set
{SG} is non empty trivial finite 1 -element V68() set
{{SG,r3},{SG}} is non empty finite V42() set
the Mult of V . [SG,r3] is set
r2 is Element of the carrier of V
SG * r2 is Element of the carrier of V
[SG,r2] is set
{SG,r2} is non empty finite set
{{SG,r2},{SG}} is non empty finite V42() set
the Mult of V . [SG,r2] is set
r2 + r3 is Element of the carrier of V
the addF of V . (r2,r3) is Element of the carrier of V
[r2,r3] is set
{r2,r3} is non empty finite set
{r2} is non empty trivial finite 1 -element set
{{r2,r3},{r2}} is non empty finite V42() set
the addF of V . [r2,r3] is set
SG * (r2 + r3) is Element of the carrier of V
[SG,(r2 + r3)] is set
{SG,(r2 + r3)} is non empty finite set
{{SG,(r2 + r3)},{SG}} is non empty finite V42() set
the Mult of V . [SG,(r2 + r3)] is set
Y is Element of the carrier of V
r2 is Element of the carrier of V
SG * r2 is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[SG,r2] is set
{SG,r2} is non empty finite set
{SG} is non empty trivial finite 1 -element V68() set
{{SG,r2},{SG}} is non empty finite V42() set
the Mult of V . [SG,r2] is set
r1 is Element of the carrier of V
r3 is Element of the carrier of V
r1 + r3 is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (r1,r3) is Element of the carrier of V
[r1,r3] is set
{r1,r3} is non empty finite set
{r1} is non empty trivial finite 1 -element set
{{r1,r3},{r1}} is non empty finite V42() set
the addF of V . [r1,r3] is set
SG * r1 is Element of the carrier of V
[SG,r1] is set
{SG,r1} is non empty finite set
{{SG,r1},{SG}} is non empty finite V42() set
the Mult of V . [SG,r1] is set
SG * r3 is Element of the carrier of V
[SG,r3] is set
{SG,r3} is non empty finite set
{{SG,r3},{SG}} is non empty finite V42() set
the Mult of V . [SG,r3] is set
(SG * r1) + (SG * r3) is Element of the carrier of V
the addF of V . ((SG * r1),(SG * r3)) is Element of the carrier of V
[(SG * r1),(SG * r3)] is set
{(SG * r1),(SG * r3)} is non empty finite set
{(SG * r1)} is non empty trivial finite 1 -element set
{{(SG * r1),(SG * r3)},{(SG * r1)}} is non empty finite V42() set
the addF of V . [(SG * r1),(SG * r3)] is set
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Element of the carrier of V
N + M is Element of bool the carrier of V
{ (N + b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
SG is Element of the carrier of V
Y is Element of the carrier of V
r2 is complex set
r2 * SG is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[r2,SG] is set
{r2,SG} is non empty finite set
{r2} is non empty trivial finite 1 -element V68() set
{{r2,SG},{r2}} is non empty finite V42() set
the Mult of V . [r2,SG] is set
1r - r2 is complex set
- r2 is complex set
1r + (- r2) is complex set
(1r - r2) * Y is Element of the carrier of V
[(1r - r2),Y] is set
{(1r - r2),Y} is non empty finite set
{(1r - r2)} is non empty trivial finite 1 -element V68() set
{{(1r - r2),Y},{(1r - r2)}} is non empty finite V42() set
the Mult of V . [(1r - r2),Y] is set
(r2 * SG) + ((1r - r2) * Y) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((r2 * SG),((1r - r2) * Y)) is Element of the carrier of V
[(r2 * SG),((1r - r2) * Y)] is set
{(r2 * SG),((1r - r2) * Y)} is non empty finite set
{(r2 * SG)} is non empty trivial finite 1 -element set
{{(r2 * SG),((1r - r2) * Y)},{(r2 * SG)}} is non empty finite V42() set
the addF of V . [(r2 * SG),((1r - r2) * Y)] is set
N + SG is Element of the carrier of V
the addF of V . (N,SG) is Element of the carrier of V
[N,SG] is set
{N,SG} is non empty finite set
{N} is non empty trivial finite 1 -element set
{{N,SG},{N}} is non empty finite V42() set
the addF of V . [N,SG] is set
N + Y is Element of the carrier of V
the addF of V . (N,Y) is Element of the carrier of V
[N,Y] is set
{N,Y} is non empty finite set
{{N,Y},{N}} is non empty finite V42() set
the addF of V . [N,Y] is set
{ (N + b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
r2 * (N + SG) is Element of the carrier of V
[r2,(N + SG)] is set
{r2,(N + SG)} is non empty finite set
{{r2,(N + SG)},{r2}} is non empty finite V42() set
the Mult of V . [r2,(N + SG)] is set
(1r - r2) * (N + Y) is Element of the carrier of V
[(1r - r2),(N + Y)] is set
{(1r - r2),(N + Y)} is non empty finite set
{{(1r - r2),(N + Y)},{(1r - r2)}} is non empty finite V42() set
the Mult of V . [(1r - r2),(N + Y)] is set
(r2 * (N + SG)) + ((1r - r2) * (N + Y)) is Element of the carrier of V
the addF of V . ((r2 * (N + SG)),((1r - r2) * (N + Y))) is Element of the carrier of V
[(r2 * (N + SG)),((1r - r2) * (N + Y))] is set
{(r2 * (N + SG)),((1r - r2) * (N + Y))} is non empty finite set
{(r2 * (N + SG))} is non empty trivial finite 1 -element set
{{(r2 * (N + SG)),((1r - r2) * (N + Y))},{(r2 * (N + SG))}} is non empty finite V42() set
the addF of V . [(r2 * (N + SG)),((1r - r2) * (N + Y))] is set
r2 is complex real ext-real Element of REAL
r2 * N is Element of the carrier of V
[r2,N] is set
{r2,N} is non empty finite set
{{r2,N},{r2}} is non empty finite V42() set
the Mult of V . [r2,N] is set
(r2 * N) + (r2 * SG) is Element of the carrier of V
the addF of V . ((r2 * N),(r2 * SG)) is Element of the carrier of V
[(r2 * N),(r2 * SG)] is set
{(r2 * N),(r2 * SG)} is non empty finite set
{(r2 * N)} is non empty trivial finite 1 -element set
{{(r2 * N),(r2 * SG)},{(r2 * N)}} is non empty finite V42() set
the addF of V . [(r2 * N),(r2 * SG)] is set
((r2 * N) + (r2 * SG)) + ((1r - r2) * (N + Y)) is Element of the carrier of V
the addF of V . (((r2 * N) + (r2 * SG)),((1r - r2) * (N + Y))) is Element of the carrier of V
[((r2 * N) + (r2 * SG)),((1r - r2) * (N + Y))] is set
{((r2 * N) + (r2 * SG)),((1r - r2) * (N + Y))} is non empty finite set
{((r2 * N) + (r2 * SG))} is non empty trivial finite 1 -element set
{{((r2 * N) + (r2 * SG)),((1r - r2) * (N + Y))},{((r2 * N) + (r2 * SG))}} is non empty finite V42() set
the addF of V . [((r2 * N) + (r2 * SG)),((1r - r2) * (N + Y))] is set
(1r - r2) * N is Element of the carrier of V
[(1r - r2),N] is set
{(1r - r2),N} is non empty finite set
{{(1r - r2),N},{(1r - r2)}} is non empty finite V42() set
the Mult of V . [(1r - r2),N] is set
((1r - r2) * N) + ((1r - r2) * Y) is Element of the carrier of V
the addF of V . (((1r - r2) * N),((1r - r2) * Y)) is Element of the carrier of V
[((1r - r2) * N),((1r - r2) * Y)] is set
{((1r - r2) * N),((1r - r2) * Y)} is non empty finite set
{((1r - r2) * N)} is non empty trivial finite 1 -element set
{{((1r - r2) * N),((1r - r2) * Y)},{((1r - r2) * N)}} is non empty finite V42() set
the addF of V . [((1r - r2) * N),((1r - r2) * Y)] is set
((r2 * N) + (r2 * SG)) + (((1r - r2) * N) + ((1r - r2) * Y)) is Element of the carrier of V
the addF of V . (((r2 * N) + (r2 * SG)),(((1r - r2) * N) + ((1r - r2) * Y))) is Element of the carrier of V
[((r2 * N) + (r2 * SG)),(((1r - r2) * N) + ((1r - r2) * Y))] is set
{((r2 * N) + (r2 * SG)),(((1r - r2) * N) + ((1r - r2) * Y))} is non empty finite set
{{((r2 * N) + (r2 * SG)),(((1r - r2) * N) + ((1r - r2) * Y))},{((r2 * N) + (r2 * SG))}} is non empty finite V42() set
the addF of V . [((r2 * N) + (r2 * SG)),(((1r - r2) * N) + ((1r - r2) * Y))] is set
((r2 * N) + (r2 * SG)) + ((1r - r2) * N) is Element of the carrier of V
the addF of V . (((r2 * N) + (r2 * SG)),((1r - r2) * N)) is Element of the carrier of V
[((r2 * N) + (r2 * SG)),((1r - r2) * N)] is set
{((r2 * N) + (r2 * SG)),((1r - r2) * N)} is non empty finite set
{{((r2 * N) + (r2 * SG)),((1r - r2) * N)},{((r2 * N) + (r2 * SG))}} is non empty finite V42() set
the addF of V . [((r2 * N) + (r2 * SG)),((1r - r2) * N)] is set
(((r2 * N) + (r2 * SG)) + ((1r - r2) * N)) + ((1r - r2) * Y) is Element of the carrier of V
the addF of V . ((((r2 * N) + (r2 * SG)) + ((1r - r2) * N)),((1r - r2) * Y)) is Element of the carrier of V
[(((r2 * N) + (r2 * SG)) + ((1r - r2) * N)),((1r - r2) * Y)] is set
{(((r2 * N) + (r2 * SG)) + ((1r - r2) * N)),((1r - r2) * Y)} is non empty finite set
{(((r2 * N) + (r2 * SG)) + ((1r - r2) * N))} is non empty trivial finite 1 -element set
{{(((r2 * N) + (r2 * SG)) + ((1r - r2) * N)),((1r - r2) * Y)},{(((r2 * N) + (r2 * SG)) + ((1r - r2) * N))}} is non empty finite V42() set
the addF of V . [(((r2 * N) + (r2 * SG)) + ((1r - r2) * N)),((1r - r2) * Y)] is set
(r2 * N) + ((1r - r2) * N) is Element of the carrier of V
the addF of V . ((r2 * N),((1r - r2) * N)) is Element of the carrier of V
[(r2 * N),((1r - r2) * N)] is set
{(r2 * N),((1r - r2) * N)} is non empty finite set
{{(r2 * N),((1r - r2) * N)},{(r2 * N)}} is non empty finite V42() set
the addF of V . [(r2 * N),((1r - r2) * N)] is set
((r2 * N) + ((1r - r2) * N)) + (r2 * SG) is Element of the carrier of V
the addF of V . (((r2 * N) + ((1r - r2) * N)),(r2 * SG)) is Element of the carrier of V
[((r2 * N) + ((1r - r2) * N)),(r2 * SG)] is set
{((r2 * N) + ((1r - r2) * N)),(r2 * SG)} is non empty finite set
{((r2 * N) + ((1r - r2) * N))} is non empty trivial finite 1 -element set
{{((r2 * N) + ((1r - r2) * N)),(r2 * SG)},{((r2 * N) + ((1r - r2) * N))}} is non empty finite V42() set
the addF of V . [((r2 * N) + ((1r - r2) * N)),(r2 * SG)] is set
(((r2 * N) + ((1r - r2) * N)) + (r2 * SG)) + ((1r - r2) * Y) is Element of the carrier of V
the addF of V . ((((r2 * N) + ((1r - r2) * N)) + (r2 * SG)),((1r - r2) * Y)) is Element of the carrier of V
[(((r2 * N) + ((1r - r2) * N)) + (r2 * SG)),((1r - r2) * Y)] is set
{(((r2 * N) + ((1r - r2) * N)) + (r2 * SG)),((1r - r2) * Y)} is non empty finite set
{(((r2 * N) + ((1r - r2) * N)) + (r2 * SG))} is non empty trivial finite 1 -element set
{{(((r2 * N) + ((1r - r2) * N)) + (r2 * SG)),((1r - r2) * Y)},{(((r2 * N) + ((1r - r2) * N)) + (r2 * SG))}} is non empty finite V42() set
the addF of V . [(((r2 * N) + ((1r - r2) * N)) + (r2 * SG)),((1r - r2) * Y)] is set
r2 + (1r - r2) is complex set
(r2 + (1r - r2)) * N is Element of the carrier of V
[(r2 + (1r - r2)),N] is set
{(r2 + (1r - r2)),N} is non empty finite set
{(r2 + (1r - r2))} is non empty trivial finite 1 -element V68() set
{{(r2 + (1r - r2)),N},{(r2 + (1r - r2))}} is non empty finite V42() set
the Mult of V . [(r2 + (1r - r2)),N] is set
((r2 + (1r - r2)) * N) + (r2 * SG) is Element of the carrier of V
the addF of V . (((r2 + (1r - r2)) * N),(r2 * SG)) is Element of the carrier of V
[((r2 + (1r - r2)) * N),(r2 * SG)] is set
{((r2 + (1r - r2)) * N),(r2 * SG)} is non empty finite set
{((r2 + (1r - r2)) * N)} is non empty trivial finite 1 -element set
{{((r2 + (1r - r2)) * N),(r2 * SG)},{((r2 + (1r - r2)) * N)}} is non empty finite V42() set
the addF of V . [((r2 + (1r - r2)) * N),(r2 * SG)] is set
(((r2 + (1r - r2)) * N) + (r2 * SG)) + ((1r - r2) * Y) is Element of the carrier of V
the addF of V . ((((r2 + (1r - r2)) * N) + (r2 * SG)),((1r - r2) * Y)) is Element of the carrier of V
[(((r2 + (1r - r2)) * N) + (r2 * SG)),((1r - r2) * Y)] is set
{(((r2 + (1r - r2)) * N) + (r2 * SG)),((1r - r2) * Y)} is non empty finite set
{(((r2 + (1r - r2)) * N) + (r2 * SG))} is non empty trivial finite 1 -element set
{{(((r2 + (1r - r2)) * N) + (r2 * SG)),((1r - r2) * Y)},{(((r2 + (1r - r2)) * N) + (r2 * SG))}} is non empty finite V42() set
the addF of V . [(((r2 + (1r - r2)) * N) + (r2 * SG)),((1r - r2) * Y)] is set
N + (r2 * SG) is Element of the carrier of V
the addF of V . (N,(r2 * SG)) is Element of the carrier of V
[N,(r2 * SG)] is set
{N,(r2 * SG)} is non empty finite set
{{N,(r2 * SG)},{N}} is non empty finite V42() set
the addF of V . [N,(r2 * SG)] is set
(N + (r2 * SG)) + ((1r - r2) * Y) is Element of the carrier of V
the addF of V . ((N + (r2 * SG)),((1r - r2) * Y)) is Element of the carrier of V
[(N + (r2 * SG)),((1r - r2) * Y)] is set
{(N + (r2 * SG)),((1r - r2) * Y)} is non empty finite set
{(N + (r2 * SG))} is non empty trivial finite 1 -element set
{{(N + (r2 * SG)),((1r - r2) * Y)},{(N + (r2 * SG))}} is non empty finite V42() set
the addF of V . [(N + (r2 * SG)),((1r - r2) * Y)] is set
(r2 * SG) + ((1r - r2) * Y) is Element of the carrier of V
N + ((r2 * SG) + ((1r - r2) * Y)) is Element of the carrier of V
the addF of V . (N,((r2 * SG) + ((1r - r2) * Y))) is Element of the carrier of V
[N,((r2 * SG) + ((1r - r2) * Y))] is set
{N,((r2 * SG) + ((1r - r2) * Y))} is non empty finite set
{{N,((r2 * SG) + ((1r - r2) * Y))},{N}} is non empty finite V42() set
the addF of V . [N,((r2 * SG) + ((1r - r2) * Y))] is set
r2 is Element of the carrier of V
N + r2 is Element of the carrier of V
the addF of V . (N,r2) is Element of the carrier of V
[N,r2] is set
{N,r2} is non empty finite set
{{N,r2},{N}} is non empty finite V42() set
the addF of V . [N,r2] is set
SG is Element of the carrier of V
Y is Element of the carrier of V
r2 is complex set
r2 * SG is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[r2,SG] is set
{r2,SG} is non empty finite set
{r2} is non empty trivial finite 1 -element V68() set
{{r2,SG},{r2}} is non empty finite V42() set
the Mult of V . [r2,SG] is set
1r - r2 is complex set
- r2 is complex set
1r + (- r2) is complex set
(1r - r2) * Y is Element of the carrier of V
[(1r - r2),Y] is set
{(1r - r2),Y} is non empty finite set
{(1r - r2)} is non empty trivial finite 1 -element V68() set
{{(1r - r2),Y},{(1r - r2)}} is non empty finite V42() set
the Mult of V . [(1r - r2),Y] is set
(r2 * SG) + ((1r - r2) * Y) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((r2 * SG),((1r - r2) * Y)) is Element of the carrier of V
[(r2 * SG),((1r - r2) * Y)] is set
{(r2 * SG),((1r - r2) * Y)} is non empty finite set
{(r2 * SG)} is non empty trivial finite 1 -element set
{{(r2 * SG),((1r - r2) * Y)},{(r2 * SG)}} is non empty finite V42() set
the addF of V . [(r2 * SG),((1r - r2) * Y)] is set
r1 is Element of the carrier of V
N + r1 is Element of the carrier of V
the addF of V . (N,r1) is Element of the carrier of V
[N,r1] is set
{N,r1} is non empty finite set
{N} is non empty trivial finite 1 -element set
{{N,r1},{N}} is non empty finite V42() set
the addF of V . [N,r1] is set
r3 is Element of the carrier of V
N + r3 is Element of the carrier of V
the addF of V . (N,r3) is Element of the carrier of V
[N,r3] is set
{N,r3} is non empty finite set
{{N,r3},{N}} is non empty finite V42() set
the addF of V . [N,r3] is set
(r2 * SG) + ((1r - r2) * Y) is Element of the carrier of V
r2 * N is Element of the carrier of V
[r2,N] is set
{r2,N} is non empty finite set
{{r2,N},{r2}} is non empty finite V42() set
the Mult of V . [r2,N] is set
r2 * r3 is Element of the carrier of V
[r2,r3] is set
{r2,r3} is non empty finite set
{{r2,r3},{r2}} is non empty finite V42() set
the Mult of V . [r2,r3] is set
(r2 * N) + (r2 * r3) is Element of the carrier of V
the addF of V . ((r2 * N),(r2 * r3)) is Element of the carrier of V
[(r2 * N),(r2 * r3)] is set
{(r2 * N),(r2 * r3)} is non empty finite set
{(r2 * N)} is non empty trivial finite 1 -element set
{{(r2 * N),(r2 * r3)},{(r2 * N)}} is non empty finite V42() set
the addF of V . [(r2 * N),(r2 * r3)] is set
(1r - r2) * (N + r1) is Element of the carrier of V
[(1r - r2),(N + r1)] is set
{(1r - r2),(N + r1)} is non empty finite set
{{(1r - r2),(N + r1)},{(1r - r2)}} is non empty finite V42() set
the Mult of V . [(1r - r2),(N + r1)] is set
((r2 * N) + (r2 * r3)) + ((1r - r2) * (N + r1)) is Element of the carrier of V
the addF of V . (((r2 * N) + (r2 * r3)),((1r - r2) * (N + r1))) is Element of the carrier of V
[((r2 * N) + (r2 * r3)),((1r - r2) * (N + r1))] is set
{((r2 * N) + (r2 * r3)),((1r - r2) * (N + r1))} is non empty finite set
{((r2 * N) + (r2 * r3))} is non empty trivial finite 1 -element set
{{((r2 * N) + (r2 * r3)),((1r - r2) * (N + r1))},{((r2 * N) + (r2 * r3))}} is non empty finite V42() set
the addF of V . [((r2 * N) + (r2 * r3)),((1r - r2) * (N + r1))] is set
(1r - r2) * N is Element of the carrier of V
[(1r - r2),N] is set
{(1r - r2),N} is non empty finite set
{{(1r - r2),N},{(1r - r2)}} is non empty finite V42() set
the Mult of V . [(1r - r2),N] is set
(1r - r2) * r1 is Element of the carrier of V
[(1r - r2),r1] is set
{(1r - r2),r1} is non empty finite set
{{(1r - r2),r1},{(1r - r2)}} is non empty finite V42() set
the Mult of V . [(1r - r2),r1] is set
((1r - r2) * N) + ((1r - r2) * r1) is Element of the carrier of V
the addF of V . (((1r - r2) * N),((1r - r2) * r1)) is Element of the carrier of V
[((1r - r2) * N),((1r - r2) * r1)] is set
{((1r - r2) * N),((1r - r2) * r1)} is non empty finite set
{((1r - r2) * N)} is non empty trivial finite 1 -element set
{{((1r - r2) * N),((1r - r2) * r1)},{((1r - r2) * N)}} is non empty finite V42() set
the addF of V . [((1r - r2) * N),((1r - r2) * r1)] is set
((r2 * N) + (r2 * r3)) + (((1r - r2) * N) + ((1r - r2) * r1)) is Element of the carrier of V
the addF of V . (((r2 * N) + (r2 * r3)),(((1r - r2) * N) + ((1r - r2) * r1))) is Element of the carrier of V
[((r2 * N) + (r2 * r3)),(((1r - r2) * N) + ((1r - r2) * r1))] is set
{((r2 * N) + (r2 * r3)),(((1r - r2) * N) + ((1r - r2) * r1))} is non empty finite set
{{((r2 * N) + (r2 * r3)),(((1r - r2) * N) + ((1r - r2) * r1))},{((r2 * N) + (r2 * r3))}} is non empty finite V42() set
the addF of V . [((r2 * N) + (r2 * r3)),(((1r - r2) * N) + ((1r - r2) * r1))] is set
((r2 * N) + (r2 * r3)) + ((1r - r2) * N) is Element of the carrier of V
the addF of V . (((r2 * N) + (r2 * r3)),((1r - r2) * N)) is Element of the carrier of V
[((r2 * N) + (r2 * r3)),((1r - r2) * N)] is set
{((r2 * N) + (r2 * r3)),((1r - r2) * N)} is non empty finite set
{{((r2 * N) + (r2 * r3)),((1r - r2) * N)},{((r2 * N) + (r2 * r3))}} is non empty finite V42() set
the addF of V . [((r2 * N) + (r2 * r3)),((1r - r2) * N)] is set
(((r2 * N) + (r2 * r3)) + ((1r - r2) * N)) + ((1r - r2) * r1) is Element of the carrier of V
the addF of V . ((((r2 * N) + (r2 * r3)) + ((1r - r2) * N)),((1r - r2) * r1)) is Element of the carrier of V
[(((r2 * N) + (r2 * r3)) + ((1r - r2) * N)),((1r - r2) * r1)] is set
{(((r2 * N) + (r2 * r3)) + ((1r - r2) * N)),((1r - r2) * r1)} is non empty finite set
{(((r2 * N) + (r2 * r3)) + ((1r - r2) * N))} is non empty trivial finite 1 -element set
{{(((r2 * N) + (r2 * r3)) + ((1r - r2) * N)),((1r - r2) * r1)},{(((r2 * N) + (r2 * r3)) + ((1r - r2) * N))}} is non empty finite V42() set
the addF of V . [(((r2 * N) + (r2 * r3)) + ((1r - r2) * N)),((1r - r2) * r1)] is set
(r2 * N) + ((1r - r2) * N) is Element of the carrier of V
the addF of V . ((r2 * N),((1r - r2) * N)) is Element of the carrier of V
[(r2 * N),((1r - r2) * N)] is set
{(r2 * N),((1r - r2) * N)} is non empty finite set
{{(r2 * N),((1r - r2) * N)},{(r2 * N)}} is non empty finite V42() set
the addF of V . [(r2 * N),((1r - r2) * N)] is set
((r2 * N) + ((1r - r2) * N)) + (r2 * r3) is Element of the carrier of V
the addF of V . (((r2 * N) + ((1r - r2) * N)),(r2 * r3)) is Element of the carrier of V
[((r2 * N) + ((1r - r2) * N)),(r2 * r3)] is set
{((r2 * N) + ((1r - r2) * N)),(r2 * r3)} is non empty finite set
{((r2 * N) + ((1r - r2) * N))} is non empty trivial finite 1 -element set
{{((r2 * N) + ((1r - r2) * N)),(r2 * r3)},{((r2 * N) + ((1r - r2) * N))}} is non empty finite V42() set
the addF of V . [((r2 * N) + ((1r - r2) * N)),(r2 * r3)] is set
(((r2 * N) + ((1r - r2) * N)) + (r2 * r3)) + ((1r - r2) * r1) is Element of the carrier of V
the addF of V . ((((r2 * N) + ((1r - r2) * N)) + (r2 * r3)),((1r - r2) * r1)) is Element of the carrier of V
[(((r2 * N) + ((1r - r2) * N)) + (r2 * r3)),((1r - r2) * r1)] is set
{(((r2 * N) + ((1r - r2) * N)) + (r2 * r3)),((1r - r2) * r1)} is non empty finite set
{(((r2 * N) + ((1r - r2) * N)) + (r2 * r3))} is non empty trivial finite 1 -element set
{{(((r2 * N) + ((1r - r2) * N)) + (r2 * r3)),((1r - r2) * r1)},{(((r2 * N) + ((1r - r2) * N)) + (r2 * r3))}} is non empty finite V42() set
the addF of V . [(((r2 * N) + ((1r - r2) * N)) + (r2 * r3)),((1r - r2) * r1)] is set
r2 + (1r - r2) is complex set
(r2 + (1r - r2)) * N is Element of the carrier of V
[(r2 + (1r - r2)),N] is set
{(r2 + (1r - r2)),N} is non empty finite set
{(r2 + (1r - r2))} is non empty trivial finite 1 -element V68() set
{{(r2 + (1r - r2)),N},{(r2 + (1r - r2))}} is non empty finite V42() set
the Mult of V . [(r2 + (1r - r2)),N] is set
((r2 + (1r - r2)) * N) + (r2 * r3) is Element of the carrier of V
the addF of V . (((r2 + (1r - r2)) * N),(r2 * r3)) is Element of the carrier of V
[((r2 + (1r - r2)) * N),(r2 * r3)] is set
{((r2 + (1r - r2)) * N),(r2 * r3)} is non empty finite set
{((r2 + (1r - r2)) * N)} is non empty trivial finite 1 -element set
{{((r2 + (1r - r2)) * N),(r2 * r3)},{((r2 + (1r - r2)) * N)}} is non empty finite V42() set
the addF of V . [((r2 + (1r - r2)) * N),(r2 * r3)] is set
(((r2 + (1r - r2)) * N) + (r2 * r3)) + ((1r - r2) * r1) is Element of the carrier of V
the addF of V . ((((r2 + (1r - r2)) * N) + (r2 * r3)),((1r - r2) * r1)) is Element of the carrier of V
[(((r2 + (1r - r2)) * N) + (r2 * r3)),((1r - r2) * r1)] is set
{(((r2 + (1r - r2)) * N) + (r2 * r3)),((1r - r2) * r1)} is non empty finite set
{(((r2 + (1r - r2)) * N) + (r2 * r3))} is non empty trivial finite 1 -element set
{{(((r2 + (1r - r2)) * N) + (r2 * r3)),((1r - r2) * r1)},{(((r2 + (1r - r2)) * N) + (r2 * r3))}} is non empty finite V42() set
the addF of V . [(((r2 + (1r - r2)) * N) + (r2 * r3)),((1r - r2) * r1)] is set
N + (r2 * r3) is Element of the carrier of V
the addF of V . (N,(r2 * r3)) is Element of the carrier of V
[N,(r2 * r3)] is set
{N,(r2 * r3)} is non empty finite set
{{N,(r2 * r3)},{N}} is non empty finite V42() set
the addF of V . [N,(r2 * r3)] is set
(N + (r2 * r3)) + ((1r - r2) * r1) is Element of the carrier of V
the addF of V . ((N + (r2 * r3)),((1r - r2) * r1)) is Element of the carrier of V
[(N + (r2 * r3)),((1r - r2) * r1)] is set
{(N + (r2 * r3)),((1r - r2) * r1)} is non empty finite set
{(N + (r2 * r3))} is non empty trivial finite 1 -element set
{{(N + (r2 * r3)),((1r - r2) * r1)},{(N + (r2 * r3))}} is non empty finite V42() set
the addF of V . [(N + (r2 * r3)),((1r - r2) * r1)] is set
(r2 * r3) + ((1r - r2) * r1) is Element of the carrier of V
the addF of V . ((r2 * r3),((1r - r2) * r1)) is Element of the carrier of V
[(r2 * r3),((1r - r2) * r1)] is set
{(r2 * r3),((1r - r2) * r1)} is non empty finite set
{(r2 * r3)} is non empty trivial finite 1 -element set
{{(r2 * r3),((1r - r2) * r1)},{(r2 * r3)}} is non empty finite V42() set
the addF of V . [(r2 * r3),((1r - r2) * r1)] is set
N + ((r2 * r3) + ((1r - r2) * r1)) is Element of the carrier of V
the addF of V . (N,((r2 * r3) + ((1r - r2) * r1))) is Element of the carrier of V
[N,((r2 * r3) + ((1r - r2) * r1))] is set
{N,((r2 * r3) + ((1r - r2) * r1))} is non empty finite set
{{N,((r2 * r3) + ((1r - r2) * r1))},{N}} is non empty finite V42() set
the addF of V . [N,((r2 * r3) + ((1r - r2) * r1))] is set
r2 is complex real ext-real Element of REAL
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
(0). V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
(V,((0). V)) is non empty Element of bool the carrier of V
the carrier of V is non empty set
bool the carrier of V is non empty set
the carrier of ((0). V) is non empty set
M is Element of the carrier of V
N is Element of the carrier of V
SG is complex set
SG * M is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[SG,M] is set
{SG,M} is non empty finite set
{SG} is non empty trivial finite 1 -element V68() set
{{SG,M},{SG}} is non empty finite V42() set
the Mult of V . [SG,M] is set
1r - SG is complex set
- SG is complex set
1r + (- SG) is complex set
(1r - SG) * N is Element of the carrier of V
[(1r - SG),N] is set
{(1r - SG),N} is non empty finite set
{(1r - SG)} is non empty trivial finite 1 -element V68() set
{{(1r - SG),N},{(1r - SG)}} is non empty finite V42() set
the Mult of V . [(1r - SG),N] is set
(SG * M) + ((1r - SG) * N) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((SG * M),((1r - SG) * N)) is Element of the carrier of V
[(SG * M),((1r - SG) * N)] is set
{(SG * M),((1r - SG) * N)} is non empty finite set
{(SG * M)} is non empty trivial finite 1 -element set
{{(SG * M),((1r - SG) * N)},{(SG * M)}} is non empty finite V42() set
the addF of V . [(SG * M),((1r - SG) * N)] is set
0. V is zero Element of the carrier of V
the ZeroF of V is Element of the carrier of V
{(0. V)} is non empty trivial finite 1 -element Element of bool the carrier of V
(SG * M) + ((1r - SG) * N) is Element of the carrier of V
(1r - SG) * (0. V) is Element of the carrier of V
[(1r - SG),(0. V)] is set
{(1r - SG),(0. V)} is non empty finite set
{{(1r - SG),(0. V)},{(1r - SG)}} is non empty finite V42() set
the Mult of V . [(1r - SG),(0. V)] is set
(0. V) + ((1r - SG) * (0. V)) is Element of the carrier of V
the addF of V . ((0. V),((1r - SG) * (0. V))) is Element of the carrier of V
[(0. V),((1r - SG) * (0. V))] is set
{(0. V),((1r - SG) * (0. V))} is non empty finite set
{(0. V)} is non empty trivial finite 1 -element set
{{(0. V),((1r - SG) * (0. V))},{(0. V)}} is non empty finite V42() set
the addF of V . [(0. V),((1r - SG) * (0. V))] is set
(0. V) + (0. V) is Element of the carrier of V
the addF of V . ((0. V),(0. V)) is Element of the carrier of V
[(0. V),(0. V)] is set
{(0. V),(0. V)} is non empty finite set
{{(0. V),(0. V)},{(0. V)}} is non empty finite V42() set
the addF of V . [(0. V),(0. V)] is set
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
(V) is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
the carrier of V is non empty set
the ZeroF of V is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
CLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is non empty strict CLSStruct
(V,(V)) is non empty Element of bool the carrier of V
bool the carrier of V is non empty set
the carrier of (V) is non empty set
M is Element of the carrier of V
N is Element of the carrier of V
SG is complex set
Y is complex real ext-real Element of REAL
SG * M is Element of the carrier of V
[SG,M] is set
{SG,M} is non empty finite set
{SG} is non empty trivial finite 1 -element V68() set
{{SG,M},{SG}} is non empty finite V42() set
the Mult of V . [SG,M] is set
1r - SG is complex set
- SG is complex set
1r + (- SG) is complex set
(1r - SG) * N is Element of the carrier of V
[(1r - SG),N] is set
{(1r - SG),N} is non empty finite set
{(1r - SG)} is non empty trivial finite 1 -element V68() set
{{(1r - SG),N},{(1r - SG)}} is non empty finite V42() set
the Mult of V . [(1r - SG),N] is set
(SG * M) + ((1r - SG) * N) is Element of the carrier of V
the addF of V . ((SG * M),((1r - SG) * N)) is Element of the carrier of V
[(SG * M),((1r - SG) * N)] is set
{(SG * M),((1r - SG) * N)} is non empty finite set
{(SG * M)} is non empty trivial finite 1 -element set
{{(SG * M),((1r - SG) * N)},{(SG * M)}} is non empty finite V42() set
the addF of V . [(SG * M),((1r - SG) * N)] is set
V is non empty CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
Y is complex set
r2 is complex real ext-real Element of REAL
N is Element of the carrier of V
SG is Element of the carrier of V
Y * N is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[Y,N] is set
{Y,N} is non empty finite set
{Y} is non empty trivial finite 1 -element V68() set
{{Y,N},{Y}} is non empty finite V42() set
the Mult of V . [Y,N] is set
1r - Y is complex set
- Y is complex set
1r + (- Y) is complex set
(1r - Y) * SG is Element of the carrier of V
[(1r - Y),SG] is set
{(1r - Y),SG} is non empty finite set
{(1r - Y)} is non empty trivial finite 1 -element V68() set
{{(1r - Y),SG},{(1r - Y)}} is non empty finite V42() set
the Mult of V . [(1r - Y),SG] is set
(Y * N) + ((1r - Y) * SG) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((Y * N),((1r - Y) * SG)) is Element of the carrier of V
[(Y * N),((1r - Y) * SG)] is set
{(Y * N),((1r - Y) * SG)} is non empty finite set
{(Y * N)} is non empty trivial finite 1 -element set
{{(Y * N),((1r - Y) * SG)},{(Y * N)}} is non empty finite V42() set
the addF of V . [(Y * N),((1r - Y) * SG)] is set
V is non empty Abelian add-associative vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Element of bool the carrier of V
SG is complex set
(V,M,SG) is Element of bool the carrier of V
{ (SG * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
Y is complex set
(V,N,Y) is Element of bool the carrier of V
{ (Y * b₁) where b₁ is Element of the carrier of V : b₁ in N } is set
(V,M,SG) + (V,N,Y) is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in (V,M,SG) & b₂ in (V,N,Y) ) } is set
r2 is Element of the carrier of V
r1 is Element of the carrier of V
r3 is complex set
r3 * r2 is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[r3,r2] is set
{r3,r2} is non empty finite set
{r3} is non empty trivial finite 1 -element V68() set
{{r3,r2},{r3}} is non empty finite V42() set
the Mult of V . [r3,r2] is set
1r - r3 is complex set
- r3 is complex set
1r + (- r3) is complex set
(1r - r3) * r1 is Element of the carrier of V
[(1r - r3),r1] is set
{(1r - r3),r1} is non empty finite set
{(1r - r3)} is non empty trivial finite 1 -element V68() set
{{(1r - r3),r1},{(1r - r3)}} is non empty finite V42() set
the Mult of V . [(1r - r3),r1] is set
(r3 * r2) + ((1r - r3) * r1) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((r3 * r2),((1r - r3) * r1)) is Element of the carrier of V
[(r3 * r2),((1r - r3) * r1)] is set
{(r3 * r2),((1r - r3) * r1)} is non empty finite set
{(r3 * r2)} is non empty trivial finite 1 -element set
{{(r3 * r2),((1r - r3) * r1)},{(r3 * r2)}} is non empty finite V42() set
the addF of V . [(r3 * r2),((1r - r3) * r1)] is set
r2 is Element of the carrier of V
r3 is Element of the carrier of V
r2 + r3 is Element of the carrier of V
the addF of V . (r2,r3) is Element of the carrier of V
[r2,r3] is set
{r2,r3} is non empty finite set
{r2} is non empty trivial finite 1 -element set
{{r2,r3},{r2}} is non empty finite V42() set
the addF of V . [r2,r3] is set
r1 is Element of the carrier of V
u2 is Element of the carrier of V
r1 + u2 is Element of the carrier of V
the addF of V . (r1,u2) is Element of the carrier of V
[r1,u2] is set
{r1,u2} is non empty finite set
{r1} is non empty trivial finite 1 -element set
{{r1,u2},{r1}} is non empty finite V42() set
the addF of V . [r1,u2] is set
y1 is Element of the carrier of V
SG * y1 is Element of the carrier of V
[SG,y1] is set
{SG,y1} is non empty finite set
{SG} is non empty trivial finite 1 -element V68() set
{{SG,y1},{SG}} is non empty finite V42() set
the Mult of V . [SG,y1] is set
x1 is Element of the carrier of V
SG * x1 is Element of the carrier of V
[SG,x1] is set
{SG,x1} is non empty finite set
{{SG,x1},{SG}} is non empty finite V42() set
the Mult of V . [SG,x1] is set
r3 * r1 is Element of the carrier of V
[r3,r1] is set
{r3,r1} is non empty finite set
{{r3,r1},{r3}} is non empty finite V42() set
the Mult of V . [r3,r1] is set
(1r - r3) * r2 is Element of the carrier of V
[(1r - r3),r2] is set
{(1r - r3),r2} is non empty finite set
{{(1r - r3),r2},{(1r - r3)}} is non empty finite V42() set
the Mult of V . [(1r - r3),r2] is set
(r3 * r1) + ((1r - r3) * r2) is Element of the carrier of V
the addF of V . ((r3 * r1),((1r - r3) * r2)) is Element of the carrier of V
[(r3 * r1),((1r - r3) * r2)] is set
{(r3 * r1),((1r - r3) * r2)} is non empty finite set
{(r3 * r1)} is non empty trivial finite 1 -element set
{{(r3 * r1),((1r - r3) * r2)},{(r3 * r1)}} is non empty finite V42() set
the addF of V . [(r3 * r1),((1r - r3) * r2)] is set
SG * r3 is complex set
(SG * r3) * x1 is Element of the carrier of V
[(SG * r3),x1] is set
{(SG * r3),x1} is non empty finite set
{(SG * r3)} is non empty trivial finite 1 -element V68() set
{{(SG * r3),x1},{(SG * r3)}} is non empty finite V42() set
the Mult of V . [(SG * r3),x1] is set
(1r - r3) * (SG * y1) is Element of the carrier of V
[(1r - r3),(SG * y1)] is set
{(1r - r3),(SG * y1)} is non empty finite set
{{(1r - r3),(SG * y1)},{(1r - r3)}} is non empty finite V42() set
the Mult of V . [(1r - r3),(SG * y1)] is set
((SG * r3) * x1) + ((1r - r3) * (SG * y1)) is Element of the carrier of V
the addF of V . (((SG * r3) * x1),((1r - r3) * (SG * y1))) is Element of the carrier of V
[((SG * r3) * x1),((1r - r3) * (SG * y1))] is set
{((SG * r3) * x1),((1r - r3) * (SG * y1))} is non empty finite set
{((SG * r3) * x1)} is non empty trivial finite 1 -element set
{{((SG * r3) * x1),((1r - r3) * (SG * y1))},{((SG * r3) * x1)}} is non empty finite V42() set
the addF of V . [((SG * r3) * x1),((1r - r3) * (SG * y1))] is set
SG * (1r - r3) is complex set
(SG * (1r - r3)) * y1 is Element of the carrier of V
[(SG * (1r - r3)),y1] is set
{(SG * (1r - r3)),y1} is non empty finite set
{(SG * (1r - r3))} is non empty trivial finite 1 -element V68() set
{{(SG * (1r - r3)),y1},{(SG * (1r - r3))}} is non empty finite V42() set
the Mult of V . [(SG * (1r - r3)),y1] is set
((SG * r3) * x1) + ((SG * (1r - r3)) * y1) is Element of the carrier of V
the addF of V . (((SG * r3) * x1),((SG * (1r - r3)) * y1)) is Element of the carrier of V
[((SG * r3) * x1),((SG * (1r - r3)) * y1)] is set
{((SG * r3) * x1),((SG * (1r - r3)) * y1)} is non empty finite set
{{((SG * r3) * x1),((SG * (1r - r3)) * y1)},{((SG * r3) * x1)}} is non empty finite V42() set
the addF of V . [((SG * r3) * x1),((SG * (1r - r3)) * y1)] is set
r3 * x1 is Element of the carrier of V
[r3,x1] is set
{r3,x1} is non empty finite set
{{r3,x1},{r3}} is non empty finite V42() set
the Mult of V . [r3,x1] is set
SG * (r3 * x1) is Element of the carrier of V
[SG,(r3 * x1)] is set
{SG,(r3 * x1)} is non empty finite set
{{SG,(r3 * x1)},{SG}} is non empty finite V42() set
the Mult of V . [SG,(r3 * x1)] is set
(SG * (r3 * x1)) + ((SG * (1r - r3)) * y1) is Element of the carrier of V
the addF of V . ((SG * (r3 * x1)),((SG * (1r - r3)) * y1)) is Element of the carrier of V
[(SG * (r3 * x1)),((SG * (1r - r3)) * y1)] is set
{(SG * (r3 * x1)),((SG * (1r - r3)) * y1)} is non empty finite set
{(SG * (r3 * x1))} is non empty trivial finite 1 -element set
{{(SG * (r3 * x1)),((SG * (1r - r3)) * y1)},{(SG * (r3 * x1))}} is non empty finite V42() set
the addF of V . [(SG * (r3 * x1)),((SG * (1r - r3)) * y1)] is set
(1r - r3) * y1 is Element of the carrier of V
[(1r - r3),y1] is set
{(1r - r3),y1} is non empty finite set
{{(1r - r3),y1},{(1r - r3)}} is non empty finite V42() set
the Mult of V . [(1r - r3),y1] is set
SG * ((1r - r3) * y1) is Element of the carrier of V
[SG,((1r - r3) * y1)] is set
{SG,((1r - r3) * y1)} is non empty finite set
{{SG,((1r - r3) * y1)},{SG}} is non empty finite V42() set
the Mult of V . [SG,((1r - r3) * y1)] is set
(SG * (r3 * x1)) + (SG * ((1r - r3) * y1)) is Element of the carrier of V
the addF of V . ((SG * (r3 * x1)),(SG * ((1r - r3) * y1))) is Element of the carrier of V
[(SG * (r3 * x1)),(SG * ((1r - r3) * y1))] is set
{(SG * (r3 * x1)),(SG * ((1r - r3) * y1))} is non empty finite set
{{(SG * (r3 * x1)),(SG * ((1r - r3) * y1))},{(SG * (r3 * x1))}} is non empty finite V42() set
the addF of V . [(SG * (r3 * x1)),(SG * ((1r - r3) * y1))] is set
(r3 * x1) + ((1r - r3) * y1) is Element of the carrier of V
the addF of V . ((r3 * x1),((1r - r3) * y1)) is Element of the carrier of V
[(r3 * x1),((1r - r3) * y1)] is set
{(r3 * x1),((1r - r3) * y1)} is non empty finite set
{(r3 * x1)} is non empty trivial finite 1 -element set
{{(r3 * x1),((1r - r3) * y1)},{(r3 * x1)}} is non empty finite V42() set
the addF of V . [(r3 * x1),((1r - r3) * y1)] is set
SG * ((r3 * x1) + ((1r - r3) * y1)) is Element of the carrier of V
[SG,((r3 * x1) + ((1r - r3) * y1))] is set
{SG,((r3 * x1) + ((1r - r3) * y1))} is non empty finite set
{{SG,((r3 * x1) + ((1r - r3) * y1))},{SG}} is non empty finite V42() set
the Mult of V . [SG,((r3 * x1) + ((1r - r3) * y1))] is set
y2 is Element of the carrier of V
Y * y2 is Element of the carrier of V
[Y,y2] is set
{Y,y2} is non empty finite set
{Y} is non empty trivial finite 1 -element V68() set
{{Y,y2},{Y}} is non empty finite V42() set
the Mult of V . [Y,y2] is set
x2 is Element of the carrier of V
Y * x2 is Element of the carrier of V
[Y,x2] is set
{Y,x2} is non empty finite set
{{Y,x2},{Y}} is non empty finite V42() set
the Mult of V . [Y,x2] is set
r3 * u2 is Element of the carrier of V
[r3,u2] is set
{r3,u2} is non empty finite set
{{r3,u2},{r3}} is non empty finite V42() set
the Mult of V . [r3,u2] is set
(1r - r3) * r3 is Element of the carrier of V
[(1r - r3),r3] is set
{(1r - r3),r3} is non empty finite set
{{(1r - r3),r3},{(1r - r3)}} is non empty finite V42() set
the Mult of V . [(1r - r3),r3] is set
(r3 * u2) + ((1r - r3) * r3) is Element of the carrier of V
the addF of V . ((r3 * u2),((1r - r3) * r3)) is Element of the carrier of V
[(r3 * u2),((1r - r3) * r3)] is set
{(r3 * u2),((1r - r3) * r3)} is non empty finite set
{(r3 * u2)} is non empty trivial finite 1 -element set
{{(r3 * u2),((1r - r3) * r3)},{(r3 * u2)}} is non empty finite V42() set
the addF of V . [(r3 * u2),((1r - r3) * r3)] is set
Y * r3 is complex set
(Y * r3) * x2 is Element of the carrier of V
[(Y * r3),x2] is set
{(Y * r3),x2} is non empty finite set
{(Y * r3)} is non empty trivial finite 1 -element V68() set
{{(Y * r3),x2},{(Y * r3)}} is non empty finite V42() set
the Mult of V . [(Y * r3),x2] is set
(1r - r3) * (Y * y2) is Element of the carrier of V
[(1r - r3),(Y * y2)] is set
{(1r - r3),(Y * y2)} is non empty finite set
{{(1r - r3),(Y * y2)},{(1r - r3)}} is non empty finite V42() set
the Mult of V . [(1r - r3),(Y * y2)] is set
((Y * r3) * x2) + ((1r - r3) * (Y * y2)) is Element of the carrier of V
the addF of V . (((Y * r3) * x2),((1r - r3) * (Y * y2))) is Element of the carrier of V
[((Y * r3) * x2),((1r - r3) * (Y * y2))] is set
{((Y * r3) * x2),((1r - r3) * (Y * y2))} is non empty finite set
{((Y * r3) * x2)} is non empty trivial finite 1 -element set
{{((Y * r3) * x2),((1r - r3) * (Y * y2))},{((Y * r3) * x2)}} is non empty finite V42() set
the addF of V . [((Y * r3) * x2),((1r - r3) * (Y * y2))] is set
Y * (1r - r3) is complex set
(Y * (1r - r3)) * y2 is Element of the carrier of V
[(Y * (1r - r3)),y2] is set
{(Y * (1r - r3)),y2} is non empty finite set
{(Y * (1r - r3))} is non empty trivial finite 1 -element V68() set
{{(Y * (1r - r3)),y2},{(Y * (1r - r3))}} is non empty finite V42() set
the Mult of V . [(Y * (1r - r3)),y2] is set
((Y * r3) * x2) + ((Y * (1r - r3)) * y2) is Element of the carrier of V
the addF of V . (((Y * r3) * x2),((Y * (1r - r3)) * y2)) is Element of the carrier of V
[((Y * r3) * x2),((Y * (1r - r3)) * y2)] is set
{((Y * r3) * x2),((Y * (1r - r3)) * y2)} is non empty finite set
{{((Y * r3) * x2),((Y * (1r - r3)) * y2)},{((Y * r3) * x2)}} is non empty finite V42() set
the addF of V . [((Y * r3) * x2),((Y * (1r - r3)) * y2)] is set
r3 * x2 is Element of the carrier of V
[r3,x2] is set
{r3,x2} is non empty finite set
{{r3,x2},{r3}} is non empty finite V42() set
the Mult of V . [r3,x2] is set
Y * (r3 * x2) is Element of the carrier of V
[Y,(r3 * x2)] is set
{Y,(r3 * x2)} is non empty finite set
{{Y,(r3 * x2)},{Y}} is non empty finite V42() set
the Mult of V . [Y,(r3 * x2)] is set
(Y * (r3 * x2)) + ((Y * (1r - r3)) * y2) is Element of the carrier of V
the addF of V . ((Y * (r3 * x2)),((Y * (1r - r3)) * y2)) is Element of the carrier of V
[(Y * (r3 * x2)),((Y * (1r - r3)) * y2)] is set
{(Y * (r3 * x2)),((Y * (1r - r3)) * y2)} is non empty finite set
{(Y * (r3 * x2))} is non empty trivial finite 1 -element set
{{(Y * (r3 * x2)),((Y * (1r - r3)) * y2)},{(Y * (r3 * x2))}} is non empty finite V42() set
the addF of V . [(Y * (r3 * x2)),((Y * (1r - r3)) * y2)] is set
(1r - r3) * y2 is Element of the carrier of V
[(1r - r3),y2] is set
{(1r - r3),y2} is non empty finite set
{{(1r - r3),y2},{(1r - r3)}} is non empty finite V42() set
the Mult of V . [(1r - r3),y2] is set
Y * ((1r - r3) * y2) is Element of the carrier of V
[Y,((1r - r3) * y2)] is set
{Y,((1r - r3) * y2)} is non empty finite set
{{Y,((1r - r3) * y2)},{Y}} is non empty finite V42() set
the Mult of V . [Y,((1r - r3) * y2)] is set
(Y * (r3 * x2)) + (Y * ((1r - r3) * y2)) is Element of the carrier of V
the addF of V . ((Y * (r3 * x2)),(Y * ((1r - r3) * y2))) is Element of the carrier of V
[(Y * (r3 * x2)),(Y * ((1r - r3) * y2))] is set
{(Y * (r3 * x2)),(Y * ((1r - r3) * y2))} is non empty finite set
{{(Y * (r3 * x2)),(Y * ((1r - r3) * y2))},{(Y * (r3 * x2))}} is non empty finite V42() set
the addF of V . [(Y * (r3 * x2)),(Y * ((1r - r3) * y2))] is set
(r3 * x2) + ((1r - r3) * y2) is Element of the carrier of V
the addF of V . ((r3 * x2),((1r - r3) * y2)) is Element of the carrier of V
[(r3 * x2),((1r - r3) * y2)] is set
{(r3 * x2),((1r - r3) * y2)} is non empty finite set
{(r3 * x2)} is non empty trivial finite 1 -element set
{{(r3 * x2),((1r - r3) * y2)},{(r3 * x2)}} is non empty finite V42() set
the addF of V . [(r3 * x2),((1r - r3) * y2)] is set
Y * ((r3 * x2) + ((1r - r3) * y2)) is Element of the carrier of V
[Y,((r3 * x2) + ((1r - r3) * y2))] is set
{Y,((r3 * x2) + ((1r - r3) * y2))} is non empty finite set
{{Y,((r3 * x2) + ((1r - r3) * y2))},{Y}} is non empty finite V42() set
the Mult of V . [Y,((r3 * x2) + ((1r - r3) * y2))] is set
bx is complex real ext-real Element of REAL
bx is complex real ext-real Element of REAL
r3 * (r1 + u2) is Element of the carrier of V
[r3,(r1 + u2)] is set
{r3,(r1 + u2)} is non empty finite set
{{r3,(r1 + u2)},{r3}} is non empty finite V42() set
the Mult of V . [r3,(r1 + u2)] is set
(1r - r3) * (r2 + r3) is Element of the carrier of V
[(1r - r3),(r2 + r3)] is set
{(1r - r3),(r2 + r3)} is non empty finite set
{{(1r - r3),(r2 + r3)},{(1r - r3)}} is non empty finite V42() set
the Mult of V . [(1r - r3),(r2 + r3)] is set
(r3 * (r1 + u2)) + ((1r - r3) * (r2 + r3)) is Element of the carrier of V
the addF of V . ((r3 * (r1 + u2)),((1r - r3) * (r2 + r3))) is Element of the carrier of V
[(r3 * (r1 + u2)),((1r - r3) * (r2 + r3))] is set
{(r3 * (r1 + u2)),((1r - r3) * (r2 + r3))} is non empty finite set
{(r3 * (r1 + u2))} is non empty trivial finite 1 -element set
{{(r3 * (r1 + u2)),((1r - r3) * (r2 + r3))},{(r3 * (r1 + u2))}} is non empty finite V42() set
the addF of V . [(r3 * (r1 + u2)),((1r - r3) * (r2 + r3))] is set
(r3 * r1) + (r3 * u2) is Element of the carrier of V
the addF of V . ((r3 * r1),(r3 * u2)) is Element of the carrier of V
[(r3 * r1),(r3 * u2)] is set
{(r3 * r1),(r3 * u2)} is non empty finite set
{{(r3 * r1),(r3 * u2)},{(r3 * r1)}} is non empty finite V42() set
the addF of V . [(r3 * r1),(r3 * u2)] is set
((r3 * r1) + (r3 * u2)) + ((1r - r3) * (r2 + r3)) is Element of the carrier of V
the addF of V . (((r3 * r1) + (r3 * u2)),((1r - r3) * (r2 + r3))) is Element of the carrier of V
[((r3 * r1) + (r3 * u2)),((1r - r3) * (r2 + r3))] is set
{((r3 * r1) + (r3 * u2)),((1r - r3) * (r2 + r3))} is non empty finite set
{((r3 * r1) + (r3 * u2))} is non empty trivial finite 1 -element set
{{((r3 * r1) + (r3 * u2)),((1r - r3) * (r2 + r3))},{((r3 * r1) + (r3 * u2))}} is non empty finite V42() set
the addF of V . [((r3 * r1) + (r3 * u2)),((1r - r3) * (r2 + r3))] is set
((1r - r3) * r2) + ((1r - r3) * r3) is Element of the carrier of V
the addF of V . (((1r - r3) * r2),((1r - r3) * r3)) is Element of the carrier of V
[((1r - r3) * r2),((1r - r3) * r3)] is set
{((1r - r3) * r2),((1r - r3) * r3)} is non empty finite set
{((1r - r3) * r2)} is non empty trivial finite 1 -element set
{{((1r - r3) * r2),((1r - r3) * r3)},{((1r - r3) * r2)}} is non empty finite V42() set
the addF of V . [((1r - r3) * r2),((1r - r3) * r3)] is set
((r3 * r1) + (r3 * u2)) + (((1r - r3) * r2) + ((1r - r3) * r3)) is Element of the carrier of V
the addF of V . (((r3 * r1) + (r3 * u2)),(((1r - r3) * r2) + ((1r - r3) * r3))) is Element of the carrier of V
[((r3 * r1) + (r3 * u2)),(((1r - r3) * r2) + ((1r - r3) * r3))] is set
{((r3 * r1) + (r3 * u2)),(((1r - r3) * r2) + ((1r - r3) * r3))} is non empty finite set
{{((r3 * r1) + (r3 * u2)),(((1r - r3) * r2) + ((1r - r3) * r3))},{((r3 * r1) + (r3 * u2))}} is non empty finite V42() set
the addF of V . [((r3 * r1) + (r3 * u2)),(((1r - r3) * r2) + ((1r - r3) * r3))] is set
((r3 * r1) + (r3 * u2)) + ((1r - r3) * r2) is Element of the carrier of V
the addF of V . (((r3 * r1) + (r3 * u2)),((1r - r3) * r2)) is Element of the carrier of V
[((r3 * r1) + (r3 * u2)),((1r - r3) * r2)] is set
{((r3 * r1) + (r3 * u2)),((1r - r3) * r2)} is non empty finite set
{{((r3 * r1) + (r3 * u2)),((1r - r3) * r2)},{((r3 * r1) + (r3 * u2))}} is non empty finite V42() set
the addF of V . [((r3 * r1) + (r3 * u2)),((1r - r3) * r2)] is set
(((r3 * r1) + (r3 * u2)) + ((1r - r3) * r2)) + ((1r - r3) * r3) is Element of the carrier of V
the addF of V . ((((r3 * r1) + (r3 * u2)) + ((1r - r3) * r2)),((1r - r3) * r3)) is Element of the carrier of V
[(((r3 * r1) + (r3 * u2)) + ((1r - r3) * r2)),((1r - r3) * r3)] is set
{(((r3 * r1) + (r3 * u2)) + ((1r - r3) * r2)),((1r - r3) * r3)} is non empty finite set
{(((r3 * r1) + (r3 * u2)) + ((1r - r3) * r2))} is non empty trivial finite 1 -element set
{{(((r3 * r1) + (r3 * u2)) + ((1r - r3) * r2)),((1r - r3) * r3)},{(((r3 * r1) + (r3 * u2)) + ((1r - r3) * r2))}} is non empty finite V42() set
the addF of V . [(((r3 * r1) + (r3 * u2)) + ((1r - r3) * r2)),((1r - r3) * r3)] is set
((r3 * r1) + ((1r - r3) * r2)) + (r3 * u2) is Element of the carrier of V
the addF of V . (((r3 * r1) + ((1r - r3) * r2)),(r3 * u2)) is Element of the carrier of V
[((r3 * r1) + ((1r - r3) * r2)),(r3 * u2)] is set
{((r3 * r1) + ((1r - r3) * r2)),(r3 * u2)} is non empty finite set
{((r3 * r1) + ((1r - r3) * r2))} is non empty trivial finite 1 -element set
{{((r3 * r1) + ((1r - r3) * r2)),(r3 * u2)},{((r3 * r1) + ((1r - r3) * r2))}} is non empty finite V42() set
the addF of V . [((r3 * r1) + ((1r - r3) * r2)),(r3 * u2)] is set
(((r3 * r1) + ((1r - r3) * r2)) + (r3 * u2)) + ((1r - r3) * r3) is Element of the carrier of V
the addF of V . ((((r3 * r1) + ((1r - r3) * r2)) + (r3 * u2)),((1r - r3) * r3)) is Element of the carrier of V
[(((r3 * r1) + ((1r - r3) * r2)) + (r3 * u2)),((1r - r3) * r3)] is set
{(((r3 * r1) + ((1r - r3) * r2)) + (r3 * u2)),((1r - r3) * r3)} is non empty finite set
{(((r3 * r1) + ((1r - r3) * r2)) + (r3 * u2))} is non empty trivial finite 1 -element set
{{(((r3 * r1) + ((1r - r3) * r2)) + (r3 * u2)),((1r - r3) * r3)},{(((r3 * r1) + ((1r - r3) * r2)) + (r3 * u2))}} is non empty finite V42() set
the addF of V . [(((r3 * r1) + ((1r - r3) * r2)) + (r3 * u2)),((1r - r3) * r3)] is set
((r3 * r1) + ((1r - r3) * r2)) + ((r3 * u2) + ((1r - r3) * r3)) is Element of the carrier of V
the addF of V . (((r3 * r1) + ((1r - r3) * r2)),((r3 * u2) + ((1r - r3) * r3))) is Element of the carrier of V
[((r3 * r1) + ((1r - r3) * r2)),((r3 * u2) + ((1r - r3) * r3))] is set
{((r3 * r1) + ((1r - r3) * r2)),((r3 * u2) + ((1r - r3) * r3))} is non empty finite set
{{((r3 * r1) + ((1r - r3) * r2)),((r3 * u2) + ((1r - r3) * r3))},{((r3 * r1) + ((1r - r3) * r2))}} is non empty finite V42() set
the addF of V . [((r3 * r1) + ((1r - r3) * r2)),((r3 * u2) + ((1r - r3) * r3))] is set
V is non empty vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is complex set
SG is complex set
N + SG is complex set
(V,M,(N + SG)) is Element of bool the carrier of V
{ ((N + SG) * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
(V,M,N) is Element of bool the carrier of V
{ (N * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
(V,M,SG) is Element of bool the carrier of V
{ (SG * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
(V,M,N) + (V,M,SG) is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in (V,M,N) & b₂ in (V,M,SG) ) } is set
Y is Element of the carrier of V
r2 is Element of the carrier of V
(N + SG) * r2 is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(N + SG),r2] is set
{(N + SG),r2} is non empty finite set
{(N + SG)} is non empty trivial finite 1 -element V68() set
{{(N + SG),r2},{(N + SG)}} is non empty finite V42() set
the Mult of V . [(N + SG),r2] is set
SG * r2 is Element of the carrier of V
[SG,r2] is set
{SG,r2} is non empty finite set
{SG} is non empty trivial finite 1 -element V68() set
{{SG,r2},{SG}} is non empty finite V42() set
the Mult of V . [SG,r2] is set
N * r2 is Element of the carrier of V
[N,r2] is set
{N,r2} is non empty finite set
{N} is non empty trivial finite 1 -element V68() set
{{N,r2},{N}} is non empty finite V42() set
the Mult of V . [N,r2] is set
(N * r2) + (SG * r2) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((N * r2),(SG * r2)) is Element of the carrier of V
[(N * r2),(SG * r2)] is set
{(N * r2),(SG * r2)} is non empty finite set
{(N * r2)} is non empty trivial finite 1 -element set
{{(N * r2),(SG * r2)},{(N * r2)}} is non empty finite V42() set
the addF of V . [(N * r2),(SG * r2)] is set
V is non empty CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Element of bool the carrier of V
SG is complex set
(V,M,SG) is Element of bool the carrier of V
{ (SG * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
(V,N,SG) is Element of bool the carrier of V
{ (SG * b₁) where b₁ is Element of the carrier of V : b₁ in N } is set
Y is Element of the carrier of V
r2 is Element of the carrier of V
SG * r2 is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[SG,r2] is set
{SG,r2} is non empty finite set
{SG} is non empty trivial finite 1 -element V68() set
{{SG,r2},{SG}} is non empty finite V42() set
the Mult of V . [SG,r2] is set
V is non empty CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is empty proper ordinal natural complex real finite V42() cardinal {} -element ext-real non positive non negative V68() V69() V70() V71() V72() V73() V74() (V) Element of bool the carrier of V
N is complex set
(V,M,N) is Element of bool the carrier of V
{ (N * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
SG is Element of the carrier of V
Y is Element of the carrier of V
N * Y is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[N,Y] is set
{N,Y} is non empty finite set
{N} is non empty trivial finite 1 -element V68() set
{{N,Y},{N}} is non empty finite V42() set
the Mult of V . [N,Y] is set
V is non empty addLoopStr
the carrier of V is non empty set
bool the carrier of V is non empty set
M is empty proper ordinal natural complex real finite V42() cardinal {} -element ext-real non positive non negative V68() V69() V70() V71() V72() V73() V74() Element of bool the carrier of V
N is Element of bool the carrier of V
M + N is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in M & b₂ in N ) } is set
SG is Element of the carrier of V
Y is Element of the carrier of V
r2 is Element of the carrier of V
Y + r2 is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (Y,r2) is Element of the carrier of V
[Y,r2] is set
{Y,r2} is non empty finite set
{Y} is non empty trivial finite 1 -element set
{{Y,r2},{Y}} is non empty finite V42() set
the addF of V . [Y,r2] is set
V is non empty right_zeroed addLoopStr
the carrier of V is non empty set
bool the carrier of V is non empty set
0. V is zero Element of the carrier of V
the ZeroF of V is Element of the carrier of V
{(0. V)} is non empty trivial finite 1 -element Element of bool the carrier of V
M is Element of bool the carrier of V
M + {(0. V)} is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in M & b₂ in {(0. V)} ) } is set
N is Element of the carrier of V
SG is Element of the carrier of V
Y is Element of the carrier of V
SG + Y is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (SG,Y) is Element of the carrier of V
[SG,Y] is set
{SG,Y} is non empty finite set
{SG} is non empty trivial finite 1 -element set
{{SG,Y},{SG}} is non empty finite V42() set
the addF of V . [SG,Y] is set
N is Element of the carrier of V
N + (0. V) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (N,(0. V)) is Element of the carrier of V
[N,(0. V)] is set
{N,(0. V)} is non empty finite set
{N} is non empty trivial finite 1 -element set
{{N,(0. V)},{N}} is non empty finite V42() set
the addF of V . [N,(0. V)] is set
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is complex set
SG is complex set
(V,M,N) is Element of bool the carrier of V
{ (N * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
(V,M,SG) is Element of bool the carrier of V
{ (SG * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
(V,M,N) + (V,M,SG) is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in (V,M,N) & b₂ in (V,M,SG) ) } is set
N + SG is complex set
(V,M,(N + SG)) is Element of bool the carrier of V
{ ((N + SG) * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
Y is complex real ext-real Element of REAL
r2 is complex real ext-real Element of REAL
Y is complex real ext-real Element of REAL
r2 is complex real ext-real Element of REAL
0. V is zero Element of the carrier of V
the ZeroF of V is Element of the carrier of V
{(0. V)} is non empty trivial finite 1 -element Element of bool the carrier of V
0. V is zero Element of the carrier of V
the ZeroF of V is Element of the carrier of V
{(0. V)} is non empty trivial finite 1 -element Element of bool the carrier of V
Y + r2 is complex real ext-real Element of REAL
Y / (Y + r2) is complex real ext-real Element of REAL
(Y + r2) " is complex real ext-real set
Y * ((Y + r2) ") is complex real ext-real set
N / (N + SG) is complex Element of COMPLEX
(N + SG) " is complex set
N * ((N + SG) ") is complex set
(V,M,(N / (N + SG))) is Element of bool the carrier of V
{ ((N / (N + SG)) * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
1r - (N / (N + SG)) is complex Element of COMPLEX
- (N / (N + SG)) is complex set
1r + (- (N / (N + SG))) is complex set
(V,M,(1r - (N / (N + SG)))) is Element of bool the carrier of V
{ ((1r - (N / (N + SG))) * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
(V,M,(N / (N + SG))) + (V,M,(1r - (N / (N + SG)))) is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in (V,M,(N / (N + SG))) & b₂ in (V,M,(1r - (N / (N + SG)))) ) } is set
(V,((V,M,(N / (N + SG))) + (V,M,(1r - (N / (N + SG))))),(N + SG)) is Element of bool the carrier of V
{ ((N + SG) * b₁) where b₁ is Element of the carrier of V : b₁ in (V,M,(N / (N + SG))) + (V,M,(1r - (N / (N + SG)))) } is set
1 - (Y / (Y + r2)) is complex real ext-real Element of REAL
- (Y / (Y + r2)) is complex real ext-real set
1 + (- (Y / (Y + r2))) is complex real ext-real set
(Y + r2) / (Y + r2) is complex real ext-real Element of REAL
(Y + r2) * ((Y + r2) ") is complex real ext-real set
((Y + r2) / (Y + r2)) - (Y / (Y + r2)) is complex real ext-real Element of REAL
((Y + r2) / (Y + r2)) + (- (Y / (Y + r2))) is complex real ext-real set
(Y + r2) - Y is complex real ext-real Element of REAL
- Y is complex real ext-real set
(Y + r2) + (- Y) is complex real ext-real set
((Y + r2) - Y) / (Y + r2) is complex real ext-real Element of REAL
((Y + r2) - Y) * ((Y + r2) ") is complex real ext-real set
(V,(V,M,(1r - (N / (N + SG)))),(N + SG)) is Element of bool the carrier of V
{ ((N + SG) * b₁) where b₁ is Element of the carrier of V : b₁ in (V,M,(1r - (N / (N + SG)))) } is set
SG / (N + SG) is complex Element of COMPLEX
SG * ((N + SG) ") is complex set
(SG / (N + SG)) * (N + SG) is complex set
(V,M,((SG / (N + SG)) * (N + SG))) is Element of bool the carrier of V
{ (((SG / (N + SG)) * (N + SG)) * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
(V,(V,M,(N / (N + SG))),(N + SG)) is Element of bool the carrier of V
{ ((N + SG) * b₁) where b₁ is Element of the carrier of V : b₁ in (V,M,(N / (N + SG))) } is set
(N / (N + SG)) * (N + SG) is complex set
(V,M,((N / (N + SG)) * (N + SG))) is Element of bool the carrier of V
{ (((N / (N + SG)) * (N + SG)) * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is complex set
SG is complex set
(V,M,N) is Element of bool the carrier of V
{ (N * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
(V,M,SG) is Element of bool the carrier of V
{ (SG * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
(V,M,N) + (V,M,SG) is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in (V,M,N) & b₂ in (V,M,SG) ) } is set
N + SG is complex set
(V,M,(N + SG)) is Element of bool the carrier of V
{ ((N + SG) * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
Y is complex real ext-real Element of REAL
r2 is complex real ext-real Element of REAL
V is non empty Abelian add-associative vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Element of bool the carrier of V
SG is Element of bool the carrier of V
Y is complex set
(V,M,Y) is Element of bool the carrier of V
{ (Y * b₁) where b₁ is Element of the carrier of V : b₁ in M } is set
r2 is complex set
(V,N,r2) is Element of bool the carrier of V
{ (r2 * b₁) where b₁ is Element of the carrier of V : b₁ in N } is set
(V,M,Y) + (V,N,r2) is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in (V,M,Y) & b₂ in (V,N,r2) ) } is set
r1 is complex set
(V,SG,r1) is Element of bool the carrier of V
{ (r1 * b₁) where b₁ is Element of the carrier of V : b₁ in SG } is set
((V,M,Y) + (V,N,r2)) + (V,SG,r1) is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in (V,M,Y) + (V,N,r2) & b₂ in (V,SG,r1) ) } is set
(V,((V,M,Y) + (V,N,r2)),1r) is Element of bool the carrier of V
{ (1r * b₁) where b₁ is Element of the carrier of V : b₁ in (V,M,Y) + (V,N,r2) } is set
(V,((V,M,Y) + (V,N,r2)),1r) + (V,SG,r1) is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is Element of the carrier of V : ( b₁ in (V,((V,M,Y) + (V,N,r2)),1r) & b₂ in (V,SG,r1) ) } is set
V is non empty CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
bool (bool the carrier of V) is non empty set
M is Element of bool (bool the carrier of V)
meet M is Element of bool the carrier of V
N is Element of the carrier of V
SG is Element of the carrier of V
Y is complex set
Y * N is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[Y,N] is set
{Y,N} is non empty finite set
{Y} is non empty trivial finite 1 -element V68() set
{{Y,N},{Y}} is non empty finite V42() set
the Mult of V . [Y,N] is set
1r - Y is complex set
- Y is complex set
1r + (- Y) is complex set
(1r - Y) * SG is Element of the carrier of V
[(1r - Y),SG] is set
{(1r - Y),SG} is non empty finite set
{(1r - Y)} is non empty trivial finite 1 -element V68() set
{{(1r - Y),SG},{(1r - Y)}} is non empty finite V42() set
the Mult of V . [(1r - Y),SG] is set
(Y * N) + ((1r - Y) * SG) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((Y * N),((1r - Y) * SG)) is Element of the carrier of V
[(Y * N),((1r - Y) * SG)] is set
{(Y * N),((1r - Y) * SG)} is non empty finite set
{(Y * N)} is non empty trivial finite 1 -element set
{{(Y * N),((1r - Y) * SG)},{(Y * N)}} is non empty finite V42() set
the addF of V . [(Y * N),((1r - Y) * SG)] is set
r2 is set
r1 is Element of bool the carrier of V
r3 is complex real ext-real Element of REAL
V is non empty CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Element of the carrier of V
SG is Element of the carrier of V
Y is complex set
Y * N is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[Y,N] is set
{Y,N} is non empty finite set
{Y} is non empty trivial finite 1 -element V68() set
{{Y,N},{Y}} is non empty finite V42() set
the Mult of V . [Y,N] is set
1r - Y is complex set
- Y is complex set
1r + (- Y) is complex set
(1r - Y) * SG is Element of the carrier of V
[(1r - Y),SG] is set
{(1r - Y),SG} is non empty finite set
{(1r - Y)} is non empty trivial finite 1 -element V68() set
{{(1r - Y),SG},{(1r - Y)}} is non empty finite V42() set
the Mult of V . [(1r - Y),SG] is set
(Y * N) + ((1r - Y) * SG) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((Y * N),((1r - Y) * SG)) is Element of the carrier of V
[(Y * N),((1r - Y) * SG)] is set
{(Y * N),((1r - Y) * SG)} is non empty finite set
{(Y * N)} is non empty trivial finite 1 -element set
{{(Y * N),((1r - Y) * SG)},{(Y * N)}} is non empty finite V42() set
the addF of V . [(Y * N),((1r - Y) * SG)] is set
r1 is complex real ext-real Element of REAL
r1 is complex real ext-real Element of REAL
1 - r1 is complex real ext-real Element of REAL
- r1 is complex real ext-real set
1 + (- r1) is complex real ext-real set
1r - (1r - Y) is complex set
- (1r - Y) is complex set
1r + (- (1r - Y)) is complex set
(1r - (1r - Y)) * N is Element of the carrier of V
[(1r - (1r - Y)),N] is set
{(1r - (1r - Y)),N} is non empty finite set
{(1r - (1r - Y))} is non empty trivial finite 1 -element V68() set
{{(1r - (1r - Y)),N},{(1r - (1r - Y))}} is non empty finite V42() set
the Mult of V . [(1r - (1r - Y)),N] is set
((1r - (1r - Y)) * N) + ((1r - Y) * SG) is Element of the carrier of V
the addF of V . (((1r - (1r - Y)) * N),((1r - Y) * SG)) is Element of the carrier of V
[((1r - (1r - Y)) * N),((1r - Y) * SG)] is set
{((1r - (1r - Y)) * N),((1r - Y) * SG)} is non empty finite set
{((1r - (1r - Y)) * N)} is non empty trivial finite 1 -element set
{{((1r - (1r - Y)) * N),((1r - Y) * SG)},{((1r - (1r - Y)) * N)}} is non empty finite V42() set
the addF of V . [((1r - (1r - Y)) * N),((1r - Y) * SG)] is set
V is non empty CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
the non empty (V) Element of bool the carrier of V is non empty (V) Element of bool the carrier of V
V is non empty CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
{} V is empty proper ordinal natural complex real finite V42() cardinal {} -element ext-real non positive non negative V68() V69() V70() V71() V72() V73() V74() (V) Element of bool the carrier of V
V is non empty ComplexUnitarySpace-like CUNITSTR
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Element of the carrier of V
SG is complex real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of V : SG <= Re (b₁ .|. N) } is set
Y is Element of the carrier of V
r2 is Element of the carrier of V
r1 is complex set
r1 * Y is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[r1,Y] is set
{r1,Y} is non empty finite set
{r1} is non empty trivial finite 1 -element V68() set
{{r1,Y},{r1}} is non empty finite V42() set
the Mult of V . [r1,Y] is set
1r - r1 is complex set
- r1 is complex set
1r + (- r1) is complex set
(1r - r1) * r2 is Element of the carrier of V
[(1r - r1),r2] is set
{(1r - r1),r2} is non empty finite set
{(1r - r1)} is non empty trivial finite 1 -element V68() set
{{(1r - r1),r2},{(1r - r1)}} is non empty finite V42() set
the Mult of V . [(1r - r1),r2] is set
(r1 * Y) + ((1r - r1) * r2) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((r1 * Y),((1r - r1) * r2)) is Element of the carrier of V
[(r1 * Y),((1r - r1) * r2)] is set
{(r1 * Y),((1r - r1) * r2)} is non empty finite set
{(r1 * Y)} is non empty trivial finite 1 -element set
{{(r1 * Y),((1r - r1) * r2)},{(r1 * Y)}} is non empty finite V42() set
the addF of V . [(r1 * Y),((1r - r1) * r2)] is set
r3 is complex real ext-real Element of REAL
r3 is complex real ext-real Element of REAL
1 - r3 is complex real ext-real Element of REAL
- r3 is complex real ext-real set
1 + (- r3) is complex real ext-real set
(1 - r3) * SG is complex real ext-real Element of REAL
r2 .|. N is complex set
Re (r2 .|. N) is complex real ext-real Element of REAL
(1 - r3) * (Re (r2 .|. N)) is complex real ext-real Element of REAL
r2 is Element of the carrier of V
r2 .|. N is complex set
Re (r2 .|. N) is complex real ext-real Element of REAL
r3 * SG is complex real ext-real Element of REAL
Y .|. N is complex set
Re (Y .|. N) is complex real ext-real Element of REAL
r3 * (Re (Y .|. N)) is complex real ext-real Element of REAL
r2 is Element of the carrier of V
r2 .|. N is complex set
Re (r2 .|. N) is complex real ext-real Element of REAL
(r3 * SG) + ((1 - r3) * SG) is complex real ext-real Element of REAL
(r3 * (Re (Y .|. N))) + ((1 - r3) * (Re (r2 .|. N))) is complex real ext-real Element of REAL
((r1 * Y) + ((1r - r1) * r2)) .|. N is complex set
Re (((r1 * Y) + ((1r - r1) * r2)) .|. N) is complex real ext-real Element of REAL
(r1 * Y) .|. N is complex set
((1r - r1) * r2) .|. N is complex set
((r1 * Y) .|. N) + (((1r - r1) * r2) .|. N) is complex set
Re (((r1 * Y) .|. N) + (((1r - r1) * r2) .|. N)) is complex real ext-real Element of REAL
r1 * (Y .|. N) is complex set
(r1 * (Y .|. N)) + (((1r - r1) * r2) .|. N) is complex set
Re ((r1 * (Y .|. N)) + (((1r - r1) * r2) .|. N)) is complex real ext-real Element of REAL
(1r - r1) * (r2 .|. N) is complex set
(r1 * (Y .|. N)) + ((1r - r1) * (r2 .|. N)) is complex set
Re ((r1 * (Y .|. N)) + ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
Re (r1 * (Y .|. N)) is complex real ext-real Element of REAL
Re ((1r - r1) * (r2 .|. N)) is complex real ext-real Element of REAL
(Re (r1 * (Y .|. N))) + (Re ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
(r3 * (Re (Y .|. N))) + (Re ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
V is non empty ComplexUnitarySpace-like CUNITSTR
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Element of the carrier of V
SG is complex real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of V : not Re (b₁ .|. N) <= SG } is set
Y is Element of the carrier of V
r2 is Element of the carrier of V
r1 is complex set
r1 * Y is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[r1,Y] is set
{r1,Y} is non empty finite set
{r1} is non empty trivial finite 1 -element V68() set
{{r1,Y},{r1}} is non empty finite V42() set
the Mult of V . [r1,Y] is set
1r - r1 is complex set
- r1 is complex set
1r + (- r1) is complex set
(1r - r1) * r2 is Element of the carrier of V
[(1r - r1),r2] is set
{(1r - r1),r2} is non empty finite set
{(1r - r1)} is non empty trivial finite 1 -element V68() set
{{(1r - r1),r2},{(1r - r1)}} is non empty finite V42() set
the Mult of V . [(1r - r1),r2] is set
(r1 * Y) + ((1r - r1) * r2) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((r1 * Y),((1r - r1) * r2)) is Element of the carrier of V
[(r1 * Y),((1r - r1) * r2)] is set
{(r1 * Y),((1r - r1) * r2)} is non empty finite set
{(r1 * Y)} is non empty trivial finite 1 -element set
{{(r1 * Y),((1r - r1) * r2)},{(r1 * Y)}} is non empty finite V42() set
the addF of V . [(r1 * Y),((1r - r1) * r2)] is set
r3 is complex real ext-real Element of REAL
r3 is complex real ext-real Element of REAL
1 - r3 is complex real ext-real Element of REAL
- r3 is complex real ext-real set
1 + (- r3) is complex real ext-real set
r2 .|. N is complex set
Re (r2 .|. N) is complex real ext-real Element of REAL
(1 - r3) * (Re (r2 .|. N)) is complex real ext-real Element of REAL
(1 - r3) * SG is complex real ext-real Element of REAL
r2 is Element of the carrier of V
r2 .|. N is complex set
Re (r2 .|. N) is complex real ext-real Element of REAL
Y .|. N is complex set
Re (Y .|. N) is complex real ext-real Element of REAL
r3 * (Re (Y .|. N)) is complex real ext-real Element of REAL
r3 * SG is complex real ext-real Element of REAL
r2 is Element of the carrier of V
r2 .|. N is complex set
Re (r2 .|. N) is complex real ext-real Element of REAL
(r3 * (Re (Y .|. N))) + ((1 - r3) * (Re (r2 .|. N))) is complex real ext-real Element of REAL
(r3 * SG) + ((1 - r3) * SG) is complex real ext-real Element of REAL
((r1 * Y) + ((1r - r1) * r2)) .|. N is complex set
Re (((r1 * Y) + ((1r - r1) * r2)) .|. N) is complex real ext-real Element of REAL
(r1 * Y) .|. N is complex set
((1r - r1) * r2) .|. N is complex set
((r1 * Y) .|. N) + (((1r - r1) * r2) .|. N) is complex set
Re (((r1 * Y) .|. N) + (((1r - r1) * r2) .|. N)) is complex real ext-real Element of REAL
r1 * (Y .|. N) is complex set
(r1 * (Y .|. N)) + (((1r - r1) * r2) .|. N) is complex set
Re ((r1 * (Y .|. N)) + (((1r - r1) * r2) .|. N)) is complex real ext-real Element of REAL
(1r - r1) * (r2 .|. N) is complex set
(r1 * (Y .|. N)) + ((1r - r1) * (r2 .|. N)) is complex set
Re ((r1 * (Y .|. N)) + ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
Re (r1 * (Y .|. N)) is complex real ext-real Element of REAL
Re ((1r - r1) * (r2 .|. N)) is complex real ext-real Element of REAL
(Re (r1 * (Y .|. N))) + (Re ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
(r3 * (Re (Y .|. N))) + (Re ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
V is non empty ComplexUnitarySpace-like CUNITSTR
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Element of the carrier of V
SG is complex real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of V : Re (b₁ .|. N) <= SG } is set
Y is Element of the carrier of V
r2 is Element of the carrier of V
r1 is complex set
r1 * Y is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[r1,Y] is set
{r1,Y} is non empty finite set
{r1} is non empty trivial finite 1 -element V68() set
{{r1,Y},{r1}} is non empty finite V42() set
the Mult of V . [r1,Y] is set
1r - r1 is complex set
- r1 is complex set
1r + (- r1) is complex set
(1r - r1) * r2 is Element of the carrier of V
[(1r - r1),r2] is set
{(1r - r1),r2} is non empty finite set
{(1r - r1)} is non empty trivial finite 1 -element V68() set
{{(1r - r1),r2},{(1r - r1)}} is non empty finite V42() set
the Mult of V . [(1r - r1),r2] is set
(r1 * Y) + ((1r - r1) * r2) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((r1 * Y),((1r - r1) * r2)) is Element of the carrier of V
[(r1 * Y),((1r - r1) * r2)] is set
{(r1 * Y),((1r - r1) * r2)} is non empty finite set
{(r1 * Y)} is non empty trivial finite 1 -element set
{{(r1 * Y),((1r - r1) * r2)},{(r1 * Y)}} is non empty finite V42() set
the addF of V . [(r1 * Y),((1r - r1) * r2)] is set
r3 is complex real ext-real Element of REAL
r3 is complex real ext-real Element of REAL
1 - r3 is complex real ext-real Element of REAL
- r3 is complex real ext-real set
1 + (- r3) is complex real ext-real set
r2 .|. N is complex set
Re (r2 .|. N) is complex real ext-real Element of REAL
(1 - r3) * (Re (r2 .|. N)) is complex real ext-real Element of REAL
(1 - r3) * SG is complex real ext-real Element of REAL
r2 is Element of the carrier of V
r2 .|. N is complex set
Re (r2 .|. N) is complex real ext-real Element of REAL
Y .|. N is complex set
Re (Y .|. N) is complex real ext-real Element of REAL
r3 * (Re (Y .|. N)) is complex real ext-real Element of REAL
r3 * SG is complex real ext-real Element of REAL
r2 is Element of the carrier of V
r2 .|. N is complex set
Re (r2 .|. N) is complex real ext-real Element of REAL
(r3 * (Re (Y .|. N))) + ((1 - r3) * (Re (r2 .|. N))) is complex real ext-real Element of REAL
(r3 * SG) + ((1 - r3) * SG) is complex real ext-real Element of REAL
((r1 * Y) + ((1r - r1) * r2)) .|. N is complex set
Re (((r1 * Y) + ((1r - r1) * r2)) .|. N) is complex real ext-real Element of REAL
(r1 * Y) .|. N is complex set
((1r - r1) * r2) .|. N is complex set
((r1 * Y) .|. N) + (((1r - r1) * r2) .|. N) is complex set
Re (((r1 * Y) .|. N) + (((1r - r1) * r2) .|. N)) is complex real ext-real Element of REAL
r1 * (Y .|. N) is complex set
(r1 * (Y .|. N)) + (((1r - r1) * r2) .|. N) is complex set
Re ((r1 * (Y .|. N)) + (((1r - r1) * r2) .|. N)) is complex real ext-real Element of REAL
(1r - r1) * (r2 .|. N) is complex set
(r1 * (Y .|. N)) + ((1r - r1) * (r2 .|. N)) is complex set
Re ((r1 * (Y .|. N)) + ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
Re (r1 * (Y .|. N)) is complex real ext-real Element of REAL
Re ((1r - r1) * (r2 .|. N)) is complex real ext-real Element of REAL
(Re (r1 * (Y .|. N))) + (Re ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
(r3 * (Re (Y .|. N))) + (Re ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
V is non empty ComplexUnitarySpace-like CUNITSTR
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Element of the carrier of V
SG is complex real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of V : not SG <= Re (b₁ .|. N) } is set
Y is Element of the carrier of V
r2 is Element of the carrier of V
r1 is complex set
r1 * Y is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[r1,Y] is set
{r1,Y} is non empty finite set
{r1} is non empty trivial finite 1 -element V68() set
{{r1,Y},{r1}} is non empty finite V42() set
the Mult of V . [r1,Y] is set
1r - r1 is complex set
- r1 is complex set
1r + (- r1) is complex set
(1r - r1) * r2 is Element of the carrier of V
[(1r - r1),r2] is set
{(1r - r1),r2} is non empty finite set
{(1r - r1)} is non empty trivial finite 1 -element V68() set
{{(1r - r1),r2},{(1r - r1)}} is non empty finite V42() set
the Mult of V . [(1r - r1),r2] is set
(r1 * Y) + ((1r - r1) * r2) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((r1 * Y),((1r - r1) * r2)) is Element of the carrier of V
[(r1 * Y),((1r - r1) * r2)] is set
{(r1 * Y),((1r - r1) * r2)} is non empty finite set
{(r1 * Y)} is non empty trivial finite 1 -element set
{{(r1 * Y),((1r - r1) * r2)},{(r1 * Y)}} is non empty finite V42() set
the addF of V . [(r1 * Y),((1r - r1) * r2)] is set
r3 is complex real ext-real Element of REAL
r3 is complex real ext-real Element of REAL
1 - r3 is complex real ext-real Element of REAL
- r3 is complex real ext-real set
1 + (- r3) is complex real ext-real set
(1 - r3) * SG is complex real ext-real Element of REAL
r2 .|. N is complex set
Re (r2 .|. N) is complex real ext-real Element of REAL
(1 - r3) * (Re (r2 .|. N)) is complex real ext-real Element of REAL
r2 is Element of the carrier of V
r2 .|. N is complex set
Re (r2 .|. N) is complex real ext-real Element of REAL
r3 * SG is complex real ext-real Element of REAL
Y .|. N is complex set
Re (Y .|. N) is complex real ext-real Element of REAL
r3 * (Re (Y .|. N)) is complex real ext-real Element of REAL
r2 is Element of the carrier of V
r2 .|. N is complex set
Re (r2 .|. N) is complex real ext-real Element of REAL
(r3 * SG) + ((1 - r3) * SG) is complex real ext-real Element of REAL
(r3 * (Re (Y .|. N))) + ((1 - r3) * (Re (r2 .|. N))) is complex real ext-real Element of REAL
((r1 * Y) + ((1r - r1) * r2)) .|. N is complex set
Re (((r1 * Y) + ((1r - r1) * r2)) .|. N) is complex real ext-real Element of REAL
(r1 * Y) .|. N is complex set
((1r - r1) * r2) .|. N is complex set
((r1 * Y) .|. N) + (((1r - r1) * r2) .|. N) is complex set
Re (((r1 * Y) .|. N) + (((1r - r1) * r2) .|. N)) is complex real ext-real Element of REAL
r1 * (Y .|. N) is complex set
(r1 * (Y .|. N)) + (((1r - r1) * r2) .|. N) is complex set
Re ((r1 * (Y .|. N)) + (((1r - r1) * r2) .|. N)) is complex real ext-real Element of REAL
(1r - r1) * (r2 .|. N) is complex set
(r1 * (Y .|. N)) + ((1r - r1) * (r2 .|. N)) is complex set
Re ((r1 * (Y .|. N)) + ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
Re (r1 * (Y .|. N)) is complex real ext-real Element of REAL
Re ((1r - r1) * (r2 .|. N)) is complex real ext-real Element of REAL
(Re (r1 * (Y .|. N))) + (Re ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
(r3 * (Re (Y .|. N))) + (Re ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
V is non empty ComplexUnitarySpace-like CUNITSTR
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Element of the carrier of V
SG is complex real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of V : SG <= Im (b₁ .|. N) } is set
Y is Element of the carrier of V
r2 is Element of the carrier of V
r1 is complex set
r1 * Y is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[r1,Y] is set
{r1,Y} is non empty finite set
{r1} is non empty trivial finite 1 -element V68() set
{{r1,Y},{r1}} is non empty finite V42() set
the Mult of V . [r1,Y] is set
1r - r1 is complex set
- r1 is complex set
1r + (- r1) is complex set
(1r - r1) * r2 is Element of the carrier of V
[(1r - r1),r2] is set
{(1r - r1),r2} is non empty finite set
{(1r - r1)} is non empty trivial finite 1 -element V68() set
{{(1r - r1),r2},{(1r - r1)}} is non empty finite V42() set
the Mult of V . [(1r - r1),r2] is set
(r1 * Y) + ((1r - r1) * r2) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((r1 * Y),((1r - r1) * r2)) is Element of the carrier of V
[(r1 * Y),((1r - r1) * r2)] is set
{(r1 * Y),((1r - r1) * r2)} is non empty finite set
{(r1 * Y)} is non empty trivial finite 1 -element set
{{(r1 * Y),((1r - r1) * r2)},{(r1 * Y)}} is non empty finite V42() set
the addF of V . [(r1 * Y),((1r - r1) * r2)] is set
r3 is complex real ext-real Element of REAL
r3 is complex real ext-real Element of REAL
1 - r3 is complex real ext-real Element of REAL
- r3 is complex real ext-real set
1 + (- r3) is complex real ext-real set
(1 - r3) * SG is complex real ext-real Element of REAL
r2 .|. N is complex set
Im (r2 .|. N) is complex real ext-real Element of REAL
(1 - r3) * (Im (r2 .|. N)) is complex real ext-real Element of REAL
r2 is Element of the carrier of V
r2 .|. N is complex set
Im (r2 .|. N) is complex real ext-real Element of REAL
r3 * SG is complex real ext-real Element of REAL
Y .|. N is complex set
Im (Y .|. N) is complex real ext-real Element of REAL
r3 * (Im (Y .|. N)) is complex real ext-real Element of REAL
r2 is Element of the carrier of V
r2 .|. N is complex set
Im (r2 .|. N) is complex real ext-real Element of REAL
(r3 * SG) + ((1 - r3) * SG) is complex real ext-real Element of REAL
(r3 * (Im (Y .|. N))) + ((1 - r3) * (Im (r2 .|. N))) is complex real ext-real Element of REAL
((r1 * Y) + ((1r - r1) * r2)) .|. N is complex set
Im (((r1 * Y) + ((1r - r1) * r2)) .|. N) is complex real ext-real Element of REAL
(r1 * Y) .|. N is complex set
((1r - r1) * r2) .|. N is complex set
((r1 * Y) .|. N) + (((1r - r1) * r2) .|. N) is complex set
Im (((r1 * Y) .|. N) + (((1r - r1) * r2) .|. N)) is complex real ext-real Element of REAL
r1 * (Y .|. N) is complex set
(r1 * (Y .|. N)) + (((1r - r1) * r2) .|. N) is complex set
Im ((r1 * (Y .|. N)) + (((1r - r1) * r2) .|. N)) is complex real ext-real Element of REAL
(1r - r1) * (r2 .|. N) is complex set
(r1 * (Y .|. N)) + ((1r - r1) * (r2 .|. N)) is complex set
Im ((r1 * (Y .|. N)) + ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
Im (r1 * (Y .|. N)) is complex real ext-real Element of REAL
Im ((1r - r1) * (r2 .|. N)) is complex real ext-real Element of REAL
(Im (r1 * (Y .|. N))) + (Im ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
(r3 * (Im (Y .|. N))) + (Im ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
V is non empty ComplexUnitarySpace-like CUNITSTR
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Element of the carrier of V
SG is complex real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of V : not Im (b₁ .|. N) <= SG } is set
Y is Element of the carrier of V
r2 is Element of the carrier of V
r1 is complex set
r1 * Y is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[r1,Y] is set
{r1,Y} is non empty finite set
{r1} is non empty trivial finite 1 -element V68() set
{{r1,Y},{r1}} is non empty finite V42() set
the Mult of V . [r1,Y] is set
1r - r1 is complex set
- r1 is complex set
1r + (- r1) is complex set
(1r - r1) * r2 is Element of the carrier of V
[(1r - r1),r2] is set
{(1r - r1),r2} is non empty finite set
{(1r - r1)} is non empty trivial finite 1 -element V68() set
{{(1r - r1),r2},{(1r - r1)}} is non empty finite V42() set
the Mult of V . [(1r - r1),r2] is set
(r1 * Y) + ((1r - r1) * r2) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((r1 * Y),((1r - r1) * r2)) is Element of the carrier of V
[(r1 * Y),((1r - r1) * r2)] is set
{(r1 * Y),((1r - r1) * r2)} is non empty finite set
{(r1 * Y)} is non empty trivial finite 1 -element set
{{(r1 * Y),((1r - r1) * r2)},{(r1 * Y)}} is non empty finite V42() set
the addF of V . [(r1 * Y),((1r - r1) * r2)] is set
r3 is complex real ext-real Element of REAL
r3 is complex real ext-real Element of REAL
1 - r3 is complex real ext-real Element of REAL
- r3 is complex real ext-real set
1 + (- r3) is complex real ext-real set
r2 .|. N is complex set
Im (r2 .|. N) is complex real ext-real Element of REAL
(1 - r3) * (Im (r2 .|. N)) is complex real ext-real Element of REAL
(1 - r3) * SG is complex real ext-real Element of REAL
r2 is Element of the carrier of V
r2 .|. N is complex set
Im (r2 .|. N) is complex real ext-real Element of REAL
Y .|. N is complex set
Im (Y .|. N) is complex real ext-real Element of REAL
r3 * (Im (Y .|. N)) is complex real ext-real Element of REAL
r3 * SG is complex real ext-real Element of REAL
r2 is Element of the carrier of V
r2 .|. N is complex set
Im (r2 .|. N) is complex real ext-real Element of REAL
(r3 * (Im (Y .|. N))) + ((1 - r3) * (Im (r2 .|. N))) is complex real ext-real Element of REAL
(r3 * SG) + ((1 - r3) * SG) is complex real ext-real Element of REAL
((r1 * Y) + ((1r - r1) * r2)) .|. N is complex set
Im (((r1 * Y) + ((1r - r1) * r2)) .|. N) is complex real ext-real Element of REAL
(r1 * Y) .|. N is complex set
((1r - r1) * r2) .|. N is complex set
((r1 * Y) .|. N) + (((1r - r1) * r2) .|. N) is complex set
Im (((r1 * Y) .|. N) + (((1r - r1) * r2) .|. N)) is complex real ext-real Element of REAL
r1 * (Y .|. N) is complex set
(r1 * (Y .|. N)) + (((1r - r1) * r2) .|. N) is complex set
Im ((r1 * (Y .|. N)) + (((1r - r1) * r2) .|. N)) is complex real ext-real Element of REAL
(1r - r1) * (r2 .|. N) is complex set
(r1 * (Y .|. N)) + ((1r - r1) * (r2 .|. N)) is complex set
Im ((r1 * (Y .|. N)) + ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
Im (r1 * (Y .|. N)) is complex real ext-real Element of REAL
Im ((1r - r1) * (r2 .|. N)) is complex real ext-real Element of REAL
(Im (r1 * (Y .|. N))) + (Im ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
(r3 * (Im (Y .|. N))) + (Im ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
V is non empty ComplexUnitarySpace-like CUNITSTR
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Element of the carrier of V
SG is complex real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of V : Im (b₁ .|. N) <= SG } is set
Y is Element of the carrier of V
r2 is Element of the carrier of V
r1 is complex set
r1 * Y is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[r1,Y] is set
{r1,Y} is non empty finite set
{r1} is non empty trivial finite 1 -element V68() set
{{r1,Y},{r1}} is non empty finite V42() set
the Mult of V . [r1,Y] is set
1r - r1 is complex set
- r1 is complex set
1r + (- r1) is complex set
(1r - r1) * r2 is Element of the carrier of V
[(1r - r1),r2] is set
{(1r - r1),r2} is non empty finite set
{(1r - r1)} is non empty trivial finite 1 -element V68() set
{{(1r - r1),r2},{(1r - r1)}} is non empty finite V42() set
the Mult of V . [(1r - r1),r2] is set
(r1 * Y) + ((1r - r1) * r2) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((r1 * Y),((1r - r1) * r2)) is Element of the carrier of V
[(r1 * Y),((1r - r1) * r2)] is set
{(r1 * Y),((1r - r1) * r2)} is non empty finite set
{(r1 * Y)} is non empty trivial finite 1 -element set
{{(r1 * Y),((1r - r1) * r2)},{(r1 * Y)}} is non empty finite V42() set
the addF of V . [(r1 * Y),((1r - r1) * r2)] is set
r3 is complex real ext-real Element of REAL
r3 is complex real ext-real Element of REAL
1 - r3 is complex real ext-real Element of REAL
- r3 is complex real ext-real set
1 + (- r3) is complex real ext-real set
r2 .|. N is complex set
Im (r2 .|. N) is complex real ext-real Element of REAL
(1 - r3) * (Im (r2 .|. N)) is complex real ext-real Element of REAL
(1 - r3) * SG is complex real ext-real Element of REAL
r2 is Element of the carrier of V
r2 .|. N is complex set
Im (r2 .|. N) is complex real ext-real Element of REAL
Y .|. N is complex set
Im (Y .|. N) is complex real ext-real Element of REAL
r3 * (Im (Y .|. N)) is complex real ext-real Element of REAL
r3 * SG is complex real ext-real Element of REAL
r2 is Element of the carrier of V
r2 .|. N is complex set
Im (r2 .|. N) is complex real ext-real Element of REAL
(r3 * (Im (Y .|. N))) + ((1 - r3) * (Im (r2 .|. N))) is complex real ext-real Element of REAL
(r3 * SG) + ((1 - r3) * SG) is complex real ext-real Element of REAL
((r1 * Y) + ((1r - r1) * r2)) .|. N is complex set
Im (((r1 * Y) + ((1r - r1) * r2)) .|. N) is complex real ext-real Element of REAL
(r1 * Y) .|. N is complex set
((1r - r1) * r2) .|. N is complex set
((r1 * Y) .|. N) + (((1r - r1) * r2) .|. N) is complex set
Im (((r1 * Y) .|. N) + (((1r - r1) * r2) .|. N)) is complex real ext-real Element of REAL
r1 * (Y .|. N) is complex set
(r1 * (Y .|. N)) + (((1r - r1) * r2) .|. N) is complex set
Im ((r1 * (Y .|. N)) + (((1r - r1) * r2) .|. N)) is complex real ext-real Element of REAL
(1r - r1) * (r2 .|. N) is complex set
(r1 * (Y .|. N)) + ((1r - r1) * (r2 .|. N)) is complex set
Im ((r1 * (Y .|. N)) + ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
Im (r1 * (Y .|. N)) is complex real ext-real Element of REAL
Im ((1r - r1) * (r2 .|. N)) is complex real ext-real Element of REAL
(Im (r1 * (Y .|. N))) + (Im ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
(r3 * (Im (Y .|. N))) + (Im ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
V is non empty ComplexUnitarySpace-like CUNITSTR
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Element of the carrier of V
SG is complex real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of V : not SG <= Im (b₁ .|. N) } is set
Y is Element of the carrier of V
r2 is Element of the carrier of V
r1 is complex set
r1 * Y is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[r1,Y] is set
{r1,Y} is non empty finite set
{r1} is non empty trivial finite 1 -element V68() set
{{r1,Y},{r1}} is non empty finite V42() set
the Mult of V . [r1,Y] is set
1r - r1 is complex set
- r1 is complex set
1r + (- r1) is complex set
(1r - r1) * r2 is Element of the carrier of V
[(1r - r1),r2] is set
{(1r - r1),r2} is non empty finite set
{(1r - r1)} is non empty trivial finite 1 -element V68() set
{{(1r - r1),r2},{(1r - r1)}} is non empty finite V42() set
the Mult of V . [(1r - r1),r2] is set
(r1 * Y) + ((1r - r1) * r2) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((r1 * Y),((1r - r1) * r2)) is Element of the carrier of V
[(r1 * Y),((1r - r1) * r2)] is set
{(r1 * Y),((1r - r1) * r2)} is non empty finite set
{(r1 * Y)} is non empty trivial finite 1 -element set
{{(r1 * Y),((1r - r1) * r2)},{(r1 * Y)}} is non empty finite V42() set
the addF of V . [(r1 * Y),((1r - r1) * r2)] is set
r3 is complex real ext-real Element of REAL
r3 is complex real ext-real Element of REAL
1 - r3 is complex real ext-real Element of REAL
- r3 is complex real ext-real set
1 + (- r3) is complex real ext-real set
(1 - r3) * SG is complex real ext-real Element of REAL
r2 .|. N is complex set
Im (r2 .|. N) is complex real ext-real Element of REAL
(1 - r3) * (Im (r2 .|. N)) is complex real ext-real Element of REAL
r2 is Element of the carrier of V
r2 .|. N is complex set
Im (r2 .|. N) is complex real ext-real Element of REAL
r3 * SG is complex real ext-real Element of REAL
Y .|. N is complex set
Im (Y .|. N) is complex real ext-real Element of REAL
r3 * (Im (Y .|. N)) is complex real ext-real Element of REAL
r2 is Element of the carrier of V
r2 .|. N is complex set
Im (r2 .|. N) is complex real ext-real Element of REAL
(r3 * SG) + ((1 - r3) * SG) is complex real ext-real Element of REAL
(r3 * (Im (Y .|. N))) + ((1 - r3) * (Im (r2 .|. N))) is complex real ext-real Element of REAL
((r1 * Y) + ((1r - r1) * r2)) .|. N is complex set
Im (((r1 * Y) + ((1r - r1) * r2)) .|. N) is complex real ext-real Element of REAL
(r1 * Y) .|. N is complex set
((1r - r1) * r2) .|. N is complex set
((r1 * Y) .|. N) + (((1r - r1) * r2) .|. N) is complex set
Im (((r1 * Y) .|. N) + (((1r - r1) * r2) .|. N)) is complex real ext-real Element of REAL
r1 * (Y .|. N) is complex set
(r1 * (Y .|. N)) + (((1r - r1) * r2) .|. N) is complex set
Im ((r1 * (Y .|. N)) + (((1r - r1) * r2) .|. N)) is complex real ext-real Element of REAL
(1r - r1) * (r2 .|. N) is complex set
(r1 * (Y .|. N)) + ((1r - r1) * (r2 .|. N)) is complex set
Im ((r1 * (Y .|. N)) + ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
Im (r1 * (Y .|. N)) is complex real ext-real Element of REAL
Im ((1r - r1) * (r2 .|. N)) is complex real ext-real Element of REAL
(Im (r1 * (Y .|. N))) + (Im ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
(r3 * (Im (Y .|. N))) + (Im ((1r - r1) * (r2 .|. N))) is complex real ext-real Element of REAL
V is non empty ComplexUnitarySpace-like CUNITSTR
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Element of the carrier of V
SG is complex real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of V : |.(b₁ .|. N).| <= SG } is set
Y is Element of the carrier of V
r2 is Element of the carrier of V
r1 is complex set
r1 * Y is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[r1,Y] is set
{r1,Y} is non empty finite set
{r1} is non empty trivial finite 1 -element V68() set
{{r1,Y},{r1}} is non empty finite V42() set
the Mult of V . [r1,Y] is set
1r - r1 is complex set
- r1 is complex set
1r + (- r1) is complex set
(1r - r1) * r2 is Element of the carrier of V
[(1r - r1),r2] is set
{(1r - r1),r2} is non empty finite set
{(1r - r1)} is non empty trivial finite 1 -element V68() set
{{(1r - r1),r2},{(1r - r1)}} is non empty finite V42() set
the Mult of V . [(1r - r1),r2] is set
(r1 * Y) + ((1r - r1) * r2) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((r1 * Y),((1r - r1) * r2)) is Element of the carrier of V
[(r1 * Y),((1r - r1) * r2)] is set
{(r1 * Y),((1r - r1) * r2)} is non empty finite set
{(r1 * Y)} is non empty trivial finite 1 -element set
{{(r1 * Y),((1r - r1) * r2)},{(r1 * Y)}} is non empty finite V42() set
the addF of V . [(r1 * Y),((1r - r1) * r2)] is set
r3 is complex real ext-real Element of REAL
r3 is complex real ext-real Element of REAL
1 - r3 is complex real ext-real Element of REAL
- r3 is complex real ext-real set
1 + (- r3) is complex real ext-real set
r2 .|. N is complex set
|.(r2 .|. N).| is complex real ext-real Element of REAL
(1 - r3) * |.(r2 .|. N).| is complex real ext-real Element of REAL
(1 - r3) * SG is complex real ext-real Element of REAL
r2 is Element of the carrier of V
r2 .|. N is complex set
|.(r2 .|. N).| is complex real ext-real Element of REAL
Y .|. N is complex set
|.(Y .|. N).| is complex real ext-real Element of REAL
r3 * |.(Y .|. N).| is complex real ext-real Element of REAL
r3 * SG is complex real ext-real Element of REAL
r2 is Element of the carrier of V
r2 .|. N is complex set
|.(r2 .|. N).| is complex real ext-real Element of REAL
(r3 * |.(Y .|. N).|) + ((1 - r3) * |.(r2 .|. N).|) is complex real ext-real Element of REAL
(r3 * SG) + ((1 - r3) * SG) is complex real ext-real Element of REAL
r1 * (Y .|. N) is complex set
|.(r1 * (Y .|. N)).| is complex real ext-real Element of REAL
(1r - r1) * (r2 .|. N) is complex set
|.((1r - r1) * (r2 .|. N)).| is complex real ext-real Element of REAL
(r1 * (Y .|. N)) + ((1r - r1) * (r2 .|. N)) is complex set
|.((r1 * (Y .|. N)) + ((1r - r1) * (r2 .|. N))).| is complex real ext-real Element of REAL
((r1 * Y) + ((1r - r1) * r2)) .|. N is complex set
|.(((r1 * Y) + ((1r - r1) * r2)) .|. N).| is complex real ext-real Element of REAL
(r1 * Y) .|. N is complex set
((1r - r1) * r2) .|. N is complex set
((r1 * Y) .|. N) + (((1r - r1) * r2) .|. N) is complex set
|.(((r1 * Y) .|. N) + (((1r - r1) * r2) .|. N)).| is complex real ext-real Element of REAL
(r1 * (Y .|. N)) + (((1r - r1) * r2) .|. N) is complex set
|.((r1 * (Y .|. N)) + (((1r - r1) * r2) .|. N)).| is complex real ext-real Element of REAL
V is non empty ComplexUnitarySpace-like CUNITSTR
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
N is Element of the carrier of V
SG is complex real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of V : not SG <= |.(b₁ .|. N).| } is set
Y is Element of the carrier of V
r2 is Element of the carrier of V
r1 is complex set
r1 * Y is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[r1,Y] is set
{r1,Y} is non empty finite set
{r1} is non empty trivial finite 1 -element V68() set
{{r1,Y},{r1}} is non empty finite V42() set
the Mult of V . [r1,Y] is set
1r - r1 is complex set
- r1 is complex set
1r + (- r1) is complex set
(1r - r1) * r2 is Element of the carrier of V
[(1r - r1),r2] is set
{(1r - r1),r2} is non empty finite set
{(1r - r1)} is non empty trivial finite 1 -element V68() set
{{(1r - r1),r2},{(1r - r1)}} is non empty finite V42() set
the Mult of V . [(1r - r1),r2] is set
(r1 * Y) + ((1r - r1) * r2) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((r1 * Y),((1r - r1) * r2)) is Element of the carrier of V
[(r1 * Y),((1r - r1) * r2)] is set
{(r1 * Y),((1r - r1) * r2)} is non empty finite set
{(r1 * Y)} is non empty trivial finite 1 -element set
{{(r1 * Y),((1r - r1) * r2)},{(r1 * Y)}} is non empty finite V42() set
the addF of V . [(r1 * Y),((1r - r1) * r2)] is set
r3 is complex real ext-real Element of REAL
r3 is complex real ext-real Element of REAL
1 - r3 is complex real ext-real Element of REAL
- r3 is complex real ext-real set
1 + (- r3) is complex real ext-real set
(1 - r3) * SG is complex real ext-real Element of REAL
r2 .|. N is complex set
|.(r2 .|. N).| is complex real ext-real Element of REAL
(1 - r3) * |.(r2 .|. N).| is complex real ext-real Element of REAL
r2 is Element of the carrier of V
r2 .|. N is complex set
|.(r2 .|. N).| is complex real ext-real Element of REAL
r3 * SG is complex real ext-real Element of REAL
Y .|. N is complex set
|.(Y .|. N).| is complex real ext-real Element of REAL
r3 * |.(Y .|. N).| is complex real ext-real Element of REAL
r2 is Element of the carrier of V
r2 .|. N is complex set
|.(r2 .|. N).| is complex real ext-real Element of REAL
(r3 * SG) + ((1 - r3) * SG) is complex real ext-real Element of REAL
(r3 * |.(Y .|. N).|) + ((1 - r3) * |.(r2 .|. N).|) is complex real ext-real Element of REAL
r1 * (Y .|. N) is complex set
|.(r1 * (Y .|. N)).| is complex real ext-real Element of REAL
(1r - r1) * (r2 .|. N) is complex set
|.((1r - r1) * (r2 .|. N)).| is complex real ext-real Element of REAL
(r1 * (Y .|. N)) + ((1r - r1) * (r2 .|. N)) is complex set
|.((r1 * (Y .|. N)) + ((1r - r1) * (r2 .|. N))).| is complex real ext-real Element of REAL
((r1 * Y) + ((1r - r1) * r2)) .|. N is complex set
|.(((r1 * Y) + ((1r - r1) * r2)) .|. N).| is complex real ext-real Element of REAL
(r1 * Y) .|. N is complex set
((1r - r1) * r2) .|. N is complex set
((r1 * Y) .|. N) + (((1r - r1) * r2) .|. N) is complex set
|.(((r1 * Y) .|. N) + (((1r - r1) * r2) .|. N)).| is complex real ext-real Element of REAL
(r1 * (Y .|. N)) + (((1r - r1) * r2) .|. N) is complex set
|.((r1 * (Y .|. N)) + (((1r - r1) * r2) .|. N)).| is complex real ext-real Element of REAL
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M) is finite Element of bool the carrier of V
bool the carrier of V is non empty set
{ b₁ where b₁ is Element of the carrier of V : not M . b₁ = 0c } is set
N is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
rng N is Element of bool the carrier of V
len N is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
SG is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V58() V59() V60() FinSequence of REAL
len SG is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
Sum SG is complex real ext-real Element of REAL
K295(REAL,SG,K267()) is complex real ext-real Element of REAL
dom SG is V68() V69() V70() V71() V72() V73() Element of bool NAT
SG is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V58() V59() V60() FinSequence of REAL
len SG is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
Sum SG is complex real ext-real Element of REAL
K295(REAL,SG,K267()) is complex real ext-real Element of REAL
dom SG is V68() V69() V70() V71() V72() V73() Element of bool NAT
<*> the carrier of V is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M) is finite Element of bool the carrier of V
bool the carrier of V is non empty set
{ b₁ where b₁ is Element of the carrier of V : not M . b₁ = 0c } is set
N is Element of the carrier of V
M . N is complex Element of COMPLEX
SG is complex real ext-real Element of REAL
SG is complex real ext-real Element of REAL
Y is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
rng Y is Element of bool the carrier of V
len Y is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
dom Y is V68() V69() V70() V71() V72() V73() Element of bool NAT
r2 is set
Y . r2 is set
r3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V58() V59() V60() FinSequence of REAL
len r3 is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
Sum r3 is complex real ext-real Element of REAL
K295(REAL,r3,K267()) is complex real ext-real Element of REAL
dom r3 is V68() V69() V70() V71() V72() V73() Element of bool NAT
r3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V58() V59() V60() FinSequence of REAL
len r3 is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
Sum r3 is complex real ext-real Element of REAL
K295(REAL,r3,K267()) is complex real ext-real Element of REAL
dom r3 is V68() V69() V70() V71() V72() V73() Element of bool NAT
r1 is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
Seg (len Y) is V68() V69() V70() V71() V72() V73() Element of bool NAT
{ b₁ where b₁ is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT : ( 1 <= b₁ & b₁ <= len Y ) } is set
r3 . r1 is complex real ext-real set
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
M is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,M) is finite Element of bool the carrier of V
bool the carrier of V is non empty set
{ b₁ where b₁ is Element of the carrier of V : not M . b₁ = 0c } is set
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
M is Element of the carrier of V
{M} is non empty trivial finite 1 -element Element of bool the carrier of V
bool the carrier of V is non empty set
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,N) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not N . b₁ = 0c } is set
N . M is complex Element of COMPLEX
(V,N) is Element of the carrier of V
(N . M) * M is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(N . M),M] is set
{(N . M),M} is non empty finite set
{(N . M)} is non empty trivial finite 1 -element V68() set
{{(N . M),M},{(N . M)}} is non empty finite V42() set
the Mult of V . [(N . M),M] is set
SG is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,{M})
(V,SG) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not SG . b₁ = 0c } is set
Y is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
rng Y is Element of bool the carrier of V
len Y is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
<*M*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
[1,M] is set
{1,M} is non empty finite set
{{1,M},{1}} is non empty finite V42() set
{[1,M]} is non empty trivial finite 1 -element set
r2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V58() V59() V60() FinSequence of REAL
len r2 is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
Sum r2 is complex real ext-real Element of REAL
K295(REAL,r2,K267()) is complex real ext-real Element of REAL
dom r2 is V68() V69() V70() V71() V72() V73() Element of bool NAT
r2 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V58() V59() V60() FinSequence of REAL
len r2 is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
Sum r2 is complex real ext-real Element of REAL
K295(REAL,r2,K267()) is complex real ext-real Element of REAL
dom r2 is V68() V69() V70() V71() V72() V73() Element of bool NAT
r2 /. 1 is complex real ext-real Element of REAL
card (V,SG) is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of omega
r2 . 1 is complex real ext-real set
r1 is complex real ext-real Element of REAL
<*r1*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V58() V59() V60() FinSequence of REAL
[1,r1] is set
{1,r1} is non empty finite V68() V69() V70() set
{{1,r1},{1}} is non empty finite V42() set
{[1,r1]} is non empty trivial finite 1 -element set
Y . 1 is set
SG . (Y . 1) is complex set
SG . M is complex Element of COMPLEX
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
M is Element of the carrier of V
N is Element of the carrier of V
{M,N} is non empty finite Element of bool the carrier of V
bool the carrier of V is non empty set
SG is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,SG) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not SG . b₁ = 0c } is set
SG . M is complex Element of COMPLEX
SG . N is complex Element of COMPLEX
(V,SG) is Element of the carrier of V
(SG . M) * M is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(SG . M),M] is set
{(SG . M),M} is non empty finite set
{(SG . M)} is non empty trivial finite 1 -element V68() set
{{(SG . M),M},{(SG . M)}} is non empty finite V42() set
the Mult of V . [(SG . M),M] is set
(SG . N) * N is Element of the carrier of V
[(SG . N),N] is set
{(SG . N),N} is non empty finite set
{(SG . N)} is non empty trivial finite 1 -element V68() set
{{(SG . N),N},{(SG . N)}} is non empty finite V42() set
the Mult of V . [(SG . N),N] is set
((SG . M) * M) + ((SG . N) * N) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (((SG . M) * M),((SG . N) * N)) is Element of the carrier of V
[((SG . M) * M),((SG . N) * N)] is set
{((SG . M) * M),((SG . N) * N)} is non empty finite set
{((SG . M) * M)} is non empty trivial finite 1 -element set
{{((SG . M) * M),((SG . N) * N)},{((SG . M) * M)}} is non empty finite V42() set
the addF of V . [((SG . M) * M),((SG . N) * N)] is set
Y is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,{M,N})
(V,Y) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not Y . b₁ = 0c } is set
r2 is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
rng r2 is Element of bool the carrier of V
len r2 is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
r1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V58() V59() V60() FinSequence of REAL
len r1 is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
Sum r1 is complex real ext-real Element of REAL
K295(REAL,r1,K267()) is complex real ext-real Element of REAL
dom r1 is V68() V69() V70() V71() V72() V73() Element of bool NAT
r1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V58() V59() V60() FinSequence of REAL
len r1 is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
Sum r1 is complex real ext-real Element of REAL
K295(REAL,r1,K267()) is complex real ext-real Element of REAL
dom r1 is V68() V69() V70() V71() V72() V73() Element of bool NAT
card {M,N} is non empty ordinal natural complex real finite cardinal V49() V50() ext-real positive non negative V68() V69() V70() V71() V72() V73() Element of omega
{1,2} is non empty finite V42() V68() V69() V70() V71() V72() V73() Element of bool REAL
r1 . 2 is complex real ext-real set
r2 . 2 is set
Y . (r2 . 2) is complex set
r1 /. 2 is complex real ext-real Element of REAL
r1 . 1 is complex real ext-real set
r2 . 1 is set
Y . (r2 . 1) is complex set
r1 /. 1 is complex real ext-real Element of REAL
r2 is complex real ext-real Element of REAL
r3 is complex real ext-real Element of REAL
<*r2,r3*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V58() V59() V60() FinSequence of REAL
<*r2*> is Relation-like Function-like set
[1,r2] is set
{1,r2} is non empty finite V68() V69() V70() set
{{1,r2},{1}} is non empty finite V42() set
{[1,r2]} is non empty trivial finite 1 -element set
<*r3*> is Relation-like Function-like set
[1,r3] is set
{1,r3} is non empty finite V68() V69() V70() set
{{1,r3},{1}} is non empty finite V42() set
{[1,r3]} is non empty trivial finite 1 -element set
K158(<*r2*>,<*r3*>) is Relation-like Function-like FinSequence-like set
Y . M is complex Element of COMPLEX
Y . N is complex Element of COMPLEX
<*M,N*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
<*M*> is Relation-like Function-like set
[1,M] is set
{1,M} is non empty finite set
{{1,M},{1}} is non empty finite V42() set
{[1,M]} is non empty trivial finite 1 -element set
<*N*> is Relation-like Function-like set
[1,N] is set
{1,N} is non empty finite set
{{1,N},{1}} is non empty finite V42() set
{[1,N]} is non empty trivial finite 1 -element set
K158(<*M*>,<*N*>) is Relation-like Function-like FinSequence-like set
r2 + r3 is complex real ext-real Element of REAL
<*N,M*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
<*N*> is Relation-like Function-like set
[1,N] is set
{1,N} is non empty finite set
{{1,N},{1}} is non empty finite V42() set
{[1,N]} is non empty trivial finite 1 -element set
<*M*> is Relation-like Function-like set
[1,M] is set
{1,M} is non empty finite set
{{1,M},{1}} is non empty finite V42() set
{[1,M]} is non empty trivial finite 1 -element set
K158(<*N*>,<*M*>) is Relation-like Function-like FinSequence-like set
r2 + r3 is complex real ext-real Element of REAL
<*M,N*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
<*M*> is Relation-like Function-like set
[1,M] is set
{1,M} is non empty finite set
{{1,M},{1}} is non empty finite V42() set
{[1,M]} is non empty trivial finite 1 -element set
<*N*> is Relation-like Function-like set
[1,N] is set
{1,N} is non empty finite set
{{1,N},{1}} is non empty finite V42() set
{[1,N]} is non empty trivial finite 1 -element set
K158(<*M*>,<*N*>) is Relation-like Function-like FinSequence-like set
<*N,M*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
K158(<*N*>,<*M*>) is Relation-like Function-like FinSequence-like set
r3 is complex real ext-real Element of REAL
r1 is complex real ext-real Element of REAL
r3 + r1 is complex real ext-real Element of REAL
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
M is Element of the carrier of V
N is Element of the carrier of V
SG is Element of the carrier of V
{M,N,SG} is non empty finite Element of bool the carrier of V
bool the carrier of V is non empty set
Y is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,{M,N,SG})
(V,Y) is Element of the carrier of V
Y . M is complex Element of COMPLEX
(Y . M) * M is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(Y . M),M] is set
{(Y . M),M} is non empty finite set
{(Y . M)} is non empty trivial finite 1 -element V68() set
{{(Y . M),M},{(Y . M)}} is non empty finite V42() set
the Mult of V . [(Y . M),M] is set
Y . N is complex Element of COMPLEX
(Y . N) * N is Element of the carrier of V
[(Y . N),N] is set
{(Y . N),N} is non empty finite set
{(Y . N)} is non empty trivial finite 1 -element V68() set
{{(Y . N),N},{(Y . N)}} is non empty finite V42() set
the Mult of V . [(Y . N),N] is set
((Y . M) * M) + ((Y . N) * N) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (((Y . M) * M),((Y . N) * N)) is Element of the carrier of V
[((Y . M) * M),((Y . N) * N)] is set
{((Y . M) * M),((Y . N) * N)} is non empty finite set
{((Y . M) * M)} is non empty trivial finite 1 -element set
{{((Y . M) * M),((Y . N) * N)},{((Y . M) * M)}} is non empty finite V42() set
the addF of V . [((Y . M) * M),((Y . N) * N)] is set
Y . SG is complex Element of COMPLEX
(Y . SG) * SG is Element of the carrier of V
[(Y . SG),SG] is set
{(Y . SG),SG} is non empty finite set
{(Y . SG)} is non empty trivial finite 1 -element V68() set
{{(Y . SG),SG},{(Y . SG)}} is non empty finite V42() set
the Mult of V . [(Y . SG),SG] is set
(((Y . M) * M) + ((Y . N) * N)) + ((Y . SG) * SG) is Element of the carrier of V
the addF of V . ((((Y . M) * M) + ((Y . N) * N)),((Y . SG) * SG)) is Element of the carrier of V
[(((Y . M) * M) + ((Y . N) * N)),((Y . SG) * SG)] is set
{(((Y . M) * M) + ((Y . N) * N)),((Y . SG) * SG)} is non empty finite set
{(((Y . M) * M) + ((Y . N) * N))} is non empty trivial finite 1 -element set
{{(((Y . M) * M) + ((Y . N) * N)),((Y . SG) * SG)},{(((Y . M) * M) + ((Y . N) * N))}} is non empty finite V42() set
the addF of V . [(((Y . M) * M) + ((Y . N) * N)),((Y . SG) * SG)] is set
(V,Y) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not Y . b₁ = 0c } is set
(V) is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
0. V is zero Element of the carrier of V
the ZeroF of V is Element of the carrier of V
(0. V) + (0. V) is Element of the carrier of V
the addF of V . ((0. V),(0. V)) is Element of the carrier of V
[(0. V),(0. V)] is set
{(0. V),(0. V)} is non empty finite set
{(0. V)} is non empty trivial finite 1 -element set
{{(0. V),(0. V)},{(0. V)}} is non empty finite V42() set
the addF of V . [(0. V),(0. V)] is set
((0. V) + (0. V)) + (0. V) is Element of the carrier of V
the addF of V . (((0. V) + (0. V)),(0. V)) is Element of the carrier of V
[((0. V) + (0. V)),(0. V)] is set
{((0. V) + (0. V)),(0. V)} is non empty finite set
{((0. V) + (0. V))} is non empty trivial finite 1 -element set
{{((0. V) + (0. V)),(0. V)},{((0. V) + (0. V))}} is non empty finite V42() set
the addF of V . [((0. V) + (0. V)),(0. V)] is set
0c * M is Element of the carrier of V
[0c,M] is set
{0c,M} is non empty finite set
{0c} is non empty trivial finite V42() 1 -element V68() V69() V70() V71() V72() V73() set
{{0c,M},{0c}} is non empty finite V42() set
the Mult of V . [0c,M] is set
(0c * M) + (0. V) is Element of the carrier of V
the addF of V . ((0c * M),(0. V)) is Element of the carrier of V
[(0c * M),(0. V)] is set
{(0c * M),(0. V)} is non empty finite set
{(0c * M)} is non empty trivial finite 1 -element set
{{(0c * M),(0. V)},{(0c * M)}} is non empty finite V42() set
the addF of V . [(0c * M),(0. V)] is set
((0c * M) + (0. V)) + (0. V) is Element of the carrier of V
the addF of V . (((0c * M) + (0. V)),(0. V)) is Element of the carrier of V
[((0c * M) + (0. V)),(0. V)] is set
{((0c * M) + (0. V)),(0. V)} is non empty finite set
{((0c * M) + (0. V))} is non empty trivial finite 1 -element set
{{((0c * M) + (0. V)),(0. V)},{((0c * M) + (0. V))}} is non empty finite V42() set
the addF of V . [((0c * M) + (0. V)),(0. V)] is set
0c * N is Element of the carrier of V
[0c,N] is set
{0c,N} is non empty finite set
{{0c,N},{0c}} is non empty finite V42() set
the Mult of V . [0c,N] is set
(0c * M) + (0c * N) is Element of the carrier of V
the addF of V . ((0c * M),(0c * N)) is Element of the carrier of V
[(0c * M),(0c * N)] is set
{(0c * M),(0c * N)} is non empty finite set
{{(0c * M),(0c * N)},{(0c * M)}} is non empty finite V42() set
the addF of V . [(0c * M),(0c * N)] is set
((0c * M) + (0c * N)) + (0. V) is Element of the carrier of V
the addF of V . (((0c * M) + (0c * N)),(0. V)) is Element of the carrier of V
[((0c * M) + (0c * N)),(0. V)] is set
{((0c * M) + (0c * N)),(0. V)} is non empty finite set
{((0c * M) + (0c * N))} is non empty trivial finite 1 -element set
{{((0c * M) + (0c * N)),(0. V)},{((0c * M) + (0c * N))}} is non empty finite V42() set
the addF of V . [((0c * M) + (0c * N)),(0. V)] is set
0c * SG is Element of the carrier of V
[0c,SG] is set
{0c,SG} is non empty finite set
{{0c,SG},{0c}} is non empty finite V42() set
the Mult of V . [0c,SG] is set
((0c * M) + (0c * N)) + (0c * SG) is Element of the carrier of V
the addF of V . (((0c * M) + (0c * N)),(0c * SG)) is Element of the carrier of V
[((0c * M) + (0c * N)),(0c * SG)] is set
{((0c * M) + (0c * N)),(0c * SG)} is non empty finite set
{{((0c * M) + (0c * N)),(0c * SG)},{((0c * M) + (0c * N))}} is non empty finite V42() set
the addF of V . [((0c * M) + (0c * N)),(0c * SG)] is set
((Y . M) * M) + (0c * N) is Element of the carrier of V
the addF of V . (((Y . M) * M),(0c * N)) is Element of the carrier of V
[((Y . M) * M),(0c * N)] is set
{((Y . M) * M),(0c * N)} is non empty finite set
{{((Y . M) * M),(0c * N)},{((Y . M) * M)}} is non empty finite V42() set
the addF of V . [((Y . M) * M),(0c * N)] is set
(((Y . M) * M) + (0c * N)) + (0c * SG) is Element of the carrier of V
the addF of V . ((((Y . M) * M) + (0c * N)),(0c * SG)) is Element of the carrier of V
[(((Y . M) * M) + (0c * N)),(0c * SG)] is set
{(((Y . M) * M) + (0c * N)),(0c * SG)} is non empty finite set
{(((Y . M) * M) + (0c * N))} is non empty trivial finite 1 -element set
{{(((Y . M) * M) + (0c * N)),(0c * SG)},{(((Y . M) * M) + (0c * N))}} is non empty finite V42() set
the addF of V . [(((Y . M) * M) + (0c * N)),(0c * SG)] is set
(((Y . M) * M) + ((Y . N) * N)) + (0c * SG) is Element of the carrier of V
the addF of V . ((((Y . M) * M) + ((Y . N) * N)),(0c * SG)) is Element of the carrier of V
[(((Y . M) * M) + ((Y . N) * N)),(0c * SG)] is set
{(((Y . M) * M) + ((Y . N) * N)),(0c * SG)} is non empty finite set
{{(((Y . M) * M) + ((Y . N) * N)),(0c * SG)},{(((Y . M) * M) + ((Y . N) * N))}} is non empty finite V42() set
the addF of V . [(((Y . M) * M) + ((Y . N) * N)),(0c * SG)] is set
{M} is non empty trivial finite 1 -element Element of bool the carrier of V
r2 is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,{M})
(V,r2) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not r2 . b₁ = 0c } is set
(V,r2) is Element of the carrier of V
r2 . M is complex Element of COMPLEX
(r2 . M) * M is Element of the carrier of V
[(r2 . M),M] is set
{(r2 . M),M} is non empty finite set
{(r2 . M)} is non empty trivial finite 1 -element V68() set
{{(r2 . M),M},{(r2 . M)}} is non empty finite V42() set
the Mult of V . [(r2 . M),M] is set
0. V is zero Element of the carrier of V
the ZeroF of V is Element of the carrier of V
((r2 . M) * M) + (0. V) is Element of the carrier of V
the addF of V . (((r2 . M) * M),(0. V)) is Element of the carrier of V
[((r2 . M) * M),(0. V)] is set
{((r2 . M) * M),(0. V)} is non empty finite set
{((r2 . M) * M)} is non empty trivial finite 1 -element set
{{((r2 . M) * M),(0. V)},{((r2 . M) * M)}} is non empty finite V42() set
the addF of V . [((r2 . M) * M),(0. V)] is set
(((r2 . M) * M) + (0. V)) + (0. V) is Element of the carrier of V
the addF of V . ((((r2 . M) * M) + (0. V)),(0. V)) is Element of the carrier of V
[(((r2 . M) * M) + (0. V)),(0. V)] is set
{(((r2 . M) * M) + (0. V)),(0. V)} is non empty finite set
{(((r2 . M) * M) + (0. V))} is non empty trivial finite 1 -element set
{{(((r2 . M) * M) + (0. V)),(0. V)},{(((r2 . M) * M) + (0. V))}} is non empty finite V42() set
the addF of V . [(((r2 . M) * M) + (0. V)),(0. V)] is set
0c * N is Element of the carrier of V
[0c,N] is set
{0c,N} is non empty finite set
{0c} is non empty trivial finite V42() 1 -element V68() V69() V70() V71() V72() V73() set
{{0c,N},{0c}} is non empty finite V42() set
the Mult of V . [0c,N] is set
((r2 . M) * M) + (0c * N) is Element of the carrier of V
the addF of V . (((r2 . M) * M),(0c * N)) is Element of the carrier of V
[((r2 . M) * M),(0c * N)] is set
{((r2 . M) * M),(0c * N)} is non empty finite set
{{((r2 . M) * M),(0c * N)},{((r2 . M) * M)}} is non empty finite V42() set
the addF of V . [((r2 . M) * M),(0c * N)] is set
(((r2 . M) * M) + (0c * N)) + (0. V) is Element of the carrier of V
the addF of V . ((((r2 . M) * M) + (0c * N)),(0. V)) is Element of the carrier of V
[(((r2 . M) * M) + (0c * N)),(0. V)] is set
{(((r2 . M) * M) + (0c * N)),(0. V)} is non empty finite set
{(((r2 . M) * M) + (0c * N))} is non empty trivial finite 1 -element set
{{(((r2 . M) * M) + (0c * N)),(0. V)},{(((r2 . M) * M) + (0c * N))}} is non empty finite V42() set
the addF of V . [(((r2 . M) * M) + (0c * N)),(0. V)] is set
0c * SG is Element of the carrier of V
[0c,SG] is set
{0c,SG} is non empty finite set
{{0c,SG},{0c}} is non empty finite V42() set
the Mult of V . [0c,SG] is set
(((r2 . M) * M) + (0c * N)) + (0c * SG) is Element of the carrier of V
the addF of V . ((((r2 . M) * M) + (0c * N)),(0c * SG)) is Element of the carrier of V
[(((r2 . M) * M) + (0c * N)),(0c * SG)] is set
{(((r2 . M) * M) + (0c * N)),(0c * SG)} is non empty finite set
{{(((r2 . M) * M) + (0c * N)),(0c * SG)},{(((r2 . M) * M) + (0c * N))}} is non empty finite V42() set
the addF of V . [(((r2 . M) * M) + (0c * N)),(0c * SG)] is set
r2 . N is complex Element of COMPLEX
(r2 . N) * N is Element of the carrier of V
[(r2 . N),N] is set
{(r2 . N),N} is non empty finite set
{(r2 . N)} is non empty trivial finite 1 -element V68() set
{{(r2 . N),N},{(r2 . N)}} is non empty finite V42() set
the Mult of V . [(r2 . N),N] is set
((r2 . M) * M) + ((r2 . N) * N) is Element of the carrier of V
the addF of V . (((r2 . M) * M),((r2 . N) * N)) is Element of the carrier of V
[((r2 . M) * M),((r2 . N) * N)] is set
{((r2 . M) * M),((r2 . N) * N)} is non empty finite set
{{((r2 . M) * M),((r2 . N) * N)},{((r2 . M) * M)}} is non empty finite V42() set
the addF of V . [((r2 . M) * M),((r2 . N) * N)] is set
(((r2 . M) * M) + ((r2 . N) * N)) + (0c * SG) is Element of the carrier of V
the addF of V . ((((r2 . M) * M) + ((r2 . N) * N)),(0c * SG)) is Element of the carrier of V
[(((r2 . M) * M) + ((r2 . N) * N)),(0c * SG)] is set
{(((r2 . M) * M) + ((r2 . N) * N)),(0c * SG)} is non empty finite set
{(((r2 . M) * M) + ((r2 . N) * N))} is non empty trivial finite 1 -element set
{{(((r2 . M) * M) + ((r2 . N) * N)),(0c * SG)},{(((r2 . M) * M) + ((r2 . N) * N))}} is non empty finite V42() set
the addF of V . [(((r2 . M) * M) + ((r2 . N) * N)),(0c * SG)] is set
r2 . SG is complex Element of COMPLEX
(r2 . SG) * SG is Element of the carrier of V
[(r2 . SG),SG] is set
{(r2 . SG),SG} is non empty finite set
{(r2 . SG)} is non empty trivial finite 1 -element V68() set
{{(r2 . SG),SG},{(r2 . SG)}} is non empty finite V42() set
the Mult of V . [(r2 . SG),SG] is set
(((r2 . M) * M) + ((r2 . N) * N)) + ((r2 . SG) * SG) is Element of the carrier of V
the addF of V . ((((r2 . M) * M) + ((r2 . N) * N)),((r2 . SG) * SG)) is Element of the carrier of V
[(((r2 . M) * M) + ((r2 . N) * N)),((r2 . SG) * SG)] is set
{(((r2 . M) * M) + ((r2 . N) * N)),((r2 . SG) * SG)} is non empty finite set
{{(((r2 . M) * M) + ((r2 . N) * N)),((r2 . SG) * SG)},{(((r2 . M) * M) + ((r2 . N) * N))}} is non empty finite V42() set
the addF of V . [(((r2 . M) * M) + ((r2 . N) * N)),((r2 . SG) * SG)] is set
{N} is non empty trivial finite 1 -element Element of bool the carrier of V
r2 is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,{N})
(V,r2) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not r2 . b₁ = 0c } is set
(V,r2) is Element of the carrier of V
r2 . N is complex Element of COMPLEX
(r2 . N) * N is Element of the carrier of V
[(r2 . N),N] is set
{(r2 . N),N} is non empty finite set
{(r2 . N)} is non empty trivial finite 1 -element V68() set
{{(r2 . N),N},{(r2 . N)}} is non empty finite V42() set
the Mult of V . [(r2 . N),N] is set
0. V is zero Element of the carrier of V
the ZeroF of V is Element of the carrier of V
(0. V) + ((r2 . N) * N) is Element of the carrier of V
the addF of V . ((0. V),((r2 . N) * N)) is Element of the carrier of V
[(0. V),((r2 . N) * N)] is set
{(0. V),((r2 . N) * N)} is non empty finite set
{(0. V)} is non empty trivial finite 1 -element set
{{(0. V),((r2 . N) * N)},{(0. V)}} is non empty finite V42() set
the addF of V . [(0. V),((r2 . N) * N)] is set
((0. V) + ((r2 . N) * N)) + (0. V) is Element of the carrier of V
the addF of V . (((0. V) + ((r2 . N) * N)),(0. V)) is Element of the carrier of V
[((0. V) + ((r2 . N) * N)),(0. V)] is set
{((0. V) + ((r2 . N) * N)),(0. V)} is non empty finite set
{((0. V) + ((r2 . N) * N))} is non empty trivial finite 1 -element set
{{((0. V) + ((r2 . N) * N)),(0. V)},{((0. V) + ((r2 . N) * N))}} is non empty finite V42() set
the addF of V . [((0. V) + ((r2 . N) * N)),(0. V)] is set
0c * M is Element of the carrier of V
[0c,M] is set
{0c,M} is non empty finite set
{0c} is non empty trivial finite V42() 1 -element V68() V69() V70() V71() V72() V73() set
{{0c,M},{0c}} is non empty finite V42() set
the Mult of V . [0c,M] is set
(0c * M) + ((r2 . N) * N) is Element of the carrier of V
the addF of V . ((0c * M),((r2 . N) * N)) is Element of the carrier of V
[(0c * M),((r2 . N) * N)] is set
{(0c * M),((r2 . N) * N)} is non empty finite set
{(0c * M)} is non empty trivial finite 1 -element set
{{(0c * M),((r2 . N) * N)},{(0c * M)}} is non empty finite V42() set
the addF of V . [(0c * M),((r2 . N) * N)] is set
((0c * M) + ((r2 . N) * N)) + (0. V) is Element of the carrier of V
the addF of V . (((0c * M) + ((r2 . N) * N)),(0. V)) is Element of the carrier of V
[((0c * M) + ((r2 . N) * N)),(0. V)] is set
{((0c * M) + ((r2 . N) * N)),(0. V)} is non empty finite set
{((0c * M) + ((r2 . N) * N))} is non empty trivial finite 1 -element set
{{((0c * M) + ((r2 . N) * N)),(0. V)},{((0c * M) + ((r2 . N) * N))}} is non empty finite V42() set
the addF of V . [((0c * M) + ((r2 . N) * N)),(0. V)] is set
0c * SG is Element of the carrier of V
[0c,SG] is set
{0c,SG} is non empty finite set
{{0c,SG},{0c}} is non empty finite V42() set
the Mult of V . [0c,SG] is set
((0c * M) + ((r2 . N) * N)) + (0c * SG) is Element of the carrier of V
the addF of V . (((0c * M) + ((r2 . N) * N)),(0c * SG)) is Element of the carrier of V
[((0c * M) + ((r2 . N) * N)),(0c * SG)] is set
{((0c * M) + ((r2 . N) * N)),(0c * SG)} is non empty finite set
{{((0c * M) + ((r2 . N) * N)),(0c * SG)},{((0c * M) + ((r2 . N) * N))}} is non empty finite V42() set
the addF of V . [((0c * M) + ((r2 . N) * N)),(0c * SG)] is set
r2 . M is complex Element of COMPLEX
(r2 . M) * M is Element of the carrier of V
[(r2 . M),M] is set
{(r2 . M),M} is non empty finite set
{(r2 . M)} is non empty trivial finite 1 -element V68() set
{{(r2 . M),M},{(r2 . M)}} is non empty finite V42() set
the Mult of V . [(r2 . M),M] is set
((r2 . M) * M) + ((r2 . N) * N) is Element of the carrier of V
the addF of V . (((r2 . M) * M),((r2 . N) * N)) is Element of the carrier of V
[((r2 . M) * M),((r2 . N) * N)] is set
{((r2 . M) * M),((r2 . N) * N)} is non empty finite set
{((r2 . M) * M)} is non empty trivial finite 1 -element set
{{((r2 . M) * M),((r2 . N) * N)},{((r2 . M) * M)}} is non empty finite V42() set
the addF of V . [((r2 . M) * M),((r2 . N) * N)] is set
(((r2 . M) * M) + ((r2 . N) * N)) + (0c * SG) is Element of the carrier of V
the addF of V . ((((r2 . M) * M) + ((r2 . N) * N)),(0c * SG)) is Element of the carrier of V
[(((r2 . M) * M) + ((r2 . N) * N)),(0c * SG)] is set
{(((r2 . M) * M) + ((r2 . N) * N)),(0c * SG)} is non empty finite set
{(((r2 . M) * M) + ((r2 . N) * N))} is non empty trivial finite 1 -element set
{{(((r2 . M) * M) + ((r2 . N) * N)),(0c * SG)},{(((r2 . M) * M) + ((r2 . N) * N))}} is non empty finite V42() set
the addF of V . [(((r2 . M) * M) + ((r2 . N) * N)),(0c * SG)] is set
r2 . SG is complex Element of COMPLEX
(r2 . SG) * SG is Element of the carrier of V
[(r2 . SG),SG] is set
{(r2 . SG),SG} is non empty finite set
{(r2 . SG)} is non empty trivial finite 1 -element V68() set
{{(r2 . SG),SG},{(r2 . SG)}} is non empty finite V42() set
the Mult of V . [(r2 . SG),SG] is set
(((r2 . M) * M) + ((r2 . N) * N)) + ((r2 . SG) * SG) is Element of the carrier of V
the addF of V . ((((r2 . M) * M) + ((r2 . N) * N)),((r2 . SG) * SG)) is Element of the carrier of V
[(((r2 . M) * M) + ((r2 . N) * N)),((r2 . SG) * SG)] is set
{(((r2 . M) * M) + ((r2 . N) * N)),((r2 . SG) * SG)} is non empty finite set
{{(((r2 . M) * M) + ((r2 . N) * N)),((r2 . SG) * SG)},{(((r2 . M) * M) + ((r2 . N) * N))}} is non empty finite V42() set
the addF of V . [(((r2 . M) * M) + ((r2 . N) * N)),((r2 . SG) * SG)] is set
{SG} is non empty trivial finite 1 -element Element of bool the carrier of V
r2 is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,{SG})
(V,r2) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not r2 . b₁ = 0c } is set
(V,r2) is Element of the carrier of V
r2 . SG is complex Element of COMPLEX
(r2 . SG) * SG is Element of the carrier of V
[(r2 . SG),SG] is set
{(r2 . SG),SG} is non empty finite set
{(r2 . SG)} is non empty trivial finite 1 -element V68() set
{{(r2 . SG),SG},{(r2 . SG)}} is non empty finite V42() set
the Mult of V . [(r2 . SG),SG] is set
0. V is zero Element of the carrier of V
the ZeroF of V is Element of the carrier of V
(0. V) + ((r2 . SG) * SG) is Element of the carrier of V
the addF of V . ((0. V),((r2 . SG) * SG)) is Element of the carrier of V
[(0. V),((r2 . SG) * SG)] is set
{(0. V),((r2 . SG) * SG)} is non empty finite set
{(0. V)} is non empty trivial finite 1 -element set
{{(0. V),((r2 . SG) * SG)},{(0. V)}} is non empty finite V42() set
the addF of V . [(0. V),((r2 . SG) * SG)] is set
(0. V) + (0. V) is Element of the carrier of V
the addF of V . ((0. V),(0. V)) is Element of the carrier of V
[(0. V),(0. V)] is set
{(0. V),(0. V)} is non empty finite set
{{(0. V),(0. V)},{(0. V)}} is non empty finite V42() set
the addF of V . [(0. V),(0. V)] is set
((0. V) + (0. V)) + ((r2 . SG) * SG) is Element of the carrier of V
the addF of V . (((0. V) + (0. V)),((r2 . SG) * SG)) is Element of the carrier of V
[((0. V) + (0. V)),((r2 . SG) * SG)] is set
{((0. V) + (0. V)),((r2 . SG) * SG)} is non empty finite set
{((0. V) + (0. V))} is non empty trivial finite 1 -element set
{{((0. V) + (0. V)),((r2 . SG) * SG)},{((0. V) + (0. V))}} is non empty finite V42() set
the addF of V . [((0. V) + (0. V)),((r2 . SG) * SG)] is set
0c * M is Element of the carrier of V
[0c,M] is set
{0c,M} is non empty finite set
{0c} is non empty trivial finite V42() 1 -element V68() V69() V70() V71() V72() V73() set
{{0c,M},{0c}} is non empty finite V42() set
the Mult of V . [0c,M] is set
(0c * M) + (0. V) is Element of the carrier of V
the addF of V . ((0c * M),(0. V)) is Element of the carrier of V
[(0c * M),(0. V)] is set
{(0c * M),(0. V)} is non empty finite set
{(0c * M)} is non empty trivial finite 1 -element set
{{(0c * M),(0. V)},{(0c * M)}} is non empty finite V42() set
the addF of V . [(0c * M),(0. V)] is set
((0c * M) + (0. V)) + ((r2 . SG) * SG) is Element of the carrier of V
the addF of V . (((0c * M) + (0. V)),((r2 . SG) * SG)) is Element of the carrier of V
[((0c * M) + (0. V)),((r2 . SG) * SG)] is set
{((0c * M) + (0. V)),((r2 . SG) * SG)} is non empty finite set
{((0c * M) + (0. V))} is non empty trivial finite 1 -element set
{{((0c * M) + (0. V)),((r2 . SG) * SG)},{((0c * M) + (0. V))}} is non empty finite V42() set
the addF of V . [((0c * M) + (0. V)),((r2 . SG) * SG)] is set
0c * N is Element of the carrier of V
[0c,N] is set
{0c,N} is non empty finite set
{{0c,N},{0c}} is non empty finite V42() set
the Mult of V . [0c,N] is set
(0c * M) + (0c * N) is Element of the carrier of V
the addF of V . ((0c * M),(0c * N)) is Element of the carrier of V
[(0c * M),(0c * N)] is set
{(0c * M),(0c * N)} is non empty finite set
{{(0c * M),(0c * N)},{(0c * M)}} is non empty finite V42() set
the addF of V . [(0c * M),(0c * N)] is set
((0c * M) + (0c * N)) + ((r2 . SG) * SG) is Element of the carrier of V
the addF of V . (((0c * M) + (0c * N)),((r2 . SG) * SG)) is Element of the carrier of V
[((0c * M) + (0c * N)),((r2 . SG) * SG)] is set
{((0c * M) + (0c * N)),((r2 . SG) * SG)} is non empty finite set
{((0c * M) + (0c * N))} is non empty trivial finite 1 -element set
{{((0c * M) + (0c * N)),((r2 . SG) * SG)},{((0c * M) + (0c * N))}} is non empty finite V42() set
the addF of V . [((0c * M) + (0c * N)),((r2 . SG) * SG)] is set
r2 . M is complex Element of COMPLEX
(r2 . M) * M is Element of the carrier of V
[(r2 . M),M] is set
{(r2 . M),M} is non empty finite set
{(r2 . M)} is non empty trivial finite 1 -element V68() set
{{(r2 . M),M},{(r2 . M)}} is non empty finite V42() set
the Mult of V . [(r2 . M),M] is set
((r2 . M) * M) + (0c * N) is Element of the carrier of V
the addF of V . (((r2 . M) * M),(0c * N)) is Element of the carrier of V
[((r2 . M) * M),(0c * N)] is set
{((r2 . M) * M),(0c * N)} is non empty finite set
{((r2 . M) * M)} is non empty trivial finite 1 -element set
{{((r2 . M) * M),(0c * N)},{((r2 . M) * M)}} is non empty finite V42() set
the addF of V . [((r2 . M) * M),(0c * N)] is set
(((r2 . M) * M) + (0c * N)) + ((r2 . SG) * SG) is Element of the carrier of V
the addF of V . ((((r2 . M) * M) + (0c * N)),((r2 . SG) * SG)) is Element of the carrier of V
[(((r2 . M) * M) + (0c * N)),((r2 . SG) * SG)] is set
{(((r2 . M) * M) + (0c * N)),((r2 . SG) * SG)} is non empty finite set
{(((r2 . M) * M) + (0c * N))} is non empty trivial finite 1 -element set
{{(((r2 . M) * M) + (0c * N)),((r2 . SG) * SG)},{(((r2 . M) * M) + (0c * N))}} is non empty finite V42() set
the addF of V . [(((r2 . M) * M) + (0c * N)),((r2 . SG) * SG)] is set
r2 . N is complex Element of COMPLEX
(r2 . N) * N is Element of the carrier of V
[(r2 . N),N] is set
{(r2 . N),N} is non empty finite set
{(r2 . N)} is non empty trivial finite 1 -element V68() set
{{(r2 . N),N},{(r2 . N)}} is non empty finite V42() set
the Mult of V . [(r2 . N),N] is set
((r2 . M) * M) + ((r2 . N) * N) is Element of the carrier of V
the addF of V . (((r2 . M) * M),((r2 . N) * N)) is Element of the carrier of V
[((r2 . M) * M),((r2 . N) * N)] is set
{((r2 . M) * M),((r2 . N) * N)} is non empty finite set
{{((r2 . M) * M),((r2 . N) * N)},{((r2 . M) * M)}} is non empty finite V42() set
the addF of V . [((r2 . M) * M),((r2 . N) * N)] is set
(((r2 . M) * M) + ((r2 . N) * N)) + ((r2 . SG) * SG) is Element of the carrier of V
the addF of V . ((((r2 . M) * M) + ((r2 . N) * N)),((r2 . SG) * SG)) is Element of the carrier of V
[(((r2 . M) * M) + ((r2 . N) * N)),((r2 . SG) * SG)] is set
{(((r2 . M) * M) + ((r2 . N) * N)),((r2 . SG) * SG)} is non empty finite set
{(((r2 . M) * M) + ((r2 . N) * N))} is non empty trivial finite 1 -element set
{{(((r2 . M) * M) + ((r2 . N) * N)),((r2 . SG) * SG)},{(((r2 . M) * M) + ((r2 . N) * N))}} is non empty finite V42() set
the addF of V . [(((r2 . M) * M) + ((r2 . N) * N)),((r2 . SG) * SG)] is set
{M,N} is non empty finite Element of bool the carrier of V
0. V is zero Element of the carrier of V
the ZeroF of V is Element of the carrier of V
(((Y . M) * M) + ((Y . N) * N)) + (0. V) is Element of the carrier of V
the addF of V . ((((Y . M) * M) + ((Y . N) * N)),(0. V)) is Element of the carrier of V
[(((Y . M) * M) + ((Y . N) * N)),(0. V)] is set
{(((Y . M) * M) + ((Y . N) * N)),(0. V)} is non empty finite set
{{(((Y . M) * M) + ((Y . N) * N)),(0. V)},{(((Y . M) * M) + ((Y . N) * N))}} is non empty finite V42() set
the addF of V . [(((Y . M) * M) + ((Y . N) * N)),(0. V)] is set
0c * SG is Element of the carrier of V
[0c,SG] is set
{0c,SG} is non empty finite set
{0c} is non empty trivial finite V42() 1 -element V68() V69() V70() V71() V72() V73() set
{{0c,SG},{0c}} is non empty finite V42() set
the Mult of V . [0c,SG] is set
(((Y . M) * M) + ((Y . N) * N)) + (0c * SG) is Element of the carrier of V
the addF of V . ((((Y . M) * M) + ((Y . N) * N)),(0c * SG)) is Element of the carrier of V
[(((Y . M) * M) + ((Y . N) * N)),(0c * SG)] is set
{(((Y . M) * M) + ((Y . N) * N)),(0c * SG)} is non empty finite set
{{(((Y . M) * M) + ((Y . N) * N)),(0c * SG)},{(((Y . M) * M) + ((Y . N) * N))}} is non empty finite V42() set
the addF of V . [(((Y . M) * M) + ((Y . N) * N)),(0c * SG)] is set
{M,SG} is non empty finite Element of bool the carrier of V
((Y . M) * M) + ((Y . SG) * SG) is Element of the carrier of V
the addF of V . (((Y . M) * M),((Y . SG) * SG)) is Element of the carrier of V
[((Y . M) * M),((Y . SG) * SG)] is set
{((Y . M) * M),((Y . SG) * SG)} is non empty finite set
{{((Y . M) * M),((Y . SG) * SG)},{((Y . M) * M)}} is non empty finite V42() set
the addF of V . [((Y . M) * M),((Y . SG) * SG)] is set
0. V is zero Element of the carrier of V
the ZeroF of V is Element of the carrier of V
((Y . M) * M) + (0. V) is Element of the carrier of V
the addF of V . (((Y . M) * M),(0. V)) is Element of the carrier of V
[((Y . M) * M),(0. V)] is set
{((Y . M) * M),(0. V)} is non empty finite set
{{((Y . M) * M),(0. V)},{((Y . M) * M)}} is non empty finite V42() set
the addF of V . [((Y . M) * M),(0. V)] is set
(((Y . M) * M) + (0. V)) + ((Y . SG) * SG) is Element of the carrier of V
the addF of V . ((((Y . M) * M) + (0. V)),((Y . SG) * SG)) is Element of the carrier of V
[(((Y . M) * M) + (0. V)),((Y . SG) * SG)] is set
{(((Y . M) * M) + (0. V)),((Y . SG) * SG)} is non empty finite set
{(((Y . M) * M) + (0. V))} is non empty trivial finite 1 -element set
{{(((Y . M) * M) + (0. V)),((Y . SG) * SG)},{(((Y . M) * M) + (0. V))}} is non empty finite V42() set
the addF of V . [(((Y . M) * M) + (0. V)),((Y . SG) * SG)] is set
0c * N is Element of the carrier of V
[0c,N] is set
{0c,N} is non empty finite set
{0c} is non empty trivial finite V42() 1 -element V68() V69() V70() V71() V72() V73() set
{{0c,N},{0c}} is non empty finite V42() set
the Mult of V . [0c,N] is set
((Y . M) * M) + (0c * N) is Element of the carrier of V
the addF of V . (((Y . M) * M),(0c * N)) is Element of the carrier of V
[((Y . M) * M),(0c * N)] is set
{((Y . M) * M),(0c * N)} is non empty finite set
{{((Y . M) * M),(0c * N)},{((Y . M) * M)}} is non empty finite V42() set
the addF of V . [((Y . M) * M),(0c * N)] is set
(((Y . M) * M) + (0c * N)) + ((Y . SG) * SG) is Element of the carrier of V
the addF of V . ((((Y . M) * M) + (0c * N)),((Y . SG) * SG)) is Element of the carrier of V
[(((Y . M) * M) + (0c * N)),((Y . SG) * SG)] is set
{(((Y . M) * M) + (0c * N)),((Y . SG) * SG)} is non empty finite set
{(((Y . M) * M) + (0c * N))} is non empty trivial finite 1 -element set
{{(((Y . M) * M) + (0c * N)),((Y . SG) * SG)},{(((Y . M) * M) + (0c * N))}} is non empty finite V42() set
the addF of V . [(((Y . M) * M) + (0c * N)),((Y . SG) * SG)] is set
{N,SG} is non empty finite Element of bool the carrier of V
((Y . N) * N) + ((Y . SG) * SG) is Element of the carrier of V
the addF of V . (((Y . N) * N),((Y . SG) * SG)) is Element of the carrier of V
[((Y . N) * N),((Y . SG) * SG)] is set
{((Y . N) * N),((Y . SG) * SG)} is non empty finite set
{((Y . N) * N)} is non empty trivial finite 1 -element set
{{((Y . N) * N),((Y . SG) * SG)},{((Y . N) * N)}} is non empty finite V42() set
the addF of V . [((Y . N) * N),((Y . SG) * SG)] is set
0. V is zero Element of the carrier of V
the ZeroF of V is Element of the carrier of V
(0. V) + ((Y . N) * N) is Element of the carrier of V
the addF of V . ((0. V),((Y . N) * N)) is Element of the carrier of V
[(0. V),((Y . N) * N)] is set
{(0. V),((Y . N) * N)} is non empty finite set
{(0. V)} is non empty trivial finite 1 -element set
{{(0. V),((Y . N) * N)},{(0. V)}} is non empty finite V42() set
the addF of V . [(0. V),((Y . N) * N)] is set
((0. V) + ((Y . N) * N)) + ((Y . SG) * SG) is Element of the carrier of V
the addF of V . (((0. V) + ((Y . N) * N)),((Y . SG) * SG)) is Element of the carrier of V
[((0. V) + ((Y . N) * N)),((Y . SG) * SG)] is set
{((0. V) + ((Y . N) * N)),((Y . SG) * SG)} is non empty finite set
{((0. V) + ((Y . N) * N))} is non empty trivial finite 1 -element set
{{((0. V) + ((Y . N) * N)),((Y . SG) * SG)},{((0. V) + ((Y . N) * N))}} is non empty finite V42() set
the addF of V . [((0. V) + ((Y . N) * N)),((Y . SG) * SG)] is set
0c * M is Element of the carrier of V
[0c,M] is set
{0c,M} is non empty finite set
{0c} is non empty trivial finite V42() 1 -element V68() V69() V70() V71() V72() V73() set
{{0c,M},{0c}} is non empty finite V42() set
the Mult of V . [0c,M] is set
(0c * M) + ((Y . N) * N) is Element of the carrier of V
the addF of V . ((0c * M),((Y . N) * N)) is Element of the carrier of V
[(0c * M),((Y . N) * N)] is set
{(0c * M),((Y . N) * N)} is non empty finite set
{(0c * M)} is non empty trivial finite 1 -element set
{{(0c * M),((Y . N) * N)},{(0c * M)}} is non empty finite V42() set
the addF of V . [(0c * M),((Y . N) * N)] is set
((0c * M) + ((Y . N) * N)) + ((Y . SG) * SG) is Element of the carrier of V
the addF of V . (((0c * M) + ((Y . N) * N)),((Y . SG) * SG)) is Element of the carrier of V
[((0c * M) + ((Y . N) * N)),((Y . SG) * SG)] is set
{((0c * M) + ((Y . N) * N)),((Y . SG) * SG)} is non empty finite set
{((0c * M) + ((Y . N) * N))} is non empty trivial finite 1 -element set
{{((0c * M) + ((Y . N) * N)),((Y . SG) * SG)},{((0c * M) + ((Y . N) * N))}} is non empty finite V42() set
the addF of V . [((0c * M) + ((Y . N) * N)),((Y . SG) * SG)] is set
r2 is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
rng r2 is Element of bool the carrier of V
(V,r2,Y) is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
Sum (V,r2,Y) is Element of the carrier of V
<*M,N,SG*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
<*M*> is Relation-like Function-like set
[1,M] is set
{1,M} is non empty finite set
{{1,M},{1}} is non empty finite V42() set
{[1,M]} is non empty trivial finite 1 -element set
<*N*> is Relation-like Function-like set
[1,N] is set
{1,N} is non empty finite set
{{1,N},{1}} is non empty finite V42() set
{[1,N]} is non empty trivial finite 1 -element set
K158(<*M*>,<*N*>) is Relation-like Function-like FinSequence-like set
<*SG*> is Relation-like Function-like set
[1,SG] is set
{1,SG} is non empty finite set
{{1,SG},{1}} is non empty finite V42() set
{[1,SG]} is non empty trivial finite 1 -element set
K158(K158(<*M*>,<*N*>),<*SG*>) is Relation-like Function-like FinSequence-like set
<*M,SG,N*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
K158(<*M*>,<*SG*>) is Relation-like Function-like FinSequence-like set
K158(K158(<*M*>,<*SG*>),<*N*>) is Relation-like Function-like FinSequence-like set
<*N,M,SG*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
K158(<*N*>,<*M*>) is Relation-like Function-like FinSequence-like set
K158(K158(<*N*>,<*M*>),<*SG*>) is Relation-like Function-like FinSequence-like set
<*N,SG,M*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
K158(<*N*>,<*SG*>) is Relation-like Function-like FinSequence-like set
K158(K158(<*N*>,<*SG*>),<*M*>) is Relation-like Function-like FinSequence-like set
<*SG,M,N*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
K158(<*SG*>,<*M*>) is Relation-like Function-like FinSequence-like set
K158(K158(<*SG*>,<*M*>),<*N*>) is Relation-like Function-like FinSequence-like set
<*SG,N,M*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
K158(<*SG*>,<*N*>) is Relation-like Function-like FinSequence-like set
K158(K158(<*SG*>,<*N*>),<*M*>) is Relation-like Function-like FinSequence-like set
<*((Y . M) * M),((Y . N) * N),((Y . SG) * SG)*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
<*((Y . M) * M)*> is Relation-like Function-like set
[1,((Y . M) * M)] is set
{1,((Y . M) * M)} is non empty finite set
{{1,((Y . M) * M)},{1}} is non empty finite V42() set
{[1,((Y . M) * M)]} is non empty trivial finite 1 -element set
<*((Y . N) * N)*> is Relation-like Function-like set
[1,((Y . N) * N)] is set
{1,((Y . N) * N)} is non empty finite set
{{1,((Y . N) * N)},{1}} is non empty finite V42() set
{[1,((Y . N) * N)]} is non empty trivial finite 1 -element set
K158(<*((Y . M) * M)*>,<*((Y . N) * N)*>) is Relation-like Function-like FinSequence-like set
<*((Y . SG) * SG)*> is Relation-like Function-like set
[1,((Y . SG) * SG)] is set
{1,((Y . SG) * SG)} is non empty finite set
{{1,((Y . SG) * SG)},{1}} is non empty finite V42() set
{[1,((Y . SG) * SG)]} is non empty trivial finite 1 -element set
K158(K158(<*((Y . M) * M)*>,<*((Y . N) * N)*>),<*((Y . SG) * SG)*>) is Relation-like Function-like FinSequence-like set
<*((Y . M) * M),((Y . SG) * SG),((Y . N) * N)*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
K158(<*((Y . M) * M)*>,<*((Y . SG) * SG)*>) is Relation-like Function-like FinSequence-like set
K158(K158(<*((Y . M) * M)*>,<*((Y . SG) * SG)*>),<*((Y . N) * N)*>) is Relation-like Function-like FinSequence-like set
<*((Y . N) * N),((Y . M) * M),((Y . SG) * SG)*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
K158(<*((Y . N) * N)*>,<*((Y . M) * M)*>) is Relation-like Function-like FinSequence-like set
K158(K158(<*((Y . N) * N)*>,<*((Y . M) * M)*>),<*((Y . SG) * SG)*>) is Relation-like Function-like FinSequence-like set
<*((Y . N) * N),((Y . SG) * SG),((Y . M) * M)*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
K158(<*((Y . N) * N)*>,<*((Y . SG) * SG)*>) is Relation-like Function-like FinSequence-like set
K158(K158(<*((Y . N) * N)*>,<*((Y . SG) * SG)*>),<*((Y . M) * M)*>) is Relation-like Function-like FinSequence-like set
<*((Y . SG) * SG),((Y . M) * M),((Y . N) * N)*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
K158(<*((Y . SG) * SG)*>,<*((Y . M) * M)*>) is Relation-like Function-like FinSequence-like set
K158(K158(<*((Y . SG) * SG)*>,<*((Y . M) * M)*>),<*((Y . N) * N)*>) is Relation-like Function-like FinSequence-like set
<*((Y . SG) * SG),((Y . N) * N),((Y . M) * M)*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
K158(<*((Y . SG) * SG)*>,<*((Y . N) * N)*>) is Relation-like Function-like FinSequence-like set
K158(K158(<*((Y . SG) * SG)*>,<*((Y . N) * N)*>),<*((Y . M) * M)*>) is Relation-like Function-like FinSequence-like set
((Y . N) * N) + ((Y . SG) * SG) is Element of the carrier of V
the addF of V . (((Y . N) * N),((Y . SG) * SG)) is Element of the carrier of V
[((Y . N) * N),((Y . SG) * SG)] is set
{((Y . N) * N),((Y . SG) * SG)} is non empty finite set
{((Y . N) * N)} is non empty trivial finite 1 -element set
{{((Y . N) * N),((Y . SG) * SG)},{((Y . N) * N)}} is non empty finite V42() set
the addF of V . [((Y . N) * N),((Y . SG) * SG)] is set
((Y . M) * M) + (((Y . N) * N) + ((Y . SG) * SG)) is Element of the carrier of V
the addF of V . (((Y . M) * M),(((Y . N) * N) + ((Y . SG) * SG))) is Element of the carrier of V
[((Y . M) * M),(((Y . N) * N) + ((Y . SG) * SG))] is set
{((Y . M) * M),(((Y . N) * N) + ((Y . SG) * SG))} is non empty finite set
{{((Y . M) * M),(((Y . N) * N) + ((Y . SG) * SG))},{((Y . M) * M)}} is non empty finite V42() set
the addF of V . [((Y . M) * M),(((Y . N) * N) + ((Y . SG) * SG))] is set
((Y . M) * M) + ((Y . SG) * SG) is Element of the carrier of V
the addF of V . (((Y . M) * M),((Y . SG) * SG)) is Element of the carrier of V
[((Y . M) * M),((Y . SG) * SG)] is set
{((Y . M) * M),((Y . SG) * SG)} is non empty finite set
{{((Y . M) * M),((Y . SG) * SG)},{((Y . M) * M)}} is non empty finite V42() set
the addF of V . [((Y . M) * M),((Y . SG) * SG)] is set
((Y . N) * N) + (((Y . M) * M) + ((Y . SG) * SG)) is Element of the carrier of V
the addF of V . (((Y . N) * N),(((Y . M) * M) + ((Y . SG) * SG))) is Element of the carrier of V
[((Y . N) * N),(((Y . M) * M) + ((Y . SG) * SG))] is set
{((Y . N) * N),(((Y . M) * M) + ((Y . SG) * SG))} is non empty finite set
{{((Y . N) * N),(((Y . M) * M) + ((Y . SG) * SG))},{((Y . N) * N)}} is non empty finite V42() set
the addF of V . [((Y . N) * N),(((Y . M) * M) + ((Y . SG) * SG))] is set
{M} is non empty trivial finite 1 -element Element of bool the carrier of V
{N} is non empty trivial finite 1 -element Element of bool the carrier of V
{SG} is non empty trivial finite 1 -element Element of bool the carrier of V
{M,N} is non empty finite Element of bool the carrier of V
{M,SG} is non empty finite Element of bool the carrier of V
{N,SG} is non empty finite Element of bool the carrier of V
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
M is Element of the carrier of V
N is Element of the carrier of V
SG is Element of the carrier of V
{M,N,SG} is non empty finite Element of bool the carrier of V
bool the carrier of V is non empty set
Y is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V)
(V,Y) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not Y . b₁ = 0c } is set
Y . M is complex Element of COMPLEX
Y . N is complex Element of COMPLEX
Y . SG is complex Element of COMPLEX
(V,Y) is Element of the carrier of V
(Y . M) * M is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(Y . M),M] is set
{(Y . M),M} is non empty finite set
{(Y . M)} is non empty trivial finite 1 -element V68() set
{{(Y . M),M},{(Y . M)}} is non empty finite V42() set
the Mult of V . [(Y . M),M] is set
(Y . N) * N is Element of the carrier of V
[(Y . N),N] is set
{(Y . N),N} is non empty finite set
{(Y . N)} is non empty trivial finite 1 -element V68() set
{{(Y . N),N},{(Y . N)}} is non empty finite V42() set
the Mult of V . [(Y . N),N] is set
((Y . M) * M) + ((Y . N) * N) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (((Y . M) * M),((Y . N) * N)) is Element of the carrier of V
[((Y . M) * M),((Y . N) * N)] is set
{((Y . M) * M),((Y . N) * N)} is non empty finite set
{((Y . M) * M)} is non empty trivial finite 1 -element set
{{((Y . M) * M),((Y . N) * N)},{((Y . M) * M)}} is non empty finite V42() set
the addF of V . [((Y . M) * M),((Y . N) * N)] is set
(Y . SG) * SG is Element of the carrier of V
[(Y . SG),SG] is set
{(Y . SG),SG} is non empty finite set
{(Y . SG)} is non empty trivial finite 1 -element V68() set
{{(Y . SG),SG},{(Y . SG)}} is non empty finite V42() set
the Mult of V . [(Y . SG),SG] is set
(((Y . M) * M) + ((Y . N) * N)) + ((Y . SG) * SG) is Element of the carrier of V
the addF of V . ((((Y . M) * M) + ((Y . N) * N)),((Y . SG) * SG)) is Element of the carrier of V
[(((Y . M) * M) + ((Y . N) * N)),((Y . SG) * SG)] is set
{(((Y . M) * M) + ((Y . N) * N)),((Y . SG) * SG)} is non empty finite set
{(((Y . M) * M) + ((Y . N) * N))} is non empty trivial finite 1 -element set
{{(((Y . M) * M) + ((Y . N) * N)),((Y . SG) * SG)},{(((Y . M) * M) + ((Y . N) * N))}} is non empty finite V42() set
the addF of V . [(((Y . M) * M) + ((Y . N) * N)),((Y . SG) * SG)] is set
r2 is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,{M,N,SG})
(V,r2) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not r2 . b₁ = 0c } is set
r1 is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
rng r1 is Element of bool the carrier of V
len r1 is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
r3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V58() V59() V60() FinSequence of REAL
len r3 is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
Sum r3 is complex real ext-real Element of REAL
K295(REAL,r3,K267()) is complex real ext-real Element of REAL
dom r3 is V68() V69() V70() V71() V72() V73() Element of bool NAT
r3 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V58() V59() V60() FinSequence of REAL
len r3 is ordinal natural complex real finite cardinal V49() V50() ext-real non negative V68() V69() V70() V71() V72() V73() Element of NAT
Sum r3 is complex real ext-real Element of REAL
K295(REAL,r3,K267()) is complex real ext-real Element of REAL
dom r3 is V68() V69() V70() V71() V72() V73() Element of bool NAT
card {M,N,SG} is non empty ordinal natural complex real finite cardinal V49() V50() ext-real positive non negative V68() V69() V70() V71() V72() V73() Element of omega
{1,2,3} is non empty finite V68() V69() V70() V71() V72() V73() Element of bool REAL
r3 . 2 is complex real ext-real set
r1 . 2 is set
r2 . (r1 . 2) is complex set
r3 /. 2 is complex real ext-real Element of REAL
r3 . 3 is complex real ext-real set
r1 . 3 is set
r2 . (r1 . 3) is complex set
r3 /. 3 is complex real ext-real Element of REAL
r3 . 1 is complex real ext-real set
r1 . 1 is set
r2 . (r1 . 1) is complex set
r3 /. 1 is complex real ext-real Element of REAL
r1 is complex real ext-real Element of REAL
r2 is complex real ext-real Element of REAL
r3 is complex real ext-real Element of REAL
<*r1,r2,r3*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V58() V59() V60() FinSequence of REAL
<*r1*> is Relation-like Function-like set
[1,r1] is set
{1,r1} is non empty finite V68() V69() V70() set
{{1,r1},{1}} is non empty finite V42() set
{[1,r1]} is non empty trivial finite 1 -element set
<*r2*> is Relation-like Function-like set
[1,r2] is set
{1,r2} is non empty finite V68() V69() V70() set
{{1,r2},{1}} is non empty finite V42() set
{[1,r2]} is non empty trivial finite 1 -element set
K158(<*r1*>,<*r2*>) is Relation-like Function-like FinSequence-like set
<*r3*> is Relation-like Function-like set
[1,r3] is set
{1,r3} is non empty finite V68() V69() V70() set
{{1,r3},{1}} is non empty finite V42() set
{[1,r3]} is non empty trivial finite 1 -element set
K158(K158(<*r1*>,<*r2*>),<*r3*>) is Relation-like Function-like FinSequence-like set
r1 + r2 is complex real ext-real Element of REAL
(r1 + r2) + r3 is complex real ext-real Element of REAL
r2 . M is complex Element of COMPLEX
r2 . N is complex Element of COMPLEX
r2 . SG is complex Element of COMPLEX
<*M,N,SG*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
<*M*> is Relation-like Function-like set
[1,M] is set
{1,M} is non empty finite set
{{1,M},{1}} is non empty finite V42() set
{[1,M]} is non empty trivial finite 1 -element set
<*N*> is Relation-like Function-like set
[1,N] is set
{1,N} is non empty finite set
{{1,N},{1}} is non empty finite V42() set
{[1,N]} is non empty trivial finite 1 -element set
K158(<*M*>,<*N*>) is Relation-like Function-like FinSequence-like set
<*SG*> is Relation-like Function-like set
[1,SG] is set
{1,SG} is non empty finite set
{{1,SG},{1}} is non empty finite V42() set
{[1,SG]} is non empty trivial finite 1 -element set
K158(K158(<*M*>,<*N*>),<*SG*>) is Relation-like Function-like FinSequence-like set
<*M,SG,N*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
<*M*> is Relation-like Function-like set
[1,M] is set
{1,M} is non empty finite set
{{1,M},{1}} is non empty finite V42() set
{[1,M]} is non empty trivial finite 1 -element set
<*SG*> is Relation-like Function-like set
[1,SG] is set
{1,SG} is non empty finite set
{{1,SG},{1}} is non empty finite V42() set
{[1,SG]} is non empty trivial finite 1 -element set
K158(<*M*>,<*SG*>) is Relation-like Function-like FinSequence-like set
<*N*> is Relation-like Function-like set
[1,N] is set
{1,N} is non empty finite set
{{1,N},{1}} is non empty finite V42() set
{[1,N]} is non empty trivial finite 1 -element set
K158(K158(<*M*>,<*SG*>),<*N*>) is Relation-like Function-like FinSequence-like set
r1 + r3 is complex real ext-real Element of REAL
(r1 + r3) + r2 is complex real ext-real Element of REAL
<*N,M,SG*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
<*N*> is Relation-like Function-like set
[1,N] is set
{1,N} is non empty finite set
{{1,N},{1}} is non empty finite V42() set
{[1,N]} is non empty trivial finite 1 -element set
<*M*> is Relation-like Function-like set
[1,M] is set
{1,M} is non empty finite set
{{1,M},{1}} is non empty finite V42() set
{[1,M]} is non empty trivial finite 1 -element set
K158(<*N*>,<*M*>) is Relation-like Function-like FinSequence-like set
<*SG*> is Relation-like Function-like set
[1,SG] is set
{1,SG} is non empty finite set
{{1,SG},{1}} is non empty finite V42() set
{[1,SG]} is non empty trivial finite 1 -element set
K158(K158(<*N*>,<*M*>),<*SG*>) is Relation-like Function-like FinSequence-like set
r2 + r1 is complex real ext-real Element of REAL
(r2 + r1) + r3 is complex real ext-real Element of REAL
<*N,SG,M*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
<*N*> is Relation-like Function-like set
[1,N] is set
{1,N} is non empty finite set
{{1,N},{1}} is non empty finite V42() set
{[1,N]} is non empty trivial finite 1 -element set
<*SG*> is Relation-like Function-like set
[1,SG] is set
{1,SG} is non empty finite set
{{1,SG},{1}} is non empty finite V42() set
{[1,SG]} is non empty trivial finite 1 -element set
K158(<*N*>,<*SG*>) is Relation-like Function-like FinSequence-like set
<*M*> is Relation-like Function-like set
[1,M] is set
{1,M} is non empty finite set
{{1,M},{1}} is non empty finite V42() set
{[1,M]} is non empty trivial finite 1 -element set
K158(K158(<*N*>,<*SG*>),<*M*>) is Relation-like Function-like FinSequence-like set
r3 + r1 is complex real ext-real Element of REAL
(r3 + r1) + r2 is complex real ext-real Element of REAL
<*SG,M,N*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
<*SG*> is Relation-like Function-like set
[1,SG] is set
{1,SG} is non empty finite set
{{1,SG},{1}} is non empty finite V42() set
{[1,SG]} is non empty trivial finite 1 -element set
<*M*> is Relation-like Function-like set
[1,M] is set
{1,M} is non empty finite set
{{1,M},{1}} is non empty finite V42() set
{[1,M]} is non empty trivial finite 1 -element set
K158(<*SG*>,<*M*>) is Relation-like Function-like FinSequence-like set
<*N*> is Relation-like Function-like set
[1,N] is set
{1,N} is non empty finite set
{{1,N},{1}} is non empty finite V42() set
{[1,N]} is non empty trivial finite 1 -element set
K158(K158(<*SG*>,<*M*>),<*N*>) is Relation-like Function-like FinSequence-like set
r2 + r3 is complex real ext-real Element of REAL
(r2 + r3) + r1 is complex real ext-real Element of REAL
<*SG,N,M*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
<*SG*> is Relation-like Function-like set
[1,SG] is set
{1,SG} is non empty finite set
{{1,SG},{1}} is non empty finite V42() set
{[1,SG]} is non empty trivial finite 1 -element set
<*N*> is Relation-like Function-like set
[1,N] is set
{1,N} is non empty finite set
{{1,N},{1}} is non empty finite V42() set
{[1,N]} is non empty trivial finite 1 -element set
K158(<*SG*>,<*N*>) is Relation-like Function-like FinSequence-like set
<*M*> is Relation-like Function-like set
[1,M] is set
{1,M} is non empty finite set
{{1,M},{1}} is non empty finite V42() set
{[1,M]} is non empty trivial finite 1 -element set
K158(K158(<*SG*>,<*N*>),<*M*>) is Relation-like Function-like FinSequence-like set
r3 + r2 is complex real ext-real Element of REAL
(r3 + r2) + r1 is complex real ext-real Element of REAL
<*M,N,SG*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
<*M*> is Relation-like Function-like set
[1,M] is set
{1,M} is non empty finite set
{{1,M},{1}} is non empty finite V42() set
{[1,M]} is non empty trivial finite 1 -element set
<*N*> is Relation-like Function-like set
[1,N] is set
{1,N} is non empty finite set
{{1,N},{1}} is non empty finite V42() set
{[1,N]} is non empty trivial finite 1 -element set
K158(<*M*>,<*N*>) is Relation-like Function-like FinSequence-like set
<*SG*> is Relation-like Function-like set
[1,SG] is set
{1,SG} is non empty finite set
{{1,SG},{1}} is non empty finite V42() set
{[1,SG]} is non empty trivial finite 1 -element set
K158(K158(<*M*>,<*N*>),<*SG*>) is Relation-like Function-like FinSequence-like set
<*M,SG,N*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
K158(<*M*>,<*SG*>) is Relation-like Function-like FinSequence-like set
K158(K158(<*M*>,<*SG*>),<*N*>) is Relation-like Function-like FinSequence-like set
<*N,M,SG*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
K158(<*N*>,<*M*>) is Relation-like Function-like FinSequence-like set
K158(K158(<*N*>,<*M*>),<*SG*>) is Relation-like Function-like FinSequence-like set
<*N,SG,M*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
K158(<*N*>,<*SG*>) is Relation-like Function-like FinSequence-like set
K158(K158(<*N*>,<*SG*>),<*M*>) is Relation-like Function-like FinSequence-like set
<*SG,M,N*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
K158(<*SG*>,<*M*>) is Relation-like Function-like FinSequence-like set
K158(K158(<*SG*>,<*M*>),<*N*>) is Relation-like Function-like FinSequence-like set
<*SG,N,M*> is Relation-like NAT -defined the carrier of V -valued Function-like FinSequence-like FinSequence of the carrier of V
K158(<*SG*>,<*N*>) is Relation-like Function-like FinSequence-like set
K158(K158(<*SG*>,<*N*>),<*M*>) is Relation-like Function-like FinSequence-like set
u2 is complex real ext-real set
y1 is complex real ext-real set
x1 is complex real ext-real set
u2 + y1 is complex real ext-real set
(u2 + y1) + x1 is complex real ext-real set
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
M is Element of the carrier of V
{M} is non empty trivial finite 1 -element Element of bool the carrier of V
bool the carrier of V is non empty set
N is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,{M})
N . M is complex Element of COMPLEX
(V,N) is Element of the carrier of V
(N . M) * M is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(N . M),M] is set
{(N . M),M} is non empty finite set
{(N . M)} is non empty trivial finite 1 -element V68() set
{{(N . M),M},{(N . M)}} is non empty finite V42() set
the Mult of V . [(N . M),M] is set
(V,N) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not N . b₁ = 0c } is set
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
M is Element of the carrier of V
N is Element of the carrier of V
{M,N} is non empty finite Element of bool the carrier of V
bool the carrier of V is non empty set
SG is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,{M,N})
SG . M is complex Element of COMPLEX
SG . N is complex Element of COMPLEX
(V,SG) is Element of the carrier of V
(SG . M) * M is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(SG . M),M] is set
{(SG . M),M} is non empty finite set
{(SG . M)} is non empty trivial finite 1 -element V68() set
{{(SG . M),M},{(SG . M)}} is non empty finite V42() set
the Mult of V . [(SG . M),M] is set
(SG . N) * N is Element of the carrier of V
[(SG . N),N] is set
{(SG . N),N} is non empty finite set
{(SG . N)} is non empty trivial finite 1 -element V68() set
{{(SG . N),N},{(SG . N)}} is non empty finite V42() set
the Mult of V . [(SG . N),N] is set
((SG . M) * M) + ((SG . N) * N) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (((SG . M) * M),((SG . N) * N)) is Element of the carrier of V
[((SG . M) * M),((SG . N) * N)] is set
{((SG . M) * M),((SG . N) * N)} is non empty finite set
{((SG . M) * M)} is non empty trivial finite 1 -element set
{{((SG . M) * M),((SG . N) * N)},{((SG . M) * M)}} is non empty finite V42() set
the addF of V . [((SG . M) * M),((SG . N) * N)] is set
(V,SG) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not SG . b₁ = 0c } is set
{M} is non empty trivial finite 1 -element Element of bool the carrier of V
Y is complex real ext-real Element of REAL
{N} is non empty trivial finite 1 -element Element of bool the carrier of V
Y is complex real ext-real Element of REAL
Y is complex real ext-real Element of REAL
r2 is complex real ext-real Element of REAL
Y + r2 is complex real ext-real Element of REAL
{M} is non empty trivial finite 1 -element Element of bool the carrier of V
{N} is non empty trivial finite 1 -element Element of bool the carrier of V
Y is complex real ext-real set
r2 is complex real ext-real set
V is non empty left_complementable right_complementable Abelian add-associative right_zeroed V138() vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V is non empty set
M is Element of the carrier of V
N is Element of the carrier of V
SG is Element of the carrier of V
{M,N,SG} is non empty finite Element of bool the carrier of V
bool the carrier of V is non empty set
Y is Relation-like the carrier of V -defined COMPLEX -valued Function-like total quasi_total V58() (V,{M,N,SG})
Y . M is complex Element of COMPLEX
Y . N is complex Element of COMPLEX
Y . SG is complex Element of COMPLEX
(V,Y) is Element of the carrier of V
(Y . M) * M is Element of the carrier of V
the Mult of V is non empty Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty non trivial non finite set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty non trivial non finite set
[(Y . M),M] is set
{(Y . M),M} is non empty finite set
{(Y . M)} is non empty trivial finite 1 -element V68() set
{{(Y . M),M},{(Y . M)}} is non empty finite V42() set
the Mult of V . [(Y . M),M] is set
(Y . N) * N is Element of the carrier of V
[(Y . N),N] is set
{(Y . N),N} is non empty finite set
{(Y . N)} is non empty trivial finite 1 -element V68() set
{{(Y . N),N},{(Y . N)}} is non empty finite V42() set
the Mult of V . [(Y . N),N] is set
((Y . M) * M) + ((Y . N) * N) is Element of the carrier of V
the addF of V is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like total quasi_total Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (((Y . M) * M),((Y . N) * N)) is Element of the carrier of V
[((Y . M) * M),((Y . N) * N)] is set
{((Y . M) * M),((Y . N) * N)} is non empty finite set
{((Y . M) * M)} is non empty trivial finite 1 -element set
{{((Y . M) * M),((Y . N) * N)},{((Y . M) * M)}} is non empty finite V42() set
the addF of V . [((Y . M) * M),((Y . N) * N)] is set
(Y . SG) * SG is Element of the carrier of V
[(Y . SG),SG] is set
{(Y . SG),SG} is non empty finite set
{(Y . SG)} is non empty trivial finite 1 -element V68() set
{{(Y . SG),SG},{(Y . SG)}} is non empty finite V42() set
the Mult of V . [(Y . SG),SG] is set
(((Y . M) * M) + ((Y . N) * N)) + ((Y . SG) * SG) is Element of the carrier of V
the addF of V . ((((Y . M) * M) + ((Y . N) * N)),((Y . SG) * SG)) is Element of the carrier of V
[(((Y . M) * M) + ((Y . N) * N)),((Y . SG) * SG)] is set
{(((Y . M) * M) + ((Y . N) * N)),((Y . SG) * SG)} is non empty finite set
{(((Y . M) * M) + ((Y . N) * N))} is non empty trivial finite 1 -element set
{{(((Y . M) * M) + ((Y . N) * N)),((Y . SG) * SG)},{(((Y . M) * M) + ((Y . N) * N))}} is non empty finite V42() set
the addF of V . [(((Y . M) * M) + ((Y . N) * N)),((Y . SG) * SG)] is set
(V,Y) is finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not Y . b₁ = 0c } is set
{M} is non empty trivial finite 1 -element Element of bool the carrier of V
1 + {} is non empty ordinal natural complex real finite cardinal ext-real positive non negative Element of REAL
(1 + {}) + {} is non empty ordinal natural complex real finite cardinal ext-real positive non negative Element of REAL
r2 is complex real ext-real Element of REAL
{N} is non empty trivial finite 1 -element Element of bool the carrier of V
{} + 1 is non empty ordinal natural complex real finite cardinal ext-real positive non negative Element of REAL
({} + 1) + {} is non empty ordinal natural complex real finite cardinal ext-real positive non negative Element of REAL
r2 is complex real ext-real Element of REAL
{SG} is non empty trivial finite 1 -element Element of bool the carrier of V
{} + {} is empty ordinal natural complex real finite V42() cardinal {} -element ext-real non positive non negative V68() V69() V70() V71() V72() V73() V74() set
({} + {}) + 1 is non empty ordinal natural complex real finite cardinal ext-real positive non negative Element of REAL
r2 is complex real ext-real Element of REAL
{M,N} is non empty finite Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : not Y . b₁ = {} } is set
r1 is complex real ext-real Element of REAL
r3 is complex real ext-real Element of REAL
r1 + r3 is complex real ext-real Element of REAL
(r1 + r3) + {} is complex real ext-real Element of REAL
{N,SG} is non empty finite Element of bool the carrier of V
r1 is complex real ext-real Element of REAL
r3 is complex real ext-real Element of REAL
r1 + r3 is complex real ext-real Element of REAL
{} + r1 is complex real ext-real Element of REAL
({} + r1) + r3 is complex real ext-real Element of REAL
{M,SG} is non empty finite Element of bool the carrier of V
r1 is complex real ext-real Element of REAL
r3 is complex real ext-real Element of REAL
r1 + r3 is complex real ext-real Element of REAL
r1 + {} is complex real ext-real Element of REAL
(r1 + {}) + r3 is complex real ext-real Element of REAL
{M} is non empty trivial finite 1 -element Element of bool the carrier of V
{N} is non empty trivial finite 1 -element Element of bool the carrier of V
{SG} is non empty trivial finite 1 -element Element of bool the carrier of V
{M,N} is non empty finite Element of bool the carrier of V
{N,SG} is non empty finite Element of bool the carrier of V
{M,SG} is non empty finite Element of bool the carrier of V
r2 is complex real ext-real set
r1 is complex real ext-real set
r3 is complex real ext-real set
r2 + r1 is complex real ext-real set
(r2 + r1) + r3 is complex real ext-real set
V is non empty CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
bool (bool the carrier of V) is non empty set
M is Element of bool the carrier of V
N is Element of bool (bool the carrier of V)
SG is Element of bool (bool the carrier of V)
Y is Element of bool the carrier of V
V is non empty CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
(V,M) is Element of bool (bool the carrier of V)
bool (bool the carrier of V) is non empty set
meet (V,M) is Element of bool the carrier of V
N is Element of bool the carrier of V
V is non empty CLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
M is Element of bool the carrier of V
(V,M) is (V) Element of bool the carrier of V
(V,M) is Element of bool (bool the carrier of V)
bool (bool the carrier of V) is non empty set
meet (V,M) is Element of bool the carrier of V
N is (V) Element of bool the carrier of V