:: HERMITAN semantic presentation

REAL is non empty V38() V175() V176() V177() V181() set
NAT is V175() V176() V177() V178() V179() V180() V181() Element of bool REAL
bool REAL is set
F_Complex is non empty non degenerated non trivial right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital V137() V139() right-distributive left-distributive right_unital well-unital V145() left_unital doubleLoopStr
the carrier of F_Complex is non empty non trivial set
COMPLEX is non empty V38() V175() V181() set
RAT is non empty V38() V175() V176() V177() V178() V181() set
INT is non empty V38() V175() V176() V177() V178() V179() V181() set
[:COMPLEX,COMPLEX:] is set
bool [:COMPLEX,COMPLEX:] is set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is set
[:REAL,REAL:] is set
bool [:REAL,REAL:] is set
[:[:REAL,REAL:],REAL:] is set
bool [:[:REAL,REAL:],REAL:] is set
[:RAT,RAT:] is set
bool [:RAT,RAT:] is set
[:[:RAT,RAT:],RAT:] is set
bool [:[:RAT,RAT:],RAT:] is set
[:INT,INT:] is set
bool [:INT,INT:] is set
[:[:INT,INT:],INT:] is set
bool [:[:INT,INT:],INT:] is set
[:NAT,NAT:] is set
[:[:NAT,NAT:],NAT:] is set
bool [:[:NAT,NAT:],NAT:] is set
omega is V175() V176() V177() V178() V179() V180() V181() set
bool omega is set
K270() is L6()
the carrier of K270() is set
bool NAT is set
ExtREAL is non empty V176() set
{} is empty V175() V176() V177() V178() V179() V180() V181() set
the empty V175() V176() V177() V178() V179() V180() V181() set is empty V175() V176() V177() V178() V179() V180() V181() set
1 is non empty natural complex real ext-real positive non negative V33() V34() V175() V176() V177() V178() V179() V180() Element of NAT
2 is non empty natural complex real ext-real positive non negative V33() V34() V175() V176() V177() V178() V179() V180() Element of NAT
[:2,REAL:] is set
bool [:2,REAL:] is set
0 is empty natural complex real ext-real non positive non negative V33() V34() V175() V176() V177() V178() V179() V180() V181() Element of NAT
Re 0 is complex real ext-real Element of REAL
Im 0 is complex real ext-real Element of REAL
<i> is complex Element of COMPLEX
Re <i> is complex real ext-real Element of REAL
Im <i> is complex real ext-real Element of REAL
|.0.| is complex real ext-real Element of REAL
(Re 0) ^2 is complex real ext-real Element of REAL
(Re 0) * (Re 0) is complex real ext-real set
(Im 0) ^2 is complex real ext-real Element of REAL
(Im 0) * (Im 0) is complex real ext-real set
((Re 0) ^2) + ((Im 0) ^2) is complex real ext-real Element of REAL
sqrt (((Re 0) ^2) + ((Im 0) ^2)) is complex real ext-real Element of REAL
1r is complex Element of COMPLEX
|.1r.| is complex real ext-real Element of REAL
Re 1r is complex real ext-real Element of REAL
(Re 1r) ^2 is complex real ext-real Element of REAL
(Re 1r) * (Re 1r) is complex real ext-real set
Im 1r is complex real ext-real Element of REAL
(Im 1r) ^2 is complex real ext-real Element of REAL
(Im 1r) * (Im 1r) is complex real ext-real set
((Re 1r) ^2) + ((Im 1r) ^2) is complex real ext-real Element of REAL
sqrt (((Re 1r) ^2) + ((Im 1r) ^2)) is complex real ext-real Element of REAL
sqrt 1 is complex real ext-real Element of REAL
K159() is V16() V19([:COMPLEX,COMPLEX:]) V20( COMPLEX ) Function-like V30([:COMPLEX,COMPLEX:], COMPLEX ) Element of bool [:[:COMPLEX,COMPLEX:],COMPLEX:]
K161() is V16() V19([:COMPLEX,COMPLEX:]) V20( COMPLEX ) Function-like V30([:COMPLEX,COMPLEX:], COMPLEX ) Element of bool [:[:COMPLEX,COMPLEX:],COMPLEX:]
0c is empty complex V175() V176() V177() V178() V179() V180() V181() Element of COMPLEX
0. F_Complex is complex zero Element of the carrier of F_Complex
1_ F_Complex is complex Element of the carrier of F_Complex
1. F_Complex is complex non zero Element of the carrier of F_Complex
(0. F_Complex) *' is complex Element of the carrier of F_Complex
Re (0. F_Complex) is complex real ext-real Element of REAL
Im (0. F_Complex) is complex real ext-real Element of REAL
(Im (0. F_Complex)) * <i> is complex set
(Re (0. F_Complex)) - ((Im (0. F_Complex)) * <i>) is complex set
(1. F_Complex) *' is complex Element of the carrier of F_Complex
Re (1. F_Complex) is complex real ext-real Element of REAL
Im (1. F_Complex) is complex real ext-real Element of REAL
(Im (1. F_Complex)) * <i> is complex set
(Re (1. F_Complex)) - ((Im (1. F_Complex)) * <i>) is complex set
|.(0. F_Complex).| is complex real ext-real Element of REAL
(Re (0. F_Complex)) ^2 is complex real ext-real Element of REAL
(Re (0. F_Complex)) * (Re (0. F_Complex)) is complex real ext-real set
(Im (0. F_Complex)) ^2 is complex real ext-real Element of REAL
(Im (0. F_Complex)) * (Im (0. F_Complex)) is complex real ext-real set
((Re (0. F_Complex)) ^2) + ((Im (0. F_Complex)) ^2) is complex real ext-real Element of REAL
sqrt (((Re (0. F_Complex)) ^2) + ((Im (0. F_Complex)) ^2)) is complex real ext-real Element of REAL
|.(1. F_Complex).| is complex real ext-real Element of REAL
(Re (1. F_Complex)) ^2 is complex real ext-real Element of REAL
(Re (1. F_Complex)) * (Re (1. F_Complex)) is complex real ext-real set
(Im (1. F_Complex)) ^2 is complex real ext-real Element of REAL
(Im (1. F_Complex)) * (Im (1. F_Complex)) is complex real ext-real set
((Re (1. F_Complex)) ^2) + ((Im (1. F_Complex)) ^2) is complex real ext-real Element of REAL
sqrt (((Re (1. F_Complex)) ^2) + ((Im (1. F_Complex)) ^2)) is complex real ext-real Element of REAL
i_FC is complex Element of the carrier of F_Complex
i_FC * i_FC is complex Element of the carrier of F_Complex
the multF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
[: the carrier of F_Complex, the carrier of F_Complex:] is set
[:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:] is set
bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:] is set
the multF of F_Complex . (i_FC,i_FC) is complex Element of the carrier of F_Complex
[i_FC,i_FC] is set
{i_FC,i_FC} is non empty V175() set
{i_FC} is non empty V175() set
{{i_FC,i_FC},{i_FC}} is non empty set
the multF of F_Complex . [i_FC,i_FC] is set
K137(i_FC,i_FC) is complex Element of COMPLEX
- (1_ F_Complex) is complex Element of the carrier of F_Complex
0 * <i> is complex set
0 + (0 * <i>) is complex set
V is complex set
V *' is complex Element of COMPLEX
Re V is complex real ext-real Element of REAL
Im V is complex real ext-real Element of REAL
(Im V) * <i> is complex set
(Re V) - ((Im V) * <i>) is complex set
- (Im V) is complex real ext-real Element of REAL
0 + (- (Im V)) is complex real ext-real Element of REAL
V is complex Element of COMPLEX
Re V is complex real ext-real Element of REAL
|.V.| is complex real ext-real Element of REAL
(Re V) ^2 is complex real ext-real Element of REAL
(Re V) * (Re V) is complex real ext-real set
Im V is complex real ext-real Element of REAL
(Im V) ^2 is complex real ext-real Element of REAL
(Im V) * (Im V) is complex real ext-real set
((Re V) ^2) + ((Im V) ^2) is complex real ext-real Element of REAL
sqrt (((Re V) ^2) + ((Im V) ^2)) is complex real ext-real Element of REAL
(Re V) / |.V.| is complex real ext-real Element of COMPLEX
- (Im V) is complex real ext-real Element of REAL
(- (Im V)) / |.V.| is complex real ext-real Element of COMPLEX
((- (Im V)) / |.V.|) * <i> is complex Element of COMPLEX
((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>) is complex Element of COMPLEX
|.(((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>)).| is complex real ext-real Element of REAL
Re (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>)) is complex real ext-real Element of REAL
(Re (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>))) ^2 is complex real ext-real Element of REAL
(Re (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>))) * (Re (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>))) is complex real ext-real set
Im (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>)) is complex real ext-real Element of REAL
(Im (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>))) ^2 is complex real ext-real Element of REAL
(Im (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>))) * (Im (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>))) is complex real ext-real set
((Re (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>))) ^2) + ((Im (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>))) ^2) + ((Im (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>))) ^2)) is complex real ext-real Element of REAL
(((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>)) * V is complex Element of COMPLEX
Re ((((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>)) * V) is complex real ext-real Element of REAL
Im ((((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>)) * V) is complex real ext-real Element of REAL
V * V is complex Element of COMPLEX
|.(V * V).| is complex real ext-real Element of REAL
Re (V * V) is complex real ext-real Element of REAL
(Re (V * V)) ^2 is complex real ext-real Element of REAL
(Re (V * V)) * (Re (V * V)) is complex real ext-real set
Im (V * V) is complex real ext-real Element of REAL
(Im (V * V)) ^2 is complex real ext-real Element of REAL
(Im (V * V)) * (Im (V * V)) is complex real ext-real set
((Re (V * V)) ^2) + ((Im (V * V)) ^2) is complex real ext-real Element of REAL
sqrt (((Re (V * V)) ^2) + ((Im (V * V)) ^2)) is complex real ext-real Element of REAL
|.V.| ^2 is complex real ext-real Element of REAL
|.V.| * |.V.| is complex real ext-real set
((Re V) ^2) / (|.V.| ^2) is complex real ext-real Element of COMPLEX
((- (Im V)) / |.V.|) ^2 is complex real ext-real Element of COMPLEX
((- (Im V)) / |.V.|) * ((- (Im V)) / |.V.|) is complex real ext-real set
(((Re V) ^2) / (|.V.| ^2)) + (((- (Im V)) / |.V.|) ^2) is complex real ext-real Element of COMPLEX
(- (Im V)) ^2 is complex real ext-real Element of REAL
(- (Im V)) * (- (Im V)) is complex real ext-real set
((- (Im V)) ^2) / (|.V.| ^2) is complex real ext-real Element of COMPLEX
(((Re V) ^2) / (|.V.| ^2)) + (((- (Im V)) ^2) / (|.V.| ^2)) is complex real ext-real Element of COMPLEX
(((Re V) ^2) + ((Im V) ^2)) / (|.V.| ^2) is complex real ext-real Element of COMPLEX
|.V.| / |.V.| is complex real ext-real Element of COMPLEX
(|.V.| / |.V.|) ^2 is complex real ext-real Element of COMPLEX
(|.V.| / |.V.|) * (|.V.| / |.V.|) is complex real ext-real set
1 ^2 is complex real ext-real Element of REAL
1 * 1 is non empty complex real ext-real positive non negative set
((Re V) / |.V.|) * (Re V) is complex real ext-real Element of REAL
((- (Im V)) / |.V.|) * (Im V) is complex real ext-real Element of REAL
(((Re V) / |.V.|) * (Re V)) - (((- (Im V)) / |.V.|) * (Im V)) is complex real ext-real Element of REAL
(Re V) * (Re V) is complex real ext-real Element of REAL
((Re V) * (Re V)) / |.V.| is complex real ext-real Element of COMPLEX
(((Re V) * (Re V)) / |.V.|) - (((- (Im V)) / |.V.|) * (Im V)) is complex real ext-real Element of REAL
((Re V) ^2) / |.V.| is complex real ext-real Element of COMPLEX
(- (Im V)) * (Im V) is complex real ext-real Element of REAL
((- (Im V)) * (Im V)) / |.V.| is complex real ext-real Element of COMPLEX
(((Re V) ^2) / |.V.|) - (((- (Im V)) * (Im V)) / |.V.|) is complex real ext-real Element of COMPLEX
(Im V) * (Im V) is complex real ext-real Element of REAL
- ((Im V) * (Im V)) is complex real ext-real Element of REAL
((Re V) ^2) - (- ((Im V) * (Im V))) is complex real ext-real Element of REAL
(((Re V) ^2) - (- ((Im V) * (Im V)))) / |.V.| is complex real ext-real Element of COMPLEX
((Re V) / |.V.|) * (Im V) is complex real ext-real Element of REAL
(Re V) * ((- (Im V)) / |.V.|) is complex real ext-real Element of REAL
(((Re V) / |.V.|) * (Im V)) + ((Re V) * ((- (Im V)) / |.V.|)) is complex real ext-real Element of REAL
(Re V) * (Im V) is complex real ext-real Element of REAL
((Re V) * (Im V)) / |.V.| is complex real ext-real Element of COMPLEX
(((Re V) * (Im V)) / |.V.|) + ((Re V) * ((- (Im V)) / |.V.|)) is complex real ext-real Element of REAL
(- (Im V)) * (Re V) is complex real ext-real Element of REAL
((- (Im V)) * (Re V)) / |.V.| is complex real ext-real Element of COMPLEX
(((Re V) * (Im V)) / |.V.|) + (((- (Im V)) * (Re V)) / |.V.|) is complex real ext-real Element of COMPLEX
(Im V) * (Re V) is complex real ext-real Element of REAL
- ((Im V) * (Re V)) is complex real ext-real Element of REAL
((Re V) * (Im V)) + (- ((Im V) * (Re V))) is complex real ext-real Element of REAL
(((Re V) * (Im V)) + (- ((Im V) * (Re V)))) / |.V.| is complex real ext-real Element of COMPLEX
V is complex Element of COMPLEX
|.V.| is complex real ext-real Element of REAL
Re V is complex real ext-real Element of REAL
(Re V) ^2 is complex real ext-real Element of REAL
(Re V) * (Re V) is complex real ext-real set
Im V is complex real ext-real Element of REAL
(Im V) ^2 is complex real ext-real Element of REAL
(Im V) * (Im V) is complex real ext-real set
((Re V) ^2) + ((Im V) ^2) is complex real ext-real Element of REAL
sqrt (((Re V) ^2) + ((Im V) ^2)) is complex real ext-real Element of REAL
1r * V is complex Element of COMPLEX
Re (1r * V) is complex real ext-real Element of REAL
Im (1r * V) is complex real ext-real Element of REAL
(Re V) / |.V.| is complex real ext-real Element of COMPLEX
- (Im V) is complex real ext-real Element of REAL
(- (Im V)) / |.V.| is complex real ext-real Element of COMPLEX
((- (Im V)) / |.V.|) * <i> is complex Element of COMPLEX
((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>) is complex Element of COMPLEX
|.(((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>)).| is complex real ext-real Element of REAL
Re (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>)) is complex real ext-real Element of REAL
(Re (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>))) ^2 is complex real ext-real Element of REAL
(Re (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>))) * (Re (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>))) is complex real ext-real set
Im (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>)) is complex real ext-real Element of REAL
(Im (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>))) ^2 is complex real ext-real Element of REAL
(Im (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>))) * (Im (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>))) is complex real ext-real set
((Re (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>))) ^2) + ((Im (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>))) ^2) + ((Im (((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>))) ^2)) is complex real ext-real Element of REAL
(((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>)) * V is complex Element of COMPLEX
Re ((((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>)) * V) is complex real ext-real Element of REAL
Im ((((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>)) * V) is complex real ext-real Element of REAL
vq is complex Element of COMPLEX
|.vq.| is complex real ext-real Element of REAL
Re vq is complex real ext-real Element of REAL
(Re vq) ^2 is complex real ext-real Element of REAL
(Re vq) * (Re vq) is complex real ext-real set
Im vq is complex real ext-real Element of REAL
(Im vq) ^2 is complex real ext-real Element of REAL
(Im vq) * (Im vq) is complex real ext-real set
((Re vq) ^2) + ((Im vq) ^2) is complex real ext-real Element of REAL
sqrt (((Re vq) ^2) + ((Im vq) ^2)) is complex real ext-real Element of REAL
vq * V is complex Element of COMPLEX
Re (vq * V) is complex real ext-real Element of REAL
Im (vq * V) is complex real ext-real Element of REAL
vr is complex Element of COMPLEX
|.vr.| is complex real ext-real Element of REAL
Re vr is complex real ext-real Element of REAL
(Re vr) ^2 is complex real ext-real Element of REAL
(Re vr) * (Re vr) is complex real ext-real set
Im vr is complex real ext-real Element of REAL
(Im vr) ^2 is complex real ext-real Element of REAL
(Im vr) * (Im vr) is complex real ext-real set
((Re vr) ^2) + ((Im vr) ^2) is complex real ext-real Element of REAL
sqrt (((Re vr) ^2) + ((Im vr) ^2)) is complex real ext-real Element of REAL
vr * V is complex Element of COMPLEX
Re (vr * V) is complex real ext-real Element of REAL
Im (vr * V) is complex real ext-real Element of REAL
V is complex Element of COMPLEX
V *' is complex Element of COMPLEX
Re V is complex real ext-real Element of REAL
Im V is complex real ext-real Element of REAL
(Im V) * <i> is complex set
(Re V) - ((Im V) * <i>) is complex set
V * (V *') is complex Element of COMPLEX
|.V.| is complex real ext-real Element of REAL
(Re V) ^2 is complex real ext-real Element of REAL
(Re V) * (Re V) is complex real ext-real set
(Im V) ^2 is complex real ext-real Element of REAL
(Im V) * (Im V) is complex real ext-real set
((Re V) ^2) + ((Im V) ^2) is complex real ext-real Element of REAL
sqrt (((Re V) ^2) + ((Im V) ^2)) is complex real ext-real Element of REAL
|.V.| ^2 is complex real ext-real Element of REAL
|.V.| * |.V.| is complex real ext-real set
(|.V.| ^2) + (0 * <i>) is complex set
Re (V * (V *')) is complex real ext-real Element of REAL
Im (V * (V *')) is complex real ext-real Element of REAL
V is complex Element of the carrier of F_Complex
V *' is complex Element of the carrier of F_Complex
Re V is complex real ext-real Element of REAL
Im V is complex real ext-real Element of REAL
(Im V) * <i> is complex set
(Re V) - ((Im V) * <i>) is complex set
i_FC *' is complex Element of the carrier of F_Complex
Re i_FC is complex real ext-real Element of REAL
Im i_FC is complex real ext-real Element of REAL
(Im i_FC) * <i> is complex set
(Re i_FC) - ((Im i_FC) * <i>) is complex set
i_FC * (i_FC *') is complex Element of the carrier of F_Complex
the multF of F_Complex . (i_FC,(i_FC *')) is complex Element of the carrier of F_Complex
[i_FC,(i_FC *')] is set
{i_FC,(i_FC *')} is non empty V175() set
{{i_FC,(i_FC *')},{i_FC}} is non empty set
the multF of F_Complex . [i_FC,(i_FC *')] is set
K137(i_FC,(i_FC *')) is complex Element of COMPLEX
V is complex Element of the carrier of F_Complex
Re V is complex real ext-real Element of REAL
|.V.| is complex real ext-real Element of REAL
(Re V) ^2 is complex real ext-real Element of REAL
(Re V) * (Re V) is complex real ext-real set
Im V is complex real ext-real Element of REAL
(Im V) ^2 is complex real ext-real Element of REAL
(Im V) * (Im V) is complex real ext-real set
((Re V) ^2) + ((Im V) ^2) is complex real ext-real Element of REAL
sqrt (((Re V) ^2) + ((Im V) ^2)) is complex real ext-real Element of REAL
(Re V) / |.V.| is complex real ext-real Element of COMPLEX
- (Im V) is complex real ext-real Element of REAL
(- (Im V)) / |.V.| is complex real ext-real Element of COMPLEX
[**((Re V) / |.V.|),((- (Im V)) / |.V.|)**] is complex Element of the carrier of F_Complex
((- (Im V)) / |.V.|) * <i> is complex set
((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>) is complex set
|.[**((Re V) / |.V.|),((- (Im V)) / |.V.|)**].| is complex real ext-real Element of REAL
Re [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**] is complex real ext-real Element of REAL
(Re [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]) ^2 is complex real ext-real Element of REAL
(Re [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]) * (Re [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]) is complex real ext-real set
Im [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**] is complex real ext-real Element of REAL
(Im [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]) ^2 is complex real ext-real Element of REAL
(Im [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]) * (Im [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]) is complex real ext-real set
((Re [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]) ^2) + ((Im [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]) ^2) is complex real ext-real Element of REAL
sqrt (((Re [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]) ^2) + ((Im [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]) ^2)) is complex real ext-real Element of REAL
[**((Re V) / |.V.|),((- (Im V)) / |.V.|)**] * V is complex Element of the carrier of F_Complex
the multF of F_Complex . ([**((Re V) / |.V.|),((- (Im V)) / |.V.|)**],V) is complex Element of the carrier of F_Complex
[[**((Re V) / |.V.|),((- (Im V)) / |.V.|)**],V] is set
{[**((Re V) / |.V.|),((- (Im V)) / |.V.|)**],V} is non empty V175() set
{[**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]} is non empty V175() set
{{[**((Re V) / |.V.|),((- (Im V)) / |.V.|)**],V},{[**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]}} is non empty set
the multF of F_Complex . [[**((Re V) / |.V.|),((- (Im V)) / |.V.|)**],V] is set
K137([**((Re V) / |.V.|),((- (Im V)) / |.V.|)**],V) is complex Element of COMPLEX
Re ([**((Re V) / |.V.|),((- (Im V)) / |.V.|)**] * V) is complex real ext-real Element of REAL
Im ([**((Re V) / |.V.|),((- (Im V)) / |.V.|)**] * V) is complex real ext-real Element of REAL
((- (Im V)) / |.V.|) * <i> is complex Element of COMPLEX
((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>) is complex Element of COMPLEX
f is complex Element of COMPLEX
(((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>)) * f is complex Element of COMPLEX
V is complex Element of the carrier of F_Complex
|.V.| is complex real ext-real Element of REAL
Re V is complex real ext-real Element of REAL
(Re V) ^2 is complex real ext-real Element of REAL
(Re V) * (Re V) is complex real ext-real set
Im V is complex real ext-real Element of REAL
(Im V) ^2 is complex real ext-real Element of REAL
(Im V) * (Im V) is complex real ext-real set
((Re V) ^2) + ((Im V) ^2) is complex real ext-real Element of REAL
sqrt (((Re V) ^2) + ((Im V) ^2)) is complex real ext-real Element of REAL
vq is complex non zero Element of the carrier of F_Complex
|.vq.| is complex real ext-real Element of REAL
Re vq is complex real ext-real Element of REAL
(Re vq) ^2 is complex real ext-real Element of REAL
(Re vq) * (Re vq) is complex real ext-real set
Im vq is complex real ext-real Element of REAL
(Im vq) ^2 is complex real ext-real Element of REAL
(Im vq) * (Im vq) is complex real ext-real set
((Re vq) ^2) + ((Im vq) ^2) is complex real ext-real Element of REAL
sqrt (((Re vq) ^2) + ((Im vq) ^2)) is complex real ext-real Element of REAL
vq * V is complex Element of the carrier of F_Complex
the multF of F_Complex . (vq,V) is complex Element of the carrier of F_Complex
[vq,V] is set
{vq,V} is non empty V175() set
{vq} is non empty V175() set
{{vq,V},{vq}} is non empty set
the multF of F_Complex . [vq,V] is set
K137(vq,V) is complex Element of COMPLEX
Re (vq * V) is complex real ext-real Element of REAL
Im (vq * V) is complex real ext-real Element of REAL
(Re V) / |.V.| is complex real ext-real Element of COMPLEX
- (Im V) is complex real ext-real Element of REAL
(- (Im V)) / |.V.| is complex real ext-real Element of COMPLEX
[**((Re V) / |.V.|),((- (Im V)) / |.V.|)**] is complex Element of the carrier of F_Complex
((- (Im V)) / |.V.|) * <i> is complex set
((Re V) / |.V.|) + (((- (Im V)) / |.V.|) * <i>) is complex set
|.[**((Re V) / |.V.|),((- (Im V)) / |.V.|)**].| is complex real ext-real Element of REAL
Re [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**] is complex real ext-real Element of REAL
(Re [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]) ^2 is complex real ext-real Element of REAL
(Re [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]) * (Re [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]) is complex real ext-real set
Im [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**] is complex real ext-real Element of REAL
(Im [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]) ^2 is complex real ext-real Element of REAL
(Im [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]) * (Im [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]) is complex real ext-real set
((Re [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]) ^2) + ((Im [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]) ^2) is complex real ext-real Element of REAL
sqrt (((Re [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]) ^2) + ((Im [**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]) ^2)) is complex real ext-real Element of REAL
[**((Re V) / |.V.|),((- (Im V)) / |.V.|)**] * V is complex Element of the carrier of F_Complex
the multF of F_Complex . ([**((Re V) / |.V.|),((- (Im V)) / |.V.|)**],V) is complex Element of the carrier of F_Complex
[[**((Re V) / |.V.|),((- (Im V)) / |.V.|)**],V] is set
{[**((Re V) / |.V.|),((- (Im V)) / |.V.|)**],V} is non empty V175() set
{[**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]} is non empty V175() set
{{[**((Re V) / |.V.|),((- (Im V)) / |.V.|)**],V},{[**((Re V) / |.V.|),((- (Im V)) / |.V.|)**]}} is non empty set
the multF of F_Complex . [[**((Re V) / |.V.|),((- (Im V)) / |.V.|)**],V] is set
K137([**((Re V) / |.V.|),((- (Im V)) / |.V.|)**],V) is complex Element of COMPLEX
Re ([**((Re V) / |.V.|),((- (Im V)) / |.V.|)**] * V) is complex real ext-real Element of REAL
Im ([**((Re V) / |.V.|),((- (Im V)) / |.V.|)**] * V) is complex real ext-real Element of REAL
vq is complex Element of the carrier of F_Complex
|.vq.| is complex real ext-real Element of REAL
Re vq is complex real ext-real Element of REAL
(Re vq) ^2 is complex real ext-real Element of REAL
(Re vq) * (Re vq) is complex real ext-real set
Im vq is complex real ext-real Element of REAL
(Im vq) ^2 is complex real ext-real Element of REAL
(Im vq) * (Im vq) is complex real ext-real set
((Re vq) ^2) + ((Im vq) ^2) is complex real ext-real Element of REAL
sqrt (((Re vq) ^2) + ((Im vq) ^2)) is complex real ext-real Element of REAL
vq * V is complex Element of the carrier of F_Complex
the multF of F_Complex . (vq,V) is complex Element of the carrier of F_Complex
[vq,V] is set
{vq,V} is non empty V175() set
{vq} is non empty V175() set
{{vq,V},{vq}} is non empty set
the multF of F_Complex . [vq,V] is set
K137(vq,V) is complex Element of COMPLEX
Re (vq * V) is complex real ext-real Element of REAL
Im (vq * V) is complex real ext-real Element of REAL
vr is complex Element of the carrier of F_Complex
|.vr.| is complex real ext-real Element of REAL
Re vr is complex real ext-real Element of REAL
(Re vr) ^2 is complex real ext-real Element of REAL
(Re vr) * (Re vr) is complex real ext-real set
Im vr is complex real ext-real Element of REAL
(Im vr) ^2 is complex real ext-real Element of REAL
(Im vr) * (Im vr) is complex real ext-real set
((Re vr) ^2) + ((Im vr) ^2) is complex real ext-real Element of REAL
sqrt (((Re vr) ^2) + ((Im vr) ^2)) is complex real ext-real Element of REAL
vr * V is complex Element of the carrier of F_Complex
the multF of F_Complex . (vr,V) is complex Element of the carrier of F_Complex
[vr,V] is set
{vr,V} is non empty V175() set
{vr} is non empty V175() set
{{vr,V},{vr}} is non empty set
the multF of F_Complex . [vr,V] is set
K137(vr,V) is complex Element of COMPLEX
Re (vr * V) is complex real ext-real Element of REAL
Im (vr * V) is complex real ext-real Element of REAL
V is complex Element of the carrier of F_Complex
f is complex Element of the carrier of F_Complex
V - f is complex Element of the carrier of F_Complex
- f is complex Element of the carrier of F_Complex
V + (- f) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . (V,(- f)) is complex Element of the carrier of F_Complex
[V,(- f)] is set
{V,(- f)} is non empty V175() set
{V} is non empty V175() set
{{V,(- f)},{V}} is non empty set
the addF of F_Complex . [V,(- f)] is set
K135(V,(- f)) is complex Element of COMPLEX
Re (V - f) is complex real ext-real Element of REAL
Re V is complex real ext-real Element of REAL
Re f is complex real ext-real Element of REAL
(Re V) - (Re f) is complex real ext-real Element of REAL
Im (V - f) is complex real ext-real Element of REAL
Im V is complex real ext-real Element of REAL
Im f is complex real ext-real Element of REAL
(Im V) - (Im f) is complex real ext-real Element of REAL
vq is complex Element of COMPLEX
vr is complex Element of COMPLEX
vq - vr is complex Element of COMPLEX
Re (vq - vr) is complex real ext-real Element of REAL
Im (vq - vr) is complex real ext-real Element of REAL
V is complex Element of the carrier of F_Complex
Im V is complex real ext-real Element of REAL
f is complex Element of the carrier of F_Complex
V * f is complex Element of the carrier of F_Complex
the multF of F_Complex . (V,f) is complex Element of the carrier of F_Complex
[V,f] is set
{V,f} is non empty V175() set
{V} is non empty V175() set
{{V,f},{V}} is non empty set
the multF of F_Complex . [V,f] is set
K137(V,f) is complex Element of COMPLEX
Re (V * f) is complex real ext-real Element of REAL
Re V is complex real ext-real Element of REAL
Re f is complex real ext-real Element of REAL
(Re V) * (Re f) is complex real ext-real Element of REAL
Im (V * f) is complex real ext-real Element of REAL
Im f is complex real ext-real Element of REAL
(Re V) * (Im f) is complex real ext-real Element of REAL
0 * (Im f) is complex real ext-real Element of REAL
((Re V) * (Re f)) - (0 * (Im f)) is complex real ext-real Element of REAL
(Re f) * 0 is complex real ext-real Element of REAL
((Re V) * (Im f)) + ((Re f) * 0) is complex real ext-real Element of REAL
V is complex Element of the carrier of F_Complex
Im V is complex real ext-real Element of REAL
f is complex Element of the carrier of F_Complex
Im f is complex real ext-real Element of REAL
V * f is complex Element of the carrier of F_Complex
the multF of F_Complex . (V,f) is complex Element of the carrier of F_Complex
[V,f] is set
{V,f} is non empty V175() set
{V} is non empty V175() set
{{V,f},{V}} is non empty set
the multF of F_Complex . [V,f] is set
K137(V,f) is complex Element of COMPLEX
Im (V * f) is complex real ext-real Element of REAL
Re f is complex real ext-real Element of REAL
(Re f) * 0 is complex real ext-real Element of REAL
V is complex Element of the carrier of F_Complex
Im V is complex real ext-real Element of REAL
V *' is complex Element of the carrier of F_Complex
Re V is complex real ext-real Element of REAL
(Im V) * <i> is complex set
(Re V) - ((Im V) * <i>) is complex set
f is complex Element of COMPLEX
Re f is complex real ext-real Element of REAL
Im f is complex real ext-real Element of REAL
- (Im f) is complex real ext-real Element of REAL
(- (Im f)) * <i> is complex set
(Re f) + ((- (Im f)) * <i>) is complex set
V is complex Element of the carrier of F_Complex
V *' is complex Element of the carrier of F_Complex
Re V is complex real ext-real Element of REAL
Im V is complex real ext-real Element of REAL
(Im V) * <i> is complex set
(Re V) - ((Im V) * <i>) is complex set
V * (V *') is complex Element of the carrier of F_Complex
the multF of F_Complex . (V,(V *')) is complex Element of the carrier of F_Complex
[V,(V *')] is set
{V,(V *')} is non empty V175() set
{V} is non empty V175() set
{{V,(V *')},{V}} is non empty set
the multF of F_Complex . [V,(V *')] is set
K137(V,(V *')) is complex Element of COMPLEX
|.V.| is complex real ext-real Element of REAL
(Re V) ^2 is complex real ext-real Element of REAL
(Re V) * (Re V) is complex real ext-real set
(Im V) ^2 is complex real ext-real Element of REAL
(Im V) * (Im V) is complex real ext-real set
((Re V) ^2) + ((Im V) ^2) is complex real ext-real Element of REAL
sqrt (((Re V) ^2) + ((Im V) ^2)) is complex real ext-real Element of REAL
|.V.| ^2 is complex real ext-real Element of REAL
|.V.| * |.V.| is complex real ext-real set
f is complex Element of COMPLEX
|.f.| is complex real ext-real Element of REAL
Re f is complex real ext-real Element of REAL
(Re f) ^2 is complex real ext-real Element of REAL
(Re f) * (Re f) is complex real ext-real set
Im f is complex real ext-real Element of REAL
(Im f) ^2 is complex real ext-real Element of REAL
(Im f) * (Im f) is complex real ext-real set
((Re f) ^2) + ((Im f) ^2) is complex real ext-real Element of REAL
sqrt (((Re f) ^2) + ((Im f) ^2)) is complex real ext-real Element of REAL
|.f.| ^2 is complex real ext-real Element of REAL
|.f.| * |.f.| is complex real ext-real set
(|.f.| ^2) + (0 * <i>) is complex set
V is complex Element of the carrier of F_Complex
Re V is complex real ext-real Element of REAL
Im V is complex real ext-real Element of REAL
|.V.| is complex real ext-real Element of REAL
(Re V) ^2 is complex real ext-real Element of REAL
(Re V) * (Re V) is complex real ext-real set
(Im V) ^2 is complex real ext-real Element of REAL
(Im V) * (Im V) is complex real ext-real set
((Re V) ^2) + ((Im V) ^2) is complex real ext-real Element of REAL
sqrt (((Re V) ^2) + ((Im V) ^2)) is complex real ext-real Element of REAL
f is complex Element of COMPLEX
|.f.| is complex real ext-real Element of REAL
Re f is complex real ext-real Element of REAL
(Re f) ^2 is complex real ext-real Element of REAL
(Re f) * (Re f) is complex real ext-real set
Im f is complex real ext-real Element of REAL
(Im f) ^2 is complex real ext-real Element of REAL
(Im f) * (Im f) is complex real ext-real set
((Re f) ^2) + ((Im f) ^2) is complex real ext-real Element of REAL
sqrt (((Re f) ^2) + ((Im f) ^2)) is complex real ext-real Element of REAL
abs (Re f) is complex real ext-real Element of REAL
Re (Re f) is complex real ext-real Element of REAL
(Re (Re f)) ^2 is complex real ext-real Element of REAL
(Re (Re f)) * (Re (Re f)) is complex real ext-real set
Im (Re f) is complex real ext-real Element of REAL
(Im (Re f)) ^2 is complex real ext-real Element of REAL
(Im (Re f)) * (Im (Re f)) is complex real ext-real set
((Re (Re f)) ^2) + ((Im (Re f)) ^2) is complex real ext-real Element of REAL
sqrt (((Re (Re f)) ^2) + ((Im (Re f)) ^2)) is complex real ext-real Element of REAL
V is complex Element of the carrier of F_Complex
Re V is complex real ext-real Element of REAL
V *' is complex Element of the carrier of F_Complex
Im V is complex real ext-real Element of REAL
(Im V) * <i> is complex set
(Re V) - ((Im V) * <i>) is complex set
Re (V *') is complex real ext-real Element of REAL
(Re V) + (Re (V *')) is complex real ext-real Element of REAL
2 * (Re V) is complex real ext-real Element of REAL
(Re V) + (Re V) is complex real ext-real Element of REAL
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
V is non empty VectSpStr over F_Complex
0Functional V is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like constant V30( the carrier of V, the carrier of F_Complex) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of F_Complex:]
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
[#] V is non empty non proper Element of bool the carrier of V
bool the carrier of V is set
K402( the carrier of F_Complex,([#] V),(0. F_Complex)) is V16() V19( [#] V) V20( the carrier of F_Complex) Function-like V30( [#] V, the carrier of F_Complex) Element of bool [:([#] V), the carrier of F_Complex:]
[:([#] V), the carrier of F_Complex:] is set
bool [:([#] V), the carrier of F_Complex:] is set
f is Element of the carrier of V
(0Functional V) . f is complex Element of the carrier of F_Complex
vq is complex Element of the carrier of F_Complex
vq * f is Element of the carrier of V
the lmult of V is V16() V19([: the carrier of F_Complex, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of F_Complex, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:]
[: the carrier of F_Complex, the carrier of V:] is set
[:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
the lmult of V . (vq,f) is Element of the carrier of V
[vq,f] is set
{vq,f} is non empty set
{vq} is non empty V175() set
{{vq,f},{vq}} is non empty set
the lmult of V . [vq,f] is set
(0Functional V) . (vq * f) is complex Element of the carrier of F_Complex
vq *' is complex Element of the carrier of F_Complex
Re vq is complex real ext-real Element of REAL
Im vq is complex real ext-real Element of REAL
(Im vq) * <i> is complex set
(Re vq) - ((Im vq) * <i>) is complex set
(vq *') * ((0Functional V) . f) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((vq *'),((0Functional V) . f)) is complex Element of the carrier of F_Complex
[(vq *'),((0Functional V) . f)] is set
{(vq *'),((0Functional V) . f)} is non empty V175() set
{(vq *')} is non empty V175() set
{{(vq *'),((0Functional V) . f)},{(vq *')}} is non empty set
the multF of F_Complex . [(vq *'),((0Functional V) . f)] is set
K137((vq *'),((0Functional V) . f)) is complex Element of COMPLEX
V is non empty right_complementable add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
0. V is zero Element of the carrier of V
f . (0. V) is complex Element of the carrier of F_Complex
(0. F_Complex) * (0. V) is Element of the carrier of V
the lmult of V is V16() V19([: the carrier of F_Complex, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of F_Complex, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:]
[: the carrier of F_Complex, the carrier of V:] is set
[:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
the lmult of V . ((0. F_Complex),(0. V)) is Element of the carrier of V
[(0. F_Complex),(0. V)] is set
{(0. F_Complex),(0. V)} is non empty set
{(0. F_Complex)} is non empty V175() set
{{(0. F_Complex),(0. V)},{(0. F_Complex)}} is non empty set
the lmult of V . [(0. F_Complex),(0. V)] is set
f . ((0. F_Complex) * (0. V)) is complex Element of the carrier of F_Complex
((0. F_Complex) *') * (f . (0. V)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((0. F_Complex) *'),(f . (0. V))) is complex Element of the carrier of F_Complex
[((0. F_Complex) *'),(f . (0. V))] is set
{((0. F_Complex) *'),(f . (0. V))} is non empty V175() set
{((0. F_Complex) *')} is non empty V175() set
{{((0. F_Complex) *'),(f . (0. V))},{((0. F_Complex) *')}} is non empty set
the multF of F_Complex . [((0. F_Complex) *'),(f . (0. V))] is set
K137(((0. F_Complex) *'),(f . (0. V))) is complex Element of COMPLEX
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
0Functional V is V16() V19( the carrier of V) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like constant V30( the carrier of V, the carrier of F_Complex) V30( the carrier of V, the carrier of F_Complex) additive homogeneous 0-preserving (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
[#] V is non empty non proper Element of bool the carrier of V
bool the carrier of V is set
K402( the carrier of F_Complex,([#] V),(0. F_Complex)) is V16() V19( [#] V) V20( the carrier of F_Complex) Function-like V30( [#] V, the carrier of F_Complex) Element of bool [:([#] V), the carrier of F_Complex:]
[:([#] V), the carrier of F_Complex:] is set
bool [:([#] V), the carrier of F_Complex:] is set
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
vq is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
f + vq is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
vr is Element of the carrier of V
(f + vq) . vr is complex Element of the carrier of F_Complex
qh is complex Element of the carrier of F_Complex
qh * vr is Element of the carrier of V
the lmult of V is V16() V19([: the carrier of F_Complex, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of F_Complex, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:]
[: the carrier of F_Complex, the carrier of V:] is set
[:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
the lmult of V . (qh,vr) is Element of the carrier of V
[qh,vr] is set
{qh,vr} is non empty set
{qh} is non empty V175() set
{{qh,vr},{qh}} is non empty set
the lmult of V . [qh,vr] is set
(f + vq) . (qh * vr) is complex Element of the carrier of F_Complex
qh *' is complex Element of the carrier of F_Complex
Re qh is complex real ext-real Element of REAL
Im qh is complex real ext-real Element of REAL
(Im qh) * <i> is complex set
(Re qh) - ((Im qh) * <i>) is complex set
(qh *') * ((f + vq) . vr) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((qh *'),((f + vq) . vr)) is complex Element of the carrier of F_Complex
[(qh *'),((f + vq) . vr)] is set
{(qh *'),((f + vq) . vr)} is non empty V175() set
{(qh *')} is non empty V175() set
{{(qh *'),((f + vq) . vr)},{(qh *')}} is non empty set
the multF of F_Complex . [(qh *'),((f + vq) . vr)] is set
K137((qh *'),((f + vq) . vr)) is complex Element of COMPLEX
f . (qh * vr) is complex Element of the carrier of F_Complex
vq . (qh * vr) is complex Element of the carrier of F_Complex
(f . (qh * vr)) + (vq . (qh * vr)) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . ((f . (qh * vr)),(vq . (qh * vr))) is complex Element of the carrier of F_Complex
[(f . (qh * vr)),(vq . (qh * vr))] is set
{(f . (qh * vr)),(vq . (qh * vr))} is non empty V175() set
{(f . (qh * vr))} is non empty V175() set
{{(f . (qh * vr)),(vq . (qh * vr))},{(f . (qh * vr))}} is non empty set
the addF of F_Complex . [(f . (qh * vr)),(vq . (qh * vr))] is set
K135((f . (qh * vr)),(vq . (qh * vr))) is complex Element of COMPLEX
f . vr is complex Element of the carrier of F_Complex
(qh *') * (f . vr) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((qh *'),(f . vr)) is complex Element of the carrier of F_Complex
[(qh *'),(f . vr)] is set
{(qh *'),(f . vr)} is non empty V175() set
{{(qh *'),(f . vr)},{(qh *')}} is non empty set
the multF of F_Complex . [(qh *'),(f . vr)] is set
K137((qh *'),(f . vr)) is complex Element of COMPLEX
((qh *') * (f . vr)) + (vq . (qh * vr)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((qh *') * (f . vr)),(vq . (qh * vr))) is complex Element of the carrier of F_Complex
[((qh *') * (f . vr)),(vq . (qh * vr))] is set
{((qh *') * (f . vr)),(vq . (qh * vr))} is non empty V175() set
{((qh *') * (f . vr))} is non empty V175() set
{{((qh *') * (f . vr)),(vq . (qh * vr))},{((qh *') * (f . vr))}} is non empty set
the addF of F_Complex . [((qh *') * (f . vr)),(vq . (qh * vr))] is set
K135(((qh *') * (f . vr)),(vq . (qh * vr))) is complex Element of COMPLEX
vq . vr is complex Element of the carrier of F_Complex
(qh *') * (vq . vr) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((qh *'),(vq . vr)) is complex Element of the carrier of F_Complex
[(qh *'),(vq . vr)] is set
{(qh *'),(vq . vr)} is non empty V175() set
{{(qh *'),(vq . vr)},{(qh *')}} is non empty set
the multF of F_Complex . [(qh *'),(vq . vr)] is set
K137((qh *'),(vq . vr)) is complex Element of COMPLEX
((qh *') * (f . vr)) + ((qh *') * (vq . vr)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((qh *') * (f . vr)),((qh *') * (vq . vr))) is complex Element of the carrier of F_Complex
[((qh *') * (f . vr)),((qh *') * (vq . vr))] is set
{((qh *') * (f . vr)),((qh *') * (vq . vr))} is non empty V175() set
{{((qh *') * (f . vr)),((qh *') * (vq . vr))},{((qh *') * (f . vr))}} is non empty set
the addF of F_Complex . [((qh *') * (f . vr)),((qh *') * (vq . vr))] is set
K135(((qh *') * (f . vr)),((qh *') * (vq . vr))) is complex Element of COMPLEX
(f . vr) + (vq . vr) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((f . vr),(vq . vr)) is complex Element of the carrier of F_Complex
[(f . vr),(vq . vr)] is set
{(f . vr),(vq . vr)} is non empty V175() set
{(f . vr)} is non empty V175() set
{{(f . vr),(vq . vr)},{(f . vr)}} is non empty set
the addF of F_Complex . [(f . vr),(vq . vr)] is set
K135((f . vr),(vq . vr)) is complex Element of COMPLEX
(qh *') * ((f . vr) + (vq . vr)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((qh *'),((f . vr) + (vq . vr))) is complex Element of the carrier of F_Complex
[(qh *'),((f . vr) + (vq . vr))] is set
{(qh *'),((f . vr) + (vq . vr))} is non empty V175() set
{{(qh *'),((f . vr) + (vq . vr))},{(qh *')}} is non empty set
the multF of F_Complex . [(qh *'),((f . vr) + (vq . vr))] is set
K137((qh *'),((f . vr) + (vq . vr))) is complex Element of COMPLEX
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
- f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
vq is Element of the carrier of V
(- f) . vq is complex Element of the carrier of F_Complex
vr is complex Element of the carrier of F_Complex
vr * vq is Element of the carrier of V
the lmult of V is V16() V19([: the carrier of F_Complex, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of F_Complex, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:]
[: the carrier of F_Complex, the carrier of V:] is set
[:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
the lmult of V . (vr,vq) is Element of the carrier of V
[vr,vq] is set
{vr,vq} is non empty set
{vr} is non empty V175() set
{{vr,vq},{vr}} is non empty set
the lmult of V . [vr,vq] is set
(- f) . (vr * vq) is complex Element of the carrier of F_Complex
vr *' is complex Element of the carrier of F_Complex
Re vr is complex real ext-real Element of REAL
Im vr is complex real ext-real Element of REAL
(Im vr) * <i> is complex set
(Re vr) - ((Im vr) * <i>) is complex set
(vr *') * ((- f) . vq) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((vr *'),((- f) . vq)) is complex Element of the carrier of F_Complex
[(vr *'),((- f) . vq)] is set
{(vr *'),((- f) . vq)} is non empty V175() set
{(vr *')} is non empty V175() set
{{(vr *'),((- f) . vq)},{(vr *')}} is non empty set
the multF of F_Complex . [(vr *'),((- f) . vq)] is set
K137((vr *'),((- f) . vq)) is complex Element of COMPLEX
f . (vr * vq) is complex Element of the carrier of F_Complex
- (f . (vr * vq)) is complex Element of the carrier of F_Complex
f . vq is complex Element of the carrier of F_Complex
(vr *') * (f . vq) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((vr *'),(f . vq)) is complex Element of the carrier of F_Complex
[(vr *'),(f . vq)] is set
{(vr *'),(f . vq)} is non empty V175() set
{{(vr *'),(f . vq)},{(vr *')}} is non empty set
the multF of F_Complex . [(vr *'),(f . vq)] is set
K137((vr *'),(f . vq)) is complex Element of COMPLEX
- ((vr *') * (f . vq)) is complex Element of the carrier of F_Complex
- (f . vq) is complex Element of the carrier of F_Complex
(vr *') * (- (f . vq)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((vr *'),(- (f . vq))) is complex Element of the carrier of F_Complex
[(vr *'),(- (f . vq))] is set
{(vr *'),(- (f . vq))} is non empty V175() set
{{(vr *'),(- (f . vq))},{(vr *')}} is non empty set
the multF of F_Complex . [(vr *'),(- (f . vq))] is set
K137((vr *'),(- (f . vq))) is complex Element of COMPLEX
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is complex Element of the carrier of F_Complex
vq is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
f * vq is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
vr is Element of the carrier of V
(f * vq) . vr is complex Element of the carrier of F_Complex
qh is complex Element of the carrier of F_Complex
qh * vr is Element of the carrier of V
the lmult of V is V16() V19([: the carrier of F_Complex, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of F_Complex, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:]
[: the carrier of F_Complex, the carrier of V:] is set
[:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
the lmult of V . (qh,vr) is Element of the carrier of V
[qh,vr] is set
{qh,vr} is non empty set
{qh} is non empty V175() set
{{qh,vr},{qh}} is non empty set
the lmult of V . [qh,vr] is set
(f * vq) . (qh * vr) is complex Element of the carrier of F_Complex
qh *' is complex Element of the carrier of F_Complex
Re qh is complex real ext-real Element of REAL
Im qh is complex real ext-real Element of REAL
(Im qh) * <i> is complex set
(Re qh) - ((Im qh) * <i>) is complex set
(qh *') * ((f * vq) . vr) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((qh *'),((f * vq) . vr)) is complex Element of the carrier of F_Complex
[(qh *'),((f * vq) . vr)] is set
{(qh *'),((f * vq) . vr)} is non empty V175() set
{(qh *')} is non empty V175() set
{{(qh *'),((f * vq) . vr)},{(qh *')}} is non empty set
the multF of F_Complex . [(qh *'),((f * vq) . vr)] is set
K137((qh *'),((f * vq) . vr)) is complex Element of COMPLEX
vq . (qh * vr) is complex Element of the carrier of F_Complex
f * (vq . (qh * vr)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (f,(vq . (qh * vr))) is complex Element of the carrier of F_Complex
[f,(vq . (qh * vr))] is set
{f,(vq . (qh * vr))} is non empty V175() set
{f} is non empty V175() set
{{f,(vq . (qh * vr))},{f}} is non empty set
the multF of F_Complex . [f,(vq . (qh * vr))] is set
K137(f,(vq . (qh * vr))) is complex Element of COMPLEX
vq . vr is complex Element of the carrier of F_Complex
(qh *') * (vq . vr) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((qh *'),(vq . vr)) is complex Element of the carrier of F_Complex
[(qh *'),(vq . vr)] is set
{(qh *'),(vq . vr)} is non empty V175() set
{{(qh *'),(vq . vr)},{(qh *')}} is non empty set
the multF of F_Complex . [(qh *'),(vq . vr)] is set
K137((qh *'),(vq . vr)) is complex Element of COMPLEX
f * ((qh *') * (vq . vr)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (f,((qh *') * (vq . vr))) is complex Element of the carrier of F_Complex
[f,((qh *') * (vq . vr))] is set
{f,((qh *') * (vq . vr))} is non empty V175() set
{{f,((qh *') * (vq . vr))},{f}} is non empty set
the multF of F_Complex . [f,((qh *') * (vq . vr))] is set
K137(f,((qh *') * (vq . vr))) is complex Element of COMPLEX
f * (vq . vr) is complex Element of the carrier of F_Complex
the multF of F_Complex . (f,(vq . vr)) is complex Element of the carrier of F_Complex
[f,(vq . vr)] is set
{f,(vq . vr)} is non empty V175() set
{{f,(vq . vr)},{f}} is non empty set
the multF of F_Complex . [f,(vq . vr)] is set
K137(f,(vq . vr)) is complex Element of COMPLEX
(qh *') * (f * (vq . vr)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((qh *'),(f * (vq . vr))) is complex Element of the carrier of F_Complex
[(qh *'),(f * (vq . vr))] is set
{(qh *'),(f * (vq . vr))} is non empty V175() set
{{(qh *'),(f * (vq . vr))},{(qh *')}} is non empty set
the multF of F_Complex . [(qh *'),(f * (vq . vr))] is set
K137((qh *'),(f * (vq . vr))) is complex Element of COMPLEX
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
vq is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
f - vq is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
- vq is V16() V19( the carrier of V) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) V30( the carrier of V, the carrier of F_Complex) (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
f + (- vq) is V16() V19( the carrier of V) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) V30( the carrier of V, the carrier of F_Complex) (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
vq is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
vr is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
qh is Element of the carrier of V
vr . qh is complex Element of the carrier of F_Complex
f . qh is complex Element of the carrier of F_Complex
(f . qh) *' is complex Element of the carrier of F_Complex
Re (f . qh) is complex real ext-real Element of REAL
Im (f . qh) is complex real ext-real Element of REAL
(Im (f . qh)) * <i> is complex set
(Re (f . qh)) - ((Im (f . qh)) * <i>) is complex set
vq is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
vr is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
qh is Element of the carrier of V
vq . qh is complex Element of the carrier of F_Complex
f . qh is complex Element of the carrier of F_Complex
(f . qh) *' is complex Element of the carrier of F_Complex
Re (f . qh) is complex real ext-real Element of REAL
Im (f . qh) is complex real ext-real Element of REAL
(Im (f . qh)) * <i> is complex set
(Re (f . qh)) - ((Im (f . qh)) * <i>) is complex set
vr . qh is complex Element of the carrier of F_Complex
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) additive Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,f) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
vq is Element of the carrier of V
vr is Element of the carrier of V
vq + vr is Element of the carrier of V
the addF of V is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is set
the addF of V . (vq,vr) is Element of the carrier of V
[vq,vr] is set
{vq,vr} is non empty set
{vq} is non empty set
{{vq,vr},{vq}} is non empty set
the addF of V . [vq,vr] is set
(V,f) . (vq + vr) is complex Element of the carrier of F_Complex
(V,f) . vq is complex Element of the carrier of F_Complex
(V,f) . vr is complex Element of the carrier of F_Complex
((V,f) . vq) + ((V,f) . vr) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . (((V,f) . vq),((V,f) . vr)) is complex Element of the carrier of F_Complex
[((V,f) . vq),((V,f) . vr)] is set
{((V,f) . vq),((V,f) . vr)} is non empty V175() set
{((V,f) . vq)} is non empty V175() set
{{((V,f) . vq),((V,f) . vr)},{((V,f) . vq)}} is non empty set
the addF of F_Complex . [((V,f) . vq),((V,f) . vr)] is set
K135(((V,f) . vq),((V,f) . vr)) is complex Element of COMPLEX
f . (vq + vr) is complex Element of the carrier of F_Complex
(f . (vq + vr)) *' is complex Element of the carrier of F_Complex
Re (f . (vq + vr)) is complex real ext-real Element of REAL
Im (f . (vq + vr)) is complex real ext-real Element of REAL
(Im (f . (vq + vr))) * <i> is complex set
(Re (f . (vq + vr))) - ((Im (f . (vq + vr))) * <i>) is complex set
f . vq is complex Element of the carrier of F_Complex
f . vr is complex Element of the carrier of F_Complex
(f . vq) + (f . vr) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((f . vq),(f . vr)) is complex Element of the carrier of F_Complex
[(f . vq),(f . vr)] is set
{(f . vq),(f . vr)} is non empty V175() set
{(f . vq)} is non empty V175() set
{{(f . vq),(f . vr)},{(f . vq)}} is non empty set
the addF of F_Complex . [(f . vq),(f . vr)] is set
K135((f . vq),(f . vr)) is complex Element of COMPLEX
((f . vq) + (f . vr)) *' is complex Element of the carrier of F_Complex
Re ((f . vq) + (f . vr)) is complex real ext-real Element of REAL
Im ((f . vq) + (f . vr)) is complex real ext-real Element of REAL
(Im ((f . vq) + (f . vr))) * <i> is complex set
(Re ((f . vq) + (f . vr))) - ((Im ((f . vq) + (f . vr))) * <i>) is complex set
(f . vq) *' is complex Element of the carrier of F_Complex
Re (f . vq) is complex real ext-real Element of REAL
Im (f . vq) is complex real ext-real Element of REAL
(Im (f . vq)) * <i> is complex set
(Re (f . vq)) - ((Im (f . vq)) * <i>) is complex set
(f . vr) *' is complex Element of the carrier of F_Complex
Re (f . vr) is complex real ext-real Element of REAL
Im (f . vr) is complex real ext-real Element of REAL
(Im (f . vr)) * <i> is complex set
(Re (f . vr)) - ((Im (f . vr)) * <i>) is complex set
((f . vq) *') + ((f . vr) *') is complex Element of the carrier of F_Complex
the addF of F_Complex . (((f . vq) *'),((f . vr) *')) is complex Element of the carrier of F_Complex
[((f . vq) *'),((f . vr) *')] is set
{((f . vq) *'),((f . vr) *')} is non empty V175() set
{((f . vq) *')} is non empty V175() set
{{((f . vq) *'),((f . vr) *')},{((f . vq) *')}} is non empty set
the addF of F_Complex . [((f . vq) *'),((f . vr) *')] is set
K135(((f . vq) *'),((f . vr) *')) is complex Element of COMPLEX
((V,f) . vq) + ((f . vr) *') is complex Element of the carrier of F_Complex
the addF of F_Complex . (((V,f) . vq),((f . vr) *')) is complex Element of the carrier of F_Complex
[((V,f) . vq),((f . vr) *')] is set
{((V,f) . vq),((f . vr) *')} is non empty V175() set
{{((V,f) . vq),((f . vr) *')},{((V,f) . vq)}} is non empty set
the addF of F_Complex . [((V,f) . vq),((f . vr) *')] is set
K135(((V,f) . vq),((f . vr) *')) is complex Element of COMPLEX
((V,f) . vq) + ((V,f) . vr) is complex Element of the carrier of F_Complex
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) homogeneous Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,f) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
vq is Element of the carrier of V
(V,f) . vq is complex Element of the carrier of F_Complex
vr is complex Element of the carrier of F_Complex
vr * vq is Element of the carrier of V
the lmult of V is V16() V19([: the carrier of F_Complex, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of F_Complex, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:]
[: the carrier of F_Complex, the carrier of V:] is set
[:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
the lmult of V . (vr,vq) is Element of the carrier of V
[vr,vq] is set
{vr,vq} is non empty set
{vr} is non empty V175() set
{{vr,vq},{vr}} is non empty set
the lmult of V . [vr,vq] is set
(V,f) . (vr * vq) is complex Element of the carrier of F_Complex
vr *' is complex Element of the carrier of F_Complex
Re vr is complex real ext-real Element of REAL
Im vr is complex real ext-real Element of REAL
(Im vr) * <i> is complex set
(Re vr) - ((Im vr) * <i>) is complex set
(vr *') * ((V,f) . vq) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((vr *'),((V,f) . vq)) is complex Element of the carrier of F_Complex
[(vr *'),((V,f) . vq)] is set
{(vr *'),((V,f) . vq)} is non empty V175() set
{(vr *')} is non empty V175() set
{{(vr *'),((V,f) . vq)},{(vr *')}} is non empty set
the multF of F_Complex . [(vr *'),((V,f) . vq)] is set
K137((vr *'),((V,f) . vq)) is complex Element of COMPLEX
f . (vr * vq) is complex Element of the carrier of F_Complex
(f . (vr * vq)) *' is complex Element of the carrier of F_Complex
Re (f . (vr * vq)) is complex real ext-real Element of REAL
Im (f . (vr * vq)) is complex real ext-real Element of REAL
(Im (f . (vr * vq))) * <i> is complex set
(Re (f . (vr * vq))) - ((Im (f . (vr * vq))) * <i>) is complex set
f . vq is complex Element of the carrier of F_Complex
vr * (f . vq) is complex Element of the carrier of F_Complex
the multF of F_Complex . (vr,(f . vq)) is complex Element of the carrier of F_Complex
[vr,(f . vq)] is set
{vr,(f . vq)} is non empty V175() set
{{vr,(f . vq)},{vr}} is non empty set
the multF of F_Complex . [vr,(f . vq)] is set
K137(vr,(f . vq)) is complex Element of COMPLEX
(vr * (f . vq)) *' is complex Element of the carrier of F_Complex
Re (vr * (f . vq)) is complex real ext-real Element of REAL
Im (vr * (f . vq)) is complex real ext-real Element of REAL
(Im (vr * (f . vq))) * <i> is complex set
(Re (vr * (f . vq))) - ((Im (vr * (f . vq))) * <i>) is complex set
(f . vq) *' is complex Element of the carrier of F_Complex
Re (f . vq) is complex real ext-real Element of REAL
Im (f . vq) is complex real ext-real Element of REAL
(Im (f . vq)) * <i> is complex set
(Re (f . vq)) - ((Im (f . vq)) * <i>) is complex set
(vr *') * ((f . vq) *') is complex Element of the carrier of F_Complex
the multF of F_Complex . ((vr *'),((f . vq) *')) is complex Element of the carrier of F_Complex
[(vr *'),((f . vq) *')] is set
{(vr *'),((f . vq) *')} is non empty V175() set
{{(vr *'),((f . vq) *')},{(vr *')}} is non empty set
the multF of F_Complex . [(vr *'),((f . vq) *')] is set
K137((vr *'),((f . vq) *')) is complex Element of COMPLEX
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,f) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
vq is Element of the carrier of V
(V,f) . vq is complex Element of the carrier of F_Complex
vr is complex Element of the carrier of F_Complex
vr * vq is Element of the carrier of V
the lmult of V is V16() V19([: the carrier of F_Complex, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of F_Complex, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:]
[: the carrier of F_Complex, the carrier of V:] is set
[:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
the lmult of V . (vr,vq) is Element of the carrier of V
[vr,vq] is set
{vr,vq} is non empty set
{vr} is non empty V175() set
{{vr,vq},{vr}} is non empty set
the lmult of V . [vr,vq] is set
(V,f) . (vr * vq) is complex Element of the carrier of F_Complex
vr * ((V,f) . vq) is complex Element of the carrier of F_Complex
the multF of F_Complex . (vr,((V,f) . vq)) is complex Element of the carrier of F_Complex
[vr,((V,f) . vq)] is set
{vr,((V,f) . vq)} is non empty V175() set
{{vr,((V,f) . vq)},{vr}} is non empty set
the multF of F_Complex . [vr,((V,f) . vq)] is set
K137(vr,((V,f) . vq)) is complex Element of COMPLEX
f . (vr * vq) is complex Element of the carrier of F_Complex
(f . (vr * vq)) *' is complex Element of the carrier of F_Complex
Re (f . (vr * vq)) is complex real ext-real Element of REAL
Im (f . (vr * vq)) is complex real ext-real Element of REAL
(Im (f . (vr * vq))) * <i> is complex set
(Re (f . (vr * vq))) - ((Im (f . (vr * vq))) * <i>) is complex set
vr *' is complex Element of the carrier of F_Complex
Re vr is complex real ext-real Element of REAL
Im vr is complex real ext-real Element of REAL
(Im vr) * <i> is complex set
(Re vr) - ((Im vr) * <i>) is complex set
f . vq is complex Element of the carrier of F_Complex
(vr *') * (f . vq) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((vr *'),(f . vq)) is complex Element of the carrier of F_Complex
[(vr *'),(f . vq)] is set
{(vr *'),(f . vq)} is non empty V175() set
{(vr *')} is non empty V175() set
{{(vr *'),(f . vq)},{(vr *')}} is non empty set
the multF of F_Complex . [(vr *'),(f . vq)] is set
K137((vr *'),(f . vq)) is complex Element of COMPLEX
((vr *') * (f . vq)) *' is complex Element of the carrier of F_Complex
Re ((vr *') * (f . vq)) is complex real ext-real Element of REAL
Im ((vr *') * (f . vq)) is complex real ext-real Element of REAL
(Im ((vr *') * (f . vq))) * <i> is complex set
(Re ((vr *') * (f . vq))) - ((Im ((vr *') * (f . vq))) * <i>) is complex set
(vr *') *' is complex Element of the carrier of F_Complex
Re (vr *') is complex real ext-real Element of REAL
Im (vr *') is complex real ext-real Element of REAL
(Im (vr *')) * <i> is complex set
(Re (vr *')) - ((Im (vr *')) * <i>) is complex set
(f . vq) *' is complex Element of the carrier of F_Complex
Re (f . vq) is complex real ext-real Element of REAL
Im (f . vq) is complex real ext-real Element of REAL
(Im (f . vq)) * <i> is complex set
(Re (f . vq)) - ((Im (f . vq)) * <i>) is complex set
((vr *') *') * ((f . vq) *') is complex Element of the carrier of F_Complex
the multF of F_Complex . (((vr *') *'),((f . vq) *')) is complex Element of the carrier of F_Complex
[((vr *') *'),((f . vq) *')] is set
{((vr *') *'),((f . vq) *')} is non empty V175() set
{((vr *') *')} is non empty V175() set
{{((vr *') *'),((f . vq) *')},{((vr *') *')}} is non empty set
the multF of F_Complex . [((vr *') *'),((f . vq) *')] is set
K137(((vr *') *'),((f . vq) *')) is complex Element of COMPLEX
vr * ((V,f) . vq) is complex Element of the carrier of F_Complex
V is non empty non trivial right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty non trivial set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like non constant V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,f) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
dom f is Element of bool the carrier of V
bool the carrier of V is set
vq is set
vr is set
f . vq is set
f . vr is set
K93((V,f)) is set
(V,f) . vq is set
(V,f) . vr is set
qh is Element of the carrier of V
f . qh is complex Element of the carrier of F_Complex
(f . qh) *' is complex Element of the carrier of F_Complex
Re (f . qh) is complex real ext-real Element of REAL
Im (f . qh) is complex real ext-real Element of REAL
(Im (f . qh)) * <i> is complex set
(Re (f . qh)) - ((Im (f . qh)) * <i>) is complex set
A is Element of the carrier of V
f . A is complex Element of the carrier of F_Complex
(f . A) *' is complex Element of the carrier of F_Complex
Re (f . A) is complex real ext-real Element of REAL
Im (f . A) is complex real ext-real Element of REAL
(Im (f . A)) * <i> is complex set
(Re (f . A)) - ((Im (f . A)) * <i>) is complex set
((f . A) *') *' is complex Element of the carrier of F_Complex
Re ((f . A) *') is complex real ext-real Element of REAL
Im ((f . A) *') is complex real ext-real Element of REAL
(Im ((f . A) *')) * <i> is complex set
(Re ((f . A) *')) - ((Im ((f . A) *')) * <i>) is complex set
dom (V,f) is Element of bool the carrier of V
V is non empty non trivial right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty non trivial set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
the non trivial V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like non constant V30( the carrier of V, the carrier of F_Complex) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of F_Complex:] is non trivial V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like non constant V30( the carrier of V, the carrier of F_Complex) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of F_Complex:]
(V, the non trivial V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like non constant V30( the carrier of V, the carrier of F_Complex) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of F_Complex:]) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like non constant V30( the carrier of V, the carrier of F_Complex) V30( the carrier of V, the carrier of F_Complex) additive 0-preserving (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,f) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,(V,f)) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
vq is Element of the carrier of V
(V,(V,f)) . vq is complex Element of the carrier of F_Complex
(V,f) . vq is complex Element of the carrier of F_Complex
((V,f) . vq) *' is complex Element of the carrier of F_Complex
Re ((V,f) . vq) is complex real ext-real Element of REAL
Im ((V,f) . vq) is complex real ext-real Element of REAL
(Im ((V,f) . vq)) * <i> is complex set
(Re ((V,f) . vq)) - ((Im ((V,f) . vq)) * <i>) is complex set
f . vq is complex Element of the carrier of F_Complex
(f . vq) *' is complex Element of the carrier of F_Complex
Re (f . vq) is complex real ext-real Element of REAL
Im (f . vq) is complex real ext-real Element of REAL
(Im (f . vq)) * <i> is complex set
(Re (f . vq)) - ((Im (f . vq)) * <i>) is complex set
((f . vq) *') *' is complex Element of the carrier of F_Complex
Re ((f . vq) *') is complex real ext-real Element of REAL
Im ((f . vq) *') is complex real ext-real Element of REAL
(Im ((f . vq) *')) * <i> is complex set
(Re ((f . vq) *')) - ((Im ((f . vq) *')) * <i>) is complex set
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
0Functional V is V16() V19( the carrier of V) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like constant V30( the carrier of V, the carrier of F_Complex) V30( the carrier of V, the carrier of F_Complex) additive homogeneous 0-preserving (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
[#] V is non empty non proper Element of bool the carrier of V
bool the carrier of V is set
K402( the carrier of F_Complex,([#] V),(0. F_Complex)) is V16() V19( [#] V) V20( the carrier of F_Complex) Function-like V30( [#] V, the carrier of F_Complex) Element of bool [:([#] V), the carrier of F_Complex:]
[:([#] V), the carrier of F_Complex:] is set
bool [:([#] V), the carrier of F_Complex:] is set
(V,(0Functional V)) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) additive homogeneous (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
vr is Element of the carrier of V
(V,(0Functional V)) . vr is complex Element of the carrier of F_Complex
(0Functional V) . vr is complex Element of the carrier of F_Complex
((0Functional V) . vr) *' is complex Element of the carrier of F_Complex
Re ((0Functional V) . vr) is complex real ext-real Element of REAL
Im ((0Functional V) . vr) is complex real ext-real Element of REAL
(Im ((0Functional V) . vr)) * <i> is complex set
(Re ((0Functional V) . vr)) - ((Im ((0Functional V) . vr)) * <i>) is complex set
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
vq is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
f + vq is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,(f + vq)) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,f) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,vq) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,f) + (V,vq) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
vr is Element of the carrier of V
(V,(f + vq)) . vr is complex Element of the carrier of F_Complex
(f + vq) . vr is complex Element of the carrier of F_Complex
((f + vq) . vr) *' is complex Element of the carrier of F_Complex
Re ((f + vq) . vr) is complex real ext-real Element of REAL
Im ((f + vq) . vr) is complex real ext-real Element of REAL
(Im ((f + vq) . vr)) * <i> is complex set
(Re ((f + vq) . vr)) - ((Im ((f + vq) . vr)) * <i>) is complex set
f . vr is complex Element of the carrier of F_Complex
vq . vr is complex Element of the carrier of F_Complex
(f . vr) + (vq . vr) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . ((f . vr),(vq . vr)) is complex Element of the carrier of F_Complex
[(f . vr),(vq . vr)] is set
{(f . vr),(vq . vr)} is non empty V175() set
{(f . vr)} is non empty V175() set
{{(f . vr),(vq . vr)},{(f . vr)}} is non empty set
the addF of F_Complex . [(f . vr),(vq . vr)] is set
K135((f . vr),(vq . vr)) is complex Element of COMPLEX
((f . vr) + (vq . vr)) *' is complex Element of the carrier of F_Complex
Re ((f . vr) + (vq . vr)) is complex real ext-real Element of REAL
Im ((f . vr) + (vq . vr)) is complex real ext-real Element of REAL
(Im ((f . vr) + (vq . vr))) * <i> is complex set
(Re ((f . vr) + (vq . vr))) - ((Im ((f . vr) + (vq . vr))) * <i>) is complex set
(f . vr) *' is complex Element of the carrier of F_Complex
Re (f . vr) is complex real ext-real Element of REAL
Im (f . vr) is complex real ext-real Element of REAL
(Im (f . vr)) * <i> is complex set
(Re (f . vr)) - ((Im (f . vr)) * <i>) is complex set
(vq . vr) *' is complex Element of the carrier of F_Complex
Re (vq . vr) is complex real ext-real Element of REAL
Im (vq . vr) is complex real ext-real Element of REAL
(Im (vq . vr)) * <i> is complex set
(Re (vq . vr)) - ((Im (vq . vr)) * <i>) is complex set
((f . vr) *') + ((vq . vr) *') is complex Element of the carrier of F_Complex
the addF of F_Complex . (((f . vr) *'),((vq . vr) *')) is complex Element of the carrier of F_Complex
[((f . vr) *'),((vq . vr) *')] is set
{((f . vr) *'),((vq . vr) *')} is non empty V175() set
{((f . vr) *')} is non empty V175() set
{{((f . vr) *'),((vq . vr) *')},{((f . vr) *')}} is non empty set
the addF of F_Complex . [((f . vr) *'),((vq . vr) *')] is set
K135(((f . vr) *'),((vq . vr) *')) is complex Element of COMPLEX
(V,f) . vr is complex Element of the carrier of F_Complex
((V,f) . vr) + ((vq . vr) *') is complex Element of the carrier of F_Complex
the addF of F_Complex . (((V,f) . vr),((vq . vr) *')) is complex Element of the carrier of F_Complex
[((V,f) . vr),((vq . vr) *')] is set
{((V,f) . vr),((vq . vr) *')} is non empty V175() set
{((V,f) . vr)} is non empty V175() set
{{((V,f) . vr),((vq . vr) *')},{((V,f) . vr)}} is non empty set
the addF of F_Complex . [((V,f) . vr),((vq . vr) *')] is set
K135(((V,f) . vr),((vq . vr) *')) is complex Element of COMPLEX
(V,vq) . vr is complex Element of the carrier of F_Complex
((V,f) . vr) + ((V,vq) . vr) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((V,f) . vr),((V,vq) . vr)) is complex Element of the carrier of F_Complex
[((V,f) . vr),((V,vq) . vr)] is set
{((V,f) . vr),((V,vq) . vr)} is non empty V175() set
{{((V,f) . vr),((V,vq) . vr)},{((V,f) . vr)}} is non empty set
the addF of F_Complex . [((V,f) . vr),((V,vq) . vr)] is set
K135(((V,f) . vr),((V,vq) . vr)) is complex Element of COMPLEX
((V,f) + (V,vq)) . vr is complex Element of the carrier of F_Complex
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
- f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,(- f)) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,f) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
- (V,f) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
vq is Element of the carrier of V
(V,(- f)) . vq is complex Element of the carrier of F_Complex
(- f) . vq is complex Element of the carrier of F_Complex
((- f) . vq) *' is complex Element of the carrier of F_Complex
Re ((- f) . vq) is complex real ext-real Element of REAL
Im ((- f) . vq) is complex real ext-real Element of REAL
(Im ((- f) . vq)) * <i> is complex set
(Re ((- f) . vq)) - ((Im ((- f) . vq)) * <i>) is complex set
f . vq is complex Element of the carrier of F_Complex
- (f . vq) is complex Element of the carrier of F_Complex
(- (f . vq)) *' is complex Element of the carrier of F_Complex
Re (- (f . vq)) is complex real ext-real Element of REAL
Im (- (f . vq)) is complex real ext-real Element of REAL
(Im (- (f . vq))) * <i> is complex set
(Re (- (f . vq))) - ((Im (- (f . vq))) * <i>) is complex set
(f . vq) *' is complex Element of the carrier of F_Complex
Re (f . vq) is complex real ext-real Element of REAL
Im (f . vq) is complex real ext-real Element of REAL
(Im (f . vq)) * <i> is complex set
(Re (f . vq)) - ((Im (f . vq)) * <i>) is complex set
- ((f . vq) *') is complex Element of the carrier of F_Complex
(V,f) . vq is complex Element of the carrier of F_Complex
- ((V,f) . vq) is complex Element of the carrier of F_Complex
(- (V,f)) . vq is complex Element of the carrier of F_Complex
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,f) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
vq is complex Element of the carrier of F_Complex
vq * f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,(vq * f)) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
vq *' is complex Element of the carrier of F_Complex
Re vq is complex real ext-real Element of REAL
Im vq is complex real ext-real Element of REAL
(Im vq) * <i> is complex set
(Re vq) - ((Im vq) * <i>) is complex set
(vq *') * (V,f) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
vr is Element of the carrier of V
(V,(vq * f)) . vr is complex Element of the carrier of F_Complex
(vq * f) . vr is complex Element of the carrier of F_Complex
((vq * f) . vr) *' is complex Element of the carrier of F_Complex
Re ((vq * f) . vr) is complex real ext-real Element of REAL
Im ((vq * f) . vr) is complex real ext-real Element of REAL
(Im ((vq * f) . vr)) * <i> is complex set
(Re ((vq * f) . vr)) - ((Im ((vq * f) . vr)) * <i>) is complex set
f . vr is complex Element of the carrier of F_Complex
vq * (f . vr) is complex Element of the carrier of F_Complex
the multF of F_Complex . (vq,(f . vr)) is complex Element of the carrier of F_Complex
[vq,(f . vr)] is set
{vq,(f . vr)} is non empty V175() set
{vq} is non empty V175() set
{{vq,(f . vr)},{vq}} is non empty set
the multF of F_Complex . [vq,(f . vr)] is set
K137(vq,(f . vr)) is complex Element of COMPLEX
(vq * (f . vr)) *' is complex Element of the carrier of F_Complex
Re (vq * (f . vr)) is complex real ext-real Element of REAL
Im (vq * (f . vr)) is complex real ext-real Element of REAL
(Im (vq * (f . vr))) * <i> is complex set
(Re (vq * (f . vr))) - ((Im (vq * (f . vr))) * <i>) is complex set
(f . vr) *' is complex Element of the carrier of F_Complex
Re (f . vr) is complex real ext-real Element of REAL
Im (f . vr) is complex real ext-real Element of REAL
(Im (f . vr)) * <i> is complex set
(Re (f . vr)) - ((Im (f . vr)) * <i>) is complex set
(vq *') * ((f . vr) *') is complex Element of the carrier of F_Complex
the multF of F_Complex . ((vq *'),((f . vr) *')) is complex Element of the carrier of F_Complex
[(vq *'),((f . vr) *')] is set
{(vq *'),((f . vr) *')} is non empty V175() set
{(vq *')} is non empty V175() set
{{(vq *'),((f . vr) *')},{(vq *')}} is non empty set
the multF of F_Complex . [(vq *'),((f . vr) *')] is set
K137((vq *'),((f . vr) *')) is complex Element of COMPLEX
(V,f) . vr is complex Element of the carrier of F_Complex
(vq *') * ((V,f) . vr) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((vq *'),((V,f) . vr)) is complex Element of the carrier of F_Complex
[(vq *'),((V,f) . vr)] is set
{(vq *'),((V,f) . vr)} is non empty V175() set
{{(vq *'),((V,f) . vr)},{(vq *')}} is non empty set
the multF of F_Complex . [(vq *'),((V,f) . vr)] is set
K137((vq *'),((V,f) . vr)) is complex Element of COMPLEX
((vq *') * (V,f)) . vr is complex Element of the carrier of F_Complex
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
vq is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
f - vq is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
- vq is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
f + (- vq) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,(f - vq)) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,f) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,vq) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,f) - (V,vq) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
- (V,vq) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,f) + (- (V,vq)) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,(- vq)) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,f) + (V,(- vq)) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,f) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
vq is Element of the carrier of V
f . vq is complex Element of the carrier of F_Complex
(V,f) . vq is complex Element of the carrier of F_Complex
(f . vq) *' is complex Element of the carrier of F_Complex
Re (f . vq) is complex real ext-real Element of REAL
Im (f . vq) is complex real ext-real Element of REAL
(Im (f . vq)) * <i> is complex set
(Re (f . vq)) - ((Im (f . vq)) * <i>) is complex set
((f . vq) *') *' is complex Element of the carrier of F_Complex
Re ((f . vq) *') is complex real ext-real Element of REAL
Im ((f . vq) *') is complex real ext-real Element of REAL
(Im ((f . vq) *')) * <i> is complex set
(Re ((f . vq) *')) - ((Im ((f . vq) *')) * <i>) is complex set
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
ker f is Element of bool the carrier of V
bool the carrier of V is set
{ b₁ where b₁ is Element of the carrier of V : f . b₁ = 0. F_Complex } is set
(V,f) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
ker (V,f) is Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : (V,f) . b₁ = 0. F_Complex } is set
vq is set
vr is Element of the carrier of V
f . vr is complex Element of the carrier of F_Complex
(V,f) . vr is complex Element of the carrier of F_Complex
vq is set
vr is Element of the carrier of V
(V,f) . vr is complex Element of the carrier of F_Complex
f . vr is complex Element of the carrier of F_Complex
V is non empty right_complementable add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) additive 0-preserving (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
ker f is non empty Element of bool the carrier of V
bool the carrier of V is set
{ b₁ where b₁ is Element of the carrier of V : f . b₁ = 0. F_Complex } is set
(V,f) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) V30( the carrier of V, the carrier of F_Complex) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of F_Complex:]
ker (V,f) is non empty Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : (V,f) . b₁ = 0. F_Complex } is set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
the carrier of f is non empty set
VectQuot (V,f) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
vq is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) additive 0-preserving (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,vq) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) V30( the carrier of V, the carrier of F_Complex) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of F_Complex:]
ker (V,vq) is non empty Element of bool the carrier of V
bool the carrier of V is set
{ b₁ where b₁ is Element of the carrier of V : (V,vq) . b₁ = 0. F_Complex } is set
QFunctional (vq,f) is V16() V19( the carrier of (VectQuot (V,f))) V20( the carrier of F_Complex) Function-like V30( the carrier of (VectQuot (V,f)), the carrier of F_Complex) additive 0-preserving Element of bool [: the carrier of (VectQuot (V,f)), the carrier of F_Complex:]
the carrier of (VectQuot (V,f)) is non empty set
[: the carrier of (VectQuot (V,f)), the carrier of F_Complex:] is set
bool [: the carrier of (VectQuot (V,f)), the carrier of F_Complex:] is set
ker vq is non empty Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : vq . b₁ = 0. F_Complex } is set
CosetSet (V,f) is non empty Element of bool (bool the carrier of V)
bool (bool the carrier of V) is set
{ b₁ where b₁ is Coset of f : verum } is set
K is Element of the carrier of (VectQuot (V,f))
A is Coset of f
B is Element of the carrier of V
B + f is Element of bool the carrier of V
{ (B + b₁) where b₁ is Element of the carrier of V : b₁ in f } is set
x is complex Element of the carrier of F_Complex
x * K is Element of the carrier of (VectQuot (V,f))
the lmult of (VectQuot (V,f)) is V16() V19([: the carrier of F_Complex, the carrier of (VectQuot (V,f)):]) V20( the carrier of (VectQuot (V,f))) Function-like V30([: the carrier of F_Complex, the carrier of (VectQuot (V,f)):], the carrier of (VectQuot (V,f))) Element of bool [:[: the carrier of F_Complex, the carrier of (VectQuot (V,f)):], the carrier of (VectQuot (V,f)):]
[: the carrier of F_Complex, the carrier of (VectQuot (V,f)):] is set
[:[: the carrier of F_Complex, the carrier of (VectQuot (V,f)):], the carrier of (VectQuot (V,f)):] is set
bool [:[: the carrier of F_Complex, the carrier of (VectQuot (V,f)):], the carrier of (VectQuot (V,f)):] is set
the lmult of (VectQuot (V,f)) . (x,K) is Element of the carrier of (VectQuot (V,f))
[x,K] is set
{x,K} is non empty set
{x} is non empty V175() set
{{x,K},{x}} is non empty set
the lmult of (VectQuot (V,f)) . [x,K] is set
lmultCoset (V,f) is V16() V19([: the carrier of F_Complex,(CosetSet (V,f)):]) V20( CosetSet (V,f)) Function-like V30([: the carrier of F_Complex,(CosetSet (V,f)):], CosetSet (V,f)) Element of bool [:[: the carrier of F_Complex,(CosetSet (V,f)):],(CosetSet (V,f)):]
[: the carrier of F_Complex,(CosetSet (V,f)):] is set
[:[: the carrier of F_Complex,(CosetSet (V,f)):],(CosetSet (V,f)):] is set
bool [:[: the carrier of F_Complex,(CosetSet (V,f)):],(CosetSet (V,f)):] is set
(lmultCoset (V,f)) . (x,K) is set
(lmultCoset (V,f)) . [x,K] is set
x * B is Element of the carrier of V
the lmult of V is V16() V19([: the carrier of F_Complex, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of F_Complex, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:]
[: the carrier of F_Complex, the carrier of V:] is set
[:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
the lmult of V . (x,B) is Element of the carrier of V
[x,B] is set
{x,B} is non empty set
{{x,B},{x}} is non empty set
the lmult of V . [x,B] is set
(x * B) + f is Element of bool the carrier of V
{ ((x * B) + b₁) where b₁ is Element of the carrier of V : b₁ in f } is set
(QFunctional (vq,f)) . (x * K) is complex Element of the carrier of F_Complex
vq . (x * B) is complex Element of the carrier of F_Complex
x *' is complex Element of the carrier of F_Complex
Re x is complex real ext-real Element of REAL
Im x is complex real ext-real Element of REAL
(Im x) * <i> is complex set
(Re x) - ((Im x) * <i>) is complex set
vq . B is complex Element of the carrier of F_Complex
(x *') * (vq . B) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((x *'),(vq . B)) is complex Element of the carrier of F_Complex
[(x *'),(vq . B)] is set
{(x *'),(vq . B)} is non empty V175() set
{(x *')} is non empty V175() set
{{(x *'),(vq . B)},{(x *')}} is non empty set
the multF of F_Complex . [(x *'),(vq . B)] is set
K137((x *'),(vq . B)) is complex Element of COMPLEX
(QFunctional (vq,f)) . K is complex Element of the carrier of F_Complex
(x *') * ((QFunctional (vq,f)) . K) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((x *'),((QFunctional (vq,f)) . K)) is complex Element of the carrier of F_Complex
[(x *'),((QFunctional (vq,f)) . K)] is set
{(x *'),((QFunctional (vq,f)) . K)} is non empty V175() set
{{(x *'),((QFunctional (vq,f)) . K)},{(x *')}} is non empty set
the multF of F_Complex . [(x *'),((QFunctional (vq,f)) . K)] is set
K137((x *'),((QFunctional (vq,f)) . K)) is complex Element of COMPLEX
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) additive 0-preserving (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,f) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) V30( the carrier of V, the carrier of F_Complex) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of F_Complex:]
Ker (V,f) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
QFunctional (f,(Ker (V,f))) is V16() V19( the carrier of (VectQuot (V,(Ker (V,f))))) V20( the carrier of F_Complex) Function-like V30( the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex) additive 0-preserving Element of bool [: the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex:]
VectQuot (V,(Ker (V,f))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of (VectQuot (V,(Ker (V,f)))) is non empty set
[: the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex:] is set
bool [: the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex:] is set
the carrier of (Ker (V,f)) is non empty set
ker (V,f) is non empty Element of bool the carrier of V
bool the carrier of V is set
{ b₁ where b₁ is Element of the carrier of V : (V,f) . b₁ = 0. F_Complex } is set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) additive 0-preserving (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,f) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) V30( the carrier of V, the carrier of F_Complex) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of F_Complex:]
Ker (V,f) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(Ker (V,f))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of (VectQuot (V,(Ker (V,f)))) is non empty set
(V,f) is V16() V19( the carrier of (VectQuot (V,(Ker (V,f))))) V20( the carrier of F_Complex) Function-like V30( the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex) additive 0-preserving ( VectQuot (V,(Ker (V,f)))) Element of bool [: the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex:]
[: the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex:] is set
bool [: the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex:] is set
QFunctional (f,(Ker (V,f))) is V16() V19( the carrier of (VectQuot (V,(Ker (V,f))))) V20( the carrier of F_Complex) Function-like V30( the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex) additive 0-preserving Element of bool [: the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex:]
vq is Element of the carrier of (VectQuot (V,(Ker (V,f))))
(V,f) . vq is complex Element of the carrier of F_Complex
vr is Element of the carrier of V
vr + (Ker (V,f)) is Element of bool the carrier of V
bool the carrier of V is set
{ (vr + b₁) where b₁ is Element of the carrier of V : b₁ in Ker (V,f) } is set
f . vr is complex Element of the carrier of F_Complex
the carrier of (Ker (V,f)) is non empty set
ker (V,f) is non empty Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : (V,f) . b₁ = 0. F_Complex } is set
ker f is non empty Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : f . b₁ = 0. F_Complex } is set
V is non empty non trivial right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty non trivial set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like non constant V30( the carrier of V, the carrier of F_Complex) additive 0-preserving (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,f) is V16() V19( the carrier of (VectQuot (V,(Ker (V,f))))) V20( the carrier of F_Complex) Function-like V30( the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex) additive 0-preserving ( VectQuot (V,(Ker (V,f)))) Element of bool [: the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex:]
(V,f) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like non constant V30( the carrier of V, the carrier of F_Complex) V30( the carrier of V, the carrier of F_Complex) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of F_Complex:]
Ker (V,f) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(Ker (V,f))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of (VectQuot (V,(Ker (V,f)))) is non empty set
[: the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex:] is set
bool [: the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex:] is set
QFunctional (f,(Ker (V,f))) is V16() V19( the carrier of (VectQuot (V,(Ker (V,f))))) V20( the carrier of F_Complex) Function-like V30( the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex) additive 0-preserving Element of bool [: the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex:]
0. V is zero Element of the carrier of V
A is Element of the carrier of V
f . A is complex Element of the carrier of F_Complex
A + (Ker (V,f)) is Element of bool the carrier of V
bool the carrier of V is set
{ (A + b₁) where b₁ is Element of the carrier of V : b₁ in Ker (V,f) } is set
0Functional (VectQuot (V,(Ker (V,f)))) is V16() V19( the carrier of (VectQuot (V,(Ker (V,f))))) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like constant V30( the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex) V30( the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex) additive homogeneous 0-preserving ( VectQuot (V,(Ker (V,f)))) Element of bool [: the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex:]
[#] (VectQuot (V,(Ker (V,f)))) is non empty non proper Element of bool the carrier of (VectQuot (V,(Ker (V,f))))
bool the carrier of (VectQuot (V,(Ker (V,f)))) is set
K402( the carrier of F_Complex,([#] (VectQuot (V,(Ker (V,f))))),(0. F_Complex)) is V16() V19( [#] (VectQuot (V,(Ker (V,f))))) V20( the carrier of F_Complex) Function-like V30( [#] (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex) Element of bool [:([#] (VectQuot (V,(Ker (V,f))))), the carrier of F_Complex:]
[:([#] (VectQuot (V,(Ker (V,f))))), the carrier of F_Complex:] is set
bool [:([#] (VectQuot (V,(Ker (V,f))))), the carrier of F_Complex:] is set
K is Element of the carrier of (VectQuot (V,(Ker (V,f))))
(V,f) . K is complex Element of the carrier of F_Complex
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) additive 0-preserving (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,f) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) V30( the carrier of V, the carrier of F_Complex) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of F_Complex:]
Ker (V,f) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(Ker (V,f))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
(V,f) is V16() V19( the carrier of (VectQuot (V,(Ker (V,f))))) V20( the carrier of F_Complex) Function-like V30( the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex) additive 0-preserving ( VectQuot (V,(Ker (V,f)))) Element of bool [: the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex:]
the carrier of (VectQuot (V,(Ker (V,f)))) is non empty set
[: the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex:] is set
bool [: the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex:] is set
QFunctional (f,(Ker (V,f))) is V16() V19( the carrier of (VectQuot (V,(Ker (V,f))))) V20( the carrier of F_Complex) Function-like V30( the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex) additive 0-preserving Element of bool [: the carrier of (VectQuot (V,(Ker (V,f)))), the carrier of F_Complex:]
the carrier of (Ker (V,f)) is non empty set
ker (V,f) is non empty Element of bool the carrier of V
bool the carrier of V is set
{ b₁ where b₁ is Element of the carrier of V : (V,f) . b₁ = 0. F_Complex } is set
ker f is non empty Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : f . b₁ = 0. F_Complex } is set
CosetSet (V,(Ker (V,f))) is non empty Element of bool (bool the carrier of V)
bool (bool the carrier of V) is set
{ b₁ where b₁ is Coset of Ker (V,f) : verum } is set
ker (V,f) is non empty Element of bool the carrier of (VectQuot (V,(Ker (V,f))))
bool the carrier of (VectQuot (V,(Ker (V,f)))) is set
{ b₁ where b₁ is Element of the carrier of (VectQuot (V,(Ker (V,f)))) : (V,f) . b₁ = 0. F_Complex } is set
0. (VectQuot (V,(Ker (V,f)))) is zero Element of the carrier of (VectQuot (V,(Ker (V,f))))
{(0. (VectQuot (V,(Ker (V,f)))))} is non empty set
K is set
x is Element of the carrier of (VectQuot (V,(Ker (V,f))))
(V,f) . x is complex Element of the carrier of F_Complex
A is Coset of Ker (V,f)
B is Element of the carrier of V
B + (Ker (V,f)) is Element of bool the carrier of V
{ (B + b₁) where b₁ is Element of the carrier of V : b₁ in Ker (V,f) } is set
f . B is complex Element of the carrier of F_Complex
zeroCoset (V,(Ker (V,f))) is Element of CosetSet (V,(Ker (V,f)))
K203( the carrier of (VectQuot (V,(Ker (V,f)))),(0. (VectQuot (V,(Ker (V,f)))))) is non empty Element of bool the carrier of (VectQuot (V,(Ker (V,f))))
K is set
(V,f) . (0. (VectQuot (V,(Ker (V,f))))) is complex Element of the carrier of F_Complex
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is Element of the carrier of V
vr is Element of the carrier of f
qh is complex Element of the carrier of F_Complex
qh * vr is Element of the carrier of f
the lmult of f is V16() V19([: the carrier of F_Complex, the carrier of f:]) V20( the carrier of f) Function-like V30([: the carrier of F_Complex, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of F_Complex, the carrier of f:], the carrier of f:]
[: the carrier of F_Complex, the carrier of f:] is set
[:[: the carrier of F_Complex, the carrier of f:], the carrier of f:] is set
bool [:[: the carrier of F_Complex, the carrier of f:], the carrier of f:] is set
the lmult of f . (qh,vr) is Element of the carrier of f
[qh,vr] is set
{qh,vr} is non empty set
{qh} is non empty V175() set
{{qh,vr},{qh}} is non empty set
the lmult of f . [qh,vr] is set
qh *' is complex Element of the carrier of F_Complex
Re qh is complex real ext-real Element of REAL
Im qh is complex real ext-real Element of REAL
(Im qh) * <i> is complex set
(Re qh) - ((Im qh) * <i>) is complex set
A is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
A . (vq,(qh * vr)) is complex Element of the carrier of F_Complex
[vq,(qh * vr)] is set
{vq,(qh * vr)} is non empty set
{vq} is non empty set
{{vq,(qh * vr)},{vq}} is non empty set
A . [vq,(qh * vr)] is set
A . (vq,vr) is complex Element of the carrier of F_Complex
[vq,vr] is set
{vq,vr} is non empty set
{{vq,vr},{vq}} is non empty set
A . [vq,vr] is set
(qh *') * (A . (vq,vr)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((qh *'),(A . (vq,vr))) is complex Element of the carrier of F_Complex
[(qh *'),(A . (vq,vr))] is set
{(qh *'),(A . (vq,vr))} is non empty V175() set
{(qh *')} is non empty V175() set
{{(qh *'),(A . (vq,vr))},{(qh *')}} is non empty set
the multF of F_Complex . [(qh *'),(A . (vq,vr))] is set
K137((qh *'),(A . (vq,vr))) is complex Element of COMPLEX
FunctionalFAF (A,vq) is V16() V19( the carrier of f) V20( the carrier of F_Complex) Function-like V30( the carrier of f, the carrier of F_Complex) Element of bool [: the carrier of f, the carrier of F_Complex:]
[: the carrier of f, the carrier of F_Complex:] is set
bool [: the carrier of f, the carrier of F_Complex:] is set
(FunctionalFAF (A,vq)) . (qh * vr) is complex Element of the carrier of F_Complex
(FunctionalFAF (A,vq)) . vr is complex Element of the carrier of F_Complex
(qh *') * ((FunctionalFAF (A,vq)) . vr) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((qh *'),((FunctionalFAF (A,vq)) . vr)) is complex Element of the carrier of F_Complex
[(qh *'),((FunctionalFAF (A,vq)) . vr)] is set
{(qh *'),((FunctionalFAF (A,vq)) . vr)} is non empty V175() set
{{(qh *'),((FunctionalFAF (A,vq)) . vr)},{(qh *')}} is non empty set
the multF of F_Complex . [(qh *'),((FunctionalFAF (A,vq)) . vr)] is set
K137((qh *'),((FunctionalFAF (A,vq)) . vr)) is complex Element of COMPLEX
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
0Functional V is V16() V19( the carrier of V) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like constant V30( the carrier of V, the carrier of F_Complex) V30( the carrier of V, the carrier of F_Complex) additive homogeneous 0-preserving (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
[#] V is non empty non proper Element of bool the carrier of V
bool the carrier of V is set
K402( the carrier of F_Complex,([#] V),(0. F_Complex)) is V16() V19( [#] V) V20( the carrier of F_Complex) Function-like V30( [#] V, the carrier of F_Complex) Element of bool [:([#] V), the carrier of F_Complex:]
[:([#] V), the carrier of F_Complex:] is set
bool [:([#] V), the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
FormFunctional (f,(0Functional V)) is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF homogeneousFAF Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
vr is Element of the carrier of V
qh is Element of the carrier of V
(FormFunctional (f,(0Functional V))) . (vr,qh) is complex Element of the carrier of F_Complex
[vr,qh] is set
{vr,qh} is non empty set
{vr} is non empty set
{{vr,qh},{vr}} is non empty set
(FormFunctional (f,(0Functional V))) . [vr,qh] is set
f . vr is complex Element of the carrier of F_Complex
(0Functional V) . qh is complex Element of the carrier of F_Complex
(f . vr) * ((0Functional V) . qh) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((f . vr),((0Functional V) . qh)) is complex Element of the carrier of F_Complex
[(f . vr),((0Functional V) . qh)] is set
{(f . vr),((0Functional V) . qh)} is non empty V175() set
{(f . vr)} is non empty V175() set
{{(f . vr),((0Functional V) . qh)},{(f . vr)}} is non empty set
the multF of F_Complex . [(f . vr),((0Functional V) . qh)] is set
K137((f . vr),((0Functional V) . qh)) is complex Element of COMPLEX
(f . vr) * (0. F_Complex) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((f . vr),(0. F_Complex)) is complex Element of the carrier of F_Complex
[(f . vr),(0. F_Complex)] is set
{(f . vr),(0. F_Complex)} is non empty V175() set
{{(f . vr),(0. F_Complex)},{(f . vr)}} is non empty set
the multF of F_Complex . [(f . vr),(0. F_Complex)] is set
K137((f . vr),(0. F_Complex)) is complex Element of COMPLEX
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
0Functional V is V16() V19( the carrier of V) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like constant V30( the carrier of V, the carrier of F_Complex) V30( the carrier of V, the carrier of F_Complex) additive homogeneous 0-preserving (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
[#] V is non empty non proper Element of bool the carrier of V
bool the carrier of V is set
K402( the carrier of F_Complex,([#] V),(0. F_Complex)) is V16() V19( [#] V) V20( the carrier of F_Complex) Function-like V30( [#] V, the carrier of F_Complex) Element of bool [:([#] V), the carrier of F_Complex:]
[:([#] V), the carrier of F_Complex:] is set
bool [:([#] V), the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
FormFunctional (f,(0Functional V)) is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF homogeneousFAF Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
vq is Element of the carrier of V
vr is Element of the carrier of V
(FormFunctional (f,(0Functional V))) . (vq,vr) is complex Element of the carrier of F_Complex
[vq,vr] is set
{vq,vr} is non empty set
{vq} is non empty set
{{vq,vr},{vq}} is non empty set
(FormFunctional (f,(0Functional V))) . [vq,vr] is set
(FormFunctional (f,(0Functional V))) . (vr,vq) is complex Element of the carrier of F_Complex
[vr,vq] is set
{vr,vq} is non empty set
{vr} is non empty set
{{vr,vq},{vr}} is non empty set
(FormFunctional (f,(0Functional V))) . [vr,vq] is set
((FormFunctional (f,(0Functional V))) . (vr,vq)) *' is complex Element of the carrier of F_Complex
Re ((FormFunctional (f,(0Functional V))) . (vr,vq)) is complex real ext-real Element of REAL
Im ((FormFunctional (f,(0Functional V))) . (vr,vq)) is complex real ext-real Element of REAL
(Im ((FormFunctional (f,(0Functional V))) . (vr,vq))) * <i> is complex set
(Re ((FormFunctional (f,(0Functional V))) . (vr,vq))) - ((Im ((FormFunctional (f,(0Functional V))) . (vr,vq))) * <i>) is complex set
V is non empty VectSpStr over F_Complex
f is non empty VectSpStr over F_Complex
NulForm (V,f) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF homogeneousSAF Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
the carrier of V is non empty set
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
K402( the carrier of F_Complex,[: the carrier of V, the carrier of f:],(0. F_Complex)) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
vq is Element of the carrier of V
FunctionalFAF ((NulForm (V,f)),vq) is V16() V19( the carrier of f) V20( the carrier of F_Complex) Function-like V30( the carrier of f, the carrier of F_Complex) additive homogeneous Element of bool [: the carrier of f, the carrier of F_Complex:]
[: the carrier of f, the carrier of F_Complex:] is set
bool [: the carrier of f, the carrier of F_Complex:] is set
0Functional f is V16() V19( the carrier of f) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like constant V30( the carrier of f, the carrier of F_Complex) V30( the carrier of f, the carrier of F_Complex) additive homogeneous 0-preserving (f) Element of bool [: the carrier of f, the carrier of F_Complex:]
[#] f is non empty non proper Element of bool the carrier of f
bool the carrier of f is set
K402( the carrier of F_Complex,([#] f),(0. F_Complex)) is V16() V19( [#] f) V20( the carrier of F_Complex) Function-like V30( [#] f, the carrier of F_Complex) Element of bool [:([#] f), the carrier of F_Complex:]
[:([#] f), the carrier of F_Complex:] is set
bool [:([#] f), the carrier of F_Complex:] is set
V is non empty VectSpStr over F_Complex
NulForm (V,V) is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF homogeneousSAF V171( F_Complex ,V) V172( F_Complex ,V) (V,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
K402( the carrier of F_Complex,[: the carrier of V, the carrier of V:],(0. F_Complex)) is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
0Functional V is V16() V19( the carrier of V) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like constant V30( the carrier of V, the carrier of F_Complex) V30( the carrier of V, the carrier of F_Complex) additive homogeneous 0-preserving (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
[#] V is non empty non proper Element of bool the carrier of V
bool the carrier of V is set
K402( the carrier of F_Complex,([#] V),(0. F_Complex)) is V16() V19( [#] V) V20( the carrier of F_Complex) Function-like V30( [#] V, the carrier of F_Complex) Element of bool [:([#] V), the carrier of F_Complex:]
[:([#] V), the carrier of F_Complex:] is set
bool [:([#] V), the carrier of F_Complex:] is set
FormFunctional ((0Functional V),(0Functional V)) is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF homogeneousSAF Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
f is Element of the carrier of V
(NulForm (V,V)) . (f,f) is complex Element of the carrier of F_Complex
[f,f] is set
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
(NulForm (V,V)) . [f,f] is set
Re ((NulForm (V,V)) . (f,f)) is complex real ext-real Element of REAL
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
vq is Element of the carrier of V
f . (vq,vq) is complex Element of the carrier of F_Complex
[vq,vq] is set
{vq,vq} is non empty set
{vq} is non empty set
{{vq,vq},{vq}} is non empty set
f . [vq,vq] is set
Im (f . (vq,vq)) is complex real ext-real Element of REAL
(f . (vq,vq)) *' is complex Element of the carrier of F_Complex
Re (f . (vq,vq)) is complex real ext-real Element of REAL
(Im (f . (vq,vq))) * <i> is complex set
(Re (f . (vq,vq))) - ((Im (f . (vq,vq))) * <i>) is complex set
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
NulForm (V,V) is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF homogeneousSAF V171( F_Complex ,V) V172( F_Complex ,V) (V,V) (V) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
K402( the carrier of F_Complex,[: the carrier of V, the carrier of V:],(0. F_Complex)) is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
NulForm (V,f) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF homogeneousSAF (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
K402( the carrier of F_Complex,[: the carrier of V, the carrier of f:],(0. F_Complex)) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
vq is Element of the carrier of V
FunctionalSAF (f,vq) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
FunctionalFAF (f,vq) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
A is Element of the carrier of V
K is Element of the carrier of V
A + K is Element of the carrier of V
the addF of V is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[:[: the carrier of V, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is set
the addF of V . (A,K) is Element of the carrier of V
[A,K] is set
{A,K} is non empty set
{A} is non empty set
{{A,K},{A}} is non empty set
the addF of V . [A,K] is set
(FunctionalSAF (f,vq)) . (A + K) is complex Element of the carrier of F_Complex
f . ((A + K),vq) is complex Element of the carrier of F_Complex
[(A + K),vq] is set
{(A + K),vq} is non empty set
{(A + K)} is non empty set
{{(A + K),vq},{(A + K)}} is non empty set
f . [(A + K),vq] is set
f . (vq,(A + K)) is complex Element of the carrier of F_Complex
[vq,(A + K)] is set
{vq,(A + K)} is non empty set
{vq} is non empty set
{{vq,(A + K)},{vq}} is non empty set
f . [vq,(A + K)] is set
(f . (vq,(A + K))) *' is complex Element of the carrier of F_Complex
Re (f . (vq,(A + K))) is complex real ext-real Element of REAL
Im (f . (vq,(A + K))) is complex real ext-real Element of REAL
(Im (f . (vq,(A + K)))) * <i> is complex set
(Re (f . (vq,(A + K)))) - ((Im (f . (vq,(A + K)))) * <i>) is complex set
(FunctionalFAF (f,vq)) . (A + K) is complex Element of the carrier of F_Complex
((FunctionalFAF (f,vq)) . (A + K)) *' is complex Element of the carrier of F_Complex
Re ((FunctionalFAF (f,vq)) . (A + K)) is complex real ext-real Element of REAL
Im ((FunctionalFAF (f,vq)) . (A + K)) is complex real ext-real Element of REAL
(Im ((FunctionalFAF (f,vq)) . (A + K))) * <i> is complex set
(Re ((FunctionalFAF (f,vq)) . (A + K))) - ((Im ((FunctionalFAF (f,vq)) . (A + K))) * <i>) is complex set
(FunctionalFAF (f,vq)) . A is complex Element of the carrier of F_Complex
(FunctionalFAF (f,vq)) . K is complex Element of the carrier of F_Complex
((FunctionalFAF (f,vq)) . A) + ((FunctionalFAF (f,vq)) . K) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . (((FunctionalFAF (f,vq)) . A),((FunctionalFAF (f,vq)) . K)) is complex Element of the carrier of F_Complex
[((FunctionalFAF (f,vq)) . A),((FunctionalFAF (f,vq)) . K)] is set
{((FunctionalFAF (f,vq)) . A),((FunctionalFAF (f,vq)) . K)} is non empty V175() set
{((FunctionalFAF (f,vq)) . A)} is non empty V175() set
{{((FunctionalFAF (f,vq)) . A),((FunctionalFAF (f,vq)) . K)},{((FunctionalFAF (f,vq)) . A)}} is non empty set
the addF of F_Complex . [((FunctionalFAF (f,vq)) . A),((FunctionalFAF (f,vq)) . K)] is set
K135(((FunctionalFAF (f,vq)) . A),((FunctionalFAF (f,vq)) . K)) is complex Element of COMPLEX
(((FunctionalFAF (f,vq)) . A) + ((FunctionalFAF (f,vq)) . K)) *' is complex Element of the carrier of F_Complex
Re (((FunctionalFAF (f,vq)) . A) + ((FunctionalFAF (f,vq)) . K)) is complex real ext-real Element of REAL
Im (((FunctionalFAF (f,vq)) . A) + ((FunctionalFAF (f,vq)) . K)) is complex real ext-real Element of REAL
(Im (((FunctionalFAF (f,vq)) . A) + ((FunctionalFAF (f,vq)) . K))) * <i> is complex set
(Re (((FunctionalFAF (f,vq)) . A) + ((FunctionalFAF (f,vq)) . K))) - ((Im (((FunctionalFAF (f,vq)) . A) + ((FunctionalFAF (f,vq)) . K))) * <i>) is complex set
f . (vq,A) is complex Element of the carrier of F_Complex
[vq,A] is set
{vq,A} is non empty set
{{vq,A},{vq}} is non empty set
f . [vq,A] is set
(f . (vq,A)) + ((FunctionalFAF (f,vq)) . K) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((f . (vq,A)),((FunctionalFAF (f,vq)) . K)) is complex Element of the carrier of F_Complex
[(f . (vq,A)),((FunctionalFAF (f,vq)) . K)] is set
{(f . (vq,A)),((FunctionalFAF (f,vq)) . K)} is non empty V175() set
{(f . (vq,A))} is non empty V175() set
{{(f . (vq,A)),((FunctionalFAF (f,vq)) . K)},{(f . (vq,A))}} is non empty set
the addF of F_Complex . [(f . (vq,A)),((FunctionalFAF (f,vq)) . K)] is set
K135((f . (vq,A)),((FunctionalFAF (f,vq)) . K)) is complex Element of COMPLEX
((f . (vq,A)) + ((FunctionalFAF (f,vq)) . K)) *' is complex Element of the carrier of F_Complex
Re ((f . (vq,A)) + ((FunctionalFAF (f,vq)) . K)) is complex real ext-real Element of REAL
Im ((f . (vq,A)) + ((FunctionalFAF (f,vq)) . K)) is complex real ext-real Element of REAL
(Im ((f . (vq,A)) + ((FunctionalFAF (f,vq)) . K))) * <i> is complex set
(Re ((f . (vq,A)) + ((FunctionalFAF (f,vq)) . K))) - ((Im ((f . (vq,A)) + ((FunctionalFAF (f,vq)) . K))) * <i>) is complex set
f . (vq,K) is complex Element of the carrier of F_Complex
[vq,K] is set
{vq,K} is non empty set
{{vq,K},{vq}} is non empty set
f . [vq,K] is set
(f . (vq,A)) + (f . (vq,K)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((f . (vq,A)),(f . (vq,K))) is complex Element of the carrier of F_Complex
[(f . (vq,A)),(f . (vq,K))] is set
{(f . (vq,A)),(f . (vq,K))} is non empty V175() set
{{(f . (vq,A)),(f . (vq,K))},{(f . (vq,A))}} is non empty set
the addF of F_Complex . [(f . (vq,A)),(f . (vq,K))] is set
K135((f . (vq,A)),(f . (vq,K))) is complex Element of COMPLEX
((f . (vq,A)) + (f . (vq,K))) *' is complex Element of the carrier of F_Complex
Re ((f . (vq,A)) + (f . (vq,K))) is complex real ext-real Element of REAL
Im ((f . (vq,A)) + (f . (vq,K))) is complex real ext-real Element of REAL
(Im ((f . (vq,A)) + (f . (vq,K)))) * <i> is complex set
(Re ((f . (vq,A)) + (f . (vq,K)))) - ((Im ((f . (vq,A)) + (f . (vq,K)))) * <i>) is complex set
(f . (vq,A)) *' is complex Element of the carrier of F_Complex
Re (f . (vq,A)) is complex real ext-real Element of REAL
Im (f . (vq,A)) is complex real ext-real Element of REAL
(Im (f . (vq,A))) * <i> is complex set
(Re (f . (vq,A))) - ((Im (f . (vq,A))) * <i>) is complex set
(f . (vq,K)) *' is complex Element of the carrier of F_Complex
Re (f . (vq,K)) is complex real ext-real Element of REAL
Im (f . (vq,K)) is complex real ext-real Element of REAL
(Im (f . (vq,K))) * <i> is complex set
(Re (f . (vq,K))) - ((Im (f . (vq,K))) * <i>) is complex set
((f . (vq,A)) *') + ((f . (vq,K)) *') is complex Element of the carrier of F_Complex
the addF of F_Complex . (((f . (vq,A)) *'),((f . (vq,K)) *')) is complex Element of the carrier of F_Complex
[((f . (vq,A)) *'),((f . (vq,K)) *')] is set
{((f . (vq,A)) *'),((f . (vq,K)) *')} is non empty V175() set
{((f . (vq,A)) *')} is non empty V175() set
{{((f . (vq,A)) *'),((f . (vq,K)) *')},{((f . (vq,A)) *')}} is non empty set
the addF of F_Complex . [((f . (vq,A)) *'),((f . (vq,K)) *')] is set
K135(((f . (vq,A)) *'),((f . (vq,K)) *')) is complex Element of COMPLEX
f . (A,vq) is complex Element of the carrier of F_Complex
[A,vq] is set
{A,vq} is non empty set
{{A,vq},{A}} is non empty set
f . [A,vq] is set
(f . (A,vq)) + ((f . (vq,K)) *') is complex Element of the carrier of F_Complex
the addF of F_Complex . ((f . (A,vq)),((f . (vq,K)) *')) is complex Element of the carrier of F_Complex
[(f . (A,vq)),((f . (vq,K)) *')] is set
{(f . (A,vq)),((f . (vq,K)) *')} is non empty V175() set
{(f . (A,vq))} is non empty V175() set
{{(f . (A,vq)),((f . (vq,K)) *')},{(f . (A,vq))}} is non empty set
the addF of F_Complex . [(f . (A,vq)),((f . (vq,K)) *')] is set
K135((f . (A,vq)),((f . (vq,K)) *')) is complex Element of COMPLEX
f . (K,vq) is complex Element of the carrier of F_Complex
[K,vq] is set
{K,vq} is non empty set
{K} is non empty set
{{K,vq},{K}} is non empty set
f . [K,vq] is set
(f . (A,vq)) + (f . (K,vq)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((f . (A,vq)),(f . (K,vq))) is complex Element of the carrier of F_Complex
[(f . (A,vq)),(f . (K,vq))] is set
{(f . (A,vq)),(f . (K,vq))} is non empty V175() set
{{(f . (A,vq)),(f . (K,vq))},{(f . (A,vq))}} is non empty set
the addF of F_Complex . [(f . (A,vq)),(f . (K,vq))] is set
K135((f . (A,vq)),(f . (K,vq))) is complex Element of COMPLEX
(FunctionalSAF (f,vq)) . A is complex Element of the carrier of F_Complex
((FunctionalSAF (f,vq)) . A) + (f . (K,vq)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((FunctionalSAF (f,vq)) . A),(f . (K,vq))) is complex Element of the carrier of F_Complex
[((FunctionalSAF (f,vq)) . A),(f . (K,vq))] is set
{((FunctionalSAF (f,vq)) . A),(f . (K,vq))} is non empty V175() set
{((FunctionalSAF (f,vq)) . A)} is non empty V175() set
{{((FunctionalSAF (f,vq)) . A),(f . (K,vq))},{((FunctionalSAF (f,vq)) . A)}} is non empty set
the addF of F_Complex . [((FunctionalSAF (f,vq)) . A),(f . (K,vq))] is set
K135(((FunctionalSAF (f,vq)) . A),(f . (K,vq))) is complex Element of COMPLEX
(FunctionalSAF (f,vq)) . K is complex Element of the carrier of F_Complex
((FunctionalSAF (f,vq)) . A) + ((FunctionalSAF (f,vq)) . K) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((FunctionalSAF (f,vq)) . A),((FunctionalSAF (f,vq)) . K)) is complex Element of the carrier of F_Complex
[((FunctionalSAF (f,vq)) . A),((FunctionalSAF (f,vq)) . K)] is set
{((FunctionalSAF (f,vq)) . A),((FunctionalSAF (f,vq)) . K)} is non empty V175() set
{{((FunctionalSAF (f,vq)) . A),((FunctionalSAF (f,vq)) . K)},{((FunctionalSAF (f,vq)) . A)}} is non empty set
the addF of F_Complex . [((FunctionalSAF (f,vq)) . A),((FunctionalSAF (f,vq)) . K)] is set
K135(((FunctionalSAF (f,vq)) . A),((FunctionalSAF (f,vq)) . K)) is complex Element of COMPLEX
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
vq is Element of the carrier of V
FunctionalFAF (f,vq) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
FunctionalSAF (f,vq) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
A is Element of the carrier of V
K is Element of the carrier of V
A + K is Element of the carrier of V
the addF of V is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[:[: the carrier of V, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is set
the addF of V . (A,K) is Element of the carrier of V
[A,K] is set
{A,K} is non empty set
{A} is non empty set
{{A,K},{A}} is non empty set
the addF of V . [A,K] is set
(FunctionalFAF (f,vq)) . (A + K) is complex Element of the carrier of F_Complex
f . (vq,(A + K)) is complex Element of the carrier of F_Complex
[vq,(A + K)] is set
{vq,(A + K)} is non empty set
{vq} is non empty set
{{vq,(A + K)},{vq}} is non empty set
f . [vq,(A + K)] is set
f . ((A + K),vq) is complex Element of the carrier of F_Complex
[(A + K),vq] is set
{(A + K),vq} is non empty set
{(A + K)} is non empty set
{{(A + K),vq},{(A + K)}} is non empty set
f . [(A + K),vq] is set
(f . ((A + K),vq)) *' is complex Element of the carrier of F_Complex
Re (f . ((A + K),vq)) is complex real ext-real Element of REAL
Im (f . ((A + K),vq)) is complex real ext-real Element of REAL
(Im (f . ((A + K),vq))) * <i> is complex set
(Re (f . ((A + K),vq))) - ((Im (f . ((A + K),vq))) * <i>) is complex set
(FunctionalSAF (f,vq)) . (A + K) is complex Element of the carrier of F_Complex
((FunctionalSAF (f,vq)) . (A + K)) *' is complex Element of the carrier of F_Complex
Re ((FunctionalSAF (f,vq)) . (A + K)) is complex real ext-real Element of REAL
Im ((FunctionalSAF (f,vq)) . (A + K)) is complex real ext-real Element of REAL
(Im ((FunctionalSAF (f,vq)) . (A + K))) * <i> is complex set
(Re ((FunctionalSAF (f,vq)) . (A + K))) - ((Im ((FunctionalSAF (f,vq)) . (A + K))) * <i>) is complex set
(FunctionalSAF (f,vq)) . A is complex Element of the carrier of F_Complex
(FunctionalSAF (f,vq)) . K is complex Element of the carrier of F_Complex
((FunctionalSAF (f,vq)) . A) + ((FunctionalSAF (f,vq)) . K) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . (((FunctionalSAF (f,vq)) . A),((FunctionalSAF (f,vq)) . K)) is complex Element of the carrier of F_Complex
[((FunctionalSAF (f,vq)) . A),((FunctionalSAF (f,vq)) . K)] is set
{((FunctionalSAF (f,vq)) . A),((FunctionalSAF (f,vq)) . K)} is non empty V175() set
{((FunctionalSAF (f,vq)) . A)} is non empty V175() set
{{((FunctionalSAF (f,vq)) . A),((FunctionalSAF (f,vq)) . K)},{((FunctionalSAF (f,vq)) . A)}} is non empty set
the addF of F_Complex . [((FunctionalSAF (f,vq)) . A),((FunctionalSAF (f,vq)) . K)] is set
K135(((FunctionalSAF (f,vq)) . A),((FunctionalSAF (f,vq)) . K)) is complex Element of COMPLEX
(((FunctionalSAF (f,vq)) . A) + ((FunctionalSAF (f,vq)) . K)) *' is complex Element of the carrier of F_Complex
Re (((FunctionalSAF (f,vq)) . A) + ((FunctionalSAF (f,vq)) . K)) is complex real ext-real Element of REAL
Im (((FunctionalSAF (f,vq)) . A) + ((FunctionalSAF (f,vq)) . K)) is complex real ext-real Element of REAL
(Im (((FunctionalSAF (f,vq)) . A) + ((FunctionalSAF (f,vq)) . K))) * <i> is complex set
(Re (((FunctionalSAF (f,vq)) . A) + ((FunctionalSAF (f,vq)) . K))) - ((Im (((FunctionalSAF (f,vq)) . A) + ((FunctionalSAF (f,vq)) . K))) * <i>) is complex set
f . (A,vq) is complex Element of the carrier of F_Complex
[A,vq] is set
{A,vq} is non empty set
{{A,vq},{A}} is non empty set
f . [A,vq] is set
(f . (A,vq)) + ((FunctionalSAF (f,vq)) . K) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((f . (A,vq)),((FunctionalSAF (f,vq)) . K)) is complex Element of the carrier of F_Complex
[(f . (A,vq)),((FunctionalSAF (f,vq)) . K)] is set
{(f . (A,vq)),((FunctionalSAF (f,vq)) . K)} is non empty V175() set
{(f . (A,vq))} is non empty V175() set
{{(f . (A,vq)),((FunctionalSAF (f,vq)) . K)},{(f . (A,vq))}} is non empty set
the addF of F_Complex . [(f . (A,vq)),((FunctionalSAF (f,vq)) . K)] is set
K135((f . (A,vq)),((FunctionalSAF (f,vq)) . K)) is complex Element of COMPLEX
((f . (A,vq)) + ((FunctionalSAF (f,vq)) . K)) *' is complex Element of the carrier of F_Complex
Re ((f . (A,vq)) + ((FunctionalSAF (f,vq)) . K)) is complex real ext-real Element of REAL
Im ((f . (A,vq)) + ((FunctionalSAF (f,vq)) . K)) is complex real ext-real Element of REAL
(Im ((f . (A,vq)) + ((FunctionalSAF (f,vq)) . K))) * <i> is complex set
(Re ((f . (A,vq)) + ((FunctionalSAF (f,vq)) . K))) - ((Im ((f . (A,vq)) + ((FunctionalSAF (f,vq)) . K))) * <i>) is complex set
f . (K,vq) is complex Element of the carrier of F_Complex
[K,vq] is set
{K,vq} is non empty set
{K} is non empty set
{{K,vq},{K}} is non empty set
f . [K,vq] is set
(f . (A,vq)) + (f . (K,vq)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((f . (A,vq)),(f . (K,vq))) is complex Element of the carrier of F_Complex
[(f . (A,vq)),(f . (K,vq))] is set
{(f . (A,vq)),(f . (K,vq))} is non empty V175() set
{{(f . (A,vq)),(f . (K,vq))},{(f . (A,vq))}} is non empty set
the addF of F_Complex . [(f . (A,vq)),(f . (K,vq))] is set
K135((f . (A,vq)),(f . (K,vq))) is complex Element of COMPLEX
((f . (A,vq)) + (f . (K,vq))) *' is complex Element of the carrier of F_Complex
Re ((f . (A,vq)) + (f . (K,vq))) is complex real ext-real Element of REAL
Im ((f . (A,vq)) + (f . (K,vq))) is complex real ext-real Element of REAL
(Im ((f . (A,vq)) + (f . (K,vq)))) * <i> is complex set
(Re ((f . (A,vq)) + (f . (K,vq)))) - ((Im ((f . (A,vq)) + (f . (K,vq)))) * <i>) is complex set
(f . (A,vq)) *' is complex Element of the carrier of F_Complex
Re (f . (A,vq)) is complex real ext-real Element of REAL
Im (f . (A,vq)) is complex real ext-real Element of REAL
(Im (f . (A,vq))) * <i> is complex set
(Re (f . (A,vq))) - ((Im (f . (A,vq))) * <i>) is complex set
(f . (K,vq)) *' is complex Element of the carrier of F_Complex
Re (f . (K,vq)) is complex real ext-real Element of REAL
Im (f . (K,vq)) is complex real ext-real Element of REAL
(Im (f . (K,vq))) * <i> is complex set
(Re (f . (K,vq))) - ((Im (f . (K,vq))) * <i>) is complex set
((f . (A,vq)) *') + ((f . (K,vq)) *') is complex Element of the carrier of F_Complex
the addF of F_Complex . (((f . (A,vq)) *'),((f . (K,vq)) *')) is complex Element of the carrier of F_Complex
[((f . (A,vq)) *'),((f . (K,vq)) *')] is set
{((f . (A,vq)) *'),((f . (K,vq)) *')} is non empty V175() set
{((f . (A,vq)) *')} is non empty V175() set
{{((f . (A,vq)) *'),((f . (K,vq)) *')},{((f . (A,vq)) *')}} is non empty set
the addF of F_Complex . [((f . (A,vq)) *'),((f . (K,vq)) *')] is set
K135(((f . (A,vq)) *'),((f . (K,vq)) *')) is complex Element of COMPLEX
f . (vq,A) is complex Element of the carrier of F_Complex
[vq,A] is set
{vq,A} is non empty set
{{vq,A},{vq}} is non empty set
f . [vq,A] is set
(f . (vq,A)) + ((f . (K,vq)) *') is complex Element of the carrier of F_Complex
the addF of F_Complex . ((f . (vq,A)),((f . (K,vq)) *')) is complex Element of the carrier of F_Complex
[(f . (vq,A)),((f . (K,vq)) *')] is set
{(f . (vq,A)),((f . (K,vq)) *')} is non empty V175() set
{(f . (vq,A))} is non empty V175() set
{{(f . (vq,A)),((f . (K,vq)) *')},{(f . (vq,A))}} is non empty set
the addF of F_Complex . [(f . (vq,A)),((f . (K,vq)) *')] is set
K135((f . (vq,A)),((f . (K,vq)) *')) is complex Element of COMPLEX
f . (vq,K) is complex Element of the carrier of F_Complex
[vq,K] is set
{vq,K} is non empty set
{{vq,K},{vq}} is non empty set
f . [vq,K] is set
(f . (vq,A)) + (f . (vq,K)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((f . (vq,A)),(f . (vq,K))) is complex Element of the carrier of F_Complex
[(f . (vq,A)),(f . (vq,K))] is set
{(f . (vq,A)),(f . (vq,K))} is non empty V175() set
{{(f . (vq,A)),(f . (vq,K))},{(f . (vq,A))}} is non empty set
the addF of F_Complex . [(f . (vq,A)),(f . (vq,K))] is set
K135((f . (vq,A)),(f . (vq,K))) is complex Element of COMPLEX
(FunctionalFAF (f,vq)) . A is complex Element of the carrier of F_Complex
((FunctionalFAF (f,vq)) . A) + (f . (vq,K)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((FunctionalFAF (f,vq)) . A),(f . (vq,K))) is complex Element of the carrier of F_Complex
[((FunctionalFAF (f,vq)) . A),(f . (vq,K))] is set
{((FunctionalFAF (f,vq)) . A),(f . (vq,K))} is non empty V175() set
{((FunctionalFAF (f,vq)) . A)} is non empty V175() set
{{((FunctionalFAF (f,vq)) . A),(f . (vq,K))},{((FunctionalFAF (f,vq)) . A)}} is non empty set
the addF of F_Complex . [((FunctionalFAF (f,vq)) . A),(f . (vq,K))] is set
K135(((FunctionalFAF (f,vq)) . A),(f . (vq,K))) is complex Element of COMPLEX
(FunctionalFAF (f,vq)) . K is complex Element of the carrier of F_Complex
((FunctionalFAF (f,vq)) . A) + ((FunctionalFAF (f,vq)) . K) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((FunctionalFAF (f,vq)) . A),((FunctionalFAF (f,vq)) . K)) is complex Element of the carrier of F_Complex
[((FunctionalFAF (f,vq)) . A),((FunctionalFAF (f,vq)) . K)] is set
{((FunctionalFAF (f,vq)) . A),((FunctionalFAF (f,vq)) . K)} is non empty V175() set
{{((FunctionalFAF (f,vq)) . A),((FunctionalFAF (f,vq)) . K)},{((FunctionalFAF (f,vq)) . A)}} is non empty set
the addF of F_Complex . [((FunctionalFAF (f,vq)) . A),((FunctionalFAF (f,vq)) . K)] is set
K135(((FunctionalFAF (f,vq)) . A),((FunctionalFAF (f,vq)) . K)) is complex Element of COMPLEX
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
vq is Element of the carrier of V
FunctionalFAF (f,vq) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
FunctionalSAF (f,vq) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
K is complex Element of the carrier of F_Complex
A is Element of the carrier of V
K * A is Element of the carrier of V
the lmult of V is V16() V19([: the carrier of F_Complex, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of F_Complex, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:]
[: the carrier of F_Complex, the carrier of V:] is set
[:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
the lmult of V . (K,A) is Element of the carrier of V
[K,A] is set
{K,A} is non empty set
{K} is non empty V175() set
{{K,A},{K}} is non empty set
the lmult of V . [K,A] is set
(FunctionalFAF (f,vq)) . (K * A) is complex Element of the carrier of F_Complex
f . (vq,(K * A)) is complex Element of the carrier of F_Complex
[vq,(K * A)] is set
{vq,(K * A)} is non empty set
{vq} is non empty set
{{vq,(K * A)},{vq}} is non empty set
f . [vq,(K * A)] is set
f . ((K * A),vq) is complex Element of the carrier of F_Complex
[(K * A),vq] is set
{(K * A),vq} is non empty set
{(K * A)} is non empty set
{{(K * A),vq},{(K * A)}} is non empty set
f . [(K * A),vq] is set
(f . ((K * A),vq)) *' is complex Element of the carrier of F_Complex
Re (f . ((K * A),vq)) is complex real ext-real Element of REAL
Im (f . ((K * A),vq)) is complex real ext-real Element of REAL
(Im (f . ((K * A),vq))) * <i> is complex set
(Re (f . ((K * A),vq))) - ((Im (f . ((K * A),vq))) * <i>) is complex set
(FunctionalSAF (f,vq)) . (K * A) is complex Element of the carrier of F_Complex
((FunctionalSAF (f,vq)) . (K * A)) *' is complex Element of the carrier of F_Complex
Re ((FunctionalSAF (f,vq)) . (K * A)) is complex real ext-real Element of REAL
Im ((FunctionalSAF (f,vq)) . (K * A)) is complex real ext-real Element of REAL
(Im ((FunctionalSAF (f,vq)) . (K * A))) * <i> is complex set
(Re ((FunctionalSAF (f,vq)) . (K * A))) - ((Im ((FunctionalSAF (f,vq)) . (K * A))) * <i>) is complex set
(FunctionalSAF (f,vq)) . A is complex Element of the carrier of F_Complex
K * ((FunctionalSAF (f,vq)) . A) is complex Element of the carrier of F_Complex
the multF of F_Complex . (K,((FunctionalSAF (f,vq)) . A)) is complex Element of the carrier of F_Complex
[K,((FunctionalSAF (f,vq)) . A)] is set
{K,((FunctionalSAF (f,vq)) . A)} is non empty V175() set
{{K,((FunctionalSAF (f,vq)) . A)},{K}} is non empty set
the multF of F_Complex . [K,((FunctionalSAF (f,vq)) . A)] is set
K137(K,((FunctionalSAF (f,vq)) . A)) is complex Element of COMPLEX
(K * ((FunctionalSAF (f,vq)) . A)) *' is complex Element of the carrier of F_Complex
Re (K * ((FunctionalSAF (f,vq)) . A)) is complex real ext-real Element of REAL
Im (K * ((FunctionalSAF (f,vq)) . A)) is complex real ext-real Element of REAL
(Im (K * ((FunctionalSAF (f,vq)) . A))) * <i> is complex set
(Re (K * ((FunctionalSAF (f,vq)) . A))) - ((Im (K * ((FunctionalSAF (f,vq)) . A))) * <i>) is complex set
K *' is complex Element of the carrier of F_Complex
Re K is complex real ext-real Element of REAL
Im K is complex real ext-real Element of REAL
(Im K) * <i> is complex set
(Re K) - ((Im K) * <i>) is complex set
((FunctionalSAF (f,vq)) . A) *' is complex Element of the carrier of F_Complex
Re ((FunctionalSAF (f,vq)) . A) is complex real ext-real Element of REAL
Im ((FunctionalSAF (f,vq)) . A) is complex real ext-real Element of REAL
(Im ((FunctionalSAF (f,vq)) . A)) * <i> is complex set
(Re ((FunctionalSAF (f,vq)) . A)) - ((Im ((FunctionalSAF (f,vq)) . A)) * <i>) is complex set
(K *') * (((FunctionalSAF (f,vq)) . A) *') is complex Element of the carrier of F_Complex
the multF of F_Complex . ((K *'),(((FunctionalSAF (f,vq)) . A) *')) is complex Element of the carrier of F_Complex
[(K *'),(((FunctionalSAF (f,vq)) . A) *')] is set
{(K *'),(((FunctionalSAF (f,vq)) . A) *')} is non empty V175() set
{(K *')} is non empty V175() set
{{(K *'),(((FunctionalSAF (f,vq)) . A) *')},{(K *')}} is non empty set
the multF of F_Complex . [(K *'),(((FunctionalSAF (f,vq)) . A) *')] is set
K137((K *'),(((FunctionalSAF (f,vq)) . A) *')) is complex Element of COMPLEX
f . (A,vq) is complex Element of the carrier of F_Complex
[A,vq] is set
{A,vq} is non empty set
{A} is non empty set
{{A,vq},{A}} is non empty set
f . [A,vq] is set
(f . (A,vq)) *' is complex Element of the carrier of F_Complex
Re (f . (A,vq)) is complex real ext-real Element of REAL
Im (f . (A,vq)) is complex real ext-real Element of REAL
(Im (f . (A,vq))) * <i> is complex set
(Re (f . (A,vq))) - ((Im (f . (A,vq))) * <i>) is complex set
(K *') * ((f . (A,vq)) *') is complex Element of the carrier of F_Complex
the multF of F_Complex . ((K *'),((f . (A,vq)) *')) is complex Element of the carrier of F_Complex
[(K *'),((f . (A,vq)) *')] is set
{(K *'),((f . (A,vq)) *')} is non empty V175() set
{{(K *'),((f . (A,vq)) *')},{(K *')}} is non empty set
the multF of F_Complex . [(K *'),((f . (A,vq)) *')] is set
K137((K *'),((f . (A,vq)) *')) is complex Element of COMPLEX
f . (vq,A) is complex Element of the carrier of F_Complex
[vq,A] is set
{vq,A} is non empty set
{{vq,A},{vq}} is non empty set
f . [vq,A] is set
(K *') * (f . (vq,A)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((K *'),(f . (vq,A))) is complex Element of the carrier of F_Complex
[(K *'),(f . (vq,A))] is set
{(K *'),(f . (vq,A))} is non empty V175() set
{{(K *'),(f . (vq,A))},{(K *')}} is non empty set
the multF of F_Complex . [(K *'),(f . (vq,A))] is set
K137((K *'),(f . (vq,A))) is complex Element of COMPLEX
(FunctionalFAF (f,vq)) . A is complex Element of the carrier of F_Complex
(K *') * ((FunctionalFAF (f,vq)) . A) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((K *'),((FunctionalFAF (f,vq)) . A)) is complex Element of the carrier of F_Complex
[(K *'),((FunctionalFAF (f,vq)) . A)] is set
{(K *'),((FunctionalFAF (f,vq)) . A)} is non empty V175() set
{{(K *'),((FunctionalFAF (f,vq)) . A)},{(K *')}} is non empty set
the multF of F_Complex . [(K *'),((FunctionalFAF (f,vq)) . A)] is set
K137((K *'),((FunctionalFAF (f,vq)) . A)) is complex Element of COMPLEX
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
vq is Element of the carrier of V
FunctionalSAF (f,vq) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
FunctionalFAF (f,vq) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
K is complex Element of the carrier of F_Complex
A is Element of the carrier of V
K * A is Element of the carrier of V
the lmult of V is V16() V19([: the carrier of F_Complex, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of F_Complex, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:]
[: the carrier of F_Complex, the carrier of V:] is set
[:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
the lmult of V . (K,A) is Element of the carrier of V
[K,A] is set
{K,A} is non empty set
{K} is non empty V175() set
{{K,A},{K}} is non empty set
the lmult of V . [K,A] is set
(FunctionalSAF (f,vq)) . (K * A) is complex Element of the carrier of F_Complex
f . ((K * A),vq) is complex Element of the carrier of F_Complex
[(K * A),vq] is set
{(K * A),vq} is non empty set
{(K * A)} is non empty set
{{(K * A),vq},{(K * A)}} is non empty set
f . [(K * A),vq] is set
f . (vq,(K * A)) is complex Element of the carrier of F_Complex
[vq,(K * A)] is set
{vq,(K * A)} is non empty set
{vq} is non empty set
{{vq,(K * A)},{vq}} is non empty set
f . [vq,(K * A)] is set
(f . (vq,(K * A))) *' is complex Element of the carrier of F_Complex
Re (f . (vq,(K * A))) is complex real ext-real Element of REAL
Im (f . (vq,(K * A))) is complex real ext-real Element of REAL
(Im (f . (vq,(K * A)))) * <i> is complex set
(Re (f . (vq,(K * A)))) - ((Im (f . (vq,(K * A)))) * <i>) is complex set
(FunctionalFAF (f,vq)) . (K * A) is complex Element of the carrier of F_Complex
((FunctionalFAF (f,vq)) . (K * A)) *' is complex Element of the carrier of F_Complex
Re ((FunctionalFAF (f,vq)) . (K * A)) is complex real ext-real Element of REAL
Im ((FunctionalFAF (f,vq)) . (K * A)) is complex real ext-real Element of REAL
(Im ((FunctionalFAF (f,vq)) . (K * A))) * <i> is complex set
(Re ((FunctionalFAF (f,vq)) . (K * A))) - ((Im ((FunctionalFAF (f,vq)) . (K * A))) * <i>) is complex set
K *' is complex Element of the carrier of F_Complex
Re K is complex real ext-real Element of REAL
Im K is complex real ext-real Element of REAL
(Im K) * <i> is complex set
(Re K) - ((Im K) * <i>) is complex set
(FunctionalFAF (f,vq)) . A is complex Element of the carrier of F_Complex
(K *') * ((FunctionalFAF (f,vq)) . A) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((K *'),((FunctionalFAF (f,vq)) . A)) is complex Element of the carrier of F_Complex
[(K *'),((FunctionalFAF (f,vq)) . A)] is set
{(K *'),((FunctionalFAF (f,vq)) . A)} is non empty V175() set
{(K *')} is non empty V175() set
{{(K *'),((FunctionalFAF (f,vq)) . A)},{(K *')}} is non empty set
the multF of F_Complex . [(K *'),((FunctionalFAF (f,vq)) . A)] is set
K137((K *'),((FunctionalFAF (f,vq)) . A)) is complex Element of COMPLEX
((K *') * ((FunctionalFAF (f,vq)) . A)) *' is complex Element of the carrier of F_Complex
Re ((K *') * ((FunctionalFAF (f,vq)) . A)) is complex real ext-real Element of REAL
Im ((K *') * ((FunctionalFAF (f,vq)) . A)) is complex real ext-real Element of REAL
(Im ((K *') * ((FunctionalFAF (f,vq)) . A))) * <i> is complex set
(Re ((K *') * ((FunctionalFAF (f,vq)) . A))) - ((Im ((K *') * ((FunctionalFAF (f,vq)) . A))) * <i>) is complex set
(K *') *' is complex Element of the carrier of F_Complex
Re (K *') is complex real ext-real Element of REAL
Im (K *') is complex real ext-real Element of REAL
(Im (K *')) * <i> is complex set
(Re (K *')) - ((Im (K *')) * <i>) is complex set
((FunctionalFAF (f,vq)) . A) *' is complex Element of the carrier of F_Complex
Re ((FunctionalFAF (f,vq)) . A) is complex real ext-real Element of REAL
Im ((FunctionalFAF (f,vq)) . A) is complex real ext-real Element of REAL
(Im ((FunctionalFAF (f,vq)) . A)) * <i> is complex set
(Re ((FunctionalFAF (f,vq)) . A)) - ((Im ((FunctionalFAF (f,vq)) . A)) * <i>) is complex set
((K *') *') * (((FunctionalFAF (f,vq)) . A) *') is complex Element of the carrier of F_Complex
the multF of F_Complex . (((K *') *'),(((FunctionalFAF (f,vq)) . A) *')) is complex Element of the carrier of F_Complex
[((K *') *'),(((FunctionalFAF (f,vq)) . A) *')] is set
{((K *') *'),(((FunctionalFAF (f,vq)) . A) *')} is non empty V175() set
{((K *') *')} is non empty V175() set
{{((K *') *'),(((FunctionalFAF (f,vq)) . A) *')},{((K *') *')}} is non empty set
the multF of F_Complex . [((K *') *'),(((FunctionalFAF (f,vq)) . A) *')] is set
K137(((K *') *'),(((FunctionalFAF (f,vq)) . A) *')) is complex Element of COMPLEX
f . (vq,A) is complex Element of the carrier of F_Complex
[vq,A] is set
{vq,A} is non empty set
{{vq,A},{vq}} is non empty set
f . [vq,A] is set
(f . (vq,A)) *' is complex Element of the carrier of F_Complex
Re (f . (vq,A)) is complex real ext-real Element of REAL
Im (f . (vq,A)) is complex real ext-real Element of REAL
(Im (f . (vq,A))) * <i> is complex set
(Re (f . (vq,A))) - ((Im (f . (vq,A))) * <i>) is complex set
K * ((f . (vq,A)) *') is complex Element of the carrier of F_Complex
the multF of F_Complex . (K,((f . (vq,A)) *')) is complex Element of the carrier of F_Complex
[K,((f . (vq,A)) *')] is set
{K,((f . (vq,A)) *')} is non empty V175() set
{{K,((f . (vq,A)) *')},{K}} is non empty set
the multF of F_Complex . [K,((f . (vq,A)) *')] is set
K137(K,((f . (vq,A)) *')) is complex Element of COMPLEX
f . (A,vq) is complex Element of the carrier of F_Complex
[A,vq] is set
{A,vq} is non empty set
{A} is non empty set
{{A,vq},{A}} is non empty set
f . [A,vq] is set
K * (f . (A,vq)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (K,(f . (A,vq))) is complex Element of the carrier of F_Complex
[K,(f . (A,vq))] is set
{K,(f . (A,vq))} is non empty V175() set
{{K,(f . (A,vq))},{K}} is non empty set
the multF of F_Complex . [K,(f . (A,vq))] is set
K137(K,(f . (A,vq))) is complex Element of COMPLEX
(FunctionalSAF (f,vq)) . A is complex Element of the carrier of F_Complex
K * ((FunctionalSAF (f,vq)) . A) is complex Element of the carrier of F_Complex
the multF of F_Complex . (K,((FunctionalSAF (f,vq)) . A)) is complex Element of the carrier of F_Complex
[K,((FunctionalSAF (f,vq)) . A)] is set
{K,((FunctionalSAF (f,vq)) . A)} is non empty V175() set
{{K,((FunctionalSAF (f,vq)) . A)},{K}} is non empty set
the multF of F_Complex . [K,((FunctionalSAF (f,vq)) . A)] is set
K137(K,((FunctionalSAF (f,vq)) . A)) is complex Element of COMPLEX
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is non empty VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of f, the carrier of F_Complex:] is set
bool [: the carrier of f, the carrier of F_Complex:] is set
vq is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
vr is V16() V19( the carrier of f) V20( the carrier of F_Complex) Function-like V30( the carrier of f, the carrier of F_Complex) (f) Element of bool [: the carrier of f, the carrier of F_Complex:]
FormFunctional (vq,vr) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
qh is Element of the carrier of V
FunctionalFAF ((FormFunctional (vq,vr)),qh) is V16() V19( the carrier of f) V20( the carrier of F_Complex) Function-like V30( the carrier of f, the carrier of F_Complex) Element of bool [: the carrier of f, the carrier of F_Complex:]
x is Element of the carrier of f
(FunctionalFAF ((FormFunctional (vq,vr)),qh)) . x is complex Element of the carrier of F_Complex
A is complex Element of the carrier of F_Complex
A * x is Element of the carrier of f
the lmult of f is V16() V19([: the carrier of F_Complex, the carrier of f:]) V20( the carrier of f) Function-like V30([: the carrier of F_Complex, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of F_Complex, the carrier of f:], the carrier of f:]
[: the carrier of F_Complex, the carrier of f:] is set
[:[: the carrier of F_Complex, the carrier of f:], the carrier of f:] is set
bool [:[: the carrier of F_Complex, the carrier of f:], the carrier of f:] is set
the lmult of f . (A,x) is Element of the carrier of f
[A,x] is set
{A,x} is non empty set
{A} is non empty V175() set
{{A,x},{A}} is non empty set
the lmult of f . [A,x] is set
(FunctionalFAF ((FormFunctional (vq,vr)),qh)) . (A * x) is complex Element of the carrier of F_Complex
A *' is complex Element of the carrier of F_Complex
Re A is complex real ext-real Element of REAL
Im A is complex real ext-real Element of REAL
(Im A) * <i> is complex set
(Re A) - ((Im A) * <i>) is complex set
(A *') * ((FunctionalFAF ((FormFunctional (vq,vr)),qh)) . x) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((A *'),((FunctionalFAF ((FormFunctional (vq,vr)),qh)) . x)) is complex Element of the carrier of F_Complex
[(A *'),((FunctionalFAF ((FormFunctional (vq,vr)),qh)) . x)] is set
{(A *'),((FunctionalFAF ((FormFunctional (vq,vr)),qh)) . x)} is non empty V175() set
{(A *')} is non empty V175() set
{{(A *'),((FunctionalFAF ((FormFunctional (vq,vr)),qh)) . x)},{(A *')}} is non empty set
the multF of F_Complex . [(A *'),((FunctionalFAF ((FormFunctional (vq,vr)),qh)) . x)] is set
K137((A *'),((FunctionalFAF ((FormFunctional (vq,vr)),qh)) . x)) is complex Element of COMPLEX
vq . qh is complex Element of the carrier of F_Complex
(vq . qh) * vr is V16() V19( the carrier of f) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30( the carrier of f, the carrier of F_Complex) V30( the carrier of f, the carrier of F_Complex) (f) Element of bool [: the carrier of f, the carrier of F_Complex:]
vr . (A * x) is complex Element of the carrier of F_Complex
(vq . qh) * (vr . (A * x)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((vq . qh),(vr . (A * x))) is complex Element of the carrier of F_Complex
[(vq . qh),(vr . (A * x))] is set
{(vq . qh),(vr . (A * x))} is non empty V175() set
{(vq . qh)} is non empty V175() set
{{(vq . qh),(vr . (A * x))},{(vq . qh)}} is non empty set
the multF of F_Complex . [(vq . qh),(vr . (A * x))] is set
K137((vq . qh),(vr . (A * x))) is complex Element of COMPLEX
vr . x is complex Element of the carrier of F_Complex
(A *') * (vr . x) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((A *'),(vr . x)) is complex Element of the carrier of F_Complex
[(A *'),(vr . x)] is set
{(A *'),(vr . x)} is non empty V175() set
{{(A *'),(vr . x)},{(A *')}} is non empty set
the multF of F_Complex . [(A *'),(vr . x)] is set
K137((A *'),(vr . x)) is complex Element of COMPLEX
(vq . qh) * ((A *') * (vr . x)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((vq . qh),((A *') * (vr . x))) is complex Element of the carrier of F_Complex
[(vq . qh),((A *') * (vr . x))] is set
{(vq . qh),((A *') * (vr . x))} is non empty V175() set
{{(vq . qh),((A *') * (vr . x))},{(vq . qh)}} is non empty set
the multF of F_Complex . [(vq . qh),((A *') * (vr . x))] is set
K137((vq . qh),((A *') * (vr . x))) is complex Element of COMPLEX
(vq . qh) * (vr . x) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((vq . qh),(vr . x)) is complex Element of the carrier of F_Complex
[(vq . qh),(vr . x)] is set
{(vq . qh),(vr . x)} is non empty V175() set
{{(vq . qh),(vr . x)},{(vq . qh)}} is non empty set
the multF of F_Complex . [(vq . qh),(vr . x)] is set
K137((vq . qh),(vr . x)) is complex Element of COMPLEX
(A *') * ((vq . qh) * (vr . x)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((A *'),((vq . qh) * (vr . x))) is complex Element of the carrier of F_Complex
[(A *'),((vq . qh) * (vr . x))] is set
{(A *'),((vq . qh) * (vr . x))} is non empty V175() set
{{(A *'),((vq . qh) * (vr . x))},{(A *')}} is non empty set
the multF of F_Complex . [(A *'),((vq . qh) * (vr . x))] is set
K137((A *'),((vq . qh) * (vr . x))) is complex Element of COMPLEX
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
vr is Element of the carrier of V
FunctionalFAF (vq,vr) is V16() V19( the carrier of f) V20( the carrier of F_Complex) Function-like V30( the carrier of f, the carrier of F_Complex) Element of bool [: the carrier of f, the carrier of F_Complex:]
[: the carrier of f, the carrier of F_Complex:] is set
bool [: the carrier of f, the carrier of F_Complex:] is set
qh is Element of the carrier of f
(FunctionalFAF (vq,vr)) . qh is complex Element of the carrier of F_Complex
A is complex Element of the carrier of F_Complex
A * qh is Element of the carrier of f
the lmult of f is V16() V19([: the carrier of F_Complex, the carrier of f:]) V20( the carrier of f) Function-like V30([: the carrier of F_Complex, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of F_Complex, the carrier of f:], the carrier of f:]
[: the carrier of F_Complex, the carrier of f:] is set
[:[: the carrier of F_Complex, the carrier of f:], the carrier of f:] is set
bool [:[: the carrier of F_Complex, the carrier of f:], the carrier of f:] is set
the lmult of f . (A,qh) is Element of the carrier of f
[A,qh] is set
{A,qh} is non empty set
{A} is non empty V175() set
{{A,qh},{A}} is non empty set
the lmult of f . [A,qh] is set
(FunctionalFAF (vq,vr)) . (A * qh) is complex Element of the carrier of F_Complex
A *' is complex Element of the carrier of F_Complex
Re A is complex real ext-real Element of REAL
Im A is complex real ext-real Element of REAL
(Im A) * <i> is complex set
(Re A) - ((Im A) * <i>) is complex set
(A *') * ((FunctionalFAF (vq,vr)) . qh) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((A *'),((FunctionalFAF (vq,vr)) . qh)) is complex Element of the carrier of F_Complex
[(A *'),((FunctionalFAF (vq,vr)) . qh)] is set
{(A *'),((FunctionalFAF (vq,vr)) . qh)} is non empty V175() set
{(A *')} is non empty V175() set
{{(A *'),((FunctionalFAF (vq,vr)) . qh)},{(A *')}} is non empty set
the multF of F_Complex . [(A *'),((FunctionalFAF (vq,vr)) . qh)] is set
K137((A *'),((FunctionalFAF (vq,vr)) . qh)) is complex Element of COMPLEX
vq . (vr,(A * qh)) is complex Element of the carrier of F_Complex
[vr,(A * qh)] is set
{vr,(A * qh)} is non empty set
{vr} is non empty set
{{vr,(A * qh)},{vr}} is non empty set
vq . [vr,(A * qh)] is set
vq . (vr,qh) is complex Element of the carrier of F_Complex
[vr,qh] is set
{vr,qh} is non empty set
{{vr,qh},{vr}} is non empty set
vq . [vr,qh] is set
(A *') * (vq . (vr,qh)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((A *'),(vq . (vr,qh))) is complex Element of the carrier of F_Complex
[(A *'),(vq . (vr,qh))] is set
{(A *'),(vq . (vr,qh))} is non empty V175() set
{{(A *'),(vq . (vr,qh))},{(A *')}} is non empty set
the multF of F_Complex . [(A *'),(vq . (vr,qh))] is set
K137((A *'),(vq . (vr,qh))) is complex Element of COMPLEX
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
vr is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
vq + vr is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
qh is Element of the carrier of V
FunctionalFAF ((vq + vr),qh) is V16() V19( the carrier of f) V20( the carrier of F_Complex) Function-like V30( the carrier of f, the carrier of F_Complex) Element of bool [: the carrier of f, the carrier of F_Complex:]
[: the carrier of f, the carrier of F_Complex:] is set
bool [: the carrier of f, the carrier of F_Complex:] is set
FunctionalFAF (vq,qh) is V16() V19( the carrier of f) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30( the carrier of f, the carrier of F_Complex) V30( the carrier of f, the carrier of F_Complex) (f) Element of bool [: the carrier of f, the carrier of F_Complex:]
FunctionalFAF (vr,qh) is V16() V19( the carrier of f) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30( the carrier of f, the carrier of F_Complex) V30( the carrier of f, the carrier of F_Complex) (f) Element of bool [: the carrier of f, the carrier of F_Complex:]
A is Element of the carrier of f
(FunctionalFAF ((vq + vr),qh)) . A is complex Element of the carrier of F_Complex
B is complex Element of the carrier of F_Complex
B * A is Element of the carrier of f
the lmult of f is V16() V19([: the carrier of F_Complex, the carrier of f:]) V20( the carrier of f) Function-like V30([: the carrier of F_Complex, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of F_Complex, the carrier of f:], the carrier of f:]
[: the carrier of F_Complex, the carrier of f:] is set
[:[: the carrier of F_Complex, the carrier of f:], the carrier of f:] is set
bool [:[: the carrier of F_Complex, the carrier of f:], the carrier of f:] is set
the lmult of f . (B,A) is Element of the carrier of f
[B,A] is set
{B,A} is non empty set
{B} is non empty V175() set
{{B,A},{B}} is non empty set
the lmult of f . [B,A] is set
(FunctionalFAF ((vq + vr),qh)) . (B * A) is complex Element of the carrier of F_Complex
B *' is complex Element of the carrier of F_Complex
Re B is complex real ext-real Element of REAL
Im B is complex real ext-real Element of REAL
(Im B) * <i> is complex set
(Re B) - ((Im B) * <i>) is complex set
(B *') * ((FunctionalFAF ((vq + vr),qh)) . A) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((B *'),((FunctionalFAF ((vq + vr),qh)) . A)) is complex Element of the carrier of F_Complex
[(B *'),((FunctionalFAF ((vq + vr),qh)) . A)] is set
{(B *'),((FunctionalFAF ((vq + vr),qh)) . A)} is non empty V175() set
{(B *')} is non empty V175() set
{{(B *'),((FunctionalFAF ((vq + vr),qh)) . A)},{(B *')}} is non empty set
the multF of F_Complex . [(B *'),((FunctionalFAF ((vq + vr),qh)) . A)] is set
K137((B *'),((FunctionalFAF ((vq + vr),qh)) . A)) is complex Element of COMPLEX
(FunctionalFAF (vq,qh)) + (FunctionalFAF (vr,qh)) is V16() V19( the carrier of f) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30( the carrier of f, the carrier of F_Complex) V30( the carrier of f, the carrier of F_Complex) (f) Element of bool [: the carrier of f, the carrier of F_Complex:]
((FunctionalFAF (vq,qh)) + (FunctionalFAF (vr,qh))) . (B * A) is complex Element of the carrier of F_Complex
(FunctionalFAF (vq,qh)) . (B * A) is complex Element of the carrier of F_Complex
(FunctionalFAF (vr,qh)) . (B * A) is complex Element of the carrier of F_Complex
((FunctionalFAF (vq,qh)) . (B * A)) + ((FunctionalFAF (vr,qh)) . (B * A)) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . (((FunctionalFAF (vq,qh)) . (B * A)),((FunctionalFAF (vr,qh)) . (B * A))) is complex Element of the carrier of F_Complex
[((FunctionalFAF (vq,qh)) . (B * A)),((FunctionalFAF (vr,qh)) . (B * A))] is set
{((FunctionalFAF (vq,qh)) . (B * A)),((FunctionalFAF (vr,qh)) . (B * A))} is non empty V175() set
{((FunctionalFAF (vq,qh)) . (B * A))} is non empty V175() set
{{((FunctionalFAF (vq,qh)) . (B * A)),((FunctionalFAF (vr,qh)) . (B * A))},{((FunctionalFAF (vq,qh)) . (B * A))}} is non empty set
the addF of F_Complex . [((FunctionalFAF (vq,qh)) . (B * A)),((FunctionalFAF (vr,qh)) . (B * A))] is set
K135(((FunctionalFAF (vq,qh)) . (B * A)),((FunctionalFAF (vr,qh)) . (B * A))) is complex Element of COMPLEX
(FunctionalFAF (vq,qh)) . A is complex Element of the carrier of F_Complex
(B *') * ((FunctionalFAF (vq,qh)) . A) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((B *'),((FunctionalFAF (vq,qh)) . A)) is complex Element of the carrier of F_Complex
[(B *'),((FunctionalFAF (vq,qh)) . A)] is set
{(B *'),((FunctionalFAF (vq,qh)) . A)} is non empty V175() set
{{(B *'),((FunctionalFAF (vq,qh)) . A)},{(B *')}} is non empty set
the multF of F_Complex . [(B *'),((FunctionalFAF (vq,qh)) . A)] is set
K137((B *'),((FunctionalFAF (vq,qh)) . A)) is complex Element of COMPLEX
((B *') * ((FunctionalFAF (vq,qh)) . A)) + ((FunctionalFAF (vr,qh)) . (B * A)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((B *') * ((FunctionalFAF (vq,qh)) . A)),((FunctionalFAF (vr,qh)) . (B * A))) is complex Element of the carrier of F_Complex
[((B *') * ((FunctionalFAF (vq,qh)) . A)),((FunctionalFAF (vr,qh)) . (B * A))] is set
{((B *') * ((FunctionalFAF (vq,qh)) . A)),((FunctionalFAF (vr,qh)) . (B * A))} is non empty V175() set
{((B *') * ((FunctionalFAF (vq,qh)) . A))} is non empty V175() set
{{((B *') * ((FunctionalFAF (vq,qh)) . A)),((FunctionalFAF (vr,qh)) . (B * A))},{((B *') * ((FunctionalFAF (vq,qh)) . A))}} is non empty set
the addF of F_Complex . [((B *') * ((FunctionalFAF (vq,qh)) . A)),((FunctionalFAF (vr,qh)) . (B * A))] is set
K135(((B *') * ((FunctionalFAF (vq,qh)) . A)),((FunctionalFAF (vr,qh)) . (B * A))) is complex Element of COMPLEX
(FunctionalFAF (vr,qh)) . A is complex Element of the carrier of F_Complex
(B *') * ((FunctionalFAF (vr,qh)) . A) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((B *'),((FunctionalFAF (vr,qh)) . A)) is complex Element of the carrier of F_Complex
[(B *'),((FunctionalFAF (vr,qh)) . A)] is set
{(B *'),((FunctionalFAF (vr,qh)) . A)} is non empty V175() set
{{(B *'),((FunctionalFAF (vr,qh)) . A)},{(B *')}} is non empty set
the multF of F_Complex . [(B *'),((FunctionalFAF (vr,qh)) . A)] is set
K137((B *'),((FunctionalFAF (vr,qh)) . A)) is complex Element of COMPLEX
((B *') * ((FunctionalFAF (vq,qh)) . A)) + ((B *') * ((FunctionalFAF (vr,qh)) . A)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((B *') * ((FunctionalFAF (vq,qh)) . A)),((B *') * ((FunctionalFAF (vr,qh)) . A))) is complex Element of the carrier of F_Complex
[((B *') * ((FunctionalFAF (vq,qh)) . A)),((B *') * ((FunctionalFAF (vr,qh)) . A))] is set
{((B *') * ((FunctionalFAF (vq,qh)) . A)),((B *') * ((FunctionalFAF (vr,qh)) . A))} is non empty V175() set
{{((B *') * ((FunctionalFAF (vq,qh)) . A)),((B *') * ((FunctionalFAF (vr,qh)) . A))},{((B *') * ((FunctionalFAF (vq,qh)) . A))}} is non empty set
the addF of F_Complex . [((B *') * ((FunctionalFAF (vq,qh)) . A)),((B *') * ((FunctionalFAF (vr,qh)) . A))] is set
K135(((B *') * ((FunctionalFAF (vq,qh)) . A)),((B *') * ((FunctionalFAF (vr,qh)) . A))) is complex Element of COMPLEX
((FunctionalFAF (vq,qh)) . A) + ((FunctionalFAF (vr,qh)) . A) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((FunctionalFAF (vq,qh)) . A),((FunctionalFAF (vr,qh)) . A)) is complex Element of the carrier of F_Complex
[((FunctionalFAF (vq,qh)) . A),((FunctionalFAF (vr,qh)) . A)] is set
{((FunctionalFAF (vq,qh)) . A),((FunctionalFAF (vr,qh)) . A)} is non empty V175() set
{((FunctionalFAF (vq,qh)) . A)} is non empty V175() set
{{((FunctionalFAF (vq,qh)) . A),((FunctionalFAF (vr,qh)) . A)},{((FunctionalFAF (vq,qh)) . A)}} is non empty set
the addF of F_Complex . [((FunctionalFAF (vq,qh)) . A),((FunctionalFAF (vr,qh)) . A)] is set
K135(((FunctionalFAF (vq,qh)) . A),((FunctionalFAF (vr,qh)) . A)) is complex Element of COMPLEX
(B *') * (((FunctionalFAF (vq,qh)) . A) + ((FunctionalFAF (vr,qh)) . A)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((B *'),(((FunctionalFAF (vq,qh)) . A) + ((FunctionalFAF (vr,qh)) . A))) is complex Element of the carrier of F_Complex
[(B *'),(((FunctionalFAF (vq,qh)) . A) + ((FunctionalFAF (vr,qh)) . A))] is set
{(B *'),(((FunctionalFAF (vq,qh)) . A) + ((FunctionalFAF (vr,qh)) . A))} is non empty V175() set
{{(B *'),(((FunctionalFAF (vq,qh)) . A) + ((FunctionalFAF (vr,qh)) . A))},{(B *')}} is non empty set
the multF of F_Complex . [(B *'),(((FunctionalFAF (vq,qh)) . A) + ((FunctionalFAF (vr,qh)) . A))] is set
K137((B *'),(((FunctionalFAF (vq,qh)) . A) + ((FunctionalFAF (vr,qh)) . A))) is complex Element of COMPLEX
((FunctionalFAF (vq,qh)) + (FunctionalFAF (vr,qh))) . A is complex Element of the carrier of F_Complex
(B *') * (((FunctionalFAF (vq,qh)) + (FunctionalFAF (vr,qh))) . A) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((B *'),(((FunctionalFAF (vq,qh)) + (FunctionalFAF (vr,qh))) . A)) is complex Element of the carrier of F_Complex
[(B *'),(((FunctionalFAF (vq,qh)) + (FunctionalFAF (vr,qh))) . A)] is set
{(B *'),(((FunctionalFAF (vq,qh)) + (FunctionalFAF (vr,qh))) . A)} is non empty V175() set
{{(B *'),(((FunctionalFAF (vq,qh)) + (FunctionalFAF (vr,qh))) . A)},{(B *')}} is non empty set
the multF of F_Complex . [(B *'),(((FunctionalFAF (vq,qh)) + (FunctionalFAF (vr,qh))) . A)] is set
K137((B *'),(((FunctionalFAF (vq,qh)) + (FunctionalFAF (vr,qh))) . A)) is complex Element of COMPLEX
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
vr is complex Element of the carrier of F_Complex
vr * vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
qh is Element of the carrier of V
FunctionalFAF ((vr * vq),qh) is V16() V19( the carrier of f) V20( the carrier of F_Complex) Function-like V30( the carrier of f, the carrier of F_Complex) Element of bool [: the carrier of f, the carrier of F_Complex:]
[: the carrier of f, the carrier of F_Complex:] is set
bool [: the carrier of f, the carrier of F_Complex:] is set
FunctionalFAF (vq,qh) is V16() V19( the carrier of f) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30( the carrier of f, the carrier of F_Complex) V30( the carrier of f, the carrier of F_Complex) (f) Element of bool [: the carrier of f, the carrier of F_Complex:]
x is Element of the carrier of f
(FunctionalFAF ((vr * vq),qh)) . x is complex Element of the carrier of F_Complex
A is complex Element of the carrier of F_Complex
A * x is Element of the carrier of f
the lmult of f is V16() V19([: the carrier of F_Complex, the carrier of f:]) V20( the carrier of f) Function-like V30([: the carrier of F_Complex, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of F_Complex, the carrier of f:], the carrier of f:]
[: the carrier of F_Complex, the carrier of f:] is set
[:[: the carrier of F_Complex, the carrier of f:], the carrier of f:] is set
bool [:[: the carrier of F_Complex, the carrier of f:], the carrier of f:] is set
the lmult of f . (A,x) is Element of the carrier of f
[A,x] is set
{A,x} is non empty set
{A} is non empty V175() set
{{A,x},{A}} is non empty set
the lmult of f . [A,x] is set
(FunctionalFAF ((vr * vq),qh)) . (A * x) is complex Element of the carrier of F_Complex
A *' is complex Element of the carrier of F_Complex
Re A is complex real ext-real Element of REAL
Im A is complex real ext-real Element of REAL
(Im A) * <i> is complex set
(Re A) - ((Im A) * <i>) is complex set
(A *') * ((FunctionalFAF ((vr * vq),qh)) . x) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((A *'),((FunctionalFAF ((vr * vq),qh)) . x)) is complex Element of the carrier of F_Complex
[(A *'),((FunctionalFAF ((vr * vq),qh)) . x)] is set
{(A *'),((FunctionalFAF ((vr * vq),qh)) . x)} is non empty V175() set
{(A *')} is non empty V175() set
{{(A *'),((FunctionalFAF ((vr * vq),qh)) . x)},{(A *')}} is non empty set
the multF of F_Complex . [(A *'),((FunctionalFAF ((vr * vq),qh)) . x)] is set
K137((A *'),((FunctionalFAF ((vr * vq),qh)) . x)) is complex Element of COMPLEX
vr * (FunctionalFAF (vq,qh)) is V16() V19( the carrier of f) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30( the carrier of f, the carrier of F_Complex) V30( the carrier of f, the carrier of F_Complex) (f) Element of bool [: the carrier of f, the carrier of F_Complex:]
(vr * (FunctionalFAF (vq,qh))) . (A * x) is complex Element of the carrier of F_Complex
(FunctionalFAF (vq,qh)) . (A * x) is complex Element of the carrier of F_Complex
vr * ((FunctionalFAF (vq,qh)) . (A * x)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (vr,((FunctionalFAF (vq,qh)) . (A * x))) is complex Element of the carrier of F_Complex
[vr,((FunctionalFAF (vq,qh)) . (A * x))] is set
{vr,((FunctionalFAF (vq,qh)) . (A * x))} is non empty V175() set
{vr} is non empty V175() set
{{vr,((FunctionalFAF (vq,qh)) . (A * x))},{vr}} is non empty set
the multF of F_Complex . [vr,((FunctionalFAF (vq,qh)) . (A * x))] is set
K137(vr,((FunctionalFAF (vq,qh)) . (A * x))) is complex Element of COMPLEX
(FunctionalFAF (vq,qh)) . x is complex Element of the carrier of F_Complex
(A *') * ((FunctionalFAF (vq,qh)) . x) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((A *'),((FunctionalFAF (vq,qh)) . x)) is complex Element of the carrier of F_Complex
[(A *'),((FunctionalFAF (vq,qh)) . x)] is set
{(A *'),((FunctionalFAF (vq,qh)) . x)} is non empty V175() set
{{(A *'),((FunctionalFAF (vq,qh)) . x)},{(A *')}} is non empty set
the multF of F_Complex . [(A *'),((FunctionalFAF (vq,qh)) . x)] is set
K137((A *'),((FunctionalFAF (vq,qh)) . x)) is complex Element of COMPLEX
vr * ((A *') * ((FunctionalFAF (vq,qh)) . x)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (vr,((A *') * ((FunctionalFAF (vq,qh)) . x))) is complex Element of the carrier of F_Complex
[vr,((A *') * ((FunctionalFAF (vq,qh)) . x))] is set
{vr,((A *') * ((FunctionalFAF (vq,qh)) . x))} is non empty V175() set
{{vr,((A *') * ((FunctionalFAF (vq,qh)) . x))},{vr}} is non empty set
the multF of F_Complex . [vr,((A *') * ((FunctionalFAF (vq,qh)) . x))] is set
K137(vr,((A *') * ((FunctionalFAF (vq,qh)) . x))) is complex Element of COMPLEX
vr * ((FunctionalFAF (vq,qh)) . x) is complex Element of the carrier of F_Complex
the multF of F_Complex . (vr,((FunctionalFAF (vq,qh)) . x)) is complex Element of the carrier of F_Complex
[vr,((FunctionalFAF (vq,qh)) . x)] is set
{vr,((FunctionalFAF (vq,qh)) . x)} is non empty V175() set
{{vr,((FunctionalFAF (vq,qh)) . x)},{vr}} is non empty set
the multF of F_Complex . [vr,((FunctionalFAF (vq,qh)) . x)] is set
K137(vr,((FunctionalFAF (vq,qh)) . x)) is complex Element of COMPLEX
(A *') * (vr * ((FunctionalFAF (vq,qh)) . x)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((A *'),(vr * ((FunctionalFAF (vq,qh)) . x))) is complex Element of the carrier of F_Complex
[(A *'),(vr * ((FunctionalFAF (vq,qh)) . x))] is set
{(A *'),(vr * ((FunctionalFAF (vq,qh)) . x))} is non empty V175() set
{{(A *'),(vr * ((FunctionalFAF (vq,qh)) . x))},{(A *')}} is non empty set
the multF of F_Complex . [(A *'),(vr * ((FunctionalFAF (vq,qh)) . x))] is set
K137((A *'),(vr * ((FunctionalFAF (vq,qh)) . x))) is complex Element of COMPLEX
(vr * (FunctionalFAF (vq,qh))) . x is complex Element of the carrier of F_Complex
(A *') * ((vr * (FunctionalFAF (vq,qh))) . x) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((A *'),((vr * (FunctionalFAF (vq,qh))) . x)) is complex Element of the carrier of F_Complex
[(A *'),((vr * (FunctionalFAF (vq,qh))) . x)] is set
{(A *'),((vr * (FunctionalFAF (vq,qh))) . x)} is non empty V175() set
{{(A *'),((vr * (FunctionalFAF (vq,qh))) . x)},{(A *')}} is non empty set
the multF of F_Complex . [(A *'),((vr * (FunctionalFAF (vq,qh))) . x)] is set
K137((A *'),((vr * (FunctionalFAF (vq,qh))) . x)) is complex Element of COMPLEX
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
- vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
- (1. F_Complex) is complex Element of the carrier of F_Complex
(- (1. F_Complex)) * vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
vr is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
vq - vr is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
- vr is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(- (1. F_Complex)) * vr is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
vq + (- vr) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
V is non empty non trivial right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty non trivial set
f is non empty non trivial right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of f is non empty non trivial set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
[: the carrier of f, the carrier of F_Complex:] is set
bool [: the carrier of f, the carrier of F_Complex:] is set
the non trivial V16() V19( the carrier of f) V20( the carrier of F_Complex) Function-like non constant V30( the carrier of f, the carrier of F_Complex) additive 0-preserving (f) Element of bool [: the carrier of f, the carrier of F_Complex:] is non trivial V16() V19( the carrier of f) V20( the carrier of F_Complex) Function-like non constant V30( the carrier of f, the carrier of F_Complex) additive 0-preserving (f) Element of bool [: the carrier of f, the carrier of F_Complex:]
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
the non trivial V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like non constant V30( the carrier of V, the carrier of F_Complex) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of F_Complex:] is non trivial V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like non constant V30( the carrier of V, the carrier of F_Complex) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of F_Complex:]
FormFunctional ( the non trivial V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like non constant V30( the carrier of V, the carrier of F_Complex) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of F_Complex:], the non trivial V16() V19( the carrier of f) V20( the carrier of F_Complex) Function-like non constant V30( the carrier of f, the carrier of F_Complex) additive 0-preserving (f) Element of bool [: the carrier of f, the carrier of F_Complex:]) is non trivial V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like non constant V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
x is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
A is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
B is Element of the carrier of V
w is Element of the carrier of f
A . (B,w) is complex Element of the carrier of F_Complex
[B,w] is set
{B,w} is non empty set
{B} is non empty set
{{B,w},{B}} is non empty set
A . [B,w] is set
vq . (B,w) is complex Element of the carrier of F_Complex
vq . [B,w] is set
(vq . (B,w)) *' is complex Element of the carrier of F_Complex
Re (vq . (B,w)) is complex real ext-real Element of REAL
Im (vq . (B,w)) is complex real ext-real Element of REAL
(Im (vq . (B,w))) * <i> is complex set
(Re (vq . (B,w))) - ((Im (vq . (B,w))) * <i>) is complex set
vr is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
qh is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
A is Element of the carrier of V
K is Element of the carrier of f
vr . (A,K) is complex Element of the carrier of F_Complex
[A,K] is set
{A,K} is non empty set
{A} is non empty set
{{A,K},{A}} is non empty set
vr . [A,K] is set
vq . (A,K) is complex Element of the carrier of F_Complex
vq . [A,K] is set
(vq . (A,K)) *' is complex Element of the carrier of F_Complex
Re (vq . (A,K)) is complex real ext-real Element of REAL
Im (vq . (A,K)) is complex real ext-real Element of REAL
(Im (vq . (A,K))) * <i> is complex set
(Re (vq . (A,K))) - ((Im (vq . (A,K))) * <i>) is complex set
qh . (A,K) is complex Element of the carrier of F_Complex
qh . [A,K] is set
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,vq) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
vr is Element of the carrier of V
FunctionalFAF ((V,f,vq),vr) is V16() V19( the carrier of f) V20( the carrier of F_Complex) Function-like V30( the carrier of f, the carrier of F_Complex) Element of bool [: the carrier of f, the carrier of F_Complex:]
[: the carrier of f, the carrier of F_Complex:] is set
bool [: the carrier of f, the carrier of F_Complex:] is set
qh is Element of the carrier of f
A is Element of the carrier of f
qh + A is Element of the carrier of f
the addF of f is V16() V19([: the carrier of f, the carrier of f:]) V20( the carrier of f) Function-like V30([: the carrier of f, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of f, the carrier of f:], the carrier of f:]
[: the carrier of f, the carrier of f:] is set
[:[: the carrier of f, the carrier of f:], the carrier of f:] is set
bool [:[: the carrier of f, the carrier of f:], the carrier of f:] is set
the addF of f . (qh,A) is Element of the carrier of f
[qh,A] is set
{qh,A} is non empty set
{qh} is non empty set
{{qh,A},{qh}} is non empty set
the addF of f . [qh,A] is set
(FunctionalFAF ((V,f,vq),vr)) . (qh + A) is complex Element of the carrier of F_Complex
(FunctionalFAF ((V,f,vq),vr)) . qh is complex Element of the carrier of F_Complex
(FunctionalFAF ((V,f,vq),vr)) . A is complex Element of the carrier of F_Complex
((FunctionalFAF ((V,f,vq),vr)) . qh) + ((FunctionalFAF ((V,f,vq),vr)) . A) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . (((FunctionalFAF ((V,f,vq),vr)) . qh),((FunctionalFAF ((V,f,vq),vr)) . A)) is complex Element of the carrier of F_Complex
[((FunctionalFAF ((V,f,vq),vr)) . qh),((FunctionalFAF ((V,f,vq),vr)) . A)] is set
{((FunctionalFAF ((V,f,vq),vr)) . qh),((FunctionalFAF ((V,f,vq),vr)) . A)} is non empty V175() set
{((FunctionalFAF ((V,f,vq),vr)) . qh)} is non empty V175() set
{{((FunctionalFAF ((V,f,vq),vr)) . qh),((FunctionalFAF ((V,f,vq),vr)) . A)},{((FunctionalFAF ((V,f,vq),vr)) . qh)}} is non empty set
the addF of F_Complex . [((FunctionalFAF ((V,f,vq),vr)) . qh),((FunctionalFAF ((V,f,vq),vr)) . A)] is set
K135(((FunctionalFAF ((V,f,vq),vr)) . qh),((FunctionalFAF ((V,f,vq),vr)) . A)) is complex Element of COMPLEX
(V,f,vq) . (vr,(qh + A)) is complex Element of the carrier of F_Complex
[vr,(qh + A)] is set
{vr,(qh + A)} is non empty set
{vr} is non empty set
{{vr,(qh + A)},{vr}} is non empty set
(V,f,vq) . [vr,(qh + A)] is set
vq . (vr,(qh + A)) is complex Element of the carrier of F_Complex
vq . [vr,(qh + A)] is set
(vq . (vr,(qh + A))) *' is complex Element of the carrier of F_Complex
Re (vq . (vr,(qh + A))) is complex real ext-real Element of REAL
Im (vq . (vr,(qh + A))) is complex real ext-real Element of REAL
(Im (vq . (vr,(qh + A)))) * <i> is complex set
(Re (vq . (vr,(qh + A)))) - ((Im (vq . (vr,(qh + A)))) * <i>) is complex set
vq . (vr,qh) is complex Element of the carrier of F_Complex
[vr,qh] is set
{vr,qh} is non empty set
{{vr,qh},{vr}} is non empty set
vq . [vr,qh] is set
vq . (vr,A) is complex Element of the carrier of F_Complex
[vr,A] is set
{vr,A} is non empty set
{{vr,A},{vr}} is non empty set
vq . [vr,A] is set
(vq . (vr,qh)) + (vq . (vr,A)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vq . (vr,qh)),(vq . (vr,A))) is complex Element of the carrier of F_Complex
[(vq . (vr,qh)),(vq . (vr,A))] is set
{(vq . (vr,qh)),(vq . (vr,A))} is non empty V175() set
{(vq . (vr,qh))} is non empty V175() set
{{(vq . (vr,qh)),(vq . (vr,A))},{(vq . (vr,qh))}} is non empty set
the addF of F_Complex . [(vq . (vr,qh)),(vq . (vr,A))] is set
K135((vq . (vr,qh)),(vq . (vr,A))) is complex Element of COMPLEX
((vq . (vr,qh)) + (vq . (vr,A))) *' is complex Element of the carrier of F_Complex
Re ((vq . (vr,qh)) + (vq . (vr,A))) is complex real ext-real Element of REAL
Im ((vq . (vr,qh)) + (vq . (vr,A))) is complex real ext-real Element of REAL
(Im ((vq . (vr,qh)) + (vq . (vr,A)))) * <i> is complex set
(Re ((vq . (vr,qh)) + (vq . (vr,A)))) - ((Im ((vq . (vr,qh)) + (vq . (vr,A)))) * <i>) is complex set
(vq . (vr,qh)) *' is complex Element of the carrier of F_Complex
Re (vq . (vr,qh)) is complex real ext-real Element of REAL
Im (vq . (vr,qh)) is complex real ext-real Element of REAL
(Im (vq . (vr,qh))) * <i> is complex set
(Re (vq . (vr,qh))) - ((Im (vq . (vr,qh))) * <i>) is complex set
(vq . (vr,A)) *' is complex Element of the carrier of F_Complex
Re (vq . (vr,A)) is complex real ext-real Element of REAL
Im (vq . (vr,A)) is complex real ext-real Element of REAL
(Im (vq . (vr,A))) * <i> is complex set
(Re (vq . (vr,A))) - ((Im (vq . (vr,A))) * <i>) is complex set
((vq . (vr,qh)) *') + ((vq . (vr,A)) *') is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vq . (vr,qh)) *'),((vq . (vr,A)) *')) is complex Element of the carrier of F_Complex
[((vq . (vr,qh)) *'),((vq . (vr,A)) *')] is set
{((vq . (vr,qh)) *'),((vq . (vr,A)) *')} is non empty V175() set
{((vq . (vr,qh)) *')} is non empty V175() set
{{((vq . (vr,qh)) *'),((vq . (vr,A)) *')},{((vq . (vr,qh)) *')}} is non empty set
the addF of F_Complex . [((vq . (vr,qh)) *'),((vq . (vr,A)) *')] is set
K135(((vq . (vr,qh)) *'),((vq . (vr,A)) *')) is complex Element of COMPLEX
(V,f,vq) . (vr,qh) is complex Element of the carrier of F_Complex
(V,f,vq) . [vr,qh] is set
((V,f,vq) . (vr,qh)) + ((vq . (vr,A)) *') is complex Element of the carrier of F_Complex
the addF of F_Complex . (((V,f,vq) . (vr,qh)),((vq . (vr,A)) *')) is complex Element of the carrier of F_Complex
[((V,f,vq) . (vr,qh)),((vq . (vr,A)) *')] is set
{((V,f,vq) . (vr,qh)),((vq . (vr,A)) *')} is non empty V175() set
{((V,f,vq) . (vr,qh))} is non empty V175() set
{{((V,f,vq) . (vr,qh)),((vq . (vr,A)) *')},{((V,f,vq) . (vr,qh))}} is non empty set
the addF of F_Complex . [((V,f,vq) . (vr,qh)),((vq . (vr,A)) *')] is set
K135(((V,f,vq) . (vr,qh)),((vq . (vr,A)) *')) is complex Element of COMPLEX
(V,f,vq) . (vr,A) is complex Element of the carrier of F_Complex
(V,f,vq) . [vr,A] is set
((V,f,vq) . (vr,qh)) + ((V,f,vq) . (vr,A)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((V,f,vq) . (vr,qh)),((V,f,vq) . (vr,A))) is complex Element of the carrier of F_Complex
[((V,f,vq) . (vr,qh)),((V,f,vq) . (vr,A))] is set
{((V,f,vq) . (vr,qh)),((V,f,vq) . (vr,A))} is non empty V175() set
{{((V,f,vq) . (vr,qh)),((V,f,vq) . (vr,A))},{((V,f,vq) . (vr,qh))}} is non empty set
the addF of F_Complex . [((V,f,vq) . (vr,qh)),((V,f,vq) . (vr,A))] is set
K135(((V,f,vq) . (vr,qh)),((V,f,vq) . (vr,A))) is complex Element of COMPLEX
((FunctionalFAF ((V,f,vq),vr)) . qh) + ((V,f,vq) . (vr,A)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((FunctionalFAF ((V,f,vq),vr)) . qh),((V,f,vq) . (vr,A))) is complex Element of the carrier of F_Complex
[((FunctionalFAF ((V,f,vq),vr)) . qh),((V,f,vq) . (vr,A))] is set
{((FunctionalFAF ((V,f,vq),vr)) . qh),((V,f,vq) . (vr,A))} is non empty V175() set
{{((FunctionalFAF ((V,f,vq),vr)) . qh),((V,f,vq) . (vr,A))},{((FunctionalFAF ((V,f,vq),vr)) . qh)}} is non empty set
the addF of F_Complex . [((FunctionalFAF ((V,f,vq),vr)) . qh),((V,f,vq) . (vr,A))] is set
K135(((FunctionalFAF ((V,f,vq),vr)) . qh),((V,f,vq) . (vr,A))) is complex Element of COMPLEX
((FunctionalFAF ((V,f,vq),vr)) . qh) + ((FunctionalFAF ((V,f,vq),vr)) . A) is complex Element of the carrier of F_Complex
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveSAF Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,vq) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
vr is Element of the carrier of f
FunctionalSAF ((V,f,vq),vr) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
qh is Element of the carrier of V
A is Element of the carrier of V
qh + A is Element of the carrier of V
the addF of V is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is set
the addF of V . (qh,A) is Element of the carrier of V
[qh,A] is set
{qh,A} is non empty set
{qh} is non empty set
{{qh,A},{qh}} is non empty set
the addF of V . [qh,A] is set
(FunctionalSAF ((V,f,vq),vr)) . (qh + A) is complex Element of the carrier of F_Complex
(FunctionalSAF ((V,f,vq),vr)) . qh is complex Element of the carrier of F_Complex
(FunctionalSAF ((V,f,vq),vr)) . A is complex Element of the carrier of F_Complex
((FunctionalSAF ((V,f,vq),vr)) . qh) + ((FunctionalSAF ((V,f,vq),vr)) . A) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . (((FunctionalSAF ((V,f,vq),vr)) . qh),((FunctionalSAF ((V,f,vq),vr)) . A)) is complex Element of the carrier of F_Complex
[((FunctionalSAF ((V,f,vq),vr)) . qh),((FunctionalSAF ((V,f,vq),vr)) . A)] is set
{((FunctionalSAF ((V,f,vq),vr)) . qh),((FunctionalSAF ((V,f,vq),vr)) . A)} is non empty V175() set
{((FunctionalSAF ((V,f,vq),vr)) . qh)} is non empty V175() set
{{((FunctionalSAF ((V,f,vq),vr)) . qh),((FunctionalSAF ((V,f,vq),vr)) . A)},{((FunctionalSAF ((V,f,vq),vr)) . qh)}} is non empty set
the addF of F_Complex . [((FunctionalSAF ((V,f,vq),vr)) . qh),((FunctionalSAF ((V,f,vq),vr)) . A)] is set
K135(((FunctionalSAF ((V,f,vq),vr)) . qh),((FunctionalSAF ((V,f,vq),vr)) . A)) is complex Element of COMPLEX
(V,f,vq) . ((qh + A),vr) is complex Element of the carrier of F_Complex
[(qh + A),vr] is set
{(qh + A),vr} is non empty set
{(qh + A)} is non empty set
{{(qh + A),vr},{(qh + A)}} is non empty set
(V,f,vq) . [(qh + A),vr] is set
vq . ((qh + A),vr) is complex Element of the carrier of F_Complex
vq . [(qh + A),vr] is set
(vq . ((qh + A),vr)) *' is complex Element of the carrier of F_Complex
Re (vq . ((qh + A),vr)) is complex real ext-real Element of REAL
Im (vq . ((qh + A),vr)) is complex real ext-real Element of REAL
(Im (vq . ((qh + A),vr))) * <i> is complex set
(Re (vq . ((qh + A),vr))) - ((Im (vq . ((qh + A),vr))) * <i>) is complex set
vq . (qh,vr) is complex Element of the carrier of F_Complex
[qh,vr] is set
{qh,vr} is non empty set
{{qh,vr},{qh}} is non empty set
vq . [qh,vr] is set
vq . (A,vr) is complex Element of the carrier of F_Complex
[A,vr] is set
{A,vr} is non empty set
{A} is non empty set
{{A,vr},{A}} is non empty set
vq . [A,vr] is set
(vq . (qh,vr)) + (vq . (A,vr)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vq . (qh,vr)),(vq . (A,vr))) is complex Element of the carrier of F_Complex
[(vq . (qh,vr)),(vq . (A,vr))] is set
{(vq . (qh,vr)),(vq . (A,vr))} is non empty V175() set
{(vq . (qh,vr))} is non empty V175() set
{{(vq . (qh,vr)),(vq . (A,vr))},{(vq . (qh,vr))}} is non empty set
the addF of F_Complex . [(vq . (qh,vr)),(vq . (A,vr))] is set
K135((vq . (qh,vr)),(vq . (A,vr))) is complex Element of COMPLEX
((vq . (qh,vr)) + (vq . (A,vr))) *' is complex Element of the carrier of F_Complex
Re ((vq . (qh,vr)) + (vq . (A,vr))) is complex real ext-real Element of REAL
Im ((vq . (qh,vr)) + (vq . (A,vr))) is complex real ext-real Element of REAL
(Im ((vq . (qh,vr)) + (vq . (A,vr)))) * <i> is complex set
(Re ((vq . (qh,vr)) + (vq . (A,vr)))) - ((Im ((vq . (qh,vr)) + (vq . (A,vr)))) * <i>) is complex set
(vq . (qh,vr)) *' is complex Element of the carrier of F_Complex
Re (vq . (qh,vr)) is complex real ext-real Element of REAL
Im (vq . (qh,vr)) is complex real ext-real Element of REAL
(Im (vq . (qh,vr))) * <i> is complex set
(Re (vq . (qh,vr))) - ((Im (vq . (qh,vr))) * <i>) is complex set
(vq . (A,vr)) *' is complex Element of the carrier of F_Complex
Re (vq . (A,vr)) is complex real ext-real Element of REAL
Im (vq . (A,vr)) is complex real ext-real Element of REAL
(Im (vq . (A,vr))) * <i> is complex set
(Re (vq . (A,vr))) - ((Im (vq . (A,vr))) * <i>) is complex set
((vq . (qh,vr)) *') + ((vq . (A,vr)) *') is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vq . (qh,vr)) *'),((vq . (A,vr)) *')) is complex Element of the carrier of F_Complex
[((vq . (qh,vr)) *'),((vq . (A,vr)) *')] is set
{((vq . (qh,vr)) *'),((vq . (A,vr)) *')} is non empty V175() set
{((vq . (qh,vr)) *')} is non empty V175() set
{{((vq . (qh,vr)) *'),((vq . (A,vr)) *')},{((vq . (qh,vr)) *')}} is non empty set
the addF of F_Complex . [((vq . (qh,vr)) *'),((vq . (A,vr)) *')] is set
K135(((vq . (qh,vr)) *'),((vq . (A,vr)) *')) is complex Element of COMPLEX
(V,f,vq) . (qh,vr) is complex Element of the carrier of F_Complex
(V,f,vq) . [qh,vr] is set
((V,f,vq) . (qh,vr)) + ((vq . (A,vr)) *') is complex Element of the carrier of F_Complex
the addF of F_Complex . (((V,f,vq) . (qh,vr)),((vq . (A,vr)) *')) is complex Element of the carrier of F_Complex
[((V,f,vq) . (qh,vr)),((vq . (A,vr)) *')] is set
{((V,f,vq) . (qh,vr)),((vq . (A,vr)) *')} is non empty V175() set
{((V,f,vq) . (qh,vr))} is non empty V175() set
{{((V,f,vq) . (qh,vr)),((vq . (A,vr)) *')},{((V,f,vq) . (qh,vr))}} is non empty set
the addF of F_Complex . [((V,f,vq) . (qh,vr)),((vq . (A,vr)) *')] is set
K135(((V,f,vq) . (qh,vr)),((vq . (A,vr)) *')) is complex Element of COMPLEX
(V,f,vq) . (A,vr) is complex Element of the carrier of F_Complex
(V,f,vq) . [A,vr] is set
((V,f,vq) . (qh,vr)) + ((V,f,vq) . (A,vr)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((V,f,vq) . (qh,vr)),((V,f,vq) . (A,vr))) is complex Element of the carrier of F_Complex
[((V,f,vq) . (qh,vr)),((V,f,vq) . (A,vr))] is set
{((V,f,vq) . (qh,vr)),((V,f,vq) . (A,vr))} is non empty V175() set
{{((V,f,vq) . (qh,vr)),((V,f,vq) . (A,vr))},{((V,f,vq) . (qh,vr))}} is non empty set
the addF of F_Complex . [((V,f,vq) . (qh,vr)),((V,f,vq) . (A,vr))] is set
K135(((V,f,vq) . (qh,vr)),((V,f,vq) . (A,vr))) is complex Element of COMPLEX
((FunctionalSAF ((V,f,vq),vr)) . qh) + ((V,f,vq) . (A,vr)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((FunctionalSAF ((V,f,vq),vr)) . qh),((V,f,vq) . (A,vr))) is complex Element of the carrier of F_Complex
[((FunctionalSAF ((V,f,vq),vr)) . qh),((V,f,vq) . (A,vr))] is set
{((FunctionalSAF ((V,f,vq),vr)) . qh),((V,f,vq) . (A,vr))} is non empty V175() set
{{((FunctionalSAF ((V,f,vq),vr)) . qh),((V,f,vq) . (A,vr))},{((FunctionalSAF ((V,f,vq),vr)) . qh)}} is non empty set
the addF of F_Complex . [((FunctionalSAF ((V,f,vq),vr)) . qh),((V,f,vq) . (A,vr))] is set
K135(((FunctionalSAF ((V,f,vq),vr)) . qh),((V,f,vq) . (A,vr))) is complex Element of COMPLEX
((FunctionalSAF ((V,f,vq),vr)) . qh) + ((FunctionalSAF ((V,f,vq),vr)) . A) is complex Element of the carrier of F_Complex
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) homogeneousFAF Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,vq) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
vr is Element of the carrier of V
FunctionalFAF ((V,f,vq),vr) is V16() V19( the carrier of f) V20( the carrier of F_Complex) Function-like V30( the carrier of f, the carrier of F_Complex) Element of bool [: the carrier of f, the carrier of F_Complex:]
[: the carrier of f, the carrier of F_Complex:] is set
bool [: the carrier of f, the carrier of F_Complex:] is set
qh is Element of the carrier of f
(FunctionalFAF ((V,f,vq),vr)) . qh is complex Element of the carrier of F_Complex
A is complex Element of the carrier of F_Complex
A * qh is Element of the carrier of f
the lmult of f is V16() V19([: the carrier of F_Complex, the carrier of f:]) V20( the carrier of f) Function-like V30([: the carrier of F_Complex, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of F_Complex, the carrier of f:], the carrier of f:]
[: the carrier of F_Complex, the carrier of f:] is set
[:[: the carrier of F_Complex, the carrier of f:], the carrier of f:] is set
bool [:[: the carrier of F_Complex, the carrier of f:], the carrier of f:] is set
the lmult of f . (A,qh) is Element of the carrier of f
[A,qh] is set
{A,qh} is non empty set
{A} is non empty V175() set
{{A,qh},{A}} is non empty set
the lmult of f . [A,qh] is set
(FunctionalFAF ((V,f,vq),vr)) . (A * qh) is complex Element of the carrier of F_Complex
A *' is complex Element of the carrier of F_Complex
Re A is complex real ext-real Element of REAL
Im A is complex real ext-real Element of REAL
(Im A) * <i> is complex set
(Re A) - ((Im A) * <i>) is complex set
(A *') * ((FunctionalFAF ((V,f,vq),vr)) . qh) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((A *'),((FunctionalFAF ((V,f,vq),vr)) . qh)) is complex Element of the carrier of F_Complex
[(A *'),((FunctionalFAF ((V,f,vq),vr)) . qh)] is set
{(A *'),((FunctionalFAF ((V,f,vq),vr)) . qh)} is non empty V175() set
{(A *')} is non empty V175() set
{{(A *'),((FunctionalFAF ((V,f,vq),vr)) . qh)},{(A *')}} is non empty set
the multF of F_Complex . [(A *'),((FunctionalFAF ((V,f,vq),vr)) . qh)] is set
K137((A *'),((FunctionalFAF ((V,f,vq),vr)) . qh)) is complex Element of COMPLEX
(V,f,vq) . (vr,(A * qh)) is complex Element of the carrier of F_Complex
[vr,(A * qh)] is set
{vr,(A * qh)} is non empty set
{vr} is non empty set
{{vr,(A * qh)},{vr}} is non empty set
(V,f,vq) . [vr,(A * qh)] is set
vq . (vr,(A * qh)) is complex Element of the carrier of F_Complex
vq . [vr,(A * qh)] is set
(vq . (vr,(A * qh))) *' is complex Element of the carrier of F_Complex
Re (vq . (vr,(A * qh))) is complex real ext-real Element of REAL
Im (vq . (vr,(A * qh))) is complex real ext-real Element of REAL
(Im (vq . (vr,(A * qh)))) * <i> is complex set
(Re (vq . (vr,(A * qh)))) - ((Im (vq . (vr,(A * qh)))) * <i>) is complex set
vq . (vr,qh) is complex Element of the carrier of F_Complex
[vr,qh] is set
{vr,qh} is non empty set
{{vr,qh},{vr}} is non empty set
vq . [vr,qh] is set
A * (vq . (vr,qh)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (A,(vq . (vr,qh))) is complex Element of the carrier of F_Complex
[A,(vq . (vr,qh))] is set
{A,(vq . (vr,qh))} is non empty V175() set
{{A,(vq . (vr,qh))},{A}} is non empty set
the multF of F_Complex . [A,(vq . (vr,qh))] is set
K137(A,(vq . (vr,qh))) is complex Element of COMPLEX
(A * (vq . (vr,qh))) *' is complex Element of the carrier of F_Complex
Re (A * (vq . (vr,qh))) is complex real ext-real Element of REAL
Im (A * (vq . (vr,qh))) is complex real ext-real Element of REAL
(Im (A * (vq . (vr,qh)))) * <i> is complex set
(Re (A * (vq . (vr,qh)))) - ((Im (A * (vq . (vr,qh)))) * <i>) is complex set
(vq . (vr,qh)) *' is complex Element of the carrier of F_Complex
Re (vq . (vr,qh)) is complex real ext-real Element of REAL
Im (vq . (vr,qh)) is complex real ext-real Element of REAL
(Im (vq . (vr,qh))) * <i> is complex set
(Re (vq . (vr,qh))) - ((Im (vq . (vr,qh))) * <i>) is complex set
(A *') * ((vq . (vr,qh)) *') is complex Element of the carrier of F_Complex
the multF of F_Complex . ((A *'),((vq . (vr,qh)) *')) is complex Element of the carrier of F_Complex
[(A *'),((vq . (vr,qh)) *')] is set
{(A *'),((vq . (vr,qh)) *')} is non empty V175() set
{{(A *'),((vq . (vr,qh)) *')},{(A *')}} is non empty set
the multF of F_Complex . [(A *'),((vq . (vr,qh)) *')] is set
K137((A *'),((vq . (vr,qh)) *')) is complex Element of COMPLEX
(V,f,vq) . (vr,qh) is complex Element of the carrier of F_Complex
(V,f,vq) . [vr,qh] is set
(A *') * ((V,f,vq) . (vr,qh)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((A *'),((V,f,vq) . (vr,qh))) is complex Element of the carrier of F_Complex
[(A *'),((V,f,vq) . (vr,qh))] is set
{(A *'),((V,f,vq) . (vr,qh))} is non empty V175() set
{{(A *'),((V,f,vq) . (vr,qh))},{(A *')}} is non empty set
the multF of F_Complex . [(A *'),((V,f,vq) . (vr,qh))] is set
K137((A *'),((V,f,vq) . (vr,qh))) is complex Element of COMPLEX
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,vq) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
vr is Element of the carrier of V
FunctionalFAF ((V,f,vq),vr) is V16() V19( the carrier of f) V20( the carrier of F_Complex) Function-like V30( the carrier of f, the carrier of F_Complex) Element of bool [: the carrier of f, the carrier of F_Complex:]
[: the carrier of f, the carrier of F_Complex:] is set
bool [: the carrier of f, the carrier of F_Complex:] is set
qh is Element of the carrier of f
(FunctionalFAF ((V,f,vq),vr)) . qh is complex Element of the carrier of F_Complex
A is complex Element of the carrier of F_Complex
A * qh is Element of the carrier of f
the lmult of f is V16() V19([: the carrier of F_Complex, the carrier of f:]) V20( the carrier of f) Function-like V30([: the carrier of F_Complex, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of F_Complex, the carrier of f:], the carrier of f:]
[: the carrier of F_Complex, the carrier of f:] is set
[:[: the carrier of F_Complex, the carrier of f:], the carrier of f:] is set
bool [:[: the carrier of F_Complex, the carrier of f:], the carrier of f:] is set
the lmult of f . (A,qh) is Element of the carrier of f
[A,qh] is set
{A,qh} is non empty set
{A} is non empty V175() set
{{A,qh},{A}} is non empty set
the lmult of f . [A,qh] is set
(FunctionalFAF ((V,f,vq),vr)) . (A * qh) is complex Element of the carrier of F_Complex
A * ((FunctionalFAF ((V,f,vq),vr)) . qh) is complex Element of the carrier of F_Complex
the multF of F_Complex . (A,((FunctionalFAF ((V,f,vq),vr)) . qh)) is complex Element of the carrier of F_Complex
[A,((FunctionalFAF ((V,f,vq),vr)) . qh)] is set
{A,((FunctionalFAF ((V,f,vq),vr)) . qh)} is non empty V175() set
{{A,((FunctionalFAF ((V,f,vq),vr)) . qh)},{A}} is non empty set
the multF of F_Complex . [A,((FunctionalFAF ((V,f,vq),vr)) . qh)] is set
K137(A,((FunctionalFAF ((V,f,vq),vr)) . qh)) is complex Element of COMPLEX
(V,f,vq) . (vr,(A * qh)) is complex Element of the carrier of F_Complex
[vr,(A * qh)] is set
{vr,(A * qh)} is non empty set
{vr} is non empty set
{{vr,(A * qh)},{vr}} is non empty set
(V,f,vq) . [vr,(A * qh)] is set
vq . (vr,(A * qh)) is complex Element of the carrier of F_Complex
vq . [vr,(A * qh)] is set
(vq . (vr,(A * qh))) *' is complex Element of the carrier of F_Complex
Re (vq . (vr,(A * qh))) is complex real ext-real Element of REAL
Im (vq . (vr,(A * qh))) is complex real ext-real Element of REAL
(Im (vq . (vr,(A * qh)))) * <i> is complex set
(Re (vq . (vr,(A * qh)))) - ((Im (vq . (vr,(A * qh)))) * <i>) is complex set
A *' is complex Element of the carrier of F_Complex
Re A is complex real ext-real Element of REAL
Im A is complex real ext-real Element of REAL
(Im A) * <i> is complex set
(Re A) - ((Im A) * <i>) is complex set
vq . (vr,qh) is complex Element of the carrier of F_Complex
[vr,qh] is set
{vr,qh} is non empty set
{{vr,qh},{vr}} is non empty set
vq . [vr,qh] is set
(A *') * (vq . (vr,qh)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((A *'),(vq . (vr,qh))) is complex Element of the carrier of F_Complex
[(A *'),(vq . (vr,qh))] is set
{(A *'),(vq . (vr,qh))} is non empty V175() set
{(A *')} is non empty V175() set
{{(A *'),(vq . (vr,qh))},{(A *')}} is non empty set
the multF of F_Complex . [(A *'),(vq . (vr,qh))] is set
K137((A *'),(vq . (vr,qh))) is complex Element of COMPLEX
((A *') * (vq . (vr,qh))) *' is complex Element of the carrier of F_Complex
Re ((A *') * (vq . (vr,qh))) is complex real ext-real Element of REAL
Im ((A *') * (vq . (vr,qh))) is complex real ext-real Element of REAL
(Im ((A *') * (vq . (vr,qh)))) * <i> is complex set
(Re ((A *') * (vq . (vr,qh)))) - ((Im ((A *') * (vq . (vr,qh)))) * <i>) is complex set
(A *') *' is complex Element of the carrier of F_Complex
Re (A *') is complex real ext-real Element of REAL
Im (A *') is complex real ext-real Element of REAL
(Im (A *')) * <i> is complex set
(Re (A *')) - ((Im (A *')) * <i>) is complex set
(vq . (vr,qh)) *' is complex Element of the carrier of F_Complex
Re (vq . (vr,qh)) is complex real ext-real Element of REAL
Im (vq . (vr,qh)) is complex real ext-real Element of REAL
(Im (vq . (vr,qh))) * <i> is complex set
(Re (vq . (vr,qh))) - ((Im (vq . (vr,qh))) * <i>) is complex set
((A *') *') * ((vq . (vr,qh)) *') is complex Element of the carrier of F_Complex
the multF of F_Complex . (((A *') *'),((vq . (vr,qh)) *')) is complex Element of the carrier of F_Complex
[((A *') *'),((vq . (vr,qh)) *')] is set
{((A *') *'),((vq . (vr,qh)) *')} is non empty V175() set
{((A *') *')} is non empty V175() set
{{((A *') *'),((vq . (vr,qh)) *')},{((A *') *')}} is non empty set
the multF of F_Complex . [((A *') *'),((vq . (vr,qh)) *')] is set
K137(((A *') *'),((vq . (vr,qh)) *')) is complex Element of COMPLEX
(V,f,vq) . (vr,qh) is complex Element of the carrier of F_Complex
(V,f,vq) . [vr,qh] is set
A * ((V,f,vq) . (vr,qh)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (A,((V,f,vq) . (vr,qh))) is complex Element of the carrier of F_Complex
[A,((V,f,vq) . (vr,qh))] is set
{A,((V,f,vq) . (vr,qh))} is non empty V175() set
{{A,((V,f,vq) . (vr,qh))},{A}} is non empty set
the multF of F_Complex . [A,((V,f,vq) . (vr,qh))] is set
K137(A,((V,f,vq) . (vr,qh))) is complex Element of COMPLEX
A * ((FunctionalFAF ((V,f,vq),vr)) . qh) is complex Element of the carrier of F_Complex
V is non empty non trivial right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty non trivial set
f is non empty non trivial right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of f is non empty non trivial set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like non constant V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,vq) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
dom vq is V16() V19( the carrier of V) V20( the carrier of f) Element of bool [: the carrier of V, the carrier of f:]
bool [: the carrier of V, the carrier of f:] is set
vr is set
qh is set
vq . vr is set
vq . qh is set
A is Element of the carrier of V
K is Element of the carrier of f
[A,K] is set
{A,K} is non empty set
{A} is non empty set
{{A,K},{A}} is non empty set
K93((V,f,vq)) is V16() set
(V,f,vq) . vr is set
(V,f,vq) . qh is set
x is Element of the carrier of V
A is Element of the carrier of f
[x,A] is set
{x,A} is non empty set
{x} is non empty set
{{x,A},{x}} is non empty set
(V,f,vq) . (x,A) is complex Element of the carrier of F_Complex
(V,f,vq) . [x,A] is set
(V,f,vq) . (A,K) is complex Element of the carrier of F_Complex
(V,f,vq) . [A,K] is set
vq . (x,A) is complex Element of the carrier of F_Complex
vq . [x,A] is set
(vq . (x,A)) *' is complex Element of the carrier of F_Complex
Re (vq . (x,A)) is complex real ext-real Element of REAL
Im (vq . (x,A)) is complex real ext-real Element of REAL
(Im (vq . (x,A))) * <i> is complex set
(Re (vq . (x,A))) - ((Im (vq . (x,A))) * <i>) is complex set
((vq . (x,A)) *') *' is complex Element of the carrier of F_Complex
Re ((vq . (x,A)) *') is complex real ext-real Element of REAL
Im ((vq . (x,A)) *') is complex real ext-real Element of REAL
(Im ((vq . (x,A)) *')) * <i> is complex set
(Re ((vq . (x,A)) *')) - ((Im ((vq . (x,A)) *')) * <i>) is complex set
((V,f,vq) . (A,K)) *' is complex Element of the carrier of F_Complex
Re ((V,f,vq) . (A,K)) is complex real ext-real Element of REAL
Im ((V,f,vq) . (A,K)) is complex real ext-real Element of REAL
(Im ((V,f,vq) . (A,K))) * <i> is complex set
(Re ((V,f,vq) . (A,K))) - ((Im ((V,f,vq) . (A,K))) * <i>) is complex set
vq . (A,K) is complex Element of the carrier of F_Complex
vq . [A,K] is set
(vq . (A,K)) *' is complex Element of the carrier of F_Complex
Re (vq . (A,K)) is complex real ext-real Element of REAL
Im (vq . (A,K)) is complex real ext-real Element of REAL
(Im (vq . (A,K))) * <i> is complex set
(Re (vq . (A,K))) - ((Im (vq . (A,K))) * <i>) is complex set
((vq . (A,K)) *') *' is complex Element of the carrier of F_Complex
Re ((vq . (A,K)) *') is complex real ext-real Element of REAL
Im ((vq . (A,K)) *') is complex real ext-real Element of REAL
(Im ((vq . (A,K)) *')) * <i> is complex set
(Re ((vq . (A,K)) *')) - ((Im ((vq . (A,K)) *')) * <i>) is complex set
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,f) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
FormFunctional (f,(V,f)) is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
vq is Element of the carrier of V
(FormFunctional (f,(V,f))) . (vq,vq) is complex Element of the carrier of F_Complex
[vq,vq] is set
{vq,vq} is non empty set
{vq} is non empty set
{{vq,vq},{vq}} is non empty set
(FormFunctional (f,(V,f))) . [vq,vq] is set
f . vq is complex Element of the carrier of F_Complex
|.(f . vq).| is complex real ext-real Element of REAL
Re (f . vq) is complex real ext-real Element of REAL
(Re (f . vq)) ^2 is complex real ext-real Element of REAL
(Re (f . vq)) * (Re (f . vq)) is complex real ext-real set
Im (f . vq) is complex real ext-real Element of REAL
(Im (f . vq)) ^2 is complex real ext-real Element of REAL
(Im (f . vq)) * (Im (f . vq)) is complex real ext-real set
((Re (f . vq)) ^2) + ((Im (f . vq)) ^2) is complex real ext-real Element of REAL
sqrt (((Re (f . vq)) ^2) + ((Im (f . vq)) ^2)) is complex real ext-real Element of REAL
|.(f . vq).| ^2 is complex real ext-real Element of REAL
|.(f . vq).| * |.(f . vq).| is complex real ext-real set
(V,f) . vq is complex Element of the carrier of F_Complex
(f . vq) * ((V,f) . vq) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((f . vq),((V,f) . vq)) is complex Element of the carrier of F_Complex
[(f . vq),((V,f) . vq)] is set
{(f . vq),((V,f) . vq)} is non empty V175() set
{(f . vq)} is non empty V175() set
{{(f . vq),((V,f) . vq)},{(f . vq)}} is non empty set
the multF of F_Complex . [(f . vq),((V,f) . vq)] is set
K137((f . vq),((V,f) . vq)) is complex Element of COMPLEX
(f . vq) *' is complex Element of the carrier of F_Complex
(Im (f . vq)) * <i> is complex set
(Re (f . vq)) - ((Im (f . vq)) * <i>) is complex set
(f . vq) * ((f . vq) *') is complex Element of the carrier of F_Complex
the multF of F_Complex . ((f . vq),((f . vq) *')) is complex Element of the carrier of F_Complex
[(f . vq),((f . vq) *')] is set
{(f . vq),((f . vq) *')} is non empty V175() set
{{(f . vq),((f . vq) *')},{(f . vq)}} is non empty set
the multF of F_Complex . [(f . vq),((f . vq) *')] is set
K137((f . vq),((f . vq) *')) is complex Element of COMPLEX
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
f is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
(V,f) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
FormFunctional (f,(V,f)) is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
vr is Element of the carrier of V
(FormFunctional (f,(V,f))) . (vr,vr) is complex Element of the carrier of F_Complex
[vr,vr] is set
{vr,vr} is non empty set
{vr} is non empty set
{{vr,vr},{vr}} is non empty set
(FormFunctional (f,(V,f))) . [vr,vr] is set
Re ((FormFunctional (f,(V,f))) . (vr,vr)) is complex real ext-real Element of REAL
f . vr is complex Element of the carrier of F_Complex
|.(f . vr).| is complex real ext-real Element of REAL
Re (f . vr) is complex real ext-real Element of REAL
(Re (f . vr)) ^2 is complex real ext-real Element of REAL
(Re (f . vr)) * (Re (f . vr)) is complex real ext-real set
Im (f . vr) is complex real ext-real Element of REAL
(Im (f . vr)) ^2 is complex real ext-real Element of REAL
(Im (f . vr)) * (Im (f . vr)) is complex real ext-real set
((Re (f . vr)) ^2) + ((Im (f . vr)) ^2) is complex real ext-real Element of REAL
sqrt (((Re (f . vr)) ^2) + ((Im (f . vr)) ^2)) is complex real ext-real Element of REAL
|.(f . vr).| ^2 is complex real ext-real Element of REAL
|.(f . vr).| * |.(f . vr).| is complex real ext-real set
(|.(f . vr).| ^2) + (0 * <i>) is complex set
Im ((FormFunctional (f,(V,f))) . (vr,vr)) is complex real ext-real Element of REAL
(Im ((FormFunctional (f,(V,f))) . (vr,vr))) * <i> is complex set
(Re ((FormFunctional (f,(V,f))) . (vr,vr))) + ((Im ((FormFunctional (f,(V,f))) . (vr,vr))) * <i>) is complex set
vr is Element of the carrier of V
qh is Element of the carrier of V
(FormFunctional (f,(V,f))) . (vr,qh) is complex Element of the carrier of F_Complex
[vr,qh] is set
{vr,qh} is non empty set
{vr} is non empty set
{{vr,qh},{vr}} is non empty set
(FormFunctional (f,(V,f))) . [vr,qh] is set
(FormFunctional (f,(V,f))) . (qh,vr) is complex Element of the carrier of F_Complex
[qh,vr] is set
{qh,vr} is non empty set
{qh} is non empty set
{{qh,vr},{qh}} is non empty set
(FormFunctional (f,(V,f))) . [qh,vr] is set
((FormFunctional (f,(V,f))) . (qh,vr)) *' is complex Element of the carrier of F_Complex
Re ((FormFunctional (f,(V,f))) . (qh,vr)) is complex real ext-real Element of REAL
Im ((FormFunctional (f,(V,f))) . (qh,vr)) is complex real ext-real Element of REAL
(Im ((FormFunctional (f,(V,f))) . (qh,vr))) * <i> is complex set
(Re ((FormFunctional (f,(V,f))) . (qh,vr))) - ((Im ((FormFunctional (f,(V,f))) . (qh,vr))) * <i>) is complex set
f . vr is complex Element of the carrier of F_Complex
(V,f) . qh is complex Element of the carrier of F_Complex
(f . vr) * ((V,f) . qh) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((f . vr),((V,f) . qh)) is complex Element of the carrier of F_Complex
[(f . vr),((V,f) . qh)] is set
{(f . vr),((V,f) . qh)} is non empty V175() set
{(f . vr)} is non empty V175() set
{{(f . vr),((V,f) . qh)},{(f . vr)}} is non empty set
the multF of F_Complex . [(f . vr),((V,f) . qh)] is set
K137((f . vr),((V,f) . qh)) is complex Element of COMPLEX
((f . vr) * ((V,f) . qh)) *' is complex Element of the carrier of F_Complex
Re ((f . vr) * ((V,f) . qh)) is complex real ext-real Element of REAL
Im ((f . vr) * ((V,f) . qh)) is complex real ext-real Element of REAL
(Im ((f . vr) * ((V,f) . qh))) * <i> is complex set
(Re ((f . vr) * ((V,f) . qh))) - ((Im ((f . vr) * ((V,f) . qh))) * <i>) is complex set
(((f . vr) * ((V,f) . qh)) *') *' is complex Element of the carrier of F_Complex
Re (((f . vr) * ((V,f) . qh)) *') is complex real ext-real Element of REAL
Im (((f . vr) * ((V,f) . qh)) *') is complex real ext-real Element of REAL
(Im (((f . vr) * ((V,f) . qh)) *')) * <i> is complex set
(Re (((f . vr) * ((V,f) . qh)) *')) - ((Im (((f . vr) * ((V,f) . qh)) *')) * <i>) is complex set
f . qh is complex Element of the carrier of F_Complex
(f . qh) *' is complex Element of the carrier of F_Complex
Re (f . qh) is complex real ext-real Element of REAL
Im (f . qh) is complex real ext-real Element of REAL
(Im (f . qh)) * <i> is complex set
(Re (f . qh)) - ((Im (f . qh)) * <i>) is complex set
(f . vr) * ((f . qh) *') is complex Element of the carrier of F_Complex
the multF of F_Complex . ((f . vr),((f . qh) *')) is complex Element of the carrier of F_Complex
[(f . vr),((f . qh) *')] is set
{(f . vr),((f . qh) *')} is non empty V175() set
{{(f . vr),((f . qh) *')},{(f . vr)}} is non empty set
the multF of F_Complex . [(f . vr),((f . qh) *')] is set
K137((f . vr),((f . qh) *')) is complex Element of COMPLEX
((f . vr) * ((f . qh) *')) *' is complex Element of the carrier of F_Complex
Re ((f . vr) * ((f . qh) *')) is complex real ext-real Element of REAL
Im ((f . vr) * ((f . qh) *')) is complex real ext-real Element of REAL
(Im ((f . vr) * ((f . qh) *'))) * <i> is complex set
(Re ((f . vr) * ((f . qh) *'))) - ((Im ((f . vr) * ((f . qh) *'))) * <i>) is complex set
(((f . vr) * ((f . qh) *')) *') *' is complex Element of the carrier of F_Complex
Re (((f . vr) * ((f . qh) *')) *') is complex real ext-real Element of REAL
Im (((f . vr) * ((f . qh) *')) *') is complex real ext-real Element of REAL
(Im (((f . vr) * ((f . qh) *')) *')) * <i> is complex set
(Re (((f . vr) * ((f . qh) *')) *')) - ((Im (((f . vr) * ((f . qh) *')) *')) * <i>) is complex set
(f . vr) *' is complex Element of the carrier of F_Complex
Re (f . vr) is complex real ext-real Element of REAL
Im (f . vr) is complex real ext-real Element of REAL
(Im (f . vr)) * <i> is complex set
(Re (f . vr)) - ((Im (f . vr)) * <i>) is complex set
((f . qh) *') *' is complex Element of the carrier of F_Complex
Re ((f . qh) *') is complex real ext-real Element of REAL
Im ((f . qh) *') is complex real ext-real Element of REAL
(Im ((f . qh) *')) * <i> is complex set
(Re ((f . qh) *')) - ((Im ((f . qh) *')) * <i>) is complex set
((f . vr) *') * (((f . qh) *') *') is complex Element of the carrier of F_Complex
the multF of F_Complex . (((f . vr) *'),(((f . qh) *') *')) is complex Element of the carrier of F_Complex
[((f . vr) *'),(((f . qh) *') *')] is set
{((f . vr) *'),(((f . qh) *') *')} is non empty V175() set
{((f . vr) *')} is non empty V175() set
{{((f . vr) *'),(((f . qh) *') *')},{((f . vr) *')}} is non empty set
the multF of F_Complex . [((f . vr) *'),(((f . qh) *') *')] is set
K137(((f . vr) *'),(((f . qh) *') *')) is complex Element of COMPLEX
(((f . vr) *') * (((f . qh) *') *')) *' is complex Element of the carrier of F_Complex
Re (((f . vr) *') * (((f . qh) *') *')) is complex real ext-real Element of REAL
Im (((f . vr) *') * (((f . qh) *') *')) is complex real ext-real Element of REAL
(Im (((f . vr) *') * (((f . qh) *') *'))) * <i> is complex set
(Re (((f . vr) *') * (((f . qh) *') *'))) - ((Im (((f . vr) *') * (((f . qh) *') *'))) * <i>) is complex set
(V,f) . vr is complex Element of the carrier of F_Complex
(f . qh) * ((V,f) . vr) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((f . qh),((V,f) . vr)) is complex Element of the carrier of F_Complex
[(f . qh),((V,f) . vr)] is set
{(f . qh),((V,f) . vr)} is non empty V175() set
{(f . qh)} is non empty V175() set
{{(f . qh),((V,f) . vr)},{(f . qh)}} is non empty set
the multF of F_Complex . [(f . qh),((V,f) . vr)] is set
K137((f . qh),((V,f) . vr)) is complex Element of COMPLEX
((f . qh) * ((V,f) . vr)) *' is complex Element of the carrier of F_Complex
Re ((f . qh) * ((V,f) . vr)) is complex real ext-real Element of REAL
Im ((f . qh) * ((V,f) . vr)) is complex real ext-real Element of REAL
(Im ((f . qh) * ((V,f) . vr))) * <i> is complex set
(Re ((f . qh) * ((V,f) . vr))) - ((Im ((f . qh) * ((V,f) . vr))) * <i>) is complex set
vr is Element of the carrier of V
(FormFunctional (f,(V,f))) . (vr,vr) is complex Element of the carrier of F_Complex
[vr,vr] is set
{vr,vr} is non empty set
{vr} is non empty set
{{vr,vr},{vr}} is non empty set
(FormFunctional (f,(V,f))) . [vr,vr] is set
Im ((FormFunctional (f,(V,f))) . (vr,vr)) is complex real ext-real Element of REAL
f . vr is complex Element of the carrier of F_Complex
|.(f . vr).| is complex real ext-real Element of REAL
Re (f . vr) is complex real ext-real Element of REAL
(Re (f . vr)) ^2 is complex real ext-real Element of REAL
(Re (f . vr)) * (Re (f . vr)) is complex real ext-real set
Im (f . vr) is complex real ext-real Element of REAL
(Im (f . vr)) ^2 is complex real ext-real Element of REAL
(Im (f . vr)) * (Im (f . vr)) is complex real ext-real set
((Re (f . vr)) ^2) + ((Im (f . vr)) ^2) is complex real ext-real Element of REAL
sqrt (((Re (f . vr)) ^2) + ((Im (f . vr)) ^2)) is complex real ext-real Element of REAL
|.(f . vr).| ^2 is complex real ext-real Element of REAL
|.(f . vr).| * |.(f . vr).| is complex real ext-real set
[**(|.(f . vr).| ^2),0**] is complex Element of the carrier of F_Complex
(|.(f . vr).| ^2) + (0 * <i>) is complex set
Re ((FormFunctional (f,(V,f))) . (vr,vr)) is complex real ext-real Element of REAL
(Im ((FormFunctional (f,(V,f))) . (vr,vr))) * <i> is complex set
(Re ((FormFunctional (f,(V,f))) . (vr,vr))) + ((Im ((FormFunctional (f,(V,f))) . (vr,vr))) * <i>) is complex set
V is non empty non trivial right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty non trivial set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
the non trivial V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like non constant V30( the carrier of V, the carrier of F_Complex) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of F_Complex:] is non trivial V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like non constant V30( the carrier of V, the carrier of F_Complex) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of F_Complex:]
(V, the non trivial V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like non constant V30( the carrier of V, the carrier of F_Complex) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of F_Complex:]) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like non constant V30( the carrier of V, the carrier of F_Complex) V30( the carrier of V, the carrier of F_Complex) additive 0-preserving (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
FormFunctional ( the non trivial V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like non constant V30( the carrier of V, the carrier of F_Complex) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of F_Complex:],(V, the non trivial V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like non constant V30( the carrier of V, the carrier of F_Complex) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of F_Complex:])) is non trivial V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like non constant V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,V) (V) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,vq) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,(V,f,vq)) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
vr is Element of the carrier of V
qh is Element of the carrier of f
(V,f,(V,f,vq)) . (vr,qh) is complex Element of the carrier of F_Complex
[vr,qh] is set
{vr,qh} is non empty set
{vr} is non empty set
{{vr,qh},{vr}} is non empty set
(V,f,(V,f,vq)) . [vr,qh] is set
(V,f,vq) . (vr,qh) is complex Element of the carrier of F_Complex
(V,f,vq) . [vr,qh] is set
((V,f,vq) . (vr,qh)) *' is complex Element of the carrier of F_Complex
Re ((V,f,vq) . (vr,qh)) is complex real ext-real Element of REAL
Im ((V,f,vq) . (vr,qh)) is complex real ext-real Element of REAL
(Im ((V,f,vq) . (vr,qh))) * <i> is complex set
(Re ((V,f,vq) . (vr,qh))) - ((Im ((V,f,vq) . (vr,qh))) * <i>) is complex set
vq . (vr,qh) is complex Element of the carrier of F_Complex
vq . [vr,qh] is set
(vq . (vr,qh)) *' is complex Element of the carrier of F_Complex
Re (vq . (vr,qh)) is complex real ext-real Element of REAL
Im (vq . (vr,qh)) is complex real ext-real Element of REAL
(Im (vq . (vr,qh))) * <i> is complex set
(Re (vq . (vr,qh))) - ((Im (vq . (vr,qh))) * <i>) is complex set
((vq . (vr,qh)) *') *' is complex Element of the carrier of F_Complex
Re ((vq . (vr,qh)) *') is complex real ext-real Element of REAL
Im ((vq . (vr,qh)) *') is complex real ext-real Element of REAL
(Im ((vq . (vr,qh)) *')) * <i> is complex set
(Re ((vq . (vr,qh)) *')) - ((Im ((vq . (vr,qh)) *')) * <i>) is complex set
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
NulForm (V,f) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF homogeneousSAF (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
K402( the carrier of F_Complex,[: the carrier of V, the carrier of f:],(0. F_Complex)) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,(NulForm (V,f))) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
vr is Element of the carrier of V
qh is Element of the carrier of f
(V,f,(NulForm (V,f))) . (vr,qh) is complex Element of the carrier of F_Complex
[vr,qh] is set
{vr,qh} is non empty set
{vr} is non empty set
{{vr,qh},{vr}} is non empty set
(V,f,(NulForm (V,f))) . [vr,qh] is set
(NulForm (V,f)) . (vr,qh) is complex Element of the carrier of F_Complex
(NulForm (V,f)) . [vr,qh] is set
((NulForm (V,f)) . (vr,qh)) *' is complex Element of the carrier of F_Complex
Re ((NulForm (V,f)) . (vr,qh)) is complex real ext-real Element of REAL
Im ((NulForm (V,f)) . (vr,qh)) is complex real ext-real Element of REAL
(Im ((NulForm (V,f)) . (vr,qh))) * <i> is complex set
(Re ((NulForm (V,f)) . (vr,qh))) - ((Im ((NulForm (V,f)) . (vr,qh))) * <i>) is complex set
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
vr is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
vq + vr is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,(vq + vr)) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,vq) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,vr) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,vq) + (V,f,vr) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
qh is Element of the carrier of V
A is Element of the carrier of f
(V,f,(vq + vr)) . (qh,A) is complex Element of the carrier of F_Complex
[qh,A] is set
{qh,A} is non empty set
{qh} is non empty set
{{qh,A},{qh}} is non empty set
(V,f,(vq + vr)) . [qh,A] is set
(vq + vr) . (qh,A) is complex Element of the carrier of F_Complex
(vq + vr) . [qh,A] is set
((vq + vr) . (qh,A)) *' is complex Element of the carrier of F_Complex
Re ((vq + vr) . (qh,A)) is complex real ext-real Element of REAL
Im ((vq + vr) . (qh,A)) is complex real ext-real Element of REAL
(Im ((vq + vr) . (qh,A))) * <i> is complex set
(Re ((vq + vr) . (qh,A))) - ((Im ((vq + vr) . (qh,A))) * <i>) is complex set
vq . (qh,A) is complex Element of the carrier of F_Complex
vq . [qh,A] is set
vr . (qh,A) is complex Element of the carrier of F_Complex
vr . [qh,A] is set
(vq . (qh,A)) + (vr . (qh,A)) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . ((vq . (qh,A)),(vr . (qh,A))) is complex Element of the carrier of F_Complex
[(vq . (qh,A)),(vr . (qh,A))] is set
{(vq . (qh,A)),(vr . (qh,A))} is non empty V175() set
{(vq . (qh,A))} is non empty V175() set
{{(vq . (qh,A)),(vr . (qh,A))},{(vq . (qh,A))}} is non empty set
the addF of F_Complex . [(vq . (qh,A)),(vr . (qh,A))] is set
K135((vq . (qh,A)),(vr . (qh,A))) is complex Element of COMPLEX
((vq . (qh,A)) + (vr . (qh,A))) *' is complex Element of the carrier of F_Complex
Re ((vq . (qh,A)) + (vr . (qh,A))) is complex real ext-real Element of REAL
Im ((vq . (qh,A)) + (vr . (qh,A))) is complex real ext-real Element of REAL
(Im ((vq . (qh,A)) + (vr . (qh,A)))) * <i> is complex set
(Re ((vq . (qh,A)) + (vr . (qh,A)))) - ((Im ((vq . (qh,A)) + (vr . (qh,A)))) * <i>) is complex set
(vq . (qh,A)) *' is complex Element of the carrier of F_Complex
Re (vq . (qh,A)) is complex real ext-real Element of REAL
Im (vq . (qh,A)) is complex real ext-real Element of REAL
(Im (vq . (qh,A))) * <i> is complex set
(Re (vq . (qh,A))) - ((Im (vq . (qh,A))) * <i>) is complex set
(vr . (qh,A)) *' is complex Element of the carrier of F_Complex
Re (vr . (qh,A)) is complex real ext-real Element of REAL
Im (vr . (qh,A)) is complex real ext-real Element of REAL
(Im (vr . (qh,A))) * <i> is complex set
(Re (vr . (qh,A))) - ((Im (vr . (qh,A))) * <i>) is complex set
((vq . (qh,A)) *') + ((vr . (qh,A)) *') is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vq . (qh,A)) *'),((vr . (qh,A)) *')) is complex Element of the carrier of F_Complex
[((vq . (qh,A)) *'),((vr . (qh,A)) *')] is set
{((vq . (qh,A)) *'),((vr . (qh,A)) *')} is non empty V175() set
{((vq . (qh,A)) *')} is non empty V175() set
{{((vq . (qh,A)) *'),((vr . (qh,A)) *')},{((vq . (qh,A)) *')}} is non empty set
the addF of F_Complex . [((vq . (qh,A)) *'),((vr . (qh,A)) *')] is set
K135(((vq . (qh,A)) *'),((vr . (qh,A)) *')) is complex Element of COMPLEX
(V,f,vq) . (qh,A) is complex Element of the carrier of F_Complex
(V,f,vq) . [qh,A] is set
((V,f,vq) . (qh,A)) + ((vr . (qh,A)) *') is complex Element of the carrier of F_Complex
the addF of F_Complex . (((V,f,vq) . (qh,A)),((vr . (qh,A)) *')) is complex Element of the carrier of F_Complex
[((V,f,vq) . (qh,A)),((vr . (qh,A)) *')] is set
{((V,f,vq) . (qh,A)),((vr . (qh,A)) *')} is non empty V175() set
{((V,f,vq) . (qh,A))} is non empty V175() set
{{((V,f,vq) . (qh,A)),((vr . (qh,A)) *')},{((V,f,vq) . (qh,A))}} is non empty set
the addF of F_Complex . [((V,f,vq) . (qh,A)),((vr . (qh,A)) *')] is set
K135(((V,f,vq) . (qh,A)),((vr . (qh,A)) *')) is complex Element of COMPLEX
(V,f,vr) . (qh,A) is complex Element of the carrier of F_Complex
(V,f,vr) . [qh,A] is set
((V,f,vq) . (qh,A)) + ((V,f,vr) . (qh,A)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((V,f,vq) . (qh,A)),((V,f,vr) . (qh,A))) is complex Element of the carrier of F_Complex
[((V,f,vq) . (qh,A)),((V,f,vr) . (qh,A))] is set
{((V,f,vq) . (qh,A)),((V,f,vr) . (qh,A))} is non empty V175() set
{{((V,f,vq) . (qh,A)),((V,f,vr) . (qh,A))},{((V,f,vq) . (qh,A))}} is non empty set
the addF of F_Complex . [((V,f,vq) . (qh,A)),((V,f,vr) . (qh,A))] is set
K135(((V,f,vq) . (qh,A)),((V,f,vr) . (qh,A))) is complex Element of COMPLEX
((V,f,vq) + (V,f,vr)) . (qh,A) is complex Element of the carrier of F_Complex
((V,f,vq) + (V,f,vr)) . [qh,A] is set
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
- vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(- (1. F_Complex)) * vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,(- vq)) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,vq) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
- (V,f,vq) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(- (1. F_Complex)) * (V,f,vq) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
vr is Element of the carrier of V
qh is Element of the carrier of f
(V,f,(- vq)) . (vr,qh) is complex Element of the carrier of F_Complex
[vr,qh] is set
{vr,qh} is non empty set
{vr} is non empty set
{{vr,qh},{vr}} is non empty set
(V,f,(- vq)) . [vr,qh] is set
(- vq) . (vr,qh) is complex Element of the carrier of F_Complex
(- vq) . [vr,qh] is set
((- vq) . (vr,qh)) *' is complex Element of the carrier of F_Complex
Re ((- vq) . (vr,qh)) is complex real ext-real Element of REAL
Im ((- vq) . (vr,qh)) is complex real ext-real Element of REAL
(Im ((- vq) . (vr,qh))) * <i> is complex set
(Re ((- vq) . (vr,qh))) - ((Im ((- vq) . (vr,qh))) * <i>) is complex set
vq . (vr,qh) is complex Element of the carrier of F_Complex
vq . [vr,qh] is set
- (vq . (vr,qh)) is complex Element of the carrier of F_Complex
(- (vq . (vr,qh))) *' is complex Element of the carrier of F_Complex
Re (- (vq . (vr,qh))) is complex real ext-real Element of REAL
Im (- (vq . (vr,qh))) is complex real ext-real Element of REAL
(Im (- (vq . (vr,qh)))) * <i> is complex set
(Re (- (vq . (vr,qh)))) - ((Im (- (vq . (vr,qh)))) * <i>) is complex set
(vq . (vr,qh)) *' is complex Element of the carrier of F_Complex
Re (vq . (vr,qh)) is complex real ext-real Element of REAL
Im (vq . (vr,qh)) is complex real ext-real Element of REAL
(Im (vq . (vr,qh))) * <i> is complex set
(Re (vq . (vr,qh))) - ((Im (vq . (vr,qh))) * <i>) is complex set
- ((vq . (vr,qh)) *') is complex Element of the carrier of F_Complex
(V,f,vq) . (vr,qh) is complex Element of the carrier of F_Complex
(V,f,vq) . [vr,qh] is set
- ((V,f,vq) . (vr,qh)) is complex Element of the carrier of F_Complex
(- (V,f,vq)) . (vr,qh) is complex Element of the carrier of F_Complex
(- (V,f,vq)) . [vr,qh] is set
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,vq) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
vr is complex Element of the carrier of F_Complex
vr * vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,(vr * vq)) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
vr *' is complex Element of the carrier of F_Complex
Re vr is complex real ext-real Element of REAL
Im vr is complex real ext-real Element of REAL
(Im vr) * <i> is complex set
(Re vr) - ((Im vr) * <i>) is complex set
(vr *') * (V,f,vq) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
qh is Element of the carrier of V
A is Element of the carrier of f
(V,f,(vr * vq)) . (qh,A) is complex Element of the carrier of F_Complex
[qh,A] is set
{qh,A} is non empty set
{qh} is non empty set
{{qh,A},{qh}} is non empty set
(V,f,(vr * vq)) . [qh,A] is set
(vr * vq) . (qh,A) is complex Element of the carrier of F_Complex
(vr * vq) . [qh,A] is set
((vr * vq) . (qh,A)) *' is complex Element of the carrier of F_Complex
Re ((vr * vq) . (qh,A)) is complex real ext-real Element of REAL
Im ((vr * vq) . (qh,A)) is complex real ext-real Element of REAL
(Im ((vr * vq) . (qh,A))) * <i> is complex set
(Re ((vr * vq) . (qh,A))) - ((Im ((vr * vq) . (qh,A))) * <i>) is complex set
vq . (qh,A) is complex Element of the carrier of F_Complex
vq . [qh,A] is set
vr * (vq . (qh,A)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (vr,(vq . (qh,A))) is complex Element of the carrier of F_Complex
[vr,(vq . (qh,A))] is set
{vr,(vq . (qh,A))} is non empty V175() set
{vr} is non empty V175() set
{{vr,(vq . (qh,A))},{vr}} is non empty set
the multF of F_Complex . [vr,(vq . (qh,A))] is set
K137(vr,(vq . (qh,A))) is complex Element of COMPLEX
(vr * (vq . (qh,A))) *' is complex Element of the carrier of F_Complex
Re (vr * (vq . (qh,A))) is complex real ext-real Element of REAL
Im (vr * (vq . (qh,A))) is complex real ext-real Element of REAL
(Im (vr * (vq . (qh,A)))) * <i> is complex set
(Re (vr * (vq . (qh,A)))) - ((Im (vr * (vq . (qh,A)))) * <i>) is complex set
(vq . (qh,A)) *' is complex Element of the carrier of F_Complex
Re (vq . (qh,A)) is complex real ext-real Element of REAL
Im (vq . (qh,A)) is complex real ext-real Element of REAL
(Im (vq . (qh,A))) * <i> is complex set
(Re (vq . (qh,A))) - ((Im (vq . (qh,A))) * <i>) is complex set
(vr *') * ((vq . (qh,A)) *') is complex Element of the carrier of F_Complex
the multF of F_Complex . ((vr *'),((vq . (qh,A)) *')) is complex Element of the carrier of F_Complex
[(vr *'),((vq . (qh,A)) *')] is set
{(vr *'),((vq . (qh,A)) *')} is non empty V175() set
{(vr *')} is non empty V175() set
{{(vr *'),((vq . (qh,A)) *')},{(vr *')}} is non empty set
the multF of F_Complex . [(vr *'),((vq . (qh,A)) *')] is set
K137((vr *'),((vq . (qh,A)) *')) is complex Element of COMPLEX
(V,f,vq) . (qh,A) is complex Element of the carrier of F_Complex
(V,f,vq) . [qh,A] is set
(vr *') * ((V,f,vq) . (qh,A)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((vr *'),((V,f,vq) . (qh,A))) is complex Element of the carrier of F_Complex
[(vr *'),((V,f,vq) . (qh,A))] is set
{(vr *'),((V,f,vq) . (qh,A))} is non empty V175() set
{{(vr *'),((V,f,vq) . (qh,A))},{(vr *')}} is non empty set
the multF of F_Complex . [(vr *'),((V,f,vq) . (qh,A))] is set
K137((vr *'),((V,f,vq) . (qh,A))) is complex Element of COMPLEX
((vr *') * (V,f,vq)) . (qh,A) is complex Element of the carrier of F_Complex
((vr *') * (V,f,vq)) . [qh,A] is set
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
vr is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
vq - vr is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
- vr is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(- (1. F_Complex)) * vr is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
vq + (- vr) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,(vq - vr)) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,vq) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,vr) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,vq) - (V,f,vr) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
- (V,f,vr) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(- (1. F_Complex)) * (V,f,vr) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,vq) + (- (V,f,vr)) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,(- vr)) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,vq) + (V,f,(- vr)) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of f is non empty set
vq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of vq is non empty set
[: the carrier of f, the carrier of vq:] is set
[:[: the carrier of f, the carrier of vq:], the carrier of F_Complex:] is set
bool [:[: the carrier of f, the carrier of vq:], the carrier of F_Complex:] is set
vr is Element of the carrier of f
qh is Element of the carrier of vq
A is Element of the carrier of vq
qh - A is Element of the carrier of vq
- A is Element of the carrier of vq
qh + (- A) is Element of the carrier of vq
the addF of vq is V16() V19([: the carrier of vq, the carrier of vq:]) V20( the carrier of vq) Function-like V30([: the carrier of vq, the carrier of vq:], the carrier of vq) Element of bool [:[: the carrier of vq, the carrier of vq:], the carrier of vq:]
[: the carrier of vq, the carrier of vq:] is set
[:[: the carrier of vq, the carrier of vq:], the carrier of vq:] is set
bool [:[: the carrier of vq, the carrier of vq:], the carrier of vq:] is set
the addF of vq . (qh,(- A)) is Element of the carrier of vq
[qh,(- A)] is set
{qh,(- A)} is non empty set
{qh} is non empty set
{{qh,(- A)},{qh}} is non empty set
the addF of vq . [qh,(- A)] is set
K is V16() V19([: the carrier of f, the carrier of vq:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of f, the carrier of vq:], the carrier of F_Complex) additiveFAF (f,vq) Element of bool [:[: the carrier of f, the carrier of vq:], the carrier of F_Complex:]
K . (vr,(qh - A)) is complex Element of the carrier of F_Complex
[vr,(qh - A)] is set
{vr,(qh - A)} is non empty set
{vr} is non empty set
{{vr,(qh - A)},{vr}} is non empty set
K . [vr,(qh - A)] is set
K . (vr,qh) is complex Element of the carrier of F_Complex
[vr,qh] is set
{vr,qh} is non empty set
{{vr,qh},{vr}} is non empty set
K . [vr,qh] is set
K . (vr,A) is complex Element of the carrier of F_Complex
[vr,A] is set
{vr,A} is non empty set
{{vr,A},{vr}} is non empty set
K . [vr,A] is set
(K . (vr,qh)) - (K . (vr,A)) is complex Element of the carrier of F_Complex
- (K . (vr,A)) is complex Element of the carrier of F_Complex
(K . (vr,qh)) + (- (K . (vr,A))) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . ((K . (vr,qh)),(- (K . (vr,A)))) is complex Element of the carrier of F_Complex
[(K . (vr,qh)),(- (K . (vr,A)))] is set
{(K . (vr,qh)),(- (K . (vr,A)))} is non empty V175() set
{(K . (vr,qh))} is non empty V175() set
{{(K . (vr,qh)),(- (K . (vr,A)))},{(K . (vr,qh))}} is non empty set
the addF of F_Complex . [(K . (vr,qh)),(- (K . (vr,A)))] is set
K135((K . (vr,qh)),(- (K . (vr,A)))) is complex Element of COMPLEX
K . (vr,(- A)) is complex Element of the carrier of F_Complex
[vr,(- A)] is set
{vr,(- A)} is non empty set
{{vr,(- A)},{vr}} is non empty set
K . [vr,(- A)] is set
(K . (vr,qh)) + (K . (vr,(- A))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((K . (vr,qh)),(K . (vr,(- A)))) is complex Element of the carrier of F_Complex
[(K . (vr,qh)),(K . (vr,(- A)))] is set
{(K . (vr,qh)),(K . (vr,(- A)))} is non empty V175() set
{{(K . (vr,qh)),(K . (vr,(- A)))},{(K . (vr,qh))}} is non empty set
the addF of F_Complex . [(K . (vr,qh)),(K . (vr,(- A)))] is set
K135((K . (vr,qh)),(K . (vr,(- A)))) is complex Element of COMPLEX
(- (1_ F_Complex)) * A is Element of the carrier of vq
the lmult of vq is V16() V19([: the carrier of F_Complex, the carrier of vq:]) V20( the carrier of vq) Function-like V30([: the carrier of F_Complex, the carrier of vq:], the carrier of vq) Element of bool [:[: the carrier of F_Complex, the carrier of vq:], the carrier of vq:]
[: the carrier of F_Complex, the carrier of vq:] is set
[:[: the carrier of F_Complex, the carrier of vq:], the carrier of vq:] is set
bool [:[: the carrier of F_Complex, the carrier of vq:], the carrier of vq:] is set
the lmult of vq . ((- (1_ F_Complex)),A) is Element of the carrier of vq
[(- (1_ F_Complex)),A] is set
{(- (1_ F_Complex)),A} is non empty set
{(- (1_ F_Complex))} is non empty V175() set
{{(- (1_ F_Complex)),A},{(- (1_ F_Complex))}} is non empty set
the lmult of vq . [(- (1_ F_Complex)),A] is set
K . (vr,((- (1_ F_Complex)) * A)) is complex Element of the carrier of F_Complex
[vr,((- (1_ F_Complex)) * A)] is set
{vr,((- (1_ F_Complex)) * A)} is non empty set
{{vr,((- (1_ F_Complex)) * A)},{vr}} is non empty set
K . [vr,((- (1_ F_Complex)) * A)] is set
(K . (vr,qh)) + (K . (vr,((- (1_ F_Complex)) * A))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((K . (vr,qh)),(K . (vr,((- (1_ F_Complex)) * A)))) is complex Element of the carrier of F_Complex
[(K . (vr,qh)),(K . (vr,((- (1_ F_Complex)) * A)))] is set
{(K . (vr,qh)),(K . (vr,((- (1_ F_Complex)) * A)))} is non empty V175() set
{{(K . (vr,qh)),(K . (vr,((- (1_ F_Complex)) * A)))},{(K . (vr,qh))}} is non empty set
the addF of F_Complex . [(K . (vr,qh)),(K . (vr,((- (1_ F_Complex)) * A)))] is set
K135((K . (vr,qh)),(K . (vr,((- (1_ F_Complex)) * A)))) is complex Element of COMPLEX
(- (1. F_Complex)) *' is complex Element of the carrier of F_Complex
Re (- (1. F_Complex)) is complex real ext-real Element of REAL
Im (- (1. F_Complex)) is complex real ext-real Element of REAL
(Im (- (1. F_Complex))) * <i> is complex set
(Re (- (1. F_Complex))) - ((Im (- (1. F_Complex))) * <i>) is complex set
((- (1. F_Complex)) *') * (K . (vr,A)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((- (1. F_Complex)) *'),(K . (vr,A))) is complex Element of the carrier of F_Complex
[((- (1. F_Complex)) *'),(K . (vr,A))] is set
{((- (1. F_Complex)) *'),(K . (vr,A))} is non empty V175() set
{((- (1. F_Complex)) *')} is non empty V175() set
{{((- (1. F_Complex)) *'),(K . (vr,A))},{((- (1. F_Complex)) *')}} is non empty set
the multF of F_Complex . [((- (1. F_Complex)) *'),(K . (vr,A))] is set
K137(((- (1. F_Complex)) *'),(K . (vr,A))) is complex Element of COMPLEX
(K . (vr,qh)) + (((- (1. F_Complex)) *') * (K . (vr,A))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((K . (vr,qh)),(((- (1. F_Complex)) *') * (K . (vr,A)))) is complex Element of the carrier of F_Complex
[(K . (vr,qh)),(((- (1. F_Complex)) *') * (K . (vr,A)))] is set
{(K . (vr,qh)),(((- (1. F_Complex)) *') * (K . (vr,A)))} is non empty V175() set
{{(K . (vr,qh)),(((- (1. F_Complex)) *') * (K . (vr,A)))},{(K . (vr,qh))}} is non empty set
the addF of F_Complex . [(K . (vr,qh)),(((- (1. F_Complex)) *') * (K . (vr,A)))] is set
K135((K . (vr,qh)),(((- (1. F_Complex)) *') * (K . (vr,A)))) is complex Element of COMPLEX
(- (1_ F_Complex)) * (K . (vr,A)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((- (1_ F_Complex)),(K . (vr,A))) is complex Element of the carrier of F_Complex
[(- (1_ F_Complex)),(K . (vr,A))] is set
{(- (1_ F_Complex)),(K . (vr,A))} is non empty V175() set
{{(- (1_ F_Complex)),(K . (vr,A))},{(- (1_ F_Complex))}} is non empty set
the multF of F_Complex . [(- (1_ F_Complex)),(K . (vr,A))] is set
K137((- (1_ F_Complex)),(K . (vr,A))) is complex Element of COMPLEX
(K . (vr,qh)) + ((- (1_ F_Complex)) * (K . (vr,A))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((K . (vr,qh)),((- (1_ F_Complex)) * (K . (vr,A)))) is complex Element of the carrier of F_Complex
[(K . (vr,qh)),((- (1_ F_Complex)) * (K . (vr,A)))] is set
{(K . (vr,qh)),((- (1_ F_Complex)) * (K . (vr,A)))} is non empty V175() set
{{(K . (vr,qh)),((- (1_ F_Complex)) * (K . (vr,A)))},{(K . (vr,qh))}} is non empty set
the addF of F_Complex . [(K . (vr,qh)),((- (1_ F_Complex)) * (K . (vr,A)))] is set
K135((K . (vr,qh)),((- (1_ F_Complex)) * (K . (vr,A)))) is complex Element of COMPLEX
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is Element of the carrier of V
vr is Element of the carrier of V
vq - vr is Element of the carrier of V
- vr is Element of the carrier of V
vq + (- vr) is Element of the carrier of V
the addF of V is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is set
the addF of V . (vq,(- vr)) is Element of the carrier of V
[vq,(- vr)] is set
{vq,(- vr)} is non empty set
{vq} is non empty set
{{vq,(- vr)},{vq}} is non empty set
the addF of V . [vq,(- vr)] is set
qh is Element of the carrier of f
A is Element of the carrier of f
qh - A is Element of the carrier of f
- A is Element of the carrier of f
qh + (- A) is Element of the carrier of f
the addF of f is V16() V19([: the carrier of f, the carrier of f:]) V20( the carrier of f) Function-like V30([: the carrier of f, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of f, the carrier of f:], the carrier of f:]
[: the carrier of f, the carrier of f:] is set
[:[: the carrier of f, the carrier of f:], the carrier of f:] is set
bool [:[: the carrier of f, the carrier of f:], the carrier of f:] is set
the addF of f . (qh,(- A)) is Element of the carrier of f
[qh,(- A)] is set
{qh,(- A)} is non empty set
{qh} is non empty set
{{qh,(- A)},{qh}} is non empty set
the addF of f . [qh,(- A)] is set
K is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
K . ((vq - vr),(qh - A)) is complex Element of the carrier of F_Complex
[(vq - vr),(qh - A)] is set
{(vq - vr),(qh - A)} is non empty set
{(vq - vr)} is non empty set
{{(vq - vr),(qh - A)},{(vq - vr)}} is non empty set
K . [(vq - vr),(qh - A)] is set
K . (vq,qh) is complex Element of the carrier of F_Complex
[vq,qh] is set
{vq,qh} is non empty set
{{vq,qh},{vq}} is non empty set
K . [vq,qh] is set
K . (vq,A) is complex Element of the carrier of F_Complex
[vq,A] is set
{vq,A} is non empty set
{{vq,A},{vq}} is non empty set
K . [vq,A] is set
(K . (vq,qh)) - (K . (vq,A)) is complex Element of the carrier of F_Complex
- (K . (vq,A)) is complex Element of the carrier of F_Complex
(K . (vq,qh)) + (- (K . (vq,A))) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . ((K . (vq,qh)),(- (K . (vq,A)))) is complex Element of the carrier of F_Complex
[(K . (vq,qh)),(- (K . (vq,A)))] is set
{(K . (vq,qh)),(- (K . (vq,A)))} is non empty V175() set
{(K . (vq,qh))} is non empty V175() set
{{(K . (vq,qh)),(- (K . (vq,A)))},{(K . (vq,qh))}} is non empty set
the addF of F_Complex . [(K . (vq,qh)),(- (K . (vq,A)))] is set
K135((K . (vq,qh)),(- (K . (vq,A)))) is complex Element of COMPLEX
K . (vr,qh) is complex Element of the carrier of F_Complex
[vr,qh] is set
{vr,qh} is non empty set
{vr} is non empty set
{{vr,qh},{vr}} is non empty set
K . [vr,qh] is set
K . (vr,A) is complex Element of the carrier of F_Complex
[vr,A] is set
{vr,A} is non empty set
{{vr,A},{vr}} is non empty set
K . [vr,A] is set
(K . (vr,qh)) - (K . (vr,A)) is complex Element of the carrier of F_Complex
- (K . (vr,A)) is complex Element of the carrier of F_Complex
(K . (vr,qh)) + (- (K . (vr,A))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((K . (vr,qh)),(- (K . (vr,A)))) is complex Element of the carrier of F_Complex
[(K . (vr,qh)),(- (K . (vr,A)))] is set
{(K . (vr,qh)),(- (K . (vr,A)))} is non empty V175() set
{(K . (vr,qh))} is non empty V175() set
{{(K . (vr,qh)),(- (K . (vr,A)))},{(K . (vr,qh))}} is non empty set
the addF of F_Complex . [(K . (vr,qh)),(- (K . (vr,A)))] is set
K135((K . (vr,qh)),(- (K . (vr,A)))) is complex Element of COMPLEX
((K . (vq,qh)) - (K . (vq,A))) - ((K . (vr,qh)) - (K . (vr,A))) is complex Element of the carrier of F_Complex
- ((K . (vr,qh)) - (K . (vr,A))) is complex Element of the carrier of F_Complex
((K . (vq,qh)) - (K . (vq,A))) + (- ((K . (vr,qh)) - (K . (vr,A)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((K . (vq,qh)) - (K . (vq,A))),(- ((K . (vr,qh)) - (K . (vr,A))))) is complex Element of the carrier of F_Complex
[((K . (vq,qh)) - (K . (vq,A))),(- ((K . (vr,qh)) - (K . (vr,A))))] is set
{((K . (vq,qh)) - (K . (vq,A))),(- ((K . (vr,qh)) - (K . (vr,A))))} is non empty V175() set
{((K . (vq,qh)) - (K . (vq,A)))} is non empty V175() set
{{((K . (vq,qh)) - (K . (vq,A))),(- ((K . (vr,qh)) - (K . (vr,A))))},{((K . (vq,qh)) - (K . (vq,A)))}} is non empty set
the addF of F_Complex . [((K . (vq,qh)) - (K . (vq,A))),(- ((K . (vr,qh)) - (K . (vr,A))))] is set
K135(((K . (vq,qh)) - (K . (vq,A))),(- ((K . (vr,qh)) - (K . (vr,A))))) is complex Element of COMPLEX
K . (vq,(qh - A)) is complex Element of the carrier of F_Complex
[vq,(qh - A)] is set
{vq,(qh - A)} is non empty set
{{vq,(qh - A)},{vq}} is non empty set
K . [vq,(qh - A)] is set
K . (vr,(qh - A)) is complex Element of the carrier of F_Complex
[vr,(qh - A)] is set
{vr,(qh - A)} is non empty set
{{vr,(qh - A)},{vr}} is non empty set
K . [vr,(qh - A)] is set
(K . (vq,(qh - A))) - (K . (vr,(qh - A))) is complex Element of the carrier of F_Complex
- (K . (vr,(qh - A))) is complex Element of the carrier of F_Complex
(K . (vq,(qh - A))) + (- (K . (vr,(qh - A)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((K . (vq,(qh - A))),(- (K . (vr,(qh - A))))) is complex Element of the carrier of F_Complex
[(K . (vq,(qh - A))),(- (K . (vr,(qh - A))))] is set
{(K . (vq,(qh - A))),(- (K . (vr,(qh - A))))} is non empty V175() set
{(K . (vq,(qh - A)))} is non empty V175() set
{{(K . (vq,(qh - A))),(- (K . (vr,(qh - A))))},{(K . (vq,(qh - A)))}} is non empty set
the addF of F_Complex . [(K . (vq,(qh - A))),(- (K . (vr,(qh - A))))] is set
K135((K . (vq,(qh - A))),(- (K . (vr,(qh - A))))) is complex Element of COMPLEX
((K . (vq,qh)) - (K . (vq,A))) - (K . (vr,(qh - A))) is complex Element of the carrier of F_Complex
((K . (vq,qh)) - (K . (vq,A))) + (- (K . (vr,(qh - A)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((K . (vq,qh)) - (K . (vq,A))),(- (K . (vr,(qh - A))))) is complex Element of the carrier of F_Complex
[((K . (vq,qh)) - (K . (vq,A))),(- (K . (vr,(qh - A))))] is set
{((K . (vq,qh)) - (K . (vq,A))),(- (K . (vr,(qh - A))))} is non empty V175() set
{{((K . (vq,qh)) - (K . (vq,A))),(- (K . (vr,(qh - A))))},{((K . (vq,qh)) - (K . (vq,A)))}} is non empty set
the addF of F_Complex . [((K . (vq,qh)) - (K . (vq,A))),(- (K . (vr,(qh - A))))] is set
K135(((K . (vq,qh)) - (K . (vq,A))),(- (K . (vr,(qh - A))))) is complex Element of COMPLEX
V is non empty right_complementable add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty right_complementable add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is Element of the carrier of V
vr is Element of the carrier of V
qh is Element of the carrier of f
A is Element of the carrier of f
K is complex Element of the carrier of F_Complex
K * vr is Element of the carrier of V
the lmult of V is V16() V19([: the carrier of F_Complex, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of F_Complex, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:]
[: the carrier of F_Complex, the carrier of V:] is set
[:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
the lmult of V . (K,vr) is Element of the carrier of V
[K,vr] is set
{K,vr} is non empty set
{K} is non empty V175() set
{{K,vr},{K}} is non empty set
the lmult of V . [K,vr] is set
vq + (K * vr) is Element of the carrier of V
the addF of V is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is set
the addF of V . (vq,(K * vr)) is Element of the carrier of V
[vq,(K * vr)] is set
{vq,(K * vr)} is non empty set
{vq} is non empty set
{{vq,(K * vr)},{vq}} is non empty set
the addF of V . [vq,(K * vr)] is set
x is complex Element of the carrier of F_Complex
x * A is Element of the carrier of f
the lmult of f is V16() V19([: the carrier of F_Complex, the carrier of f:]) V20( the carrier of f) Function-like V30([: the carrier of F_Complex, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of F_Complex, the carrier of f:], the carrier of f:]
[: the carrier of F_Complex, the carrier of f:] is set
[:[: the carrier of F_Complex, the carrier of f:], the carrier of f:] is set
bool [:[: the carrier of F_Complex, the carrier of f:], the carrier of f:] is set
the lmult of f . (x,A) is Element of the carrier of f
[x,A] is set
{x,A} is non empty set
{x} is non empty V175() set
{{x,A},{x}} is non empty set
the lmult of f . [x,A] is set
qh + (x * A) is Element of the carrier of f
the addF of f is V16() V19([: the carrier of f, the carrier of f:]) V20( the carrier of f) Function-like V30([: the carrier of f, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of f, the carrier of f:], the carrier of f:]
[: the carrier of f, the carrier of f:] is set
[:[: the carrier of f, the carrier of f:], the carrier of f:] is set
bool [:[: the carrier of f, the carrier of f:], the carrier of f:] is set
the addF of f . (qh,(x * A)) is Element of the carrier of f
[qh,(x * A)] is set
{qh,(x * A)} is non empty set
{qh} is non empty set
{{qh,(x * A)},{qh}} is non empty set
the addF of f . [qh,(x * A)] is set
x *' is complex Element of the carrier of F_Complex
Re x is complex real ext-real Element of REAL
Im x is complex real ext-real Element of REAL
(Im x) * <i> is complex set
(Re x) - ((Im x) * <i>) is complex set
A is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
A . ((vq + (K * vr)),(qh + (x * A))) is complex Element of the carrier of F_Complex
[(vq + (K * vr)),(qh + (x * A))] is set
{(vq + (K * vr)),(qh + (x * A))} is non empty set
{(vq + (K * vr))} is non empty set
{{(vq + (K * vr)),(qh + (x * A))},{(vq + (K * vr))}} is non empty set
A . [(vq + (K * vr)),(qh + (x * A))] is set
A . (vq,qh) is complex Element of the carrier of F_Complex
[vq,qh] is set
{vq,qh} is non empty set
{{vq,qh},{vq}} is non empty set
A . [vq,qh] is set
A . (vq,A) is complex Element of the carrier of F_Complex
[vq,A] is set
{vq,A} is non empty set
{{vq,A},{vq}} is non empty set
A . [vq,A] is set
(x *') * (A . (vq,A)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((x *'),(A . (vq,A))) is complex Element of the carrier of F_Complex
[(x *'),(A . (vq,A))] is set
{(x *'),(A . (vq,A))} is non empty V175() set
{(x *')} is non empty V175() set
{{(x *'),(A . (vq,A))},{(x *')}} is non empty set
the multF of F_Complex . [(x *'),(A . (vq,A))] is set
K137((x *'),(A . (vq,A))) is complex Element of COMPLEX
(A . (vq,qh)) + ((x *') * (A . (vq,A))) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . ((A . (vq,qh)),((x *') * (A . (vq,A)))) is complex Element of the carrier of F_Complex
[(A . (vq,qh)),((x *') * (A . (vq,A)))] is set
{(A . (vq,qh)),((x *') * (A . (vq,A)))} is non empty V175() set
{(A . (vq,qh))} is non empty V175() set
{{(A . (vq,qh)),((x *') * (A . (vq,A)))},{(A . (vq,qh))}} is non empty set
the addF of F_Complex . [(A . (vq,qh)),((x *') * (A . (vq,A)))] is set
K135((A . (vq,qh)),((x *') * (A . (vq,A)))) is complex Element of COMPLEX
A . (vr,qh) is complex Element of the carrier of F_Complex
[vr,qh] is set
{vr,qh} is non empty set
{vr} is non empty set
{{vr,qh},{vr}} is non empty set
A . [vr,qh] is set
K * (A . (vr,qh)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (K,(A . (vr,qh))) is complex Element of the carrier of F_Complex
[K,(A . (vr,qh))] is set
{K,(A . (vr,qh))} is non empty V175() set
{{K,(A . (vr,qh))},{K}} is non empty set
the multF of F_Complex . [K,(A . (vr,qh))] is set
K137(K,(A . (vr,qh))) is complex Element of COMPLEX
A . (vr,A) is complex Element of the carrier of F_Complex
[vr,A] is set
{vr,A} is non empty set
{{vr,A},{vr}} is non empty set
A . [vr,A] is set
(x *') * (A . (vr,A)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((x *'),(A . (vr,A))) is complex Element of the carrier of F_Complex
[(x *'),(A . (vr,A))] is set
{(x *'),(A . (vr,A))} is non empty V175() set
{{(x *'),(A . (vr,A))},{(x *')}} is non empty set
the multF of F_Complex . [(x *'),(A . (vr,A))] is set
K137((x *'),(A . (vr,A))) is complex Element of COMPLEX
K * ((x *') * (A . (vr,A))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (K,((x *') * (A . (vr,A)))) is complex Element of the carrier of F_Complex
[K,((x *') * (A . (vr,A)))] is set
{K,((x *') * (A . (vr,A)))} is non empty V175() set
{{K,((x *') * (A . (vr,A)))},{K}} is non empty set
the multF of F_Complex . [K,((x *') * (A . (vr,A)))] is set
K137(K,((x *') * (A . (vr,A)))) is complex Element of COMPLEX
(K * (A . (vr,qh))) + (K * ((x *') * (A . (vr,A)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((K * (A . (vr,qh))),(K * ((x *') * (A . (vr,A))))) is complex Element of the carrier of F_Complex
[(K * (A . (vr,qh))),(K * ((x *') * (A . (vr,A))))] is set
{(K * (A . (vr,qh))),(K * ((x *') * (A . (vr,A))))} is non empty V175() set
{(K * (A . (vr,qh)))} is non empty V175() set
{{(K * (A . (vr,qh))),(K * ((x *') * (A . (vr,A))))},{(K * (A . (vr,qh)))}} is non empty set
the addF of F_Complex . [(K * (A . (vr,qh))),(K * ((x *') * (A . (vr,A))))] is set
K135((K * (A . (vr,qh))),(K * ((x *') * (A . (vr,A))))) is complex Element of COMPLEX
((A . (vq,qh)) + ((x *') * (A . (vq,A)))) + ((K * (A . (vr,qh))) + (K * ((x *') * (A . (vr,A))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((K * (A . (vr,qh))) + (K * ((x *') * (A . (vr,A)))))) is complex Element of the carrier of F_Complex
[((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((K * (A . (vr,qh))) + (K * ((x *') * (A . (vr,A)))))] is set
{((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((K * (A . (vr,qh))) + (K * ((x *') * (A . (vr,A)))))} is non empty V175() set
{((A . (vq,qh)) + ((x *') * (A . (vq,A))))} is non empty V175() set
{{((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((K * (A . (vr,qh))) + (K * ((x *') * (A . (vr,A)))))},{((A . (vq,qh)) + ((x *') * (A . (vq,A))))}} is non empty set
the addF of F_Complex . [((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((K * (A . (vr,qh))) + (K * ((x *') * (A . (vr,A)))))] is set
K135(((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((K * (A . (vr,qh))) + (K * ((x *') * (A . (vr,A)))))) is complex Element of COMPLEX
A . (vq,(x * A)) is complex Element of the carrier of F_Complex
[vq,(x * A)] is set
{vq,(x * A)} is non empty set
{{vq,(x * A)},{vq}} is non empty set
A . [vq,(x * A)] is set
(A . (vq,qh)) + (A . (vq,(x * A))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((A . (vq,qh)),(A . (vq,(x * A)))) is complex Element of the carrier of F_Complex
[(A . (vq,qh)),(A . (vq,(x * A)))] is set
{(A . (vq,qh)),(A . (vq,(x * A)))} is non empty V175() set
{{(A . (vq,qh)),(A . (vq,(x * A)))},{(A . (vq,qh))}} is non empty set
the addF of F_Complex . [(A . (vq,qh)),(A . (vq,(x * A)))] is set
K135((A . (vq,qh)),(A . (vq,(x * A)))) is complex Element of COMPLEX
A . ((K * vr),qh) is complex Element of the carrier of F_Complex
[(K * vr),qh] is set
{(K * vr),qh} is non empty set
{(K * vr)} is non empty set
{{(K * vr),qh},{(K * vr)}} is non empty set
A . [(K * vr),qh] is set
A . ((K * vr),(x * A)) is complex Element of the carrier of F_Complex
[(K * vr),(x * A)] is set
{(K * vr),(x * A)} is non empty set
{{(K * vr),(x * A)},{(K * vr)}} is non empty set
A . [(K * vr),(x * A)] is set
(A . ((K * vr),qh)) + (A . ((K * vr),(x * A))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((A . ((K * vr),qh)),(A . ((K * vr),(x * A)))) is complex Element of the carrier of F_Complex
[(A . ((K * vr),qh)),(A . ((K * vr),(x * A)))] is set
{(A . ((K * vr),qh)),(A . ((K * vr),(x * A)))} is non empty V175() set
{(A . ((K * vr),qh))} is non empty V175() set
{{(A . ((K * vr),qh)),(A . ((K * vr),(x * A)))},{(A . ((K * vr),qh))}} is non empty set
the addF of F_Complex . [(A . ((K * vr),qh)),(A . ((K * vr),(x * A)))] is set
K135((A . ((K * vr),qh)),(A . ((K * vr),(x * A)))) is complex Element of COMPLEX
((A . (vq,qh)) + (A . (vq,(x * A)))) + ((A . ((K * vr),qh)) + (A . ((K * vr),(x * A)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((A . (vq,qh)) + (A . (vq,(x * A)))),((A . ((K * vr),qh)) + (A . ((K * vr),(x * A))))) is complex Element of the carrier of F_Complex
[((A . (vq,qh)) + (A . (vq,(x * A)))),((A . ((K * vr),qh)) + (A . ((K * vr),(x * A))))] is set
{((A . (vq,qh)) + (A . (vq,(x * A)))),((A . ((K * vr),qh)) + (A . ((K * vr),(x * A))))} is non empty V175() set
{((A . (vq,qh)) + (A . (vq,(x * A))))} is non empty V175() set
{{((A . (vq,qh)) + (A . (vq,(x * A)))),((A . ((K * vr),qh)) + (A . ((K * vr),(x * A))))},{((A . (vq,qh)) + (A . (vq,(x * A))))}} is non empty set
the addF of F_Complex . [((A . (vq,qh)) + (A . (vq,(x * A)))),((A . ((K * vr),qh)) + (A . ((K * vr),(x * A))))] is set
K135(((A . (vq,qh)) + (A . (vq,(x * A)))),((A . ((K * vr),qh)) + (A . ((K * vr),(x * A))))) is complex Element of COMPLEX
((A . (vq,qh)) + ((x *') * (A . (vq,A)))) + ((A . ((K * vr),qh)) + (A . ((K * vr),(x * A)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((A . ((K * vr),qh)) + (A . ((K * vr),(x * A))))) is complex Element of the carrier of F_Complex
[((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((A . ((K * vr),qh)) + (A . ((K * vr),(x * A))))] is set
{((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((A . ((K * vr),qh)) + (A . ((K * vr),(x * A))))} is non empty V175() set
{{((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((A . ((K * vr),qh)) + (A . ((K * vr),(x * A))))},{((A . (vq,qh)) + ((x *') * (A . (vq,A))))}} is non empty set
the addF of F_Complex . [((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((A . ((K * vr),qh)) + (A . ((K * vr),(x * A))))] is set
K135(((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((A . ((K * vr),qh)) + (A . ((K * vr),(x * A))))) is complex Element of COMPLEX
(K * (A . (vr,qh))) + (A . ((K * vr),(x * A))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((K * (A . (vr,qh))),(A . ((K * vr),(x * A)))) is complex Element of the carrier of F_Complex
[(K * (A . (vr,qh))),(A . ((K * vr),(x * A)))] is set
{(K * (A . (vr,qh))),(A . ((K * vr),(x * A)))} is non empty V175() set
{{(K * (A . (vr,qh))),(A . ((K * vr),(x * A)))},{(K * (A . (vr,qh)))}} is non empty set
the addF of F_Complex . [(K * (A . (vr,qh))),(A . ((K * vr),(x * A)))] is set
K135((K * (A . (vr,qh))),(A . ((K * vr),(x * A)))) is complex Element of COMPLEX
((A . (vq,qh)) + ((x *') * (A . (vq,A)))) + ((K * (A . (vr,qh))) + (A . ((K * vr),(x * A)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((K * (A . (vr,qh))) + (A . ((K * vr),(x * A))))) is complex Element of the carrier of F_Complex
[((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((K * (A . (vr,qh))) + (A . ((K * vr),(x * A))))] is set
{((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((K * (A . (vr,qh))) + (A . ((K * vr),(x * A))))} is non empty V175() set
{{((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((K * (A . (vr,qh))) + (A . ((K * vr),(x * A))))},{((A . (vq,qh)) + ((x *') * (A . (vq,A))))}} is non empty set
the addF of F_Complex . [((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((K * (A . (vr,qh))) + (A . ((K * vr),(x * A))))] is set
K135(((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((K * (A . (vr,qh))) + (A . ((K * vr),(x * A))))) is complex Element of COMPLEX
A . (vr,(x * A)) is complex Element of the carrier of F_Complex
[vr,(x * A)] is set
{vr,(x * A)} is non empty set
{{vr,(x * A)},{vr}} is non empty set
A . [vr,(x * A)] is set
K * (A . (vr,(x * A))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (K,(A . (vr,(x * A)))) is complex Element of the carrier of F_Complex
[K,(A . (vr,(x * A)))] is set
{K,(A . (vr,(x * A)))} is non empty V175() set
{{K,(A . (vr,(x * A)))},{K}} is non empty set
the multF of F_Complex . [K,(A . (vr,(x * A)))] is set
K137(K,(A . (vr,(x * A)))) is complex Element of COMPLEX
(K * (A . (vr,qh))) + (K * (A . (vr,(x * A)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((K * (A . (vr,qh))),(K * (A . (vr,(x * A))))) is complex Element of the carrier of F_Complex
[(K * (A . (vr,qh))),(K * (A . (vr,(x * A))))] is set
{(K * (A . (vr,qh))),(K * (A . (vr,(x * A))))} is non empty V175() set
{{(K * (A . (vr,qh))),(K * (A . (vr,(x * A))))},{(K * (A . (vr,qh)))}} is non empty set
the addF of F_Complex . [(K * (A . (vr,qh))),(K * (A . (vr,(x * A))))] is set
K135((K * (A . (vr,qh))),(K * (A . (vr,(x * A))))) is complex Element of COMPLEX
((A . (vq,qh)) + ((x *') * (A . (vq,A)))) + ((K * (A . (vr,qh))) + (K * (A . (vr,(x * A))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((K * (A . (vr,qh))) + (K * (A . (vr,(x * A)))))) is complex Element of the carrier of F_Complex
[((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((K * (A . (vr,qh))) + (K * (A . (vr,(x * A)))))] is set
{((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((K * (A . (vr,qh))) + (K * (A . (vr,(x * A)))))} is non empty V175() set
{{((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((K * (A . (vr,qh))) + (K * (A . (vr,(x * A)))))},{((A . (vq,qh)) + ((x *') * (A . (vq,A))))}} is non empty set
the addF of F_Complex . [((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((K * (A . (vr,qh))) + (K * (A . (vr,(x * A)))))] is set
K135(((A . (vq,qh)) + ((x *') * (A . (vq,A)))),((K * (A . (vr,qh))) + (K * (A . (vr,(x * A)))))) is complex Element of COMPLEX
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is Element of the carrier of V
vr is Element of the carrier of V
qh is Element of the carrier of f
A is Element of the carrier of f
K is complex Element of the carrier of F_Complex
K * vr is Element of the carrier of V
the lmult of V is V16() V19([: the carrier of F_Complex, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of F_Complex, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:]
[: the carrier of F_Complex, the carrier of V:] is set
[:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
the lmult of V . (K,vr) is Element of the carrier of V
[K,vr] is set
{K,vr} is non empty set
{K} is non empty V175() set
{{K,vr},{K}} is non empty set
the lmult of V . [K,vr] is set
vq - (K * vr) is Element of the carrier of V
- (K * vr) is Element of the carrier of V
vq + (- (K * vr)) is Element of the carrier of V
the addF of V is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is set
the addF of V . (vq,(- (K * vr))) is Element of the carrier of V
[vq,(- (K * vr))] is set
{vq,(- (K * vr))} is non empty set
{vq} is non empty set
{{vq,(- (K * vr))},{vq}} is non empty set
the addF of V . [vq,(- (K * vr))] is set
x is complex Element of the carrier of F_Complex
x * A is Element of the carrier of f
the lmult of f is V16() V19([: the carrier of F_Complex, the carrier of f:]) V20( the carrier of f) Function-like V30([: the carrier of F_Complex, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of F_Complex, the carrier of f:], the carrier of f:]
[: the carrier of F_Complex, the carrier of f:] is set
[:[: the carrier of F_Complex, the carrier of f:], the carrier of f:] is set
bool [:[: the carrier of F_Complex, the carrier of f:], the carrier of f:] is set
the lmult of f . (x,A) is Element of the carrier of f
[x,A] is set
{x,A} is non empty set
{x} is non empty V175() set
{{x,A},{x}} is non empty set
the lmult of f . [x,A] is set
qh - (x * A) is Element of the carrier of f
- (x * A) is Element of the carrier of f
qh + (- (x * A)) is Element of the carrier of f
the addF of f is V16() V19([: the carrier of f, the carrier of f:]) V20( the carrier of f) Function-like V30([: the carrier of f, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of f, the carrier of f:], the carrier of f:]
[: the carrier of f, the carrier of f:] is set
[:[: the carrier of f, the carrier of f:], the carrier of f:] is set
bool [:[: the carrier of f, the carrier of f:], the carrier of f:] is set
the addF of f . (qh,(- (x * A))) is Element of the carrier of f
[qh,(- (x * A))] is set
{qh,(- (x * A))} is non empty set
{qh} is non empty set
{{qh,(- (x * A))},{qh}} is non empty set
the addF of f . [qh,(- (x * A))] is set
x *' is complex Element of the carrier of F_Complex
Re x is complex real ext-real Element of REAL
Im x is complex real ext-real Element of REAL
(Im x) * <i> is complex set
(Re x) - ((Im x) * <i>) is complex set
A is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
A . ((vq - (K * vr)),(qh - (x * A))) is complex Element of the carrier of F_Complex
[(vq - (K * vr)),(qh - (x * A))] is set
{(vq - (K * vr)),(qh - (x * A))} is non empty set
{(vq - (K * vr))} is non empty set
{{(vq - (K * vr)),(qh - (x * A))},{(vq - (K * vr))}} is non empty set
A . [(vq - (K * vr)),(qh - (x * A))] is set
A . (vq,qh) is complex Element of the carrier of F_Complex
[vq,qh] is set
{vq,qh} is non empty set
{{vq,qh},{vq}} is non empty set
A . [vq,qh] is set
A . (vq,A) is complex Element of the carrier of F_Complex
[vq,A] is set
{vq,A} is non empty set
{{vq,A},{vq}} is non empty set
A . [vq,A] is set
(x *') * (A . (vq,A)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((x *'),(A . (vq,A))) is complex Element of the carrier of F_Complex
[(x *'),(A . (vq,A))] is set
{(x *'),(A . (vq,A))} is non empty V175() set
{(x *')} is non empty V175() set
{{(x *'),(A . (vq,A))},{(x *')}} is non empty set
the multF of F_Complex . [(x *'),(A . (vq,A))] is set
K137((x *'),(A . (vq,A))) is complex Element of COMPLEX
(A . (vq,qh)) - ((x *') * (A . (vq,A))) is complex Element of the carrier of F_Complex
- ((x *') * (A . (vq,A))) is complex Element of the carrier of F_Complex
(A . (vq,qh)) + (- ((x *') * (A . (vq,A)))) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . ((A . (vq,qh)),(- ((x *') * (A . (vq,A))))) is complex Element of the carrier of F_Complex
[(A . (vq,qh)),(- ((x *') * (A . (vq,A))))] is set
{(A . (vq,qh)),(- ((x *') * (A . (vq,A))))} is non empty V175() set
{(A . (vq,qh))} is non empty V175() set
{{(A . (vq,qh)),(- ((x *') * (A . (vq,A))))},{(A . (vq,qh))}} is non empty set
the addF of F_Complex . [(A . (vq,qh)),(- ((x *') * (A . (vq,A))))] is set
K135((A . (vq,qh)),(- ((x *') * (A . (vq,A))))) is complex Element of COMPLEX
A . (vr,qh) is complex Element of the carrier of F_Complex
[vr,qh] is set
{vr,qh} is non empty set
{vr} is non empty set
{{vr,qh},{vr}} is non empty set
A . [vr,qh] is set
K * (A . (vr,qh)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (K,(A . (vr,qh))) is complex Element of the carrier of F_Complex
[K,(A . (vr,qh))] is set
{K,(A . (vr,qh))} is non empty V175() set
{{K,(A . (vr,qh))},{K}} is non empty set
the multF of F_Complex . [K,(A . (vr,qh))] is set
K137(K,(A . (vr,qh))) is complex Element of COMPLEX
A . (vr,A) is complex Element of the carrier of F_Complex
[vr,A] is set
{vr,A} is non empty set
{{vr,A},{vr}} is non empty set
A . [vr,A] is set
(x *') * (A . (vr,A)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((x *'),(A . (vr,A))) is complex Element of the carrier of F_Complex
[(x *'),(A . (vr,A))] is set
{(x *'),(A . (vr,A))} is non empty V175() set
{{(x *'),(A . (vr,A))},{(x *')}} is non empty set
the multF of F_Complex . [(x *'),(A . (vr,A))] is set
K137((x *'),(A . (vr,A))) is complex Element of COMPLEX
K * ((x *') * (A . (vr,A))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (K,((x *') * (A . (vr,A)))) is complex Element of the carrier of F_Complex
[K,((x *') * (A . (vr,A)))] is set
{K,((x *') * (A . (vr,A)))} is non empty V175() set
{{K,((x *') * (A . (vr,A)))},{K}} is non empty set
the multF of F_Complex . [K,((x *') * (A . (vr,A)))] is set
K137(K,((x *') * (A . (vr,A)))) is complex Element of COMPLEX
(K * (A . (vr,qh))) - (K * ((x *') * (A . (vr,A)))) is complex Element of the carrier of F_Complex
- (K * ((x *') * (A . (vr,A)))) is complex Element of the carrier of F_Complex
(K * (A . (vr,qh))) + (- (K * ((x *') * (A . (vr,A))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((K * (A . (vr,qh))),(- (K * ((x *') * (A . (vr,A)))))) is complex Element of the carrier of F_Complex
[(K * (A . (vr,qh))),(- (K * ((x *') * (A . (vr,A)))))] is set
{(K * (A . (vr,qh))),(- (K * ((x *') * (A . (vr,A)))))} is non empty V175() set
{(K * (A . (vr,qh)))} is non empty V175() set
{{(K * (A . (vr,qh))),(- (K * ((x *') * (A . (vr,A)))))},{(K * (A . (vr,qh)))}} is non empty set
the addF of F_Complex . [(K * (A . (vr,qh))),(- (K * ((x *') * (A . (vr,A)))))] is set
K135((K * (A . (vr,qh))),(- (K * ((x *') * (A . (vr,A)))))) is complex Element of COMPLEX
((A . (vq,qh)) - ((x *') * (A . (vq,A)))) - ((K * (A . (vr,qh))) - (K * ((x *') * (A . (vr,A))))) is complex Element of the carrier of F_Complex
- ((K * (A . (vr,qh))) - (K * ((x *') * (A . (vr,A))))) is complex Element of the carrier of F_Complex
((A . (vq,qh)) - ((x *') * (A . (vq,A)))) + (- ((K * (A . (vr,qh))) - (K * ((x *') * (A . (vr,A)))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((K * (A . (vr,qh))) - (K * ((x *') * (A . (vr,A))))))) is complex Element of the carrier of F_Complex
[((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((K * (A . (vr,qh))) - (K * ((x *') * (A . (vr,A))))))] is set
{((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((K * (A . (vr,qh))) - (K * ((x *') * (A . (vr,A))))))} is non empty V175() set
{((A . (vq,qh)) - ((x *') * (A . (vq,A))))} is non empty V175() set
{{((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((K * (A . (vr,qh))) - (K * ((x *') * (A . (vr,A))))))},{((A . (vq,qh)) - ((x *') * (A . (vq,A))))}} is non empty set
the addF of F_Complex . [((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((K * (A . (vr,qh))) - (K * ((x *') * (A . (vr,A))))))] is set
K135(((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((K * (A . (vr,qh))) - (K * ((x *') * (A . (vr,A))))))) is complex Element of COMPLEX
A . (vq,(x * A)) is complex Element of the carrier of F_Complex
[vq,(x * A)] is set
{vq,(x * A)} is non empty set
{{vq,(x * A)},{vq}} is non empty set
A . [vq,(x * A)] is set
(A . (vq,qh)) - (A . (vq,(x * A))) is complex Element of the carrier of F_Complex
- (A . (vq,(x * A))) is complex Element of the carrier of F_Complex
(A . (vq,qh)) + (- (A . (vq,(x * A)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((A . (vq,qh)),(- (A . (vq,(x * A))))) is complex Element of the carrier of F_Complex
[(A . (vq,qh)),(- (A . (vq,(x * A))))] is set
{(A . (vq,qh)),(- (A . (vq,(x * A))))} is non empty V175() set
{{(A . (vq,qh)),(- (A . (vq,(x * A))))},{(A . (vq,qh))}} is non empty set
the addF of F_Complex . [(A . (vq,qh)),(- (A . (vq,(x * A))))] is set
K135((A . (vq,qh)),(- (A . (vq,(x * A))))) is complex Element of COMPLEX
A . ((K * vr),qh) is complex Element of the carrier of F_Complex
[(K * vr),qh] is set
{(K * vr),qh} is non empty set
{(K * vr)} is non empty set
{{(K * vr),qh},{(K * vr)}} is non empty set
A . [(K * vr),qh] is set
A . ((K * vr),(x * A)) is complex Element of the carrier of F_Complex
[(K * vr),(x * A)] is set
{(K * vr),(x * A)} is non empty set
{{(K * vr),(x * A)},{(K * vr)}} is non empty set
A . [(K * vr),(x * A)] is set
(A . ((K * vr),qh)) - (A . ((K * vr),(x * A))) is complex Element of the carrier of F_Complex
- (A . ((K * vr),(x * A))) is complex Element of the carrier of F_Complex
(A . ((K * vr),qh)) + (- (A . ((K * vr),(x * A)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((A . ((K * vr),qh)),(- (A . ((K * vr),(x * A))))) is complex Element of the carrier of F_Complex
[(A . ((K * vr),qh)),(- (A . ((K * vr),(x * A))))] is set
{(A . ((K * vr),qh)),(- (A . ((K * vr),(x * A))))} is non empty V175() set
{(A . ((K * vr),qh))} is non empty V175() set
{{(A . ((K * vr),qh)),(- (A . ((K * vr),(x * A))))},{(A . ((K * vr),qh))}} is non empty set
the addF of F_Complex . [(A . ((K * vr),qh)),(- (A . ((K * vr),(x * A))))] is set
K135((A . ((K * vr),qh)),(- (A . ((K * vr),(x * A))))) is complex Element of COMPLEX
((A . (vq,qh)) - (A . (vq,(x * A)))) - ((A . ((K * vr),qh)) - (A . ((K * vr),(x * A)))) is complex Element of the carrier of F_Complex
- ((A . ((K * vr),qh)) - (A . ((K * vr),(x * A)))) is complex Element of the carrier of F_Complex
((A . (vq,qh)) - (A . (vq,(x * A)))) + (- ((A . ((K * vr),qh)) - (A . ((K * vr),(x * A))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((A . (vq,qh)) - (A . (vq,(x * A)))),(- ((A . ((K * vr),qh)) - (A . ((K * vr),(x * A)))))) is complex Element of the carrier of F_Complex
[((A . (vq,qh)) - (A . (vq,(x * A)))),(- ((A . ((K * vr),qh)) - (A . ((K * vr),(x * A)))))] is set
{((A . (vq,qh)) - (A . (vq,(x * A)))),(- ((A . ((K * vr),qh)) - (A . ((K * vr),(x * A)))))} is non empty V175() set
{((A . (vq,qh)) - (A . (vq,(x * A))))} is non empty V175() set
{{((A . (vq,qh)) - (A . (vq,(x * A)))),(- ((A . ((K * vr),qh)) - (A . ((K * vr),(x * A)))))},{((A . (vq,qh)) - (A . (vq,(x * A))))}} is non empty set
the addF of F_Complex . [((A . (vq,qh)) - (A . (vq,(x * A)))),(- ((A . ((K * vr),qh)) - (A . ((K * vr),(x * A)))))] is set
K135(((A . (vq,qh)) - (A . (vq,(x * A)))),(- ((A . ((K * vr),qh)) - (A . ((K * vr),(x * A)))))) is complex Element of COMPLEX
((A . (vq,qh)) - ((x *') * (A . (vq,A)))) - ((A . ((K * vr),qh)) - (A . ((K * vr),(x * A)))) is complex Element of the carrier of F_Complex
((A . (vq,qh)) - ((x *') * (A . (vq,A)))) + (- ((A . ((K * vr),qh)) - (A . ((K * vr),(x * A))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((A . ((K * vr),qh)) - (A . ((K * vr),(x * A)))))) is complex Element of the carrier of F_Complex
[((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((A . ((K * vr),qh)) - (A . ((K * vr),(x * A)))))] is set
{((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((A . ((K * vr),qh)) - (A . ((K * vr),(x * A)))))} is non empty V175() set
{{((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((A . ((K * vr),qh)) - (A . ((K * vr),(x * A)))))},{((A . (vq,qh)) - ((x *') * (A . (vq,A))))}} is non empty set
the addF of F_Complex . [((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((A . ((K * vr),qh)) - (A . ((K * vr),(x * A)))))] is set
K135(((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((A . ((K * vr),qh)) - (A . ((K * vr),(x * A)))))) is complex Element of COMPLEX
(K * (A . (vr,qh))) - (A . ((K * vr),(x * A))) is complex Element of the carrier of F_Complex
(K * (A . (vr,qh))) + (- (A . ((K * vr),(x * A)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((K * (A . (vr,qh))),(- (A . ((K * vr),(x * A))))) is complex Element of the carrier of F_Complex
[(K * (A . (vr,qh))),(- (A . ((K * vr),(x * A))))] is set
{(K * (A . (vr,qh))),(- (A . ((K * vr),(x * A))))} is non empty V175() set
{{(K * (A . (vr,qh))),(- (A . ((K * vr),(x * A))))},{(K * (A . (vr,qh)))}} is non empty set
the addF of F_Complex . [(K * (A . (vr,qh))),(- (A . ((K * vr),(x * A))))] is set
K135((K * (A . (vr,qh))),(- (A . ((K * vr),(x * A))))) is complex Element of COMPLEX
((A . (vq,qh)) - ((x *') * (A . (vq,A)))) - ((K * (A . (vr,qh))) - (A . ((K * vr),(x * A)))) is complex Element of the carrier of F_Complex
- ((K * (A . (vr,qh))) - (A . ((K * vr),(x * A)))) is complex Element of the carrier of F_Complex
((A . (vq,qh)) - ((x *') * (A . (vq,A)))) + (- ((K * (A . (vr,qh))) - (A . ((K * vr),(x * A))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((K * (A . (vr,qh))) - (A . ((K * vr),(x * A)))))) is complex Element of the carrier of F_Complex
[((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((K * (A . (vr,qh))) - (A . ((K * vr),(x * A)))))] is set
{((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((K * (A . (vr,qh))) - (A . ((K * vr),(x * A)))))} is non empty V175() set
{{((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((K * (A . (vr,qh))) - (A . ((K * vr),(x * A)))))},{((A . (vq,qh)) - ((x *') * (A . (vq,A))))}} is non empty set
the addF of F_Complex . [((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((K * (A . (vr,qh))) - (A . ((K * vr),(x * A)))))] is set
K135(((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((K * (A . (vr,qh))) - (A . ((K * vr),(x * A)))))) is complex Element of COMPLEX
A . (vr,(x * A)) is complex Element of the carrier of F_Complex
[vr,(x * A)] is set
{vr,(x * A)} is non empty set
{{vr,(x * A)},{vr}} is non empty set
A . [vr,(x * A)] is set
K * (A . (vr,(x * A))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (K,(A . (vr,(x * A)))) is complex Element of the carrier of F_Complex
[K,(A . (vr,(x * A)))] is set
{K,(A . (vr,(x * A)))} is non empty V175() set
{{K,(A . (vr,(x * A)))},{K}} is non empty set
the multF of F_Complex . [K,(A . (vr,(x * A)))] is set
K137(K,(A . (vr,(x * A)))) is complex Element of COMPLEX
(K * (A . (vr,qh))) - (K * (A . (vr,(x * A)))) is complex Element of the carrier of F_Complex
- (K * (A . (vr,(x * A)))) is complex Element of the carrier of F_Complex
(K * (A . (vr,qh))) + (- (K * (A . (vr,(x * A))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((K * (A . (vr,qh))),(- (K * (A . (vr,(x * A)))))) is complex Element of the carrier of F_Complex
[(K * (A . (vr,qh))),(- (K * (A . (vr,(x * A)))))] is set
{(K * (A . (vr,qh))),(- (K * (A . (vr,(x * A)))))} is non empty V175() set
{{(K * (A . (vr,qh))),(- (K * (A . (vr,(x * A)))))},{(K * (A . (vr,qh)))}} is non empty set
the addF of F_Complex . [(K * (A . (vr,qh))),(- (K * (A . (vr,(x * A)))))] is set
K135((K * (A . (vr,qh))),(- (K * (A . (vr,(x * A)))))) is complex Element of COMPLEX
((A . (vq,qh)) - ((x *') * (A . (vq,A)))) - ((K * (A . (vr,qh))) - (K * (A . (vr,(x * A))))) is complex Element of the carrier of F_Complex
- ((K * (A . (vr,qh))) - (K * (A . (vr,(x * A))))) is complex Element of the carrier of F_Complex
((A . (vq,qh)) - ((x *') * (A . (vq,A)))) + (- ((K * (A . (vr,qh))) - (K * (A . (vr,(x * A)))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((K * (A . (vr,qh))) - (K * (A . (vr,(x * A))))))) is complex Element of the carrier of F_Complex
[((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((K * (A . (vr,qh))) - (K * (A . (vr,(x * A))))))] is set
{((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((K * (A . (vr,qh))) - (K * (A . (vr,(x * A))))))} is non empty V175() set
{{((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((K * (A . (vr,qh))) - (K * (A . (vr,(x * A))))))},{((A . (vq,qh)) - ((x *') * (A . (vq,A))))}} is non empty set
the addF of F_Complex . [((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((K * (A . (vr,qh))) - (K * (A . (vr,(x * A))))))] is set
K135(((A . (vq,qh)) - ((x *') * (A . (vq,A)))),(- ((K * (A . (vr,qh))) - (K * (A . (vr,(x * A))))))) is complex Element of COMPLEX
V is non empty right_complementable add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
0. V is zero Element of the carrier of V
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) (V,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
vq is Element of the carrier of V
f . (vq,(0. V)) is complex Element of the carrier of F_Complex
[vq,(0. V)] is set
{vq,(0. V)} is non empty set
{vq} is non empty set
{{vq,(0. V)},{vq}} is non empty set
f . [vq,(0. V)] is set
FunctionalFAF (f,vq) is V16() V19( the carrier of V) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) V30( the carrier of V, the carrier of F_Complex) 0-preserving (V) Element of bool [: the carrier of V, the carrier of F_Complex:]
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
(0. F_Complex) * (0. V) is Element of the carrier of V
the lmult of V is V16() V19([: the carrier of F_Complex, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of F_Complex, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:]
[: the carrier of F_Complex, the carrier of V:] is set
[:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
the lmult of V . ((0. F_Complex),(0. V)) is Element of the carrier of V
[(0. F_Complex),(0. V)] is set
{(0. F_Complex),(0. V)} is non empty set
{(0. F_Complex)} is non empty V175() set
{{(0. F_Complex),(0. V)},{(0. F_Complex)}} is non empty set
the lmult of V . [(0. F_Complex),(0. V)] is set
f . (vq,((0. F_Complex) * (0. V))) is complex Element of the carrier of F_Complex
[vq,((0. F_Complex) * (0. V))] is set
{vq,((0. F_Complex) * (0. V))} is non empty set
{{vq,((0. F_Complex) * (0. V))},{vq}} is non empty set
f . [vq,((0. F_Complex) * (0. V))] is set
(FunctionalFAF (f,vq)) . ((0. F_Complex) * (0. V)) is complex Element of the carrier of F_Complex
(FunctionalFAF (f,vq)) . (0. V) is complex Element of the carrier of F_Complex
((0. F_Complex) *') * ((FunctionalFAF (f,vq)) . (0. V)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((0. F_Complex) *'),((FunctionalFAF (f,vq)) . (0. V))) is complex Element of the carrier of F_Complex
[((0. F_Complex) *'),((FunctionalFAF (f,vq)) . (0. V))] is set
{((0. F_Complex) *'),((FunctionalFAF (f,vq)) . (0. V))} is non empty V175() set
{((0. F_Complex) *')} is non empty V175() set
{{((0. F_Complex) *'),((FunctionalFAF (f,vq)) . (0. V))},{((0. F_Complex) *')}} is non empty set
the multF of F_Complex . [((0. F_Complex) *'),((FunctionalFAF (f,vq)) . (0. V))] is set
K137(((0. F_Complex) *'),((FunctionalFAF (f,vq)) . (0. V))) is complex Element of COMPLEX
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is Element of the carrier of V
vq is Element of the carrier of V
f + vq is Element of the carrier of V
the addF of V is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[:[: the carrier of V, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is set
the addF of V . (f,vq) is Element of the carrier of V
[f,vq] is set
{f,vq} is non empty set
{f} is non empty set
{{f,vq},{f}} is non empty set
the addF of V . [f,vq] is set
f - vq is Element of the carrier of V
- vq is Element of the carrier of V
f + (- vq) is Element of the carrier of V
the addF of V . (f,(- vq)) is Element of the carrier of V
[f,(- vq)] is set
{f,(- vq)} is non empty set
{{f,(- vq)},{f}} is non empty set
the addF of V . [f,(- vq)] is set
i_FC * vq is Element of the carrier of V
the lmult of V is V16() V19([: the carrier of F_Complex, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of F_Complex, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:]
[: the carrier of F_Complex, the carrier of V:] is set
[:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
the lmult of V . (i_FC,vq) is Element of the carrier of V
[i_FC,vq] is set
{i_FC,vq} is non empty set
{{i_FC,vq},{i_FC}} is non empty set
the lmult of V . [i_FC,vq] is set
f + (i_FC * vq) is Element of the carrier of V
the addF of V . (f,(i_FC * vq)) is Element of the carrier of V
[f,(i_FC * vq)] is set
{f,(i_FC * vq)} is non empty set
{{f,(i_FC * vq)},{f}} is non empty set
the addF of V . [f,(i_FC * vq)] is set
f - (i_FC * vq) is Element of the carrier of V
- (i_FC * vq) is Element of the carrier of V
f + (- (i_FC * vq)) is Element of the carrier of V
the addF of V . (f,(- (i_FC * vq))) is Element of the carrier of V
[f,(- (i_FC * vq))] is set
{f,(- (i_FC * vq))} is non empty set
{{f,(- (i_FC * vq))},{f}} is non empty set
the addF of V . [f,(- (i_FC * vq))] is set
vr is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,V) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
vr . (f,vq) is complex Element of the carrier of F_Complex
vr . [f,vq] is set
(vr . (f,vq)) + (vr . (f,vq)) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . ((vr . (f,vq)),(vr . (f,vq))) is complex Element of the carrier of F_Complex
[(vr . (f,vq)),(vr . (f,vq))] is set
{(vr . (f,vq)),(vr . (f,vq))} is non empty V175() set
{(vr . (f,vq))} is non empty V175() set
{{(vr . (f,vq)),(vr . (f,vq))},{(vr . (f,vq))}} is non empty set
the addF of F_Complex . [(vr . (f,vq)),(vr . (f,vq))] is set
K135((vr . (f,vq)),(vr . (f,vq))) is complex Element of COMPLEX
((vr . (f,vq)) + (vr . (f,vq))) + (vr . (f,vq)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,vq)) + (vr . (f,vq))),(vr . (f,vq))) is complex Element of the carrier of F_Complex
[((vr . (f,vq)) + (vr . (f,vq))),(vr . (f,vq))] is set
{((vr . (f,vq)) + (vr . (f,vq))),(vr . (f,vq))} is non empty V175() set
{((vr . (f,vq)) + (vr . (f,vq)))} is non empty V175() set
{{((vr . (f,vq)) + (vr . (f,vq))),(vr . (f,vq))},{((vr . (f,vq)) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [((vr . (f,vq)) + (vr . (f,vq))),(vr . (f,vq))] is set
K135(((vr . (f,vq)) + (vr . (f,vq))),(vr . (f,vq))) is complex Element of COMPLEX
(((vr . (f,vq)) + (vr . (f,vq))) + (vr . (f,vq))) + (vr . (f,vq)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((vr . (f,vq)) + (vr . (f,vq))) + (vr . (f,vq))),(vr . (f,vq))) is complex Element of the carrier of F_Complex
[(((vr . (f,vq)) + (vr . (f,vq))) + (vr . (f,vq))),(vr . (f,vq))] is set
{(((vr . (f,vq)) + (vr . (f,vq))) + (vr . (f,vq))),(vr . (f,vq))} is non empty V175() set
{(((vr . (f,vq)) + (vr . (f,vq))) + (vr . (f,vq)))} is non empty V175() set
{{(((vr . (f,vq)) + (vr . (f,vq))) + (vr . (f,vq))),(vr . (f,vq))},{(((vr . (f,vq)) + (vr . (f,vq))) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [(((vr . (f,vq)) + (vr . (f,vq))) + (vr . (f,vq))),(vr . (f,vq))] is set
K135((((vr . (f,vq)) + (vr . (f,vq))) + (vr . (f,vq))),(vr . (f,vq))) is complex Element of COMPLEX
vr . ((f + vq),(f + vq)) is complex Element of the carrier of F_Complex
[(f + vq),(f + vq)] is set
{(f + vq),(f + vq)} is non empty set
{(f + vq)} is non empty set
{{(f + vq),(f + vq)},{(f + vq)}} is non empty set
vr . [(f + vq),(f + vq)] is set
vr . ((f - vq),(f - vq)) is complex Element of the carrier of F_Complex
[(f - vq),(f - vq)] is set
{(f - vq),(f - vq)} is non empty set
{(f - vq)} is non empty set
{{(f - vq),(f - vq)},{(f - vq)}} is non empty set
vr . [(f - vq),(f - vq)] is set
(vr . ((f + vq),(f + vq))) - (vr . ((f - vq),(f - vq))) is complex Element of the carrier of F_Complex
- (vr . ((f - vq),(f - vq))) is complex Element of the carrier of F_Complex
(vr . ((f + vq),(f + vq))) + (- (vr . ((f - vq),(f - vq)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . ((f + vq),(f + vq))),(- (vr . ((f - vq),(f - vq))))) is complex Element of the carrier of F_Complex
[(vr . ((f + vq),(f + vq))),(- (vr . ((f - vq),(f - vq))))] is set
{(vr . ((f + vq),(f + vq))),(- (vr . ((f - vq),(f - vq))))} is non empty V175() set
{(vr . ((f + vq),(f + vq)))} is non empty V175() set
{{(vr . ((f + vq),(f + vq))),(- (vr . ((f - vq),(f - vq))))},{(vr . ((f + vq),(f + vq)))}} is non empty set
the addF of F_Complex . [(vr . ((f + vq),(f + vq))),(- (vr . ((f - vq),(f - vq))))] is set
K135((vr . ((f + vq),(f + vq))),(- (vr . ((f - vq),(f - vq))))) is complex Element of COMPLEX
vr . ((f + (i_FC * vq)),(f + (i_FC * vq))) is complex Element of the carrier of F_Complex
[(f + (i_FC * vq)),(f + (i_FC * vq))] is set
{(f + (i_FC * vq)),(f + (i_FC * vq))} is non empty set
{(f + (i_FC * vq))} is non empty set
{{(f + (i_FC * vq)),(f + (i_FC * vq))},{(f + (i_FC * vq))}} is non empty set
vr . [(f + (i_FC * vq)),(f + (i_FC * vq))] is set
i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq)))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (i_FC,(vr . ((f + (i_FC * vq)),(f + (i_FC * vq))))) is complex Element of the carrier of F_Complex
[i_FC,(vr . ((f + (i_FC * vq)),(f + (i_FC * vq))))] is set
{i_FC,(vr . ((f + (i_FC * vq)),(f + (i_FC * vq))))} is non empty V175() set
{{i_FC,(vr . ((f + (i_FC * vq)),(f + (i_FC * vq))))},{i_FC}} is non empty set
the multF of F_Complex . [i_FC,(vr . ((f + (i_FC * vq)),(f + (i_FC * vq))))] is set
K137(i_FC,(vr . ((f + (i_FC * vq)),(f + (i_FC * vq))))) is complex Element of COMPLEX
((vr . ((f + vq),(f + vq))) - (vr . ((f - vq),(f - vq)))) + (i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . ((f + vq),(f + vq))) - (vr . ((f - vq),(f - vq)))),(i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq)))))) is complex Element of the carrier of F_Complex
[((vr . ((f + vq),(f + vq))) - (vr . ((f - vq),(f - vq)))),(i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq)))))] is set
{((vr . ((f + vq),(f + vq))) - (vr . ((f - vq),(f - vq)))),(i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq)))))} is non empty V175() set
{((vr . ((f + vq),(f + vq))) - (vr . ((f - vq),(f - vq))))} is non empty V175() set
{{((vr . ((f + vq),(f + vq))) - (vr . ((f - vq),(f - vq)))),(i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq)))))},{((vr . ((f + vq),(f + vq))) - (vr . ((f - vq),(f - vq))))}} is non empty set
the addF of F_Complex . [((vr . ((f + vq),(f + vq))) - (vr . ((f - vq),(f - vq)))),(i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq)))))] is set
K135(((vr . ((f + vq),(f + vq))) - (vr . ((f - vq),(f - vq)))),(i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq)))))) is complex Element of COMPLEX
vr . ((f - (i_FC * vq)),(f - (i_FC * vq))) is complex Element of the carrier of F_Complex
[(f - (i_FC * vq)),(f - (i_FC * vq))] is set
{(f - (i_FC * vq)),(f - (i_FC * vq))} is non empty set
{(f - (i_FC * vq))} is non empty set
{{(f - (i_FC * vq)),(f - (i_FC * vq))},{(f - (i_FC * vq))}} is non empty set
vr . [(f - (i_FC * vq)),(f - (i_FC * vq))] is set
i_FC * (vr . ((f - (i_FC * vq)),(f - (i_FC * vq)))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (i_FC,(vr . ((f - (i_FC * vq)),(f - (i_FC * vq))))) is complex Element of the carrier of F_Complex
[i_FC,(vr . ((f - (i_FC * vq)),(f - (i_FC * vq))))] is set
{i_FC,(vr . ((f - (i_FC * vq)),(f - (i_FC * vq))))} is non empty V175() set
{{i_FC,(vr . ((f - (i_FC * vq)),(f - (i_FC * vq))))},{i_FC}} is non empty set
the multF of F_Complex . [i_FC,(vr . ((f - (i_FC * vq)),(f - (i_FC * vq))))] is set
K137(i_FC,(vr . ((f - (i_FC * vq)),(f - (i_FC * vq))))) is complex Element of COMPLEX
(((vr . ((f + vq),(f + vq))) - (vr . ((f - vq),(f - vq)))) + (i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq)))))) - (i_FC * (vr . ((f - (i_FC * vq)),(f - (i_FC * vq))))) is complex Element of the carrier of F_Complex
- (i_FC * (vr . ((f - (i_FC * vq)),(f - (i_FC * vq))))) is complex Element of the carrier of F_Complex
(((vr . ((f + vq),(f + vq))) - (vr . ((f - vq),(f - vq)))) + (i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq)))))) + (- (i_FC * (vr . ((f - (i_FC * vq)),(f - (i_FC * vq)))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((vr . ((f + vq),(f + vq))) - (vr . ((f - vq),(f - vq)))) + (i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq)))))),(- (i_FC * (vr . ((f - (i_FC * vq)),(f - (i_FC * vq))))))) is complex Element of the carrier of F_Complex
[(((vr . ((f + vq),(f + vq))) - (vr . ((f - vq),(f - vq)))) + (i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq)))))),(- (i_FC * (vr . ((f - (i_FC * vq)),(f - (i_FC * vq))))))] is set
{(((vr . ((f + vq),(f + vq))) - (vr . ((f - vq),(f - vq)))) + (i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq)))))),(- (i_FC * (vr . ((f - (i_FC * vq)),(f - (i_FC * vq))))))} is non empty V175() set
{(((vr . ((f + vq),(f + vq))) - (vr . ((f - vq),(f - vq)))) + (i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq))))))} is non empty V175() set
{{(((vr . ((f + vq),(f + vq))) - (vr . ((f - vq),(f - vq)))) + (i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq)))))),(- (i_FC * (vr . ((f - (i_FC * vq)),(f - (i_FC * vq))))))},{(((vr . ((f + vq),(f + vq))) - (vr . ((f - vq),(f - vq)))) + (i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq))))))}} is non empty set
the addF of F_Complex . [(((vr . ((f + vq),(f + vq))) - (vr . ((f - vq),(f - vq)))) + (i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq)))))),(- (i_FC * (vr . ((f - (i_FC * vq)),(f - (i_FC * vq))))))] is set
K135((((vr . ((f + vq),(f + vq))) - (vr . ((f - vq),(f - vq)))) + (i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq)))))),(- (i_FC * (vr . ((f - (i_FC * vq)),(f - (i_FC * vq))))))) is complex Element of COMPLEX
vr . (f,f) is complex Element of the carrier of F_Complex
[f,f] is set
{f,f} is non empty set
{{f,f},{f}} is non empty set
vr . [f,f] is set
vr . (vq,vq) is complex Element of the carrier of F_Complex
[vq,vq] is set
{vq,vq} is non empty set
{vq} is non empty set
{{vq,vq},{vq}} is non empty set
vr . [vq,vq] is set
vr . (vq,f) is complex Element of the carrier of F_Complex
[vq,f] is set
{vq,f} is non empty set
{{vq,f},{vq}} is non empty set
vr . [vq,f] is set
(vr . (f,f)) + (vr . (f,vq)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (f,f)),(vr . (f,vq))) is complex Element of the carrier of F_Complex
[(vr . (f,f)),(vr . (f,vq))] is set
{(vr . (f,f)),(vr . (f,vq))} is non empty V175() set
{(vr . (f,f))} is non empty V175() set
{{(vr . (f,f)),(vr . (f,vq))},{(vr . (f,f))}} is non empty set
the addF of F_Complex . [(vr . (f,f)),(vr . (f,vq))] is set
K135((vr . (f,f)),(vr . (f,vq))) is complex Element of COMPLEX
(vr . (vq,f)) + (vr . (vq,vq)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (vq,f)),(vr . (vq,vq))) is complex Element of the carrier of F_Complex
[(vr . (vq,f)),(vr . (vq,vq))] is set
{(vr . (vq,f)),(vr . (vq,vq))} is non empty V175() set
{(vr . (vq,f))} is non empty V175() set
{{(vr . (vq,f)),(vr . (vq,vq))},{(vr . (vq,f))}} is non empty set
the addF of F_Complex . [(vr . (vq,f)),(vr . (vq,vq))] is set
K135((vr . (vq,f)),(vr . (vq,vq))) is complex Element of COMPLEX
((vr . (f,f)) + (vr . (f,vq))) + ((vr . (vq,f)) + (vr . (vq,vq))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,f)) + (vr . (f,vq))),((vr . (vq,f)) + (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
[((vr . (f,f)) + (vr . (f,vq))),((vr . (vq,f)) + (vr . (vq,vq)))] is set
{((vr . (f,f)) + (vr . (f,vq))),((vr . (vq,f)) + (vr . (vq,vq)))} is non empty V175() set
{((vr . (f,f)) + (vr . (f,vq)))} is non empty V175() set
{{((vr . (f,f)) + (vr . (f,vq))),((vr . (vq,f)) + (vr . (vq,vq)))},{((vr . (f,f)) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [((vr . (f,f)) + (vr . (f,vq))),((vr . (vq,f)) + (vr . (vq,vq)))] is set
K135(((vr . (f,f)) + (vr . (f,vq))),((vr . (vq,f)) + (vr . (vq,vq)))) is complex Element of COMPLEX
(vr . (f,f)) - (vr . (f,vq)) is complex Element of the carrier of F_Complex
- (vr . (f,vq)) is complex Element of the carrier of F_Complex
(vr . (f,f)) + (- (vr . (f,vq))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (f,f)),(- (vr . (f,vq)))) is complex Element of the carrier of F_Complex
[(vr . (f,f)),(- (vr . (f,vq)))] is set
{(vr . (f,f)),(- (vr . (f,vq)))} is non empty V175() set
{{(vr . (f,f)),(- (vr . (f,vq)))},{(vr . (f,f))}} is non empty set
the addF of F_Complex . [(vr . (f,f)),(- (vr . (f,vq)))] is set
K135((vr . (f,f)),(- (vr . (f,vq)))) is complex Element of COMPLEX
(vr . (vq,f)) - (vr . (vq,vq)) is complex Element of the carrier of F_Complex
- (vr . (vq,vq)) is complex Element of the carrier of F_Complex
(vr . (vq,f)) + (- (vr . (vq,vq))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (vq,f)),(- (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
[(vr . (vq,f)),(- (vr . (vq,vq)))] is set
{(vr . (vq,f)),(- (vr . (vq,vq)))} is non empty V175() set
{{(vr . (vq,f)),(- (vr . (vq,vq)))},{(vr . (vq,f))}} is non empty set
the addF of F_Complex . [(vr . (vq,f)),(- (vr . (vq,vq)))] is set
K135((vr . (vq,f)),(- (vr . (vq,vq)))) is complex Element of COMPLEX
((vr . (f,f)) - (vr . (f,vq))) - ((vr . (vq,f)) - (vr . (vq,vq))) is complex Element of the carrier of F_Complex
- ((vr . (vq,f)) - (vr . (vq,vq))) is complex Element of the carrier of F_Complex
((vr . (f,f)) - (vr . (f,vq))) + (- ((vr . (vq,f)) - (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,f)) - (vr . (f,vq))),(- ((vr . (vq,f)) - (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
[((vr . (f,f)) - (vr . (f,vq))),(- ((vr . (vq,f)) - (vr . (vq,vq))))] is set
{((vr . (f,f)) - (vr . (f,vq))),(- ((vr . (vq,f)) - (vr . (vq,vq))))} is non empty V175() set
{((vr . (f,f)) - (vr . (f,vq)))} is non empty V175() set
{{((vr . (f,f)) - (vr . (f,vq))),(- ((vr . (vq,f)) - (vr . (vq,vq))))},{((vr . (f,f)) - (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [((vr . (f,f)) - (vr . (f,vq))),(- ((vr . (vq,f)) - (vr . (vq,vq))))] is set
K135(((vr . (f,f)) - (vr . (f,vq))),(- ((vr . (vq,f)) - (vr . (vq,vq))))) is complex Element of COMPLEX
((vr . (f,f)) + (vr . (f,vq))) - (((vr . (f,f)) - (vr . (f,vq))) - ((vr . (vq,f)) - (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
- (((vr . (f,f)) - (vr . (f,vq))) - ((vr . (vq,f)) - (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
((vr . (f,f)) + (vr . (f,vq))) + (- (((vr . (f,f)) - (vr . (f,vq))) - ((vr . (vq,f)) - (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,f)) + (vr . (f,vq))),(- (((vr . (f,f)) - (vr . (f,vq))) - ((vr . (vq,f)) - (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
[((vr . (f,f)) + (vr . (f,vq))),(- (((vr . (f,f)) - (vr . (f,vq))) - ((vr . (vq,f)) - (vr . (vq,vq)))))] is set
{((vr . (f,f)) + (vr . (f,vq))),(- (((vr . (f,f)) - (vr . (f,vq))) - ((vr . (vq,f)) - (vr . (vq,vq)))))} is non empty V175() set
{{((vr . (f,f)) + (vr . (f,vq))),(- (((vr . (f,f)) - (vr . (f,vq))) - ((vr . (vq,f)) - (vr . (vq,vq)))))},{((vr . (f,f)) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [((vr . (f,f)) + (vr . (f,vq))),(- (((vr . (f,f)) - (vr . (f,vq))) - ((vr . (vq,f)) - (vr . (vq,vq)))))] is set
K135(((vr . (f,f)) + (vr . (f,vq))),(- (((vr . (f,f)) - (vr . (f,vq))) - ((vr . (vq,f)) - (vr . (vq,vq)))))) is complex Element of COMPLEX
(((vr . (f,f)) + (vr . (f,vq))) - (((vr . (f,f)) - (vr . (f,vq))) - ((vr . (vq,f)) - (vr . (vq,vq))))) + ((vr . (vq,f)) + (vr . (vq,vq))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((vr . (f,f)) + (vr . (f,vq))) - (((vr . (f,f)) - (vr . (f,vq))) - ((vr . (vq,f)) - (vr . (vq,vq))))),((vr . (vq,f)) + (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
[(((vr . (f,f)) + (vr . (f,vq))) - (((vr . (f,f)) - (vr . (f,vq))) - ((vr . (vq,f)) - (vr . (vq,vq))))),((vr . (vq,f)) + (vr . (vq,vq)))] is set
{(((vr . (f,f)) + (vr . (f,vq))) - (((vr . (f,f)) - (vr . (f,vq))) - ((vr . (vq,f)) - (vr . (vq,vq))))),((vr . (vq,f)) + (vr . (vq,vq)))} is non empty V175() set
{(((vr . (f,f)) + (vr . (f,vq))) - (((vr . (f,f)) - (vr . (f,vq))) - ((vr . (vq,f)) - (vr . (vq,vq)))))} is non empty V175() set
{{(((vr . (f,f)) + (vr . (f,vq))) - (((vr . (f,f)) - (vr . (f,vq))) - ((vr . (vq,f)) - (vr . (vq,vq))))),((vr . (vq,f)) + (vr . (vq,vq)))},{(((vr . (f,f)) + (vr . (f,vq))) - (((vr . (f,f)) - (vr . (f,vq))) - ((vr . (vq,f)) - (vr . (vq,vq)))))}} is non empty set
the addF of F_Complex . [(((vr . (f,f)) + (vr . (f,vq))) - (((vr . (f,f)) - (vr . (f,vq))) - ((vr . (vq,f)) - (vr . (vq,vq))))),((vr . (vq,f)) + (vr . (vq,vq)))] is set
K135((((vr . (f,f)) + (vr . (f,vq))) - (((vr . (f,f)) - (vr . (f,vq))) - ((vr . (vq,f)) - (vr . (vq,vq))))),((vr . (vq,f)) + (vr . (vq,vq)))) is complex Element of COMPLEX
((vr . (f,f)) + (vr . (f,vq))) - ((vr . (f,f)) - (vr . (f,vq))) is complex Element of the carrier of F_Complex
- ((vr . (f,f)) - (vr . (f,vq))) is complex Element of the carrier of F_Complex
((vr . (f,f)) + (vr . (f,vq))) + (- ((vr . (f,f)) - (vr . (f,vq)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,f)) + (vr . (f,vq))),(- ((vr . (f,f)) - (vr . (f,vq))))) is complex Element of the carrier of F_Complex
[((vr . (f,f)) + (vr . (f,vq))),(- ((vr . (f,f)) - (vr . (f,vq))))] is set
{((vr . (f,f)) + (vr . (f,vq))),(- ((vr . (f,f)) - (vr . (f,vq))))} is non empty V175() set
{{((vr . (f,f)) + (vr . (f,vq))),(- ((vr . (f,f)) - (vr . (f,vq))))},{((vr . (f,f)) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [((vr . (f,f)) + (vr . (f,vq))),(- ((vr . (f,f)) - (vr . (f,vq))))] is set
K135(((vr . (f,f)) + (vr . (f,vq))),(- ((vr . (f,f)) - (vr . (f,vq))))) is complex Element of COMPLEX
(((vr . (f,f)) + (vr . (f,vq))) - ((vr . (f,f)) - (vr . (f,vq)))) + ((vr . (vq,f)) - (vr . (vq,vq))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((vr . (f,f)) + (vr . (f,vq))) - ((vr . (f,f)) - (vr . (f,vq)))),((vr . (vq,f)) - (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
[(((vr . (f,f)) + (vr . (f,vq))) - ((vr . (f,f)) - (vr . (f,vq)))),((vr . (vq,f)) - (vr . (vq,vq)))] is set
{(((vr . (f,f)) + (vr . (f,vq))) - ((vr . (f,f)) - (vr . (f,vq)))),((vr . (vq,f)) - (vr . (vq,vq)))} is non empty V175() set
{(((vr . (f,f)) + (vr . (f,vq))) - ((vr . (f,f)) - (vr . (f,vq))))} is non empty V175() set
{{(((vr . (f,f)) + (vr . (f,vq))) - ((vr . (f,f)) - (vr . (f,vq)))),((vr . (vq,f)) - (vr . (vq,vq)))},{(((vr . (f,f)) + (vr . (f,vq))) - ((vr . (f,f)) - (vr . (f,vq))))}} is non empty set
the addF of F_Complex . [(((vr . (f,f)) + (vr . (f,vq))) - ((vr . (f,f)) - (vr . (f,vq)))),((vr . (vq,f)) - (vr . (vq,vq)))] is set
K135((((vr . (f,f)) + (vr . (f,vq))) - ((vr . (f,f)) - (vr . (f,vq)))),((vr . (vq,f)) - (vr . (vq,vq)))) is complex Element of COMPLEX
((((vr . (f,f)) + (vr . (f,vq))) - ((vr . (f,f)) - (vr . (f,vq)))) + ((vr . (vq,f)) - (vr . (vq,vq)))) + ((vr . (vq,f)) + (vr . (vq,vq))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((((vr . (f,f)) + (vr . (f,vq))) - ((vr . (f,f)) - (vr . (f,vq)))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
[((((vr . (f,f)) + (vr . (f,vq))) - ((vr . (f,f)) - (vr . (f,vq)))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))] is set
{((((vr . (f,f)) + (vr . (f,vq))) - ((vr . (f,f)) - (vr . (f,vq)))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))} is non empty V175() set
{((((vr . (f,f)) + (vr . (f,vq))) - ((vr . (f,f)) - (vr . (f,vq)))) + ((vr . (vq,f)) - (vr . (vq,vq))))} is non empty V175() set
{{((((vr . (f,f)) + (vr . (f,vq))) - ((vr . (f,f)) - (vr . (f,vq)))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))},{((((vr . (f,f)) + (vr . (f,vq))) - ((vr . (f,f)) - (vr . (f,vq)))) + ((vr . (vq,f)) - (vr . (vq,vq))))}} is non empty set
the addF of F_Complex . [((((vr . (f,f)) + (vr . (f,vq))) - ((vr . (f,f)) - (vr . (f,vq)))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))] is set
K135(((((vr . (f,f)) + (vr . (f,vq))) - ((vr . (f,f)) - (vr . (f,vq)))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))) is complex Element of COMPLEX
(vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq))) is complex Element of the carrier of F_Complex
(vr . (f,f)) + (- ((vr . (f,f)) - (vr . (f,vq)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (f,f)),(- ((vr . (f,f)) - (vr . (f,vq))))) is complex Element of the carrier of F_Complex
[(vr . (f,f)),(- ((vr . (f,f)) - (vr . (f,vq))))] is set
{(vr . (f,f)),(- ((vr . (f,f)) - (vr . (f,vq))))} is non empty V175() set
{{(vr . (f,f)),(- ((vr . (f,f)) - (vr . (f,vq))))},{(vr . (f,f))}} is non empty set
the addF of F_Complex . [(vr . (f,f)),(- ((vr . (f,f)) - (vr . (f,vq))))] is set
K135((vr . (f,f)),(- ((vr . (f,f)) - (vr . (f,vq))))) is complex Element of COMPLEX
((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))) + (vr . (f,vq)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))),(vr . (f,vq))) is complex Element of the carrier of F_Complex
[((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))),(vr . (f,vq))] is set
{((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))),(vr . (f,vq))} is non empty V175() set
{((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq))))} is non empty V175() set
{{((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))),(vr . (f,vq))},{((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq))))}} is non empty set
the addF of F_Complex . [((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))),(vr . (f,vq))] is set
K135(((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))),(vr . (f,vq))) is complex Element of COMPLEX
(((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
[(((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))] is set
{(((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))} is non empty V175() set
{(((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))) + (vr . (f,vq)))} is non empty V175() set
{{(((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))},{(((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [(((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))] is set
K135((((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))) is complex Element of COMPLEX
((((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))) + ((vr . (vq,f)) + (vr . (vq,vq))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
[((((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))] is set
{((((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))} is non empty V175() set
{((((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq))))} is non empty V175() set
{{((((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))},{((((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq))))}} is non empty set
the addF of F_Complex . [((((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))] is set
K135(((((vr . (f,f)) - ((vr . (f,f)) - (vr . (f,vq)))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))) is complex Element of COMPLEX
(vr . (f,f)) - (vr . (f,f)) is complex Element of the carrier of F_Complex
- (vr . (f,f)) is complex Element of the carrier of F_Complex
(vr . (f,f)) + (- (vr . (f,f))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (f,f)),(- (vr . (f,f)))) is complex Element of the carrier of F_Complex
[(vr . (f,f)),(- (vr . (f,f)))] is set
{(vr . (f,f)),(- (vr . (f,f)))} is non empty V175() set
{{(vr . (f,f)),(- (vr . (f,f)))},{(vr . (f,f))}} is non empty set
the addF of F_Complex . [(vr . (f,f)),(- (vr . (f,f)))] is set
K135((vr . (f,f)),(- (vr . (f,f)))) is complex Element of COMPLEX
((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,f)) - (vr . (f,f))),(vr . (f,vq))) is complex Element of the carrier of F_Complex
[((vr . (f,f)) - (vr . (f,f))),(vr . (f,vq))] is set
{((vr . (f,f)) - (vr . (f,f))),(vr . (f,vq))} is non empty V175() set
{((vr . (f,f)) - (vr . (f,f)))} is non empty V175() set
{{((vr . (f,f)) - (vr . (f,f))),(vr . (f,vq))},{((vr . (f,f)) - (vr . (f,f)))}} is non empty set
the addF of F_Complex . [((vr . (f,f)) - (vr . (f,f))),(vr . (f,vq))] is set
K135(((vr . (f,f)) - (vr . (f,f))),(vr . (f,vq))) is complex Element of COMPLEX
(((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))) + (vr . (f,vq)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))),(vr . (f,vq))) is complex Element of the carrier of F_Complex
[(((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))),(vr . (f,vq))] is set
{(((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))),(vr . (f,vq))} is non empty V175() set
{(((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq)))} is non empty V175() set
{{(((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))),(vr . (f,vq))},{(((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [(((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))),(vr . (f,vq))] is set
K135((((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))),(vr . (f,vq))) is complex Element of COMPLEX
((((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
[((((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))] is set
{((((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))} is non empty V175() set
{((((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))) + (vr . (f,vq)))} is non empty V175() set
{{((((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))},{((((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [((((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))] is set
K135(((((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))) is complex Element of COMPLEX
(((((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))) + ((vr . (vq,f)) + (vr . (vq,vq))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
[(((((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))] is set
{(((((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))} is non empty V175() set
{(((((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq))))} is non empty V175() set
{{(((((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))},{(((((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq))))}} is non empty set
the addF of F_Complex . [(((((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))] is set
K135((((((vr . (f,f)) - (vr . (f,f))) + (vr . (f,vq))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))) is complex Element of COMPLEX
(0. F_Complex) + (vr . (f,vq)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((0. F_Complex),(vr . (f,vq))) is complex Element of the carrier of F_Complex
[(0. F_Complex),(vr . (f,vq))] is set
{(0. F_Complex),(vr . (f,vq))} is non empty V175() set
{(0. F_Complex)} is non empty V175() set
{{(0. F_Complex),(vr . (f,vq))},{(0. F_Complex)}} is non empty set
the addF of F_Complex . [(0. F_Complex),(vr . (f,vq))] is set
K135((0. F_Complex),(vr . (f,vq))) is complex Element of COMPLEX
((0. F_Complex) + (vr . (f,vq))) + (vr . (f,vq)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((0. F_Complex) + (vr . (f,vq))),(vr . (f,vq))) is complex Element of the carrier of F_Complex
[((0. F_Complex) + (vr . (f,vq))),(vr . (f,vq))] is set
{((0. F_Complex) + (vr . (f,vq))),(vr . (f,vq))} is non empty V175() set
{((0. F_Complex) + (vr . (f,vq)))} is non empty V175() set
{{((0. F_Complex) + (vr . (f,vq))),(vr . (f,vq))},{((0. F_Complex) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [((0. F_Complex) + (vr . (f,vq))),(vr . (f,vq))] is set
K135(((0. F_Complex) + (vr . (f,vq))),(vr . (f,vq))) is complex Element of COMPLEX
(((0. F_Complex) + (vr . (f,vq))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((0. F_Complex) + (vr . (f,vq))) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
[(((0. F_Complex) + (vr . (f,vq))) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))] is set
{(((0. F_Complex) + (vr . (f,vq))) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))} is non empty V175() set
{(((0. F_Complex) + (vr . (f,vq))) + (vr . (f,vq)))} is non empty V175() set
{{(((0. F_Complex) + (vr . (f,vq))) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))},{(((0. F_Complex) + (vr . (f,vq))) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [(((0. F_Complex) + (vr . (f,vq))) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))] is set
K135((((0. F_Complex) + (vr . (f,vq))) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))) is complex Element of COMPLEX
((((0. F_Complex) + (vr . (f,vq))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))) + ((vr . (vq,f)) + (vr . (vq,vq))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((((0. F_Complex) + (vr . (f,vq))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
[((((0. F_Complex) + (vr . (f,vq))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))] is set
{((((0. F_Complex) + (vr . (f,vq))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))} is non empty V175() set
{((((0. F_Complex) + (vr . (f,vq))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq))))} is non empty V175() set
{{((((0. F_Complex) + (vr . (f,vq))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))},{((((0. F_Complex) + (vr . (f,vq))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq))))}} is non empty set
the addF of F_Complex . [((((0. F_Complex) + (vr . (f,vq))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))] is set
K135(((((0. F_Complex) + (vr . (f,vq))) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))) is complex Element of COMPLEX
((vr . (f,vq)) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,vq)) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
[((vr . (f,vq)) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))] is set
{((vr . (f,vq)) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))} is non empty V175() set
{{((vr . (f,vq)) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))},{((vr . (f,vq)) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [((vr . (f,vq)) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))] is set
K135(((vr . (f,vq)) + (vr . (f,vq))),((vr . (vq,f)) - (vr . (vq,vq)))) is complex Element of COMPLEX
(((vr . (f,vq)) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))) + ((vr . (vq,f)) + (vr . (vq,vq))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((vr . (f,vq)) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
[(((vr . (f,vq)) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))] is set
{(((vr . (f,vq)) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))} is non empty V175() set
{(((vr . (f,vq)) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq))))} is non empty V175() set
{{(((vr . (f,vq)) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))},{(((vr . (f,vq)) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq))))}} is non empty set
the addF of F_Complex . [(((vr . (f,vq)) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))] is set
K135((((vr . (f,vq)) + (vr . (f,vq))) + ((vr . (vq,f)) - (vr . (vq,vq)))),((vr . (vq,f)) + (vr . (vq,vq)))) is complex Element of COMPLEX
((vr . (vq,f)) - (vr . (vq,vq))) + (vr . (vq,vq)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (vq,f)) - (vr . (vq,vq))),(vr . (vq,vq))) is complex Element of the carrier of F_Complex
[((vr . (vq,f)) - (vr . (vq,vq))),(vr . (vq,vq))] is set
{((vr . (vq,f)) - (vr . (vq,vq))),(vr . (vq,vq))} is non empty V175() set
{((vr . (vq,f)) - (vr . (vq,vq)))} is non empty V175() set
{{((vr . (vq,f)) - (vr . (vq,vq))),(vr . (vq,vq))},{((vr . (vq,f)) - (vr . (vq,vq)))}} is non empty set
the addF of F_Complex . [((vr . (vq,f)) - (vr . (vq,vq))),(vr . (vq,vq))] is set
K135(((vr . (vq,f)) - (vr . (vq,vq))),(vr . (vq,vq))) is complex Element of COMPLEX
(((vr . (vq,f)) - (vr . (vq,vq))) + (vr . (vq,vq))) + (vr . (vq,f)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((vr . (vq,f)) - (vr . (vq,vq))) + (vr . (vq,vq))),(vr . (vq,f))) is complex Element of the carrier of F_Complex
[(((vr . (vq,f)) - (vr . (vq,vq))) + (vr . (vq,vq))),(vr . (vq,f))] is set
{(((vr . (vq,f)) - (vr . (vq,vq))) + (vr . (vq,vq))),(vr . (vq,f))} is non empty V175() set
{(((vr . (vq,f)) - (vr . (vq,vq))) + (vr . (vq,vq)))} is non empty V175() set
{{(((vr . (vq,f)) - (vr . (vq,vq))) + (vr . (vq,vq))),(vr . (vq,f))},{(((vr . (vq,f)) - (vr . (vq,vq))) + (vr . (vq,vq)))}} is non empty set
the addF of F_Complex . [(((vr . (vq,f)) - (vr . (vq,vq))) + (vr . (vq,vq))),(vr . (vq,f))] is set
K135((((vr . (vq,f)) - (vr . (vq,vq))) + (vr . (vq,vq))),(vr . (vq,f))) is complex Element of COMPLEX
((vr . (f,vq)) + (vr . (f,vq))) + ((((vr . (vq,f)) - (vr . (vq,vq))) + (vr . (vq,vq))) + (vr . (vq,f))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,vq)) + (vr . (f,vq))),((((vr . (vq,f)) - (vr . (vq,vq))) + (vr . (vq,vq))) + (vr . (vq,f)))) is complex Element of the carrier of F_Complex
[((vr . (f,vq)) + (vr . (f,vq))),((((vr . (vq,f)) - (vr . (vq,vq))) + (vr . (vq,vq))) + (vr . (vq,f)))] is set
{((vr . (f,vq)) + (vr . (f,vq))),((((vr . (vq,f)) - (vr . (vq,vq))) + (vr . (vq,vq))) + (vr . (vq,f)))} is non empty V175() set
{{((vr . (f,vq)) + (vr . (f,vq))),((((vr . (vq,f)) - (vr . (vq,vq))) + (vr . (vq,vq))) + (vr . (vq,f)))},{((vr . (f,vq)) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [((vr . (f,vq)) + (vr . (f,vq))),((((vr . (vq,f)) - (vr . (vq,vq))) + (vr . (vq,vq))) + (vr . (vq,f)))] is set
K135(((vr . (f,vq)) + (vr . (f,vq))),((((vr . (vq,f)) - (vr . (vq,vq))) + (vr . (vq,vq))) + (vr . (vq,f)))) is complex Element of COMPLEX
(vr . (vq,vq)) - (vr . (vq,vq)) is complex Element of the carrier of F_Complex
(vr . (vq,vq)) + (- (vr . (vq,vq))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (vq,vq)),(- (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
[(vr . (vq,vq)),(- (vr . (vq,vq)))] is set
{(vr . (vq,vq)),(- (vr . (vq,vq)))} is non empty V175() set
{(vr . (vq,vq))} is non empty V175() set
{{(vr . (vq,vq)),(- (vr . (vq,vq)))},{(vr . (vq,vq))}} is non empty set
the addF of F_Complex . [(vr . (vq,vq)),(- (vr . (vq,vq)))] is set
K135((vr . (vq,vq)),(- (vr . (vq,vq)))) is complex Element of COMPLEX
(vr . (vq,f)) - ((vr . (vq,vq)) - (vr . (vq,vq))) is complex Element of the carrier of F_Complex
- ((vr . (vq,vq)) - (vr . (vq,vq))) is complex Element of the carrier of F_Complex
(vr . (vq,f)) + (- ((vr . (vq,vq)) - (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (vq,f)),(- ((vr . (vq,vq)) - (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
[(vr . (vq,f)),(- ((vr . (vq,vq)) - (vr . (vq,vq))))] is set
{(vr . (vq,f)),(- ((vr . (vq,vq)) - (vr . (vq,vq))))} is non empty V175() set
{{(vr . (vq,f)),(- ((vr . (vq,vq)) - (vr . (vq,vq))))},{(vr . (vq,f))}} is non empty set
the addF of F_Complex . [(vr . (vq,f)),(- ((vr . (vq,vq)) - (vr . (vq,vq))))] is set
K135((vr . (vq,f)),(- ((vr . (vq,vq)) - (vr . (vq,vq))))) is complex Element of COMPLEX
((vr . (vq,f)) - ((vr . (vq,vq)) - (vr . (vq,vq)))) + (vr . (vq,f)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (vq,f)) - ((vr . (vq,vq)) - (vr . (vq,vq)))),(vr . (vq,f))) is complex Element of the carrier of F_Complex
[((vr . (vq,f)) - ((vr . (vq,vq)) - (vr . (vq,vq)))),(vr . (vq,f))] is set
{((vr . (vq,f)) - ((vr . (vq,vq)) - (vr . (vq,vq)))),(vr . (vq,f))} is non empty V175() set
{((vr . (vq,f)) - ((vr . (vq,vq)) - (vr . (vq,vq))))} is non empty V175() set
{{((vr . (vq,f)) - ((vr . (vq,vq)) - (vr . (vq,vq)))),(vr . (vq,f))},{((vr . (vq,f)) - ((vr . (vq,vq)) - (vr . (vq,vq))))}} is non empty set
the addF of F_Complex . [((vr . (vq,f)) - ((vr . (vq,vq)) - (vr . (vq,vq)))),(vr . (vq,f))] is set
K135(((vr . (vq,f)) - ((vr . (vq,vq)) - (vr . (vq,vq)))),(vr . (vq,f))) is complex Element of COMPLEX
((vr . (f,vq)) + (vr . (f,vq))) + (((vr . (vq,f)) - ((vr . (vq,vq)) - (vr . (vq,vq)))) + (vr . (vq,f))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,vq)) + (vr . (f,vq))),(((vr . (vq,f)) - ((vr . (vq,vq)) - (vr . (vq,vq)))) + (vr . (vq,f)))) is complex Element of the carrier of F_Complex
[((vr . (f,vq)) + (vr . (f,vq))),(((vr . (vq,f)) - ((vr . (vq,vq)) - (vr . (vq,vq)))) + (vr . (vq,f)))] is set
{((vr . (f,vq)) + (vr . (f,vq))),(((vr . (vq,f)) - ((vr . (vq,vq)) - (vr . (vq,vq)))) + (vr . (vq,f)))} is non empty V175() set
{{((vr . (f,vq)) + (vr . (f,vq))),(((vr . (vq,f)) - ((vr . (vq,vq)) - (vr . (vq,vq)))) + (vr . (vq,f)))},{((vr . (f,vq)) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [((vr . (f,vq)) + (vr . (f,vq))),(((vr . (vq,f)) - ((vr . (vq,vq)) - (vr . (vq,vq)))) + (vr . (vq,f)))] is set
K135(((vr . (f,vq)) + (vr . (f,vq))),(((vr . (vq,f)) - ((vr . (vq,vq)) - (vr . (vq,vq)))) + (vr . (vq,f)))) is complex Element of COMPLEX
(vr . (vq,f)) - (0. F_Complex) is complex Element of the carrier of F_Complex
- (0. F_Complex) is complex Element of the carrier of F_Complex
(vr . (vq,f)) + (- (0. F_Complex)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (vq,f)),(- (0. F_Complex))) is complex Element of the carrier of F_Complex
[(vr . (vq,f)),(- (0. F_Complex))] is set
{(vr . (vq,f)),(- (0. F_Complex))} is non empty V175() set
{{(vr . (vq,f)),(- (0. F_Complex))},{(vr . (vq,f))}} is non empty set
the addF of F_Complex . [(vr . (vq,f)),(- (0. F_Complex))] is set
K135((vr . (vq,f)),(- (0. F_Complex))) is complex Element of COMPLEX
((vr . (vq,f)) - (0. F_Complex)) + (vr . (vq,f)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (vq,f)) - (0. F_Complex)),(vr . (vq,f))) is complex Element of the carrier of F_Complex
[((vr . (vq,f)) - (0. F_Complex)),(vr . (vq,f))] is set
{((vr . (vq,f)) - (0. F_Complex)),(vr . (vq,f))} is non empty V175() set
{((vr . (vq,f)) - (0. F_Complex))} is non empty V175() set
{{((vr . (vq,f)) - (0. F_Complex)),(vr . (vq,f))},{((vr . (vq,f)) - (0. F_Complex))}} is non empty set
the addF of F_Complex . [((vr . (vq,f)) - (0. F_Complex)),(vr . (vq,f))] is set
K135(((vr . (vq,f)) - (0. F_Complex)),(vr . (vq,f))) is complex Element of COMPLEX
((vr . (f,vq)) + (vr . (f,vq))) + (((vr . (vq,f)) - (0. F_Complex)) + (vr . (vq,f))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,vq)) + (vr . (f,vq))),(((vr . (vq,f)) - (0. F_Complex)) + (vr . (vq,f)))) is complex Element of the carrier of F_Complex
[((vr . (f,vq)) + (vr . (f,vq))),(((vr . (vq,f)) - (0. F_Complex)) + (vr . (vq,f)))] is set
{((vr . (f,vq)) + (vr . (f,vq))),(((vr . (vq,f)) - (0. F_Complex)) + (vr . (vq,f)))} is non empty V175() set
{{((vr . (f,vq)) + (vr . (f,vq))),(((vr . (vq,f)) - (0. F_Complex)) + (vr . (vq,f)))},{((vr . (f,vq)) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [((vr . (f,vq)) + (vr . (f,vq))),(((vr . (vq,f)) - (0. F_Complex)) + (vr . (vq,f)))] is set
K135(((vr . (f,vq)) + (vr . (f,vq))),(((vr . (vq,f)) - (0. F_Complex)) + (vr . (vq,f)))) is complex Element of COMPLEX
(vr . (vq,f)) + (vr . (vq,f)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (vq,f)),(vr . (vq,f))) is complex Element of the carrier of F_Complex
[(vr . (vq,f)),(vr . (vq,f))] is set
{(vr . (vq,f)),(vr . (vq,f))} is non empty V175() set
{{(vr . (vq,f)),(vr . (vq,f))},{(vr . (vq,f))}} is non empty set
the addF of F_Complex . [(vr . (vq,f)),(vr . (vq,f))] is set
K135((vr . (vq,f)),(vr . (vq,f))) is complex Element of COMPLEX
((vr . (f,vq)) + (vr . (f,vq))) + ((vr . (vq,f)) + (vr . (vq,f))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,vq)) + (vr . (f,vq))),((vr . (vq,f)) + (vr . (vq,f)))) is complex Element of the carrier of F_Complex
[((vr . (f,vq)) + (vr . (f,vq))),((vr . (vq,f)) + (vr . (vq,f)))] is set
{((vr . (f,vq)) + (vr . (f,vq))),((vr . (vq,f)) + (vr . (vq,f)))} is non empty V175() set
{{((vr . (f,vq)) + (vr . (f,vq))),((vr . (vq,f)) + (vr . (vq,f)))},{((vr . (f,vq)) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [((vr . (f,vq)) + (vr . (f,vq))),((vr . (vq,f)) + (vr . (vq,f)))] is set
K135(((vr . (f,vq)) + (vr . (f,vq))),((vr . (vq,f)) + (vr . (vq,f)))) is complex Element of COMPLEX
(i_FC *') * (vr . (f,vq)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((i_FC *'),(vr . (f,vq))) is complex Element of the carrier of F_Complex
[(i_FC *'),(vr . (f,vq))] is set
{(i_FC *'),(vr . (f,vq))} is non empty V175() set
{(i_FC *')} is non empty V175() set
{{(i_FC *'),(vr . (f,vq))},{(i_FC *')}} is non empty set
the multF of F_Complex . [(i_FC *'),(vr . (f,vq))] is set
K137((i_FC *'),(vr . (f,vq))) is complex Element of COMPLEX
(vr . (f,f)) + ((i_FC *') * (vr . (f,vq))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (f,f)),((i_FC *') * (vr . (f,vq)))) is complex Element of the carrier of F_Complex
[(vr . (f,f)),((i_FC *') * (vr . (f,vq)))] is set
{(vr . (f,f)),((i_FC *') * (vr . (f,vq)))} is non empty V175() set
{{(vr . (f,f)),((i_FC *') * (vr . (f,vq)))},{(vr . (f,f))}} is non empty set
the addF of F_Complex . [(vr . (f,f)),((i_FC *') * (vr . (f,vq)))] is set
K135((vr . (f,f)),((i_FC *') * (vr . (f,vq)))) is complex Element of COMPLEX
i_FC * (vr . (vq,f)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (i_FC,(vr . (vq,f))) is complex Element of the carrier of F_Complex
[i_FC,(vr . (vq,f))] is set
{i_FC,(vr . (vq,f))} is non empty V175() set
{{i_FC,(vr . (vq,f))},{i_FC}} is non empty set
the multF of F_Complex . [i_FC,(vr . (vq,f))] is set
K137(i_FC,(vr . (vq,f))) is complex Element of COMPLEX
(i_FC *') * (vr . (vq,vq)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((i_FC *'),(vr . (vq,vq))) is complex Element of the carrier of F_Complex
[(i_FC *'),(vr . (vq,vq))] is set
{(i_FC *'),(vr . (vq,vq))} is non empty V175() set
{{(i_FC *'),(vr . (vq,vq))},{(i_FC *')}} is non empty set
the multF of F_Complex . [(i_FC *'),(vr . (vq,vq))] is set
K137((i_FC *'),(vr . (vq,vq))) is complex Element of COMPLEX
i_FC * ((i_FC *') * (vr . (vq,vq))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (i_FC,((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
[i_FC,((i_FC *') * (vr . (vq,vq)))] is set
{i_FC,((i_FC *') * (vr . (vq,vq)))} is non empty V175() set
{{i_FC,((i_FC *') * (vr . (vq,vq)))},{i_FC}} is non empty set
the multF of F_Complex . [i_FC,((i_FC *') * (vr . (vq,vq)))] is set
K137(i_FC,((i_FC *') * (vr . (vq,vq)))) is complex Element of COMPLEX
(i_FC * (vr . (vq,f))) + (i_FC * ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((i_FC * (vr . (vq,f))),(i_FC * ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
[(i_FC * (vr . (vq,f))),(i_FC * ((i_FC *') * (vr . (vq,vq))))] is set
{(i_FC * (vr . (vq,f))),(i_FC * ((i_FC *') * (vr . (vq,vq))))} is non empty V175() set
{(i_FC * (vr . (vq,f)))} is non empty V175() set
{{(i_FC * (vr . (vq,f))),(i_FC * ((i_FC *') * (vr . (vq,vq))))},{(i_FC * (vr . (vq,f)))}} is non empty set
the addF of F_Complex . [(i_FC * (vr . (vq,f))),(i_FC * ((i_FC *') * (vr . (vq,vq))))] is set
K135((i_FC * (vr . (vq,f))),(i_FC * ((i_FC *') * (vr . (vq,vq))))) is complex Element of COMPLEX
((vr . (f,f)) + ((i_FC *') * (vr . (f,vq)))) + ((i_FC * (vr . (vq,f))) + (i_FC * ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,f)) + ((i_FC *') * (vr . (f,vq)))),((i_FC * (vr . (vq,f))) + (i_FC * ((i_FC *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
[((vr . (f,f)) + ((i_FC *') * (vr . (f,vq)))),((i_FC * (vr . (vq,f))) + (i_FC * ((i_FC *') * (vr . (vq,vq)))))] is set
{((vr . (f,f)) + ((i_FC *') * (vr . (f,vq)))),((i_FC * (vr . (vq,f))) + (i_FC * ((i_FC *') * (vr . (vq,vq)))))} is non empty V175() set
{((vr . (f,f)) + ((i_FC *') * (vr . (f,vq))))} is non empty V175() set
{{((vr . (f,f)) + ((i_FC *') * (vr . (f,vq)))),((i_FC * (vr . (vq,f))) + (i_FC * ((i_FC *') * (vr . (vq,vq)))))},{((vr . (f,f)) + ((i_FC *') * (vr . (f,vq))))}} is non empty set
the addF of F_Complex . [((vr . (f,f)) + ((i_FC *') * (vr . (f,vq)))),((i_FC * (vr . (vq,f))) + (i_FC * ((i_FC *') * (vr . (vq,vq)))))] is set
K135(((vr . (f,f)) + ((i_FC *') * (vr . (f,vq)))),((i_FC * (vr . (vq,f))) + (i_FC * ((i_FC *') * (vr . (vq,vq)))))) is complex Element of COMPLEX
(vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (vq,f)),((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
[(vr . (vq,f)),((i_FC *') * (vr . (vq,vq)))] is set
{(vr . (vq,f)),((i_FC *') * (vr . (vq,vq)))} is non empty V175() set
{{(vr . (vq,f)),((i_FC *') * (vr . (vq,vq)))},{(vr . (vq,f))}} is non empty set
the addF of F_Complex . [(vr . (vq,f)),((i_FC *') * (vr . (vq,vq)))] is set
K135((vr . (vq,f)),((i_FC *') * (vr . (vq,vq)))) is complex Element of COMPLEX
i_FC * ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (i_FC,((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
[i_FC,((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))] is set
{i_FC,((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))} is non empty V175() set
{{i_FC,((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))},{i_FC}} is non empty set
the multF of F_Complex . [i_FC,((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))] is set
K137(i_FC,((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) is complex Element of COMPLEX
((vr . (f,f)) + ((i_FC *') * (vr . (f,vq)))) + (i_FC * ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,f)) + ((i_FC *') * (vr . (f,vq)))),(i_FC * ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
[((vr . (f,f)) + ((i_FC *') * (vr . (f,vq)))),(i_FC * ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))] is set
{((vr . (f,f)) + ((i_FC *') * (vr . (f,vq)))),(i_FC * ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))} is non empty V175() set
{{((vr . (f,f)) + ((i_FC *') * (vr . (f,vq)))),(i_FC * ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))},{((vr . (f,f)) + ((i_FC *') * (vr . (f,vq))))}} is non empty set
the addF of F_Complex . [((vr . (f,f)) + ((i_FC *') * (vr . (f,vq)))),(i_FC * ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))] is set
K135(((vr . (f,f)) + ((i_FC *') * (vr . (f,vq)))),(i_FC * ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))) is complex Element of COMPLEX
i_FC * ((vr . (f,f)) + ((i_FC *') * (vr . (f,vq)))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (i_FC,((vr . (f,f)) + ((i_FC *') * (vr . (f,vq))))) is complex Element of the carrier of F_Complex
[i_FC,((vr . (f,f)) + ((i_FC *') * (vr . (f,vq))))] is set
{i_FC,((vr . (f,f)) + ((i_FC *') * (vr . (f,vq))))} is non empty V175() set
{{i_FC,((vr . (f,f)) + ((i_FC *') * (vr . (f,vq))))},{i_FC}} is non empty set
the multF of F_Complex . [i_FC,((vr . (f,f)) + ((i_FC *') * (vr . (f,vq))))] is set
K137(i_FC,((vr . (f,f)) + ((i_FC *') * (vr . (f,vq))))) is complex Element of COMPLEX
(i_FC * i_FC) * ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((i_FC * i_FC),((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
[(i_FC * i_FC),((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))] is set
{(i_FC * i_FC),((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))} is non empty V175() set
{(i_FC * i_FC)} is non empty V175() set
{{(i_FC * i_FC),((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))},{(i_FC * i_FC)}} is non empty set
the multF of F_Complex . [(i_FC * i_FC),((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))] is set
K137((i_FC * i_FC),((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) is complex Element of COMPLEX
(i_FC * ((vr . (f,f)) + ((i_FC *') * (vr . (f,vq))))) + ((i_FC * i_FC) * ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((i_FC * ((vr . (f,f)) + ((i_FC *') * (vr . (f,vq))))),((i_FC * i_FC) * ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
[(i_FC * ((vr . (f,f)) + ((i_FC *') * (vr . (f,vq))))),((i_FC * i_FC) * ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))] is set
{(i_FC * ((vr . (f,f)) + ((i_FC *') * (vr . (f,vq))))),((i_FC * i_FC) * ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))} is non empty V175() set
{(i_FC * ((vr . (f,f)) + ((i_FC *') * (vr . (f,vq)))))} is non empty V175() set
{{(i_FC * ((vr . (f,f)) + ((i_FC *') * (vr . (f,vq))))),((i_FC * i_FC) * ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))},{(i_FC * ((vr . (f,f)) + ((i_FC *') * (vr . (f,vq)))))}} is non empty set
the addF of F_Complex . [(i_FC * ((vr . (f,f)) + ((i_FC *') * (vr . (f,vq))))),((i_FC * i_FC) * ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))] is set
K135((i_FC * ((vr . (f,f)) + ((i_FC *') * (vr . (f,vq))))),((i_FC * i_FC) * ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))) is complex Element of COMPLEX
i_FC * (vr . (f,f)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (i_FC,(vr . (f,f))) is complex Element of the carrier of F_Complex
[i_FC,(vr . (f,f))] is set
{i_FC,(vr . (f,f))} is non empty V175() set
{{i_FC,(vr . (f,f))},{i_FC}} is non empty set
the multF of F_Complex . [i_FC,(vr . (f,f))] is set
K137(i_FC,(vr . (f,f))) is complex Element of COMPLEX
(i_FC * (vr . (f,f))) + (vr . (f,vq)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((i_FC * (vr . (f,f))),(vr . (f,vq))) is complex Element of the carrier of F_Complex
[(i_FC * (vr . (f,f))),(vr . (f,vq))] is set
{(i_FC * (vr . (f,f))),(vr . (f,vq))} is non empty V175() set
{(i_FC * (vr . (f,f)))} is non empty V175() set
{{(i_FC * (vr . (f,f))),(vr . (f,vq))},{(i_FC * (vr . (f,f)))}} is non empty set
the addF of F_Complex . [(i_FC * (vr . (f,f))),(vr . (f,vq))] is set
K135((i_FC * (vr . (f,f))),(vr . (f,vq))) is complex Element of COMPLEX
((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
((i_FC * (vr . (f,f))) + (vr . (f,vq))) + (- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((i_FC * (vr . (f,f))) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
[((i_FC * (vr . (f,f))) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))] is set
{((i_FC * (vr . (f,f))) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))} is non empty V175() set
{((i_FC * (vr . (f,f))) + (vr . (f,vq)))} is non empty V175() set
{{((i_FC * (vr . (f,f))) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))},{((i_FC * (vr . (f,f))) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [((i_FC * (vr . (f,f))) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))] is set
K135(((i_FC * (vr . (f,f))) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))) is complex Element of COMPLEX
vr . (f,(f - (i_FC * vq))) is complex Element of the carrier of F_Complex
[f,(f - (i_FC * vq))] is set
{f,(f - (i_FC * vq))} is non empty set
{{f,(f - (i_FC * vq))},{f}} is non empty set
vr . [f,(f - (i_FC * vq))] is set
vr . ((i_FC * vq),(f - (i_FC * vq))) is complex Element of the carrier of F_Complex
[(i_FC * vq),(f - (i_FC * vq))] is set
{(i_FC * vq),(f - (i_FC * vq))} is non empty set
{(i_FC * vq)} is non empty set
{{(i_FC * vq),(f - (i_FC * vq))},{(i_FC * vq)}} is non empty set
vr . [(i_FC * vq),(f - (i_FC * vq))] is set
(vr . (f,(f - (i_FC * vq)))) - (vr . ((i_FC * vq),(f - (i_FC * vq)))) is complex Element of the carrier of F_Complex
- (vr . ((i_FC * vq),(f - (i_FC * vq)))) is complex Element of the carrier of F_Complex
(vr . (f,(f - (i_FC * vq)))) + (- (vr . ((i_FC * vq),(f - (i_FC * vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (f,(f - (i_FC * vq)))),(- (vr . ((i_FC * vq),(f - (i_FC * vq)))))) is complex Element of the carrier of F_Complex
[(vr . (f,(f - (i_FC * vq)))),(- (vr . ((i_FC * vq),(f - (i_FC * vq)))))] is set
{(vr . (f,(f - (i_FC * vq)))),(- (vr . ((i_FC * vq),(f - (i_FC * vq)))))} is non empty V175() set
{(vr . (f,(f - (i_FC * vq))))} is non empty V175() set
{{(vr . (f,(f - (i_FC * vq)))),(- (vr . ((i_FC * vq),(f - (i_FC * vq)))))},{(vr . (f,(f - (i_FC * vq))))}} is non empty set
the addF of F_Complex . [(vr . (f,(f - (i_FC * vq)))),(- (vr . ((i_FC * vq),(f - (i_FC * vq)))))] is set
K135((vr . (f,(f - (i_FC * vq)))),(- (vr . ((i_FC * vq),(f - (i_FC * vq)))))) is complex Element of COMPLEX
vr . (f,(i_FC * vq)) is complex Element of the carrier of F_Complex
vr . [f,(i_FC * vq)] is set
(vr . (f,f)) - (vr . (f,(i_FC * vq))) is complex Element of the carrier of F_Complex
- (vr . (f,(i_FC * vq))) is complex Element of the carrier of F_Complex
(vr . (f,f)) + (- (vr . (f,(i_FC * vq)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (f,f)),(- (vr . (f,(i_FC * vq))))) is complex Element of the carrier of F_Complex
[(vr . (f,f)),(- (vr . (f,(i_FC * vq))))] is set
{(vr . (f,f)),(- (vr . (f,(i_FC * vq))))} is non empty V175() set
{{(vr . (f,f)),(- (vr . (f,(i_FC * vq))))},{(vr . (f,f))}} is non empty set
the addF of F_Complex . [(vr . (f,f)),(- (vr . (f,(i_FC * vq))))] is set
K135((vr . (f,f)),(- (vr . (f,(i_FC * vq))))) is complex Element of COMPLEX
((vr . (f,f)) - (vr . (f,(i_FC * vq)))) - (vr . ((i_FC * vq),(f - (i_FC * vq)))) is complex Element of the carrier of F_Complex
((vr . (f,f)) - (vr . (f,(i_FC * vq)))) + (- (vr . ((i_FC * vq),(f - (i_FC * vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,f)) - (vr . (f,(i_FC * vq)))),(- (vr . ((i_FC * vq),(f - (i_FC * vq)))))) is complex Element of the carrier of F_Complex
[((vr . (f,f)) - (vr . (f,(i_FC * vq)))),(- (vr . ((i_FC * vq),(f - (i_FC * vq)))))] is set
{((vr . (f,f)) - (vr . (f,(i_FC * vq)))),(- (vr . ((i_FC * vq),(f - (i_FC * vq)))))} is non empty V175() set
{((vr . (f,f)) - (vr . (f,(i_FC * vq))))} is non empty V175() set
{{((vr . (f,f)) - (vr . (f,(i_FC * vq)))),(- (vr . ((i_FC * vq),(f - (i_FC * vq)))))},{((vr . (f,f)) - (vr . (f,(i_FC * vq))))}} is non empty set
the addF of F_Complex . [((vr . (f,f)) - (vr . (f,(i_FC * vq)))),(- (vr . ((i_FC * vq),(f - (i_FC * vq)))))] is set
K135(((vr . (f,f)) - (vr . (f,(i_FC * vq)))),(- (vr . ((i_FC * vq),(f - (i_FC * vq)))))) is complex Element of COMPLEX
(vr . (f,f)) - ((i_FC *') * (vr . (f,vq))) is complex Element of the carrier of F_Complex
- ((i_FC *') * (vr . (f,vq))) is complex Element of the carrier of F_Complex
(vr . (f,f)) + (- ((i_FC *') * (vr . (f,vq)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (f,f)),(- ((i_FC *') * (vr . (f,vq))))) is complex Element of the carrier of F_Complex
[(vr . (f,f)),(- ((i_FC *') * (vr . (f,vq))))] is set
{(vr . (f,f)),(- ((i_FC *') * (vr . (f,vq))))} is non empty V175() set
{{(vr . (f,f)),(- ((i_FC *') * (vr . (f,vq))))},{(vr . (f,f))}} is non empty set
the addF of F_Complex . [(vr . (f,f)),(- ((i_FC *') * (vr . (f,vq))))] is set
K135((vr . (f,f)),(- ((i_FC *') * (vr . (f,vq))))) is complex Element of COMPLEX
((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))) - (vr . ((i_FC * vq),(f - (i_FC * vq)))) is complex Element of the carrier of F_Complex
((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))) + (- (vr . ((i_FC * vq),(f - (i_FC * vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (vr . ((i_FC * vq),(f - (i_FC * vq)))))) is complex Element of the carrier of F_Complex
[((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (vr . ((i_FC * vq),(f - (i_FC * vq)))))] is set
{((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (vr . ((i_FC * vq),(f - (i_FC * vq)))))} is non empty V175() set
{((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))} is non empty V175() set
{{((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (vr . ((i_FC * vq),(f - (i_FC * vq)))))},{((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))}} is non empty set
the addF of F_Complex . [((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (vr . ((i_FC * vq),(f - (i_FC * vq)))))] is set
K135(((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (vr . ((i_FC * vq),(f - (i_FC * vq)))))) is complex Element of COMPLEX
vr . (vq,(f - (i_FC * vq))) is complex Element of the carrier of F_Complex
[vq,(f - (i_FC * vq))] is set
{vq,(f - (i_FC * vq))} is non empty set
{{vq,(f - (i_FC * vq))},{vq}} is non empty set
vr . [vq,(f - (i_FC * vq))] is set
i_FC * (vr . (vq,(f - (i_FC * vq)))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (i_FC,(vr . (vq,(f - (i_FC * vq))))) is complex Element of the carrier of F_Complex
[i_FC,(vr . (vq,(f - (i_FC * vq))))] is set
{i_FC,(vr . (vq,(f - (i_FC * vq))))} is non empty V175() set
{{i_FC,(vr . (vq,(f - (i_FC * vq))))},{i_FC}} is non empty set
the multF of F_Complex . [i_FC,(vr . (vq,(f - (i_FC * vq))))] is set
K137(i_FC,(vr . (vq,(f - (i_FC * vq))))) is complex Element of COMPLEX
((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))) - (i_FC * (vr . (vq,(f - (i_FC * vq))))) is complex Element of the carrier of F_Complex
- (i_FC * (vr . (vq,(f - (i_FC * vq))))) is complex Element of the carrier of F_Complex
((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))) + (- (i_FC * (vr . (vq,(f - (i_FC * vq)))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (i_FC * (vr . (vq,(f - (i_FC * vq))))))) is complex Element of the carrier of F_Complex
[((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (i_FC * (vr . (vq,(f - (i_FC * vq))))))] is set
{((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (i_FC * (vr . (vq,(f - (i_FC * vq))))))} is non empty V175() set
{{((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (i_FC * (vr . (vq,(f - (i_FC * vq))))))},{((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))}} is non empty set
the addF of F_Complex . [((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (i_FC * (vr . (vq,(f - (i_FC * vq))))))] is set
K135(((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (i_FC * (vr . (vq,(f - (i_FC * vq))))))) is complex Element of COMPLEX
vr . (vq,(i_FC * vq)) is complex Element of the carrier of F_Complex
[vq,(i_FC * vq)] is set
{vq,(i_FC * vq)} is non empty set
{{vq,(i_FC * vq)},{vq}} is non empty set
vr . [vq,(i_FC * vq)] is set
(vr . (vq,f)) - (vr . (vq,(i_FC * vq))) is complex Element of the carrier of F_Complex
- (vr . (vq,(i_FC * vq))) is complex Element of the carrier of F_Complex
(vr . (vq,f)) + (- (vr . (vq,(i_FC * vq)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (vq,f)),(- (vr . (vq,(i_FC * vq))))) is complex Element of the carrier of F_Complex
[(vr . (vq,f)),(- (vr . (vq,(i_FC * vq))))] is set
{(vr . (vq,f)),(- (vr . (vq,(i_FC * vq))))} is non empty V175() set
{{(vr . (vq,f)),(- (vr . (vq,(i_FC * vq))))},{(vr . (vq,f))}} is non empty set
the addF of F_Complex . [(vr . (vq,f)),(- (vr . (vq,(i_FC * vq))))] is set
K135((vr . (vq,f)),(- (vr . (vq,(i_FC * vq))))) is complex Element of COMPLEX
i_FC * ((vr . (vq,f)) - (vr . (vq,(i_FC * vq)))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (i_FC,((vr . (vq,f)) - (vr . (vq,(i_FC * vq))))) is complex Element of the carrier of F_Complex
[i_FC,((vr . (vq,f)) - (vr . (vq,(i_FC * vq))))] is set
{i_FC,((vr . (vq,f)) - (vr . (vq,(i_FC * vq))))} is non empty V175() set
{{i_FC,((vr . (vq,f)) - (vr . (vq,(i_FC * vq))))},{i_FC}} is non empty set
the multF of F_Complex . [i_FC,((vr . (vq,f)) - (vr . (vq,(i_FC * vq))))] is set
K137(i_FC,((vr . (vq,f)) - (vr . (vq,(i_FC * vq))))) is complex Element of COMPLEX
((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))) - (i_FC * ((vr . (vq,f)) - (vr . (vq,(i_FC * vq))))) is complex Element of the carrier of F_Complex
- (i_FC * ((vr . (vq,f)) - (vr . (vq,(i_FC * vq))))) is complex Element of the carrier of F_Complex
((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))) + (- (i_FC * ((vr . (vq,f)) - (vr . (vq,(i_FC * vq)))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (i_FC * ((vr . (vq,f)) - (vr . (vq,(i_FC * vq))))))) is complex Element of the carrier of F_Complex
[((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (i_FC * ((vr . (vq,f)) - (vr . (vq,(i_FC * vq))))))] is set
{((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (i_FC * ((vr . (vq,f)) - (vr . (vq,(i_FC * vq))))))} is non empty V175() set
{{((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (i_FC * ((vr . (vq,f)) - (vr . (vq,(i_FC * vq))))))},{((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))}} is non empty set
the addF of F_Complex . [((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (i_FC * ((vr . (vq,f)) - (vr . (vq,(i_FC * vq))))))] is set
K135(((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (i_FC * ((vr . (vq,f)) - (vr . (vq,(i_FC * vq))))))) is complex Element of COMPLEX
(vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))) is complex Element of the carrier of F_Complex
- ((i_FC *') * (vr . (vq,vq))) is complex Element of the carrier of F_Complex
(vr . (vq,f)) + (- ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (vq,f)),(- ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
[(vr . (vq,f)),(- ((i_FC *') * (vr . (vq,vq))))] is set
{(vr . (vq,f)),(- ((i_FC *') * (vr . (vq,vq))))} is non empty V175() set
{{(vr . (vq,f)),(- ((i_FC *') * (vr . (vq,vq))))},{(vr . (vq,f))}} is non empty set
the addF of F_Complex . [(vr . (vq,f)),(- ((i_FC *') * (vr . (vq,vq))))] is set
K135((vr . (vq,f)),(- ((i_FC *') * (vr . (vq,vq))))) is complex Element of COMPLEX
i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (i_FC,((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
[i_FC,((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))] is set
{i_FC,((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))} is non empty V175() set
{{i_FC,((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))},{i_FC}} is non empty set
the multF of F_Complex . [i_FC,((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))] is set
K137(i_FC,((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of COMPLEX
((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))) - (i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
- (i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))) + (- (i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))) is complex Element of the carrier of F_Complex
[((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))] is set
{((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))} is non empty V175() set
{{((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))},{((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))}} is non empty set
the addF of F_Complex . [((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))] is set
K135(((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))),(- (i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))) is complex Element of COMPLEX
i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (i_FC,((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))) is complex Element of the carrier of F_Complex
[i_FC,((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))] is set
{i_FC,((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))} is non empty V175() set
{{i_FC,((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))},{i_FC}} is non empty set
the multF of F_Complex . [i_FC,((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))] is set
K137(i_FC,((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))) is complex Element of COMPLEX
i_FC * (i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (i_FC,(i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
[i_FC,(i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))] is set
{i_FC,(i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))} is non empty V175() set
{{i_FC,(i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))},{i_FC}} is non empty set
the multF of F_Complex . [i_FC,(i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))] is set
K137(i_FC,(i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))) is complex Element of COMPLEX
(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))) - (i_FC * (i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
- (i_FC * (i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))) + (- (i_FC * (i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),(- (i_FC * (i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))))) is complex Element of the carrier of F_Complex
[(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),(- (i_FC * (i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))))] is set
{(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),(- (i_FC * (i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))))} is non empty V175() set
{(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))))} is non empty V175() set
{{(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),(- (i_FC * (i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))))},{(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))))}} is non empty set
the addF of F_Complex . [(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),(- (i_FC * (i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))))] is set
K135((i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),(- (i_FC * (i_FC * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))))) is complex Element of COMPLEX
(i_FC * i_FC) * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((i_FC * i_FC),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
[(i_FC * i_FC),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))] is set
{(i_FC * i_FC),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))} is non empty V175() set
{{(i_FC * i_FC),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))},{(i_FC * i_FC)}} is non empty set
the multF of F_Complex . [(i_FC * i_FC),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))] is set
K137((i_FC * i_FC),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of COMPLEX
(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))) - ((i_FC * i_FC) * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
- ((i_FC * i_FC) * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))) + (- ((i_FC * i_FC) * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),(- ((i_FC * i_FC) * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))) is complex Element of the carrier of F_Complex
[(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),(- ((i_FC * i_FC) * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))] is set
{(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),(- ((i_FC * i_FC) * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))} is non empty V175() set
{{(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),(- ((i_FC * i_FC) * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))},{(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))))}} is non empty set
the addF of F_Complex . [(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),(- ((i_FC * i_FC) * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))] is set
K135((i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),(- ((i_FC * i_FC) * ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))) is complex Element of COMPLEX
- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))) - (- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
- (- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))) + (- (- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),(- (- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))) is complex Element of the carrier of F_Complex
[(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),(- (- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))] is set
{(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),(- (- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))} is non empty V175() set
{{(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),(- (- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))},{(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))))}} is non empty set
the addF of F_Complex . [(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),(- (- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))] is set
K135((i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),(- (- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))) is complex Element of COMPLEX
(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))) + ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
[(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))] is set
{(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))} is non empty V175() set
{{(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))},{(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq)))))}} is non empty set
the addF of F_Complex . [(i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))] is set
K135((i_FC * ((vr . (f,f)) - ((i_FC *') * (vr . (f,vq))))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of COMPLEX
i_FC * ((i_FC *') * (vr . (f,vq))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (i_FC,((i_FC *') * (vr . (f,vq)))) is complex Element of the carrier of F_Complex
[i_FC,((i_FC *') * (vr . (f,vq)))] is set
{i_FC,((i_FC *') * (vr . (f,vq)))} is non empty V175() set
{{i_FC,((i_FC *') * (vr . (f,vq)))},{i_FC}} is non empty set
the multF of F_Complex . [i_FC,((i_FC *') * (vr . (f,vq)))] is set
K137(i_FC,((i_FC *') * (vr . (f,vq)))) is complex Element of COMPLEX
(i_FC * (vr . (f,f))) - (i_FC * ((i_FC *') * (vr . (f,vq)))) is complex Element of the carrier of F_Complex
- (i_FC * ((i_FC *') * (vr . (f,vq)))) is complex Element of the carrier of F_Complex
(i_FC * (vr . (f,f))) + (- (i_FC * ((i_FC *') * (vr . (f,vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((i_FC * (vr . (f,f))),(- (i_FC * ((i_FC *') * (vr . (f,vq)))))) is complex Element of the carrier of F_Complex
[(i_FC * (vr . (f,f))),(- (i_FC * ((i_FC *') * (vr . (f,vq)))))] is set
{(i_FC * (vr . (f,f))),(- (i_FC * ((i_FC *') * (vr . (f,vq)))))} is non empty V175() set
{{(i_FC * (vr . (f,f))),(- (i_FC * ((i_FC *') * (vr . (f,vq)))))},{(i_FC * (vr . (f,f)))}} is non empty set
the addF of F_Complex . [(i_FC * (vr . (f,f))),(- (i_FC * ((i_FC *') * (vr . (f,vq)))))] is set
K135((i_FC * (vr . (f,f))),(- (i_FC * ((i_FC *') * (vr . (f,vq)))))) is complex Element of COMPLEX
((i_FC * (vr . (f,f))) - (i_FC * ((i_FC *') * (vr . (f,vq))))) + ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((i_FC * (vr . (f,f))) - (i_FC * ((i_FC *') * (vr . (f,vq))))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
[((i_FC * (vr . (f,f))) - (i_FC * ((i_FC *') * (vr . (f,vq))))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))] is set
{((i_FC * (vr . (f,f))) - (i_FC * ((i_FC *') * (vr . (f,vq))))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))} is non empty V175() set
{((i_FC * (vr . (f,f))) - (i_FC * ((i_FC *') * (vr . (f,vq)))))} is non empty V175() set
{{((i_FC * (vr . (f,f))) - (i_FC * ((i_FC *') * (vr . (f,vq))))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))},{((i_FC * (vr . (f,f))) - (i_FC * ((i_FC *') * (vr . (f,vq)))))}} is non empty set
the addF of F_Complex . [((i_FC * (vr . (f,f))) - (i_FC * ((i_FC *') * (vr . (f,vq))))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))] is set
K135(((i_FC * (vr . (f,f))) - (i_FC * ((i_FC *') * (vr . (f,vq))))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of COMPLEX
(i_FC * (vr . (f,f))) - (vr . (f,vq)) is complex Element of the carrier of F_Complex
(i_FC * (vr . (f,f))) + (- (vr . (f,vq))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((i_FC * (vr . (f,f))),(- (vr . (f,vq)))) is complex Element of the carrier of F_Complex
[(i_FC * (vr . (f,f))),(- (vr . (f,vq)))] is set
{(i_FC * (vr . (f,f))),(- (vr . (f,vq)))} is non empty V175() set
{{(i_FC * (vr . (f,f))),(- (vr . (f,vq)))},{(i_FC * (vr . (f,f)))}} is non empty set
the addF of F_Complex . [(i_FC * (vr . (f,f))),(- (vr . (f,vq)))] is set
K135((i_FC * (vr . (f,f))),(- (vr . (f,vq)))) is complex Element of COMPLEX
((i_FC * (vr . (f,f))) - (vr . (f,vq))) + ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((i_FC * (vr . (f,f))) - (vr . (f,vq))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
[((i_FC * (vr . (f,f))) - (vr . (f,vq))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))] is set
{((i_FC * (vr . (f,f))) - (vr . (f,vq))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))} is non empty V175() set
{((i_FC * (vr . (f,f))) - (vr . (f,vq)))} is non empty V175() set
{{((i_FC * (vr . (f,f))) - (vr . (f,vq))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))},{((i_FC * (vr . (f,f))) - (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [((i_FC * (vr . (f,f))) - (vr . (f,vq))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))] is set
K135(((i_FC * (vr . (f,f))) - (vr . (f,vq))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of COMPLEX
(i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq))))) - (i_FC * (vr . ((f - (i_FC * vq)),(f - (i_FC * vq))))) is complex Element of the carrier of F_Complex
(i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq))))) + (- (i_FC * (vr . ((f - (i_FC * vq)),(f - (i_FC * vq)))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq))))),(- (i_FC * (vr . ((f - (i_FC * vq)),(f - (i_FC * vq))))))) is complex Element of the carrier of F_Complex
[(i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq))))),(- (i_FC * (vr . ((f - (i_FC * vq)),(f - (i_FC * vq))))))] is set
{(i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq))))),(- (i_FC * (vr . ((f - (i_FC * vq)),(f - (i_FC * vq))))))} is non empty V175() set
{(i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq)))))} is non empty V175() set
{{(i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq))))),(- (i_FC * (vr . ((f - (i_FC * vq)),(f - (i_FC * vq))))))},{(i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq)))))}} is non empty set
the addF of F_Complex . [(i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq))))),(- (i_FC * (vr . ((f - (i_FC * vq)),(f - (i_FC * vq))))))] is set
K135((i_FC * (vr . ((f + (i_FC * vq)),(f + (i_FC * vq))))),(- (i_FC * (vr . ((f - (i_FC * vq)),(f - (i_FC * vq))))))) is complex Element of COMPLEX
(((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq))) is complex Element of the carrier of F_Complex
- ((i_FC * (vr . (f,f))) - (vr . (f,vq))) is complex Element of the carrier of F_Complex
(((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) + (- ((i_FC * (vr . (f,f))) - (vr . (f,vq)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((i_FC * (vr . (f,f))) - (vr . (f,vq))))) is complex Element of the carrier of F_Complex
[(((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((i_FC * (vr . (f,f))) - (vr . (f,vq))))] is set
{(((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((i_FC * (vr . (f,f))) - (vr . (f,vq))))} is non empty V175() set
{(((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))} is non empty V175() set
{{(((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((i_FC * (vr . (f,f))) - (vr . (f,vq))))},{(((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))}} is non empty set
the addF of F_Complex . [(((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((i_FC * (vr . (f,f))) - (vr . (f,vq))))] is set
K135((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((i_FC * (vr . (f,f))) - (vr . (f,vq))))) is complex Element of COMPLEX
((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))) - ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))) + (- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
[((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))] is set
{((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))} is non empty V175() set
{((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq))))} is non empty V175() set
{{((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))},{((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq))))}} is non empty set
the addF of F_Complex . [((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))] is set
K135(((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))) is complex Element of COMPLEX
((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq))) is complex Element of the carrier of F_Complex
((i_FC * (vr . (f,f))) + (vr . (f,vq))) + (- ((i_FC * (vr . (f,f))) - (vr . (f,vq)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((i_FC * (vr . (f,f))) + (vr . (f,vq))),(- ((i_FC * (vr . (f,f))) - (vr . (f,vq))))) is complex Element of the carrier of F_Complex
[((i_FC * (vr . (f,f))) + (vr . (f,vq))),(- ((i_FC * (vr . (f,f))) - (vr . (f,vq))))] is set
{((i_FC * (vr . (f,f))) + (vr . (f,vq))),(- ((i_FC * (vr . (f,f))) - (vr . (f,vq))))} is non empty V175() set
{{((i_FC * (vr . (f,f))) + (vr . (f,vq))),(- ((i_FC * (vr . (f,f))) - (vr . (f,vq))))},{((i_FC * (vr . (f,f))) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [((i_FC * (vr . (f,f))) + (vr . (f,vq))),(- ((i_FC * (vr . (f,f))) - (vr . (f,vq))))] is set
K135(((i_FC * (vr . (f,f))) + (vr . (f,vq))),(- ((i_FC * (vr . (f,f))) - (vr . (f,vq))))) is complex Element of COMPLEX
(((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
(((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))) + (- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
[(((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))] is set
{(((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))} is non empty V175() set
{(((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq))))} is non empty V175() set
{{(((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))},{(((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq))))}} is non empty set
the addF of F_Complex . [(((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))] is set
K135((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))) is complex Element of COMPLEX
((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) - ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) + (- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
[((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))] is set
{((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))} is non empty V175() set
{((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))} is non empty V175() set
{{((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))},{((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))}} is non empty set
the addF of F_Complex . [((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))] is set
K135(((((i_FC * (vr . (f,f))) + (vr . (f,vq))) - ((i_FC * (vr . (f,f))) - (vr . (f,vq)))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))) is complex Element of COMPLEX
(vr . (f,vq)) + (i_FC * (vr . (f,f))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (f,vq)),(i_FC * (vr . (f,f)))) is complex Element of the carrier of F_Complex
[(vr . (f,vq)),(i_FC * (vr . (f,f)))] is set
{(vr . (f,vq)),(i_FC * (vr . (f,f)))} is non empty V175() set
{{(vr . (f,vq)),(i_FC * (vr . (f,f)))},{(vr . (f,vq))}} is non empty set
the addF of F_Complex . [(vr . (f,vq)),(i_FC * (vr . (f,f)))] is set
K135((vr . (f,vq)),(i_FC * (vr . (f,f)))) is complex Element of COMPLEX
((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f))) is complex Element of the carrier of F_Complex
- (i_FC * (vr . (f,f))) is complex Element of the carrier of F_Complex
((vr . (f,vq)) + (i_FC * (vr . (f,f)))) + (- (i_FC * (vr . (f,f)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,vq)) + (i_FC * (vr . (f,f)))),(- (i_FC * (vr . (f,f))))) is complex Element of the carrier of F_Complex
[((vr . (f,vq)) + (i_FC * (vr . (f,f)))),(- (i_FC * (vr . (f,f))))] is set
{((vr . (f,vq)) + (i_FC * (vr . (f,f)))),(- (i_FC * (vr . (f,f))))} is non empty V175() set
{((vr . (f,vq)) + (i_FC * (vr . (f,f))))} is non empty V175() set
{{((vr . (f,vq)) + (i_FC * (vr . (f,f)))),(- (i_FC * (vr . (f,f))))},{((vr . (f,vq)) + (i_FC * (vr . (f,f))))}} is non empty set
the addF of F_Complex . [((vr . (f,vq)) + (i_FC * (vr . (f,f)))),(- (i_FC * (vr . (f,f))))] is set
K135(((vr . (f,vq)) + (i_FC * (vr . (f,f)))),(- (i_FC * (vr . (f,f))))) is complex Element of COMPLEX
(((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))) + (vr . (f,vq)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))),(vr . (f,vq))) is complex Element of the carrier of F_Complex
[(((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))),(vr . (f,vq))] is set
{(((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))),(vr . (f,vq))} is non empty V175() set
{(((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f))))} is non empty V175() set
{{(((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))),(vr . (f,vq))},{(((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f))))}} is non empty set
the addF of F_Complex . [(((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))),(vr . (f,vq))] is set
K135((((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))),(vr . (f,vq))) is complex Element of COMPLEX
((((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
((((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))) + (vr . (f,vq))) + (- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
[((((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))] is set
{((((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))} is non empty V175() set
{((((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))) + (vr . (f,vq)))} is non empty V175() set
{{((((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))},{((((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [((((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))] is set
K135(((((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))) is complex Element of COMPLEX
(((((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) - ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
(((((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) + (- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
[(((((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))] is set
{(((((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))} is non empty V175() set
{(((((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))} is non empty V175() set
{{(((((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))},{(((((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))}} is non empty set
the addF of F_Complex . [(((((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))] is set
K135((((((vr . (f,vq)) + (i_FC * (vr . (f,f)))) - (i_FC * (vr . (f,f)))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))) is complex Element of COMPLEX
(i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))) is complex Element of the carrier of F_Complex
(i_FC * (vr . (f,f))) + (- (i_FC * (vr . (f,f)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((i_FC * (vr . (f,f))),(- (i_FC * (vr . (f,f))))) is complex Element of the carrier of F_Complex
[(i_FC * (vr . (f,f))),(- (i_FC * (vr . (f,f))))] is set
{(i_FC * (vr . (f,f))),(- (i_FC * (vr . (f,f))))} is non empty V175() set
{{(i_FC * (vr . (f,f))),(- (i_FC * (vr . (f,f))))},{(i_FC * (vr . (f,f)))}} is non empty set
the addF of F_Complex . [(i_FC * (vr . (f,f))),(- (i_FC * (vr . (f,f))))] is set
K135((i_FC * (vr . (f,f))),(- (i_FC * (vr . (f,f))))) is complex Element of COMPLEX
(vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (f,vq)),((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))) is complex Element of the carrier of F_Complex
[(vr . (f,vq)),((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))] is set
{(vr . (f,vq)),((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))} is non empty V175() set
{{(vr . (f,vq)),((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))},{(vr . (f,vq))}} is non empty set
the addF of F_Complex . [(vr . (f,vq)),((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))] is set
K135((vr . (f,vq)),((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))) is complex Element of COMPLEX
((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))) + (vr . (f,vq)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))),(vr . (f,vq))) is complex Element of the carrier of F_Complex
[((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))),(vr . (f,vq))] is set
{((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))),(vr . (f,vq))} is non empty V175() set
{((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f)))))} is non empty V175() set
{{((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))),(vr . (f,vq))},{((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f)))))}} is non empty set
the addF of F_Complex . [((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))),(vr . (f,vq))] is set
K135(((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))),(vr . (f,vq))) is complex Element of COMPLEX
(((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
(((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))) + (vr . (f,vq))) + (- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
[(((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))] is set
{(((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))} is non empty V175() set
{(((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))) + (vr . (f,vq)))} is non empty V175() set
{{(((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))},{(((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [(((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))] is set
K135((((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))) is complex Element of COMPLEX
((((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) - ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
((((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) + (- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
[((((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))] is set
{((((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))} is non empty V175() set
{((((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))} is non empty V175() set
{{((((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))},{((((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))}} is non empty set
the addF of F_Complex . [((((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))] is set
K135(((((vr . (f,vq)) + ((i_FC * (vr . (f,f))) - (i_FC * (vr . (f,f))))) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))) is complex Element of COMPLEX
(vr . (f,vq)) + (0. F_Complex) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (f,vq)),(0. F_Complex)) is complex Element of the carrier of F_Complex
[(vr . (f,vq)),(0. F_Complex)] is set
{(vr . (f,vq)),(0. F_Complex)} is non empty V175() set
{{(vr . (f,vq)),(0. F_Complex)},{(vr . (f,vq))}} is non empty set
the addF of F_Complex . [(vr . (f,vq)),(0. F_Complex)] is set
K135((vr . (f,vq)),(0. F_Complex)) is complex Element of COMPLEX
((vr . (f,vq)) + (0. F_Complex)) + (vr . (f,vq)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,vq)) + (0. F_Complex)),(vr . (f,vq))) is complex Element of the carrier of F_Complex
[((vr . (f,vq)) + (0. F_Complex)),(vr . (f,vq))] is set
{((vr . (f,vq)) + (0. F_Complex)),(vr . (f,vq))} is non empty V175() set
{((vr . (f,vq)) + (0. F_Complex))} is non empty V175() set
{{((vr . (f,vq)) + (0. F_Complex)),(vr . (f,vq))},{((vr . (f,vq)) + (0. F_Complex))}} is non empty set
the addF of F_Complex . [((vr . (f,vq)) + (0. F_Complex)),(vr . (f,vq))] is set
K135(((vr . (f,vq)) + (0. F_Complex)),(vr . (f,vq))) is complex Element of COMPLEX
(((vr . (f,vq)) + (0. F_Complex)) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
(((vr . (f,vq)) + (0. F_Complex)) + (vr . (f,vq))) + (- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((vr . (f,vq)) + (0. F_Complex)) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
[(((vr . (f,vq)) + (0. F_Complex)) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))] is set
{(((vr . (f,vq)) + (0. F_Complex)) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))} is non empty V175() set
{(((vr . (f,vq)) + (0. F_Complex)) + (vr . (f,vq)))} is non empty V175() set
{{(((vr . (f,vq)) + (0. F_Complex)) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))},{(((vr . (f,vq)) + (0. F_Complex)) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [(((vr . (f,vq)) + (0. F_Complex)) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))] is set
K135((((vr . (f,vq)) + (0. F_Complex)) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))) is complex Element of COMPLEX
((((vr . (f,vq)) + (0. F_Complex)) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) - ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
((((vr . (f,vq)) + (0. F_Complex)) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) + (- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((((vr . (f,vq)) + (0. F_Complex)) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
[((((vr . (f,vq)) + (0. F_Complex)) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))] is set
{((((vr . (f,vq)) + (0. F_Complex)) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))} is non empty V175() set
{((((vr . (f,vq)) + (0. F_Complex)) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))} is non empty V175() set
{{((((vr . (f,vq)) + (0. F_Complex)) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))},{((((vr . (f,vq)) + (0. F_Complex)) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))}} is non empty set
the addF of F_Complex . [((((vr . (f,vq)) + (0. F_Complex)) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))] is set
K135(((((vr . (f,vq)) + (0. F_Complex)) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))) is complex Element of COMPLEX
((vr . (f,vq)) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
((vr . (f,vq)) + (vr . (f,vq))) + (- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,vq)) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
[((vr . (f,vq)) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))] is set
{((vr . (f,vq)) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))} is non empty V175() set
{{((vr . (f,vq)) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))},{((vr . (f,vq)) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [((vr . (f,vq)) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))] is set
K135(((vr . (f,vq)) + (vr . (f,vq))),(- ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))) is complex Element of COMPLEX
(((vr . (f,vq)) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) - ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
(((vr . (f,vq)) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))) + (- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((vr . (f,vq)) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
[(((vr . (f,vq)) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))] is set
{(((vr . (f,vq)) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))} is non empty V175() set
{(((vr . (f,vq)) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))} is non empty V175() set
{{(((vr . (f,vq)) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))},{(((vr . (f,vq)) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))))}} is non empty set
the addF of F_Complex . [(((vr . (f,vq)) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))] is set
K135((((vr . (f,vq)) + (vr . (f,vq))) - ((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))),(- ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))) is complex Element of COMPLEX
((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))) + ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
[((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))] is set
{((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))} is non empty V175() set
{((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))} is non empty V175() set
{{((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))},{((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq))))}} is non empty set
the addF of F_Complex . [((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))] is set
K135(((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))),((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of COMPLEX
((vr . (f,vq)) + (vr . (f,vq))) - (((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))) + ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
- (((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))) + ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
((vr . (f,vq)) + (vr . (f,vq))) + (- (((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))) + ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,vq)) + (vr . (f,vq))),(- (((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))) + ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))) is complex Element of the carrier of F_Complex
[((vr . (f,vq)) + (vr . (f,vq))),(- (((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))) + ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))] is set
{((vr . (f,vq)) + (vr . (f,vq))),(- (((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))) + ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))} is non empty V175() set
{{((vr . (f,vq)) + (vr . (f,vq))),(- (((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))) + ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))},{((vr . (f,vq)) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [((vr . (f,vq)) + (vr . (f,vq))),(- (((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))) + ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))] is set
K135(((vr . (f,vq)) + (vr . (f,vq))),(- (((vr . (vq,f)) + ((i_FC *') * (vr . (vq,vq)))) + ((vr . (vq,f)) - ((i_FC *') * (vr . (vq,vq))))))) is complex Element of COMPLEX
((i_FC *') * (vr . (vq,vq))) - ((i_FC *') * (vr . (vq,vq))) is complex Element of the carrier of F_Complex
((i_FC *') * (vr . (vq,vq))) + (- ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((i_FC *') * (vr . (vq,vq))),(- ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
[((i_FC *') * (vr . (vq,vq))),(- ((i_FC *') * (vr . (vq,vq))))] is set
{((i_FC *') * (vr . (vq,vq))),(- ((i_FC *') * (vr . (vq,vq))))} is non empty V175() set
{((i_FC *') * (vr . (vq,vq)))} is non empty V175() set
{{((i_FC *') * (vr . (vq,vq))),(- ((i_FC *') * (vr . (vq,vq))))},{((i_FC *') * (vr . (vq,vq)))}} is non empty set
the addF of F_Complex . [((i_FC *') * (vr . (vq,vq))),(- ((i_FC *') * (vr . (vq,vq))))] is set
K135(((i_FC *') * (vr . (vq,vq))),(- ((i_FC *') * (vr . (vq,vq))))) is complex Element of COMPLEX
((vr . (vq,f)) + (vr . (vq,f))) + (((i_FC *') * (vr . (vq,vq))) - ((i_FC *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (vq,f)) + (vr . (vq,f))),(((i_FC *') * (vr . (vq,vq))) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
[((vr . (vq,f)) + (vr . (vq,f))),(((i_FC *') * (vr . (vq,vq))) - ((i_FC *') * (vr . (vq,vq))))] is set
{((vr . (vq,f)) + (vr . (vq,f))),(((i_FC *') * (vr . (vq,vq))) - ((i_FC *') * (vr . (vq,vq))))} is non empty V175() set
{((vr . (vq,f)) + (vr . (vq,f)))} is non empty V175() set
{{((vr . (vq,f)) + (vr . (vq,f))),(((i_FC *') * (vr . (vq,vq))) - ((i_FC *') * (vr . (vq,vq))))},{((vr . (vq,f)) + (vr . (vq,f)))}} is non empty set
the addF of F_Complex . [((vr . (vq,f)) + (vr . (vq,f))),(((i_FC *') * (vr . (vq,vq))) - ((i_FC *') * (vr . (vq,vq))))] is set
K135(((vr . (vq,f)) + (vr . (vq,f))),(((i_FC *') * (vr . (vq,vq))) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of COMPLEX
((vr . (f,vq)) + (vr . (f,vq))) - (((vr . (vq,f)) + (vr . (vq,f))) + (((i_FC *') * (vr . (vq,vq))) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
- (((vr . (vq,f)) + (vr . (vq,f))) + (((i_FC *') * (vr . (vq,vq))) - ((i_FC *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
((vr . (f,vq)) + (vr . (f,vq))) + (- (((vr . (vq,f)) + (vr . (vq,f))) + (((i_FC *') * (vr . (vq,vq))) - ((i_FC *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,vq)) + (vr . (f,vq))),(- (((vr . (vq,f)) + (vr . (vq,f))) + (((i_FC *') * (vr . (vq,vq))) - ((i_FC *') * (vr . (vq,vq))))))) is complex Element of the carrier of F_Complex
[((vr . (f,vq)) + (vr . (f,vq))),(- (((vr . (vq,f)) + (vr . (vq,f))) + (((i_FC *') * (vr . (vq,vq))) - ((i_FC *') * (vr . (vq,vq))))))] is set
{((vr . (f,vq)) + (vr . (f,vq))),(- (((vr . (vq,f)) + (vr . (vq,f))) + (((i_FC *') * (vr . (vq,vq))) - ((i_FC *') * (vr . (vq,vq))))))} is non empty V175() set
{{((vr . (f,vq)) + (vr . (f,vq))),(- (((vr . (vq,f)) + (vr . (vq,f))) + (((i_FC *') * (vr . (vq,vq))) - ((i_FC *') * (vr . (vq,vq))))))},{((vr . (f,vq)) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [((vr . (f,vq)) + (vr . (f,vq))),(- (((vr . (vq,f)) + (vr . (vq,f))) + (((i_FC *') * (vr . (vq,vq))) - ((i_FC *') * (vr . (vq,vq))))))] is set
K135(((vr . (f,vq)) + (vr . (f,vq))),(- (((vr . (vq,f)) + (vr . (vq,f))) + (((i_FC *') * (vr . (vq,vq))) - ((i_FC *') * (vr . (vq,vq))))))) is complex Element of COMPLEX
((vr . (vq,f)) + (vr . (vq,f))) + (0. F_Complex) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (vq,f)) + (vr . (vq,f))),(0. F_Complex)) is complex Element of the carrier of F_Complex
[((vr . (vq,f)) + (vr . (vq,f))),(0. F_Complex)] is set
{((vr . (vq,f)) + (vr . (vq,f))),(0. F_Complex)} is non empty V175() set
{{((vr . (vq,f)) + (vr . (vq,f))),(0. F_Complex)},{((vr . (vq,f)) + (vr . (vq,f)))}} is non empty set
the addF of F_Complex . [((vr . (vq,f)) + (vr . (vq,f))),(0. F_Complex)] is set
K135(((vr . (vq,f)) + (vr . (vq,f))),(0. F_Complex)) is complex Element of COMPLEX
((vr . (f,vq)) + (vr . (f,vq))) - (((vr . (vq,f)) + (vr . (vq,f))) + (0. F_Complex)) is complex Element of the carrier of F_Complex
- (((vr . (vq,f)) + (vr . (vq,f))) + (0. F_Complex)) is complex Element of the carrier of F_Complex
((vr . (f,vq)) + (vr . (f,vq))) + (- (((vr . (vq,f)) + (vr . (vq,f))) + (0. F_Complex))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,vq)) + (vr . (f,vq))),(- (((vr . (vq,f)) + (vr . (vq,f))) + (0. F_Complex)))) is complex Element of the carrier of F_Complex
[((vr . (f,vq)) + (vr . (f,vq))),(- (((vr . (vq,f)) + (vr . (vq,f))) + (0. F_Complex)))] is set
{((vr . (f,vq)) + (vr . (f,vq))),(- (((vr . (vq,f)) + (vr . (vq,f))) + (0. F_Complex)))} is non empty V175() set
{{((vr . (f,vq)) + (vr . (f,vq))),(- (((vr . (vq,f)) + (vr . (vq,f))) + (0. F_Complex)))},{((vr . (f,vq)) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [((vr . (f,vq)) + (vr . (f,vq))),(- (((vr . (vq,f)) + (vr . (vq,f))) + (0. F_Complex)))] is set
K135(((vr . (f,vq)) + (vr . (f,vq))),(- (((vr . (vq,f)) + (vr . (vq,f))) + (0. F_Complex)))) is complex Element of COMPLEX
((vr . (f,vq)) + (vr . (f,vq))) - ((vr . (vq,f)) + (vr . (vq,f))) is complex Element of the carrier of F_Complex
- ((vr . (vq,f)) + (vr . (vq,f))) is complex Element of the carrier of F_Complex
((vr . (f,vq)) + (vr . (f,vq))) + (- ((vr . (vq,f)) + (vr . (vq,f)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,vq)) + (vr . (f,vq))),(- ((vr . (vq,f)) + (vr . (vq,f))))) is complex Element of the carrier of F_Complex
[((vr . (f,vq)) + (vr . (f,vq))),(- ((vr . (vq,f)) + (vr . (vq,f))))] is set
{((vr . (f,vq)) + (vr . (f,vq))),(- ((vr . (vq,f)) + (vr . (vq,f))))} is non empty V175() set
{{((vr . (f,vq)) + (vr . (f,vq))),(- ((vr . (vq,f)) + (vr . (vq,f))))},{((vr . (f,vq)) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [((vr . (f,vq)) + (vr . (f,vq))),(- ((vr . (vq,f)) + (vr . (vq,f))))] is set
K135(((vr . (f,vq)) + (vr . (f,vq))),(- ((vr . (vq,f)) + (vr . (vq,f))))) is complex Element of COMPLEX
((vr . (vq,f)) + (vr . (vq,f))) + ((vr . (f,vq)) + (vr . (f,vq))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (vq,f)) + (vr . (vq,f))),((vr . (f,vq)) + (vr . (f,vq)))) is complex Element of the carrier of F_Complex
[((vr . (vq,f)) + (vr . (vq,f))),((vr . (f,vq)) + (vr . (f,vq)))] is set
{((vr . (vq,f)) + (vr . (vq,f))),((vr . (f,vq)) + (vr . (f,vq)))} is non empty V175() set
{{((vr . (vq,f)) + (vr . (vq,f))),((vr . (f,vq)) + (vr . (f,vq)))},{((vr . (vq,f)) + (vr . (vq,f)))}} is non empty set
the addF of F_Complex . [((vr . (vq,f)) + (vr . (vq,f))),((vr . (f,vq)) + (vr . (f,vq)))] is set
K135(((vr . (vq,f)) + (vr . (vq,f))),((vr . (f,vq)) + (vr . (f,vq)))) is complex Element of COMPLEX
(((vr . (vq,f)) + (vr . (vq,f))) + ((vr . (f,vq)) + (vr . (f,vq)))) - ((vr . (vq,f)) + (vr . (vq,f))) is complex Element of the carrier of F_Complex
(((vr . (vq,f)) + (vr . (vq,f))) + ((vr . (f,vq)) + (vr . (f,vq)))) + (- ((vr . (vq,f)) + (vr . (vq,f)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((vr . (vq,f)) + (vr . (vq,f))) + ((vr . (f,vq)) + (vr . (f,vq)))),(- ((vr . (vq,f)) + (vr . (vq,f))))) is complex Element of the carrier of F_Complex
[(((vr . (vq,f)) + (vr . (vq,f))) + ((vr . (f,vq)) + (vr . (f,vq)))),(- ((vr . (vq,f)) + (vr . (vq,f))))] is set
{(((vr . (vq,f)) + (vr . (vq,f))) + ((vr . (f,vq)) + (vr . (f,vq)))),(- ((vr . (vq,f)) + (vr . (vq,f))))} is non empty V175() set
{(((vr . (vq,f)) + (vr . (vq,f))) + ((vr . (f,vq)) + (vr . (f,vq))))} is non empty V175() set
{{(((vr . (vq,f)) + (vr . (vq,f))) + ((vr . (f,vq)) + (vr . (f,vq)))),(- ((vr . (vq,f)) + (vr . (vq,f))))},{(((vr . (vq,f)) + (vr . (vq,f))) + ((vr . (f,vq)) + (vr . (f,vq))))}} is non empty set
the addF of F_Complex . [(((vr . (vq,f)) + (vr . (vq,f))) + ((vr . (f,vq)) + (vr . (f,vq)))),(- ((vr . (vq,f)) + (vr . (vq,f))))] is set
K135((((vr . (vq,f)) + (vr . (vq,f))) + ((vr . (f,vq)) + (vr . (f,vq)))),(- ((vr . (vq,f)) + (vr . (vq,f))))) is complex Element of COMPLEX
((vr . (f,vq)) + (vr . (f,vq))) + ((((vr . (vq,f)) + (vr . (vq,f))) + ((vr . (f,vq)) + (vr . (f,vq)))) - ((vr . (vq,f)) + (vr . (vq,f)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,vq)) + (vr . (f,vq))),((((vr . (vq,f)) + (vr . (vq,f))) + ((vr . (f,vq)) + (vr . (f,vq)))) - ((vr . (vq,f)) + (vr . (vq,f))))) is complex Element of the carrier of F_Complex
[((vr . (f,vq)) + (vr . (f,vq))),((((vr . (vq,f)) + (vr . (vq,f))) + ((vr . (f,vq)) + (vr . (f,vq)))) - ((vr . (vq,f)) + (vr . (vq,f))))] is set
{((vr . (f,vq)) + (vr . (f,vq))),((((vr . (vq,f)) + (vr . (vq,f))) + ((vr . (f,vq)) + (vr . (f,vq)))) - ((vr . (vq,f)) + (vr . (vq,f))))} is non empty V175() set
{{((vr . (f,vq)) + (vr . (f,vq))),((((vr . (vq,f)) + (vr . (vq,f))) + ((vr . (f,vq)) + (vr . (f,vq)))) - ((vr . (vq,f)) + (vr . (vq,f))))},{((vr . (f,vq)) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [((vr . (f,vq)) + (vr . (f,vq))),((((vr . (vq,f)) + (vr . (vq,f))) + ((vr . (f,vq)) + (vr . (f,vq)))) - ((vr . (vq,f)) + (vr . (vq,f))))] is set
K135(((vr . (f,vq)) + (vr . (f,vq))),((((vr . (vq,f)) + (vr . (vq,f))) + ((vr . (f,vq)) + (vr . (f,vq)))) - ((vr . (vq,f)) + (vr . (vq,f))))) is complex Element of COMPLEX
((vr . (f,vq)) + (vr . (f,vq))) + ((vr . (f,vq)) + (vr . (f,vq))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,vq)) + (vr . (f,vq))),((vr . (f,vq)) + (vr . (f,vq)))) is complex Element of the carrier of F_Complex
[((vr . (f,vq)) + (vr . (f,vq))),((vr . (f,vq)) + (vr . (f,vq)))] is set
{((vr . (f,vq)) + (vr . (f,vq))),((vr . (f,vq)) + (vr . (f,vq)))} is non empty V175() set
{{((vr . (f,vq)) + (vr . (f,vq))),((vr . (f,vq)) + (vr . (f,vq)))},{((vr . (f,vq)) + (vr . (f,vq)))}} is non empty set
the addF of F_Complex . [((vr . (f,vq)) + (vr . (f,vq))),((vr . (f,vq)) + (vr . (f,vq)))] is set
K135(((vr . (f,vq)) + (vr . (f,vq))),((vr . (f,vq)) + (vr . (f,vq)))) is complex Element of COMPLEX
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
vq is Element of the carrier of V
f . (vq,vq) is complex Element of the carrier of F_Complex
[vq,vq] is set
{vq,vq} is non empty set
{vq} is non empty set
{{vq,vq},{vq}} is non empty set
f . [vq,vq] is set
Re (f . (vq,vq)) is complex real ext-real Element of REAL
V is non empty right_complementable add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
vq is Element of the carrier of V
f . (vq,vq) is complex Element of the carrier of F_Complex
[vq,vq] is set
{vq,vq} is non empty set
{vq} is non empty set
{{vq,vq},{vq}} is non empty set
f . [vq,vq] is set
|.(f . (vq,vq)).| is complex real ext-real Element of REAL
Re (f . (vq,vq)) is complex real ext-real Element of REAL
(Re (f . (vq,vq))) ^2 is complex real ext-real Element of REAL
(Re (f . (vq,vq))) * (Re (f . (vq,vq))) is complex real ext-real set
Im (f . (vq,vq)) is complex real ext-real Element of REAL
(Im (f . (vq,vq))) ^2 is complex real ext-real Element of REAL
(Im (f . (vq,vq))) * (Im (f . (vq,vq))) is complex real ext-real set
((Re (f . (vq,vq))) ^2) + ((Im (f . (vq,vq))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (f . (vq,vq))) ^2) + ((Im (f . (vq,vq))) ^2)) is complex real ext-real Element of REAL
(V,f,vq) is complex real ext-real set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is Element of the carrier of V
vq is Element of the carrier of V
vr is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
vr . (f,f) is complex Element of the carrier of F_Complex
[f,f] is set
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
vr . [f,f] is set
vr . (vq,f) is complex Element of the carrier of F_Complex
[vq,f] is set
{vq,f} is non empty set
{vq} is non empty set
{{vq,f},{vq}} is non empty set
vr . [vq,f] is set
vr . (f,vq) is complex Element of the carrier of F_Complex
[f,vq] is set
{f,vq} is non empty set
{{f,vq},{f}} is non empty set
vr . [f,vq] is set
vr . (vq,vq) is complex Element of the carrier of F_Complex
[vq,vq] is set
{vq,vq} is non empty set
{{vq,vq},{vq}} is non empty set
vr . [vq,vq] is set
qh is complex real ext-real set
[**qh,0**] is complex Element of the carrier of F_Complex
qh + (0 * <i>) is complex set
qh ^2 is complex real ext-real set
qh * qh is complex real ext-real set
[**(qh ^2),0**] is complex Element of the carrier of F_Complex
(qh ^2) + (0 * <i>) is complex set
[**(qh ^2),0**] * (vr . (vq,vq)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ([**(qh ^2),0**],(vr . (vq,vq))) is complex Element of the carrier of F_Complex
[[**(qh ^2),0**],(vr . (vq,vq))] is set
{[**(qh ^2),0**],(vr . (vq,vq))} is non empty V175() set
{[**(qh ^2),0**]} is non empty V175() set
{{[**(qh ^2),0**],(vr . (vq,vq))},{[**(qh ^2),0**]}} is non empty set
the multF of F_Complex . [[**(qh ^2),0**],(vr . (vq,vq))] is set
K137([**(qh ^2),0**],(vr . (vq,vq))) is complex Element of COMPLEX
A is complex Element of the carrier of F_Complex
|.A.| is complex real ext-real Element of REAL
Re A is complex real ext-real Element of REAL
(Re A) ^2 is complex real ext-real Element of REAL
(Re A) * (Re A) is complex real ext-real set
Im A is complex real ext-real Element of REAL
(Im A) ^2 is complex real ext-real Element of REAL
(Im A) * (Im A) is complex real ext-real set
((Re A) ^2) + ((Im A) ^2) is complex real ext-real Element of REAL
sqrt (((Re A) ^2) + ((Im A) ^2)) is complex real ext-real Element of REAL
[**qh,0**] * A is complex Element of the carrier of F_Complex
the multF of F_Complex . ([**qh,0**],A) is complex Element of the carrier of F_Complex
[[**qh,0**],A] is set
{[**qh,0**],A} is non empty V175() set
{[**qh,0**]} is non empty V175() set
{{[**qh,0**],A},{[**qh,0**]}} is non empty set
the multF of F_Complex . [[**qh,0**],A] is set
K137([**qh,0**],A) is complex Element of COMPLEX
([**qh,0**] * A) * vq is Element of the carrier of V
the lmult of V is V16() V19([: the carrier of F_Complex, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of F_Complex, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:]
[: the carrier of F_Complex, the carrier of V:] is set
[:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
the lmult of V . (([**qh,0**] * A),vq) is Element of the carrier of V
[([**qh,0**] * A),vq] is set
{([**qh,0**] * A),vq} is non empty set
{([**qh,0**] * A)} is non empty V175() set
{{([**qh,0**] * A),vq},{([**qh,0**] * A)}} is non empty set
the lmult of V . [([**qh,0**] * A),vq] is set
f - (([**qh,0**] * A) * vq) is Element of the carrier of V
- (([**qh,0**] * A) * vq) is Element of the carrier of V
f + (- (([**qh,0**] * A) * vq)) is Element of the carrier of V
the addF of V is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[:[: the carrier of V, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is set
the addF of V . (f,(- (([**qh,0**] * A) * vq))) is Element of the carrier of V
[f,(- (([**qh,0**] * A) * vq))] is set
{f,(- (([**qh,0**] * A) * vq))} is non empty set
{{f,(- (([**qh,0**] * A) * vq))},{f}} is non empty set
the addF of V . [f,(- (([**qh,0**] * A) * vq))] is set
vr . ((f - (([**qh,0**] * A) * vq)),(f - (([**qh,0**] * A) * vq))) is complex Element of the carrier of F_Complex
[(f - (([**qh,0**] * A) * vq)),(f - (([**qh,0**] * A) * vq))] is set
{(f - (([**qh,0**] * A) * vq)),(f - (([**qh,0**] * A) * vq))} is non empty set
{(f - (([**qh,0**] * A) * vq))} is non empty set
{{(f - (([**qh,0**] * A) * vq)),(f - (([**qh,0**] * A) * vq))},{(f - (([**qh,0**] * A) * vq))}} is non empty set
vr . [(f - (([**qh,0**] * A) * vq)),(f - (([**qh,0**] * A) * vq))] is set
A * (vr . (vq,f)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (A,(vr . (vq,f))) is complex Element of the carrier of F_Complex
[A,(vr . (vq,f))] is set
{A,(vr . (vq,f))} is non empty V175() set
{A} is non empty V175() set
{{A,(vr . (vq,f))},{A}} is non empty set
the multF of F_Complex . [A,(vr . (vq,f))] is set
K137(A,(vr . (vq,f))) is complex Element of COMPLEX
[**qh,0**] * (A * (vr . (vq,f))) is complex Element of the carrier of F_Complex
the multF of F_Complex . ([**qh,0**],(A * (vr . (vq,f)))) is complex Element of the carrier of F_Complex
[[**qh,0**],(A * (vr . (vq,f)))] is set
{[**qh,0**],(A * (vr . (vq,f)))} is non empty V175() set
{{[**qh,0**],(A * (vr . (vq,f)))},{[**qh,0**]}} is non empty set
the multF of F_Complex . [[**qh,0**],(A * (vr . (vq,f)))] is set
K137([**qh,0**],(A * (vr . (vq,f)))) is complex Element of COMPLEX
(vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f)))) is complex Element of the carrier of F_Complex
- ([**qh,0**] * (A * (vr . (vq,f)))) is complex Element of the carrier of F_Complex
(vr . (f,f)) + (- ([**qh,0**] * (A * (vr . (vq,f))))) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . ((vr . (f,f)),(- ([**qh,0**] * (A * (vr . (vq,f)))))) is complex Element of the carrier of F_Complex
[(vr . (f,f)),(- ([**qh,0**] * (A * (vr . (vq,f)))))] is set
{(vr . (f,f)),(- ([**qh,0**] * (A * (vr . (vq,f)))))} is non empty V175() set
{(vr . (f,f))} is non empty V175() set
{{(vr . (f,f)),(- ([**qh,0**] * (A * (vr . (vq,f)))))},{(vr . (f,f))}} is non empty set
the addF of F_Complex . [(vr . (f,f)),(- ([**qh,0**] * (A * (vr . (vq,f)))))] is set
K135((vr . (f,f)),(- ([**qh,0**] * (A * (vr . (vq,f)))))) is complex Element of COMPLEX
A *' is complex Element of the carrier of F_Complex
(Im A) * <i> is complex set
(Re A) - ((Im A) * <i>) is complex set
(A *') * (vr . (f,vq)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((A *'),(vr . (f,vq))) is complex Element of the carrier of F_Complex
[(A *'),(vr . (f,vq))] is set
{(A *'),(vr . (f,vq))} is non empty V175() set
{(A *')} is non empty V175() set
{{(A *'),(vr . (f,vq))},{(A *')}} is non empty set
the multF of F_Complex . [(A *'),(vr . (f,vq))] is set
K137((A *'),(vr . (f,vq))) is complex Element of COMPLEX
[**qh,0**] * ((A *') * (vr . (f,vq))) is complex Element of the carrier of F_Complex
the multF of F_Complex . ([**qh,0**],((A *') * (vr . (f,vq)))) is complex Element of the carrier of F_Complex
[[**qh,0**],((A *') * (vr . (f,vq)))] is set
{[**qh,0**],((A *') * (vr . (f,vq)))} is non empty V175() set
{{[**qh,0**],((A *') * (vr . (f,vq)))},{[**qh,0**]}} is non empty set
the multF of F_Complex . [[**qh,0**],((A *') * (vr . (f,vq)))] is set
K137([**qh,0**],((A *') * (vr . (f,vq)))) is complex Element of COMPLEX
((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq)))) is complex Element of the carrier of F_Complex
- ([**qh,0**] * ((A *') * (vr . (f,vq)))) is complex Element of the carrier of F_Complex
((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) + (- ([**qh,0**] * ((A *') * (vr . (f,vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))),(- ([**qh,0**] * ((A *') * (vr . (f,vq)))))) is complex Element of the carrier of F_Complex
[((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))),(- ([**qh,0**] * ((A *') * (vr . (f,vq)))))] is set
{((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))),(- ([**qh,0**] * ((A *') * (vr . (f,vq)))))} is non empty V175() set
{((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f)))))} is non empty V175() set
{{((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))),(- ([**qh,0**] * ((A *') * (vr . (f,vq)))))},{((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f)))))}} is non empty set
the addF of F_Complex . [((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))),(- ([**qh,0**] * ((A *') * (vr . (f,vq)))))] is set
K135(((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))),(- ([**qh,0**] * ((A *') * (vr . (f,vq)))))) is complex Element of COMPLEX
(((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq))))) + ([**(qh ^2),0**] * (vr . (vq,vq))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),([**(qh ^2),0**] * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
[(((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),([**(qh ^2),0**] * (vr . (vq,vq)))] is set
{(((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),([**(qh ^2),0**] * (vr . (vq,vq)))} is non empty V175() set
{(((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq)))))} is non empty V175() set
{{(((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),([**(qh ^2),0**] * (vr . (vq,vq)))},{(((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq)))))}} is non empty set
the addF of F_Complex . [(((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),([**(qh ^2),0**] * (vr . (vq,vq)))] is set
K135((((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),([**(qh ^2),0**] * (vr . (vq,vq)))) is complex Element of COMPLEX
[**qh,0**] * (A *') is complex Element of the carrier of F_Complex
the multF of F_Complex . ([**qh,0**],(A *')) is complex Element of the carrier of F_Complex
[[**qh,0**],(A *')] is set
{[**qh,0**],(A *')} is non empty V175() set
{{[**qh,0**],(A *')},{[**qh,0**]}} is non empty set
the multF of F_Complex . [[**qh,0**],(A *')] is set
K137([**qh,0**],(A *')) is complex Element of COMPLEX
([**qh,0**] * (A *')) * (vr . (vq,vq)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (([**qh,0**] * (A *')),(vr . (vq,vq))) is complex Element of the carrier of F_Complex
[([**qh,0**] * (A *')),(vr . (vq,vq))] is set
{([**qh,0**] * (A *')),(vr . (vq,vq))} is non empty V175() set
{([**qh,0**] * (A *'))} is non empty V175() set
{{([**qh,0**] * (A *')),(vr . (vq,vq))},{([**qh,0**] * (A *'))}} is non empty set
the multF of F_Complex . [([**qh,0**] * (A *')),(vr . (vq,vq))] is set
K137(([**qh,0**] * (A *')),(vr . (vq,vq))) is complex Element of COMPLEX
([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (([**qh,0**] * A),(([**qh,0**] * (A *')) * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
[([**qh,0**] * A),(([**qh,0**] * (A *')) * (vr . (vq,vq)))] is set
{([**qh,0**] * A),(([**qh,0**] * (A *')) * (vr . (vq,vq)))} is non empty V175() set
{{([**qh,0**] * A),(([**qh,0**] * (A *')) * (vr . (vq,vq)))},{([**qh,0**] * A)}} is non empty set
the multF of F_Complex . [([**qh,0**] * A),(([**qh,0**] * (A *')) * (vr . (vq,vq)))] is set
K137(([**qh,0**] * A),(([**qh,0**] * (A *')) * (vr . (vq,vq)))) is complex Element of COMPLEX
A * (A *') is complex Element of the carrier of F_Complex
the multF of F_Complex . (A,(A *')) is complex Element of the carrier of F_Complex
[A,(A *')] is set
{A,(A *')} is non empty V175() set
{{A,(A *')},{A}} is non empty set
the multF of F_Complex . [A,(A *')] is set
K137(A,(A *')) is complex Element of COMPLEX
[**(qh ^2),0**] * (A * (A *')) is complex Element of the carrier of F_Complex
the multF of F_Complex . ([**(qh ^2),0**],(A * (A *'))) is complex Element of the carrier of F_Complex
[[**(qh ^2),0**],(A * (A *'))] is set
{[**(qh ^2),0**],(A * (A *'))} is non empty V175() set
{{[**(qh ^2),0**],(A * (A *'))},{[**(qh ^2),0**]}} is non empty set
the multF of F_Complex . [[**(qh ^2),0**],(A * (A *'))] is set
K137([**(qh ^2),0**],(A * (A *'))) is complex Element of COMPLEX
([**(qh ^2),0**] * (A * (A *'))) * (vr . (vq,vq)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (([**(qh ^2),0**] * (A * (A *'))),(vr . (vq,vq))) is complex Element of the carrier of F_Complex
[([**(qh ^2),0**] * (A * (A *'))),(vr . (vq,vq))] is set
{([**(qh ^2),0**] * (A * (A *'))),(vr . (vq,vq))} is non empty V175() set
{([**(qh ^2),0**] * (A * (A *')))} is non empty V175() set
{{([**(qh ^2),0**] * (A * (A *'))),(vr . (vq,vq))},{([**(qh ^2),0**] * (A * (A *')))}} is non empty set
the multF of F_Complex . [([**(qh ^2),0**] * (A * (A *'))),(vr . (vq,vq))] is set
K137(([**(qh ^2),0**] * (A * (A *'))),(vr . (vq,vq))) is complex Element of COMPLEX
1 ^2 is complex real ext-real Element of REAL
1 * 1 is non empty complex real ext-real positive non negative set
(qh ^2) * (1 ^2) is complex real ext-real Element of REAL
[**((qh ^2) * (1 ^2)),0**] is complex Element of the carrier of F_Complex
((qh ^2) * (1 ^2)) + (0 * <i>) is complex set
[**((qh ^2) * (1 ^2)),0**] * (vr . (vq,vq)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ([**((qh ^2) * (1 ^2)),0**],(vr . (vq,vq))) is complex Element of the carrier of F_Complex
[[**((qh ^2) * (1 ^2)),0**],(vr . (vq,vq))] is set
{[**((qh ^2) * (1 ^2)),0**],(vr . (vq,vq))} is non empty V175() set
{[**((qh ^2) * (1 ^2)),0**]} is non empty V175() set
{{[**((qh ^2) * (1 ^2)),0**],(vr . (vq,vq))},{[**((qh ^2) * (1 ^2)),0**]}} is non empty set
the multF of F_Complex . [[**((qh ^2) * (1 ^2)),0**],(vr . (vq,vq))] is set
K137([**((qh ^2) * (1 ^2)),0**],(vr . (vq,vq))) is complex Element of COMPLEX
([**qh,0**] * A) *' is complex Element of the carrier of F_Complex
Re ([**qh,0**] * A) is complex real ext-real Element of REAL
Im ([**qh,0**] * A) is complex real ext-real Element of REAL
(Im ([**qh,0**] * A)) * <i> is complex set
(Re ([**qh,0**] * A)) - ((Im ([**qh,0**] * A)) * <i>) is complex set
(([**qh,0**] * A) *') * (vr . (f,vq)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((([**qh,0**] * A) *'),(vr . (f,vq))) is complex Element of the carrier of F_Complex
[(([**qh,0**] * A) *'),(vr . (f,vq))] is set
{(([**qh,0**] * A) *'),(vr . (f,vq))} is non empty V175() set
{(([**qh,0**] * A) *')} is non empty V175() set
{{(([**qh,0**] * A) *'),(vr . (f,vq))},{(([**qh,0**] * A) *')}} is non empty set
the multF of F_Complex . [(([**qh,0**] * A) *'),(vr . (f,vq))] is set
K137((([**qh,0**] * A) *'),(vr . (f,vq))) is complex Element of COMPLEX
(vr . (f,f)) - ((([**qh,0**] * A) *') * (vr . (f,vq))) is complex Element of the carrier of F_Complex
- ((([**qh,0**] * A) *') * (vr . (f,vq))) is complex Element of the carrier of F_Complex
(vr . (f,f)) + (- ((([**qh,0**] * A) *') * (vr . (f,vq)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (f,f)),(- ((([**qh,0**] * A) *') * (vr . (f,vq))))) is complex Element of the carrier of F_Complex
[(vr . (f,f)),(- ((([**qh,0**] * A) *') * (vr . (f,vq))))] is set
{(vr . (f,f)),(- ((([**qh,0**] * A) *') * (vr . (f,vq))))} is non empty V175() set
{{(vr . (f,f)),(- ((([**qh,0**] * A) *') * (vr . (f,vq))))},{(vr . (f,f))}} is non empty set
the addF of F_Complex . [(vr . (f,f)),(- ((([**qh,0**] * A) *') * (vr . (f,vq))))] is set
K135((vr . (f,f)),(- ((([**qh,0**] * A) *') * (vr . (f,vq))))) is complex Element of COMPLEX
([**qh,0**] * A) * (vr . (vq,f)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (([**qh,0**] * A),(vr . (vq,f))) is complex Element of the carrier of F_Complex
[([**qh,0**] * A),(vr . (vq,f))] is set
{([**qh,0**] * A),(vr . (vq,f))} is non empty V175() set
{{([**qh,0**] * A),(vr . (vq,f))},{([**qh,0**] * A)}} is non empty set
the multF of F_Complex . [([**qh,0**] * A),(vr . (vq,f))] is set
K137(([**qh,0**] * A),(vr . (vq,f))) is complex Element of COMPLEX
(([**qh,0**] * A) *') * (vr . (vq,vq)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((([**qh,0**] * A) *'),(vr . (vq,vq))) is complex Element of the carrier of F_Complex
[(([**qh,0**] * A) *'),(vr . (vq,vq))] is set
{(([**qh,0**] * A) *'),(vr . (vq,vq))} is non empty V175() set
{{(([**qh,0**] * A) *'),(vr . (vq,vq))},{(([**qh,0**] * A) *')}} is non empty set
the multF of F_Complex . [(([**qh,0**] * A) *'),(vr . (vq,vq))] is set
K137((([**qh,0**] * A) *'),(vr . (vq,vq))) is complex Element of COMPLEX
([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (([**qh,0**] * A),((([**qh,0**] * A) *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
[([**qh,0**] * A),((([**qh,0**] * A) *') * (vr . (vq,vq)))] is set
{([**qh,0**] * A),((([**qh,0**] * A) *') * (vr . (vq,vq)))} is non empty V175() set
{{([**qh,0**] * A),((([**qh,0**] * A) *') * (vr . (vq,vq)))},{([**qh,0**] * A)}} is non empty set
the multF of F_Complex . [([**qh,0**] * A),((([**qh,0**] * A) *') * (vr . (vq,vq)))] is set
K137(([**qh,0**] * A),((([**qh,0**] * A) *') * (vr . (vq,vq)))) is complex Element of COMPLEX
(([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
- (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
(([**qh,0**] * A) * (vr . (vq,f))) + (- (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((([**qh,0**] * A) * (vr . (vq,f))),(- (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
[(([**qh,0**] * A) * (vr . (vq,f))),(- (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq)))))] is set
{(([**qh,0**] * A) * (vr . (vq,f))),(- (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq)))))} is non empty V175() set
{(([**qh,0**] * A) * (vr . (vq,f)))} is non empty V175() set
{{(([**qh,0**] * A) * (vr . (vq,f))),(- (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq)))))},{(([**qh,0**] * A) * (vr . (vq,f)))}} is non empty set
the addF of F_Complex . [(([**qh,0**] * A) * (vr . (vq,f))),(- (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq)))))] is set
K135((([**qh,0**] * A) * (vr . (vq,f))),(- (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq)))))) is complex Element of COMPLEX
((vr . (f,f)) - ((([**qh,0**] * A) *') * (vr . (f,vq)))) - ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
((vr . (f,f)) - ((([**qh,0**] * A) *') * (vr . (f,vq)))) + (- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,f)) - ((([**qh,0**] * A) *') * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))))))) is complex Element of the carrier of F_Complex
[((vr . (f,f)) - ((([**qh,0**] * A) *') * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))))))] is set
{((vr . (f,f)) - ((([**qh,0**] * A) *') * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))))))} is non empty V175() set
{((vr . (f,f)) - ((([**qh,0**] * A) *') * (vr . (f,vq))))} is non empty V175() set
{{((vr . (f,f)) - ((([**qh,0**] * A) *') * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))))))},{((vr . (f,f)) - ((([**qh,0**] * A) *') * (vr . (f,vq))))}} is non empty set
the addF of F_Complex . [((vr . (f,f)) - ((([**qh,0**] * A) *') * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))))))] is set
K135(((vr . (f,f)) - ((([**qh,0**] * A) *') * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))))))) is complex Element of COMPLEX
[**qh,0**] *' is complex Element of the carrier of F_Complex
Re [**qh,0**] is complex real ext-real Element of REAL
Im [**qh,0**] is complex real ext-real Element of REAL
(Im [**qh,0**]) * <i> is complex set
(Re [**qh,0**]) - ((Im [**qh,0**]) * <i>) is complex set
([**qh,0**] *') * (A *') is complex Element of the carrier of F_Complex
the multF of F_Complex . (([**qh,0**] *'),(A *')) is complex Element of the carrier of F_Complex
[([**qh,0**] *'),(A *')] is set
{([**qh,0**] *'),(A *')} is non empty V175() set
{([**qh,0**] *')} is non empty V175() set
{{([**qh,0**] *'),(A *')},{([**qh,0**] *')}} is non empty set
the multF of F_Complex . [([**qh,0**] *'),(A *')] is set
K137(([**qh,0**] *'),(A *')) is complex Element of COMPLEX
(([**qh,0**] *') * (A *')) * (vr . (f,vq)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((([**qh,0**] *') * (A *')),(vr . (f,vq))) is complex Element of the carrier of F_Complex
[(([**qh,0**] *') * (A *')),(vr . (f,vq))] is set
{(([**qh,0**] *') * (A *')),(vr . (f,vq))} is non empty V175() set
{(([**qh,0**] *') * (A *'))} is non empty V175() set
{{(([**qh,0**] *') * (A *')),(vr . (f,vq))},{(([**qh,0**] *') * (A *'))}} is non empty set
the multF of F_Complex . [(([**qh,0**] *') * (A *')),(vr . (f,vq))] is set
K137((([**qh,0**] *') * (A *')),(vr . (f,vq))) is complex Element of COMPLEX
(vr . (f,f)) - ((([**qh,0**] *') * (A *')) * (vr . (f,vq))) is complex Element of the carrier of F_Complex
- ((([**qh,0**] *') * (A *')) * (vr . (f,vq))) is complex Element of the carrier of F_Complex
(vr . (f,f)) + (- ((([**qh,0**] *') * (A *')) * (vr . (f,vq)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (f,f)),(- ((([**qh,0**] *') * (A *')) * (vr . (f,vq))))) is complex Element of the carrier of F_Complex
[(vr . (f,f)),(- ((([**qh,0**] *') * (A *')) * (vr . (f,vq))))] is set
{(vr . (f,f)),(- ((([**qh,0**] *') * (A *')) * (vr . (f,vq))))} is non empty V175() set
{{(vr . (f,f)),(- ((([**qh,0**] *') * (A *')) * (vr . (f,vq))))},{(vr . (f,f))}} is non empty set
the addF of F_Complex . [(vr . (f,f)),(- ((([**qh,0**] *') * (A *')) * (vr . (f,vq))))] is set
K135((vr . (f,f)),(- ((([**qh,0**] *') * (A *')) * (vr . (f,vq))))) is complex Element of COMPLEX
((vr . (f,f)) - ((([**qh,0**] *') * (A *')) * (vr . (f,vq)))) - ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
((vr . (f,f)) - ((([**qh,0**] *') * (A *')) * (vr . (f,vq)))) + (- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,f)) - ((([**qh,0**] *') * (A *')) * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))))))) is complex Element of the carrier of F_Complex
[((vr . (f,f)) - ((([**qh,0**] *') * (A *')) * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))))))] is set
{((vr . (f,f)) - ((([**qh,0**] *') * (A *')) * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))))))} is non empty V175() set
{((vr . (f,f)) - ((([**qh,0**] *') * (A *')) * (vr . (f,vq))))} is non empty V175() set
{{((vr . (f,f)) - ((([**qh,0**] *') * (A *')) * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))))))},{((vr . (f,f)) - ((([**qh,0**] *') * (A *')) * (vr . (f,vq))))}} is non empty set
the addF of F_Complex . [((vr . (f,f)) - ((([**qh,0**] *') * (A *')) * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))))))] is set
K135(((vr . (f,f)) - ((([**qh,0**] *') * (A *')) * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))))))) is complex Element of COMPLEX
([**qh,0**] * (A *')) * (vr . (f,vq)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (([**qh,0**] * (A *')),(vr . (f,vq))) is complex Element of the carrier of F_Complex
[([**qh,0**] * (A *')),(vr . (f,vq))] is set
{([**qh,0**] * (A *')),(vr . (f,vq))} is non empty V175() set
{{([**qh,0**] * (A *')),(vr . (f,vq))},{([**qh,0**] * (A *'))}} is non empty set
the multF of F_Complex . [([**qh,0**] * (A *')),(vr . (f,vq))] is set
K137(([**qh,0**] * (A *')),(vr . (f,vq))) is complex Element of COMPLEX
(vr . (f,f)) - (([**qh,0**] * (A *')) * (vr . (f,vq))) is complex Element of the carrier of F_Complex
- (([**qh,0**] * (A *')) * (vr . (f,vq))) is complex Element of the carrier of F_Complex
(vr . (f,f)) + (- (([**qh,0**] * (A *')) * (vr . (f,vq)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (f,f)),(- (([**qh,0**] * (A *')) * (vr . (f,vq))))) is complex Element of the carrier of F_Complex
[(vr . (f,f)),(- (([**qh,0**] * (A *')) * (vr . (f,vq))))] is set
{(vr . (f,f)),(- (([**qh,0**] * (A *')) * (vr . (f,vq))))} is non empty V175() set
{{(vr . (f,f)),(- (([**qh,0**] * (A *')) * (vr . (f,vq))))},{(vr . (f,f))}} is non empty set
the addF of F_Complex . [(vr . (f,f)),(- (([**qh,0**] * (A *')) * (vr . (f,vq))))] is set
K135((vr . (f,f)),(- (([**qh,0**] * (A *')) * (vr . (f,vq))))) is complex Element of COMPLEX
((vr . (f,f)) - (([**qh,0**] * (A *')) * (vr . (f,vq)))) - ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
((vr . (f,f)) - (([**qh,0**] * (A *')) * (vr . (f,vq)))) + (- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,f)) - (([**qh,0**] * (A *')) * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))))))) is complex Element of the carrier of F_Complex
[((vr . (f,f)) - (([**qh,0**] * (A *')) * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))))))] is set
{((vr . (f,f)) - (([**qh,0**] * (A *')) * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))))))} is non empty V175() set
{((vr . (f,f)) - (([**qh,0**] * (A *')) * (vr . (f,vq))))} is non empty V175() set
{{((vr . (f,f)) - (([**qh,0**] * (A *')) * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))))))},{((vr . (f,f)) - (([**qh,0**] * (A *')) * (vr . (f,vq))))}} is non empty set
the addF of F_Complex . [((vr . (f,f)) - (([**qh,0**] * (A *')) * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))))))] is set
K135(((vr . (f,f)) - (([**qh,0**] * (A *')) * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] * A) *') * (vr . (vq,vq))))))) is complex Element of COMPLEX
(([**qh,0**] *') * (A *')) * (vr . (vq,vq)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((([**qh,0**] *') * (A *')),(vr . (vq,vq))) is complex Element of the carrier of F_Complex
[(([**qh,0**] *') * (A *')),(vr . (vq,vq))] is set
{(([**qh,0**] *') * (A *')),(vr . (vq,vq))} is non empty V175() set
{{(([**qh,0**] *') * (A *')),(vr . (vq,vq))},{(([**qh,0**] *') * (A *'))}} is non empty set
the multF of F_Complex . [(([**qh,0**] *') * (A *')),(vr . (vq,vq))] is set
K137((([**qh,0**] *') * (A *')),(vr . (vq,vq))) is complex Element of COMPLEX
([**qh,0**] * A) * ((([**qh,0**] *') * (A *')) * (vr . (vq,vq))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (([**qh,0**] * A),((([**qh,0**] *') * (A *')) * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
[([**qh,0**] * A),((([**qh,0**] *') * (A *')) * (vr . (vq,vq)))] is set
{([**qh,0**] * A),((([**qh,0**] *') * (A *')) * (vr . (vq,vq)))} is non empty V175() set
{{([**qh,0**] * A),((([**qh,0**] *') * (A *')) * (vr . (vq,vq)))},{([**qh,0**] * A)}} is non empty set
the multF of F_Complex . [([**qh,0**] * A),((([**qh,0**] *') * (A *')) * (vr . (vq,vq)))] is set
K137(([**qh,0**] * A),((([**qh,0**] *') * (A *')) * (vr . (vq,vq)))) is complex Element of COMPLEX
(([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] *') * (A *')) * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
- (([**qh,0**] * A) * ((([**qh,0**] *') * (A *')) * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
(([**qh,0**] * A) * (vr . (vq,f))) + (- (([**qh,0**] * A) * ((([**qh,0**] *') * (A *')) * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((([**qh,0**] * A) * (vr . (vq,f))),(- (([**qh,0**] * A) * ((([**qh,0**] *') * (A *')) * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
[(([**qh,0**] * A) * (vr . (vq,f))),(- (([**qh,0**] * A) * ((([**qh,0**] *') * (A *')) * (vr . (vq,vq)))))] is set
{(([**qh,0**] * A) * (vr . (vq,f))),(- (([**qh,0**] * A) * ((([**qh,0**] *') * (A *')) * (vr . (vq,vq)))))} is non empty V175() set
{{(([**qh,0**] * A) * (vr . (vq,f))),(- (([**qh,0**] * A) * ((([**qh,0**] *') * (A *')) * (vr . (vq,vq)))))},{(([**qh,0**] * A) * (vr . (vq,f)))}} is non empty set
the addF of F_Complex . [(([**qh,0**] * A) * (vr . (vq,f))),(- (([**qh,0**] * A) * ((([**qh,0**] *') * (A *')) * (vr . (vq,vq)))))] is set
K135((([**qh,0**] * A) * (vr . (vq,f))),(- (([**qh,0**] * A) * ((([**qh,0**] *') * (A *')) * (vr . (vq,vq)))))) is complex Element of COMPLEX
((vr . (f,f)) - (([**qh,0**] * (A *')) * (vr . (f,vq)))) - ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] *') * (A *')) * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] *') * (A *')) * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
((vr . (f,f)) - (([**qh,0**] * (A *')) * (vr . (f,vq)))) + (- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] *') * (A *')) * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,f)) - (([**qh,0**] * (A *')) * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] *') * (A *')) * (vr . (vq,vq))))))) is complex Element of the carrier of F_Complex
[((vr . (f,f)) - (([**qh,0**] * (A *')) * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] *') * (A *')) * (vr . (vq,vq))))))] is set
{((vr . (f,f)) - (([**qh,0**] * (A *')) * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] *') * (A *')) * (vr . (vq,vq))))))} is non empty V175() set
{{((vr . (f,f)) - (([**qh,0**] * (A *')) * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] *') * (A *')) * (vr . (vq,vq))))))},{((vr . (f,f)) - (([**qh,0**] * (A *')) * (vr . (f,vq))))}} is non empty set
the addF of F_Complex . [((vr . (f,f)) - (([**qh,0**] * (A *')) * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] *') * (A *')) * (vr . (vq,vq))))))] is set
K135(((vr . (f,f)) - (([**qh,0**] * (A *')) * (vr . (f,vq)))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * ((([**qh,0**] *') * (A *')) * (vr . (vq,vq))))))) is complex Element of COMPLEX
(vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq)))) is complex Element of the carrier of F_Complex
(vr . (f,f)) + (- ([**qh,0**] * ((A *') * (vr . (f,vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vr . (f,f)),(- ([**qh,0**] * ((A *') * (vr . (f,vq)))))) is complex Element of the carrier of F_Complex
[(vr . (f,f)),(- ([**qh,0**] * ((A *') * (vr . (f,vq)))))] is set
{(vr . (f,f)),(- ([**qh,0**] * ((A *') * (vr . (f,vq)))))} is non empty V175() set
{{(vr . (f,f)),(- ([**qh,0**] * ((A *') * (vr . (f,vq)))))},{(vr . (f,f))}} is non empty set
the addF of F_Complex . [(vr . (f,f)),(- ([**qh,0**] * ((A *') * (vr . (f,vq)))))] is set
K135((vr . (f,f)),(- ([**qh,0**] * ((A *') * (vr . (f,vq)))))) is complex Element of COMPLEX
(([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
- (([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
(([**qh,0**] * A) * (vr . (vq,f))) + (- (([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((([**qh,0**] * A) * (vr . (vq,f))),(- (([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
[(([**qh,0**] * A) * (vr . (vq,f))),(- (([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq)))))] is set
{(([**qh,0**] * A) * (vr . (vq,f))),(- (([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq)))))} is non empty V175() set
{{(([**qh,0**] * A) * (vr . (vq,f))),(- (([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq)))))},{(([**qh,0**] * A) * (vr . (vq,f)))}} is non empty set
the addF of F_Complex . [(([**qh,0**] * A) * (vr . (vq,f))),(- (([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq)))))] is set
K135((([**qh,0**] * A) * (vr . (vq,f))),(- (([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq)))))) is complex Element of COMPLEX
((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))) - ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))) + (- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq)))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq))))))) is complex Element of the carrier of F_Complex
[((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq))))))] is set
{((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq))))))} is non empty V175() set
{((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq)))))} is non empty V175() set
{{((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq))))))},{((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq)))))}} is non empty set
the addF of F_Complex . [((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq))))))] is set
K135(((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),(- ((([**qh,0**] * A) * (vr . (vq,f))) - (([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq))))))) is complex Element of COMPLEX
((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))) - ([**qh,0**] * (A * (vr . (vq,f)))) is complex Element of the carrier of F_Complex
((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))) + (- ([**qh,0**] * (A * (vr . (vq,f))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),(- ([**qh,0**] * (A * (vr . (vq,f)))))) is complex Element of the carrier of F_Complex
[((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),(- ([**qh,0**] * (A * (vr . (vq,f)))))] is set
{((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),(- ([**qh,0**] * (A * (vr . (vq,f)))))} is non empty V175() set
{{((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),(- ([**qh,0**] * (A * (vr . (vq,f)))))},{((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq)))))}} is non empty set
the addF of F_Complex . [((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),(- ([**qh,0**] * (A * (vr . (vq,f)))))] is set
K135(((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),(- ([**qh,0**] * (A * (vr . (vq,f)))))) is complex Element of COMPLEX
(((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))) - ([**qh,0**] * (A * (vr . (vq,f))))) + (([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))) - ([**qh,0**] * (A * (vr . (vq,f))))),(([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
[(((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))) - ([**qh,0**] * (A * (vr . (vq,f))))),(([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq))))] is set
{(((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))) - ([**qh,0**] * (A * (vr . (vq,f))))),(([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq))))} is non empty V175() set
{(((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))) - ([**qh,0**] * (A * (vr . (vq,f)))))} is non empty V175() set
{{(((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))) - ([**qh,0**] * (A * (vr . (vq,f))))),(([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq))))},{(((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))) - ([**qh,0**] * (A * (vr . (vq,f)))))}} is non empty set
the addF of F_Complex . [(((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))) - ([**qh,0**] * (A * (vr . (vq,f))))),(([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq))))] is set
K135((((vr . (f,f)) - ([**qh,0**] * ((A *') * (vr . (f,vq))))) - ([**qh,0**] * (A * (vr . (vq,f))))),(([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq))))) is complex Element of COMPLEX
(((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq))))) + (([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),(([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq))))) is complex Element of the carrier of F_Complex
[(((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),(([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq))))] is set
{(((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),(([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq))))} is non empty V175() set
{{(((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),(([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq))))},{(((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq)))))}} is non empty set
the addF of F_Complex . [(((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),(([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq))))] is set
K135((((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),(([**qh,0**] * A) * (([**qh,0**] * (A *')) * (vr . (vq,vq))))) is complex Element of COMPLEX
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
vq is Element of the carrier of V
f is Element of the carrier of V
vr is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,V) (V) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
vr . (vq,f) is complex Element of the carrier of F_Complex
[vq,f] is set
{vq,f} is non empty set
{vq} is non empty set
{{vq,f},{vq}} is non empty set
vr . [vq,f] is set
|.(vr . (vq,f)).| is complex real ext-real Element of REAL
Re (vr . (vq,f)) is complex real ext-real Element of REAL
(Re (vr . (vq,f))) ^2 is complex real ext-real Element of REAL
(Re (vr . (vq,f))) * (Re (vr . (vq,f))) is complex real ext-real set
Im (vr . (vq,f)) is complex real ext-real Element of REAL
(Im (vr . (vq,f))) ^2 is complex real ext-real Element of REAL
(Im (vr . (vq,f))) * (Im (vr . (vq,f))) is complex real ext-real set
((Re (vr . (vq,f))) ^2) + ((Im (vr . (vq,f))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (vr . (vq,f))) ^2) + ((Im (vr . (vq,f))) ^2)) is complex real ext-real Element of REAL
(V,vr,f) is complex real ext-real set
vr . (f,f) is complex Element of the carrier of F_Complex
[f,f] is set
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
vr . [f,f] is set
Re (vr . (f,f)) is complex real ext-real Element of REAL
2 * |.(vr . (vq,f)).| is complex real ext-real Element of REAL
(V,vr,vq) is complex real ext-real set
vr . (vq,vq) is complex Element of the carrier of F_Complex
[vq,vq] is set
{vq,vq} is non empty set
{{vq,vq},{vq}} is non empty set
vr . [vq,vq] is set
Re (vr . (vq,vq)) is complex real ext-real Element of REAL
qh is complex real ext-real set
[**qh,0**] is complex Element of the carrier of F_Complex
qh + (0 * <i>) is complex set
(2 * |.(vr . (vq,f)).|) * qh is complex real ext-real Element of REAL
(V,vr,f) - ((2 * |.(vr . (vq,f)).|) * qh) is complex real ext-real Element of REAL
qh ^2 is complex real ext-real set
qh * qh is complex real ext-real set
(V,vr,vq) * (qh ^2) is complex real ext-real set
((V,vr,f) - ((2 * |.(vr . (vq,f)).|) * qh)) + ((V,vr,vq) * (qh ^2)) is complex real ext-real Element of REAL
A is complex Element of the carrier of F_Complex
|.A.| is complex real ext-real Element of REAL
Re A is complex real ext-real Element of REAL
(Re A) ^2 is complex real ext-real Element of REAL
(Re A) * (Re A) is complex real ext-real set
Im A is complex real ext-real Element of REAL
(Im A) ^2 is complex real ext-real Element of REAL
(Im A) * (Im A) is complex real ext-real set
((Re A) ^2) + ((Im A) ^2) is complex real ext-real Element of REAL
sqrt (((Re A) ^2) + ((Im A) ^2)) is complex real ext-real Element of REAL
A * (vr . (vq,f)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (A,(vr . (vq,f))) is complex Element of the carrier of F_Complex
[A,(vr . (vq,f))] is set
{A,(vr . (vq,f))} is non empty V175() set
{A} is non empty V175() set
{{A,(vr . (vq,f))},{A}} is non empty set
the multF of F_Complex . [A,(vr . (vq,f))] is set
K137(A,(vr . (vq,f))) is complex Element of COMPLEX
Re (A * (vr . (vq,f))) is complex real ext-real Element of REAL
[**qh,0**] * A is complex Element of the carrier of F_Complex
the multF of F_Complex . ([**qh,0**],A) is complex Element of the carrier of F_Complex
[[**qh,0**],A] is set
{[**qh,0**],A} is non empty V175() set
{[**qh,0**]} is non empty V175() set
{{[**qh,0**],A},{[**qh,0**]}} is non empty set
the multF of F_Complex . [[**qh,0**],A] is set
K137([**qh,0**],A) is complex Element of COMPLEX
([**qh,0**] * A) * vq is Element of the carrier of V
the lmult of V is V16() V19([: the carrier of F_Complex, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of F_Complex, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:]
[: the carrier of F_Complex, the carrier of V:] is set
[:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
the lmult of V . (([**qh,0**] * A),vq) is Element of the carrier of V
[([**qh,0**] * A),vq] is set
{([**qh,0**] * A),vq} is non empty set
{([**qh,0**] * A)} is non empty V175() set
{{([**qh,0**] * A),vq},{([**qh,0**] * A)}} is non empty set
the lmult of V . [([**qh,0**] * A),vq] is set
f - (([**qh,0**] * A) * vq) is Element of the carrier of V
- (([**qh,0**] * A) * vq) is Element of the carrier of V
f + (- (([**qh,0**] * A) * vq)) is Element of the carrier of V
the addF of V is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[:[: the carrier of V, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is set
the addF of V . (f,(- (([**qh,0**] * A) * vq))) is Element of the carrier of V
[f,(- (([**qh,0**] * A) * vq))] is set
{f,(- (([**qh,0**] * A) * vq))} is non empty set
{{f,(- (([**qh,0**] * A) * vq))},{f}} is non empty set
the addF of V . [f,(- (([**qh,0**] * A) * vq))] is set
vr . ((f - (([**qh,0**] * A) * vq)),(f - (([**qh,0**] * A) * vq))) is complex Element of the carrier of F_Complex
[(f - (([**qh,0**] * A) * vq)),(f - (([**qh,0**] * A) * vq))] is set
{(f - (([**qh,0**] * A) * vq)),(f - (([**qh,0**] * A) * vq))} is non empty set
{(f - (([**qh,0**] * A) * vq))} is non empty set
{{(f - (([**qh,0**] * A) * vq)),(f - (([**qh,0**] * A) * vq))},{(f - (([**qh,0**] * A) * vq))}} is non empty set
vr . [(f - (([**qh,0**] * A) * vq)),(f - (([**qh,0**] * A) * vq))] is set
Re (vr . ((f - (([**qh,0**] * A) * vq)),(f - (([**qh,0**] * A) * vq)))) is complex real ext-real Element of REAL
vr . (f,vq) is complex Element of the carrier of F_Complex
[f,vq] is set
{f,vq} is non empty set
{{f,vq},{f}} is non empty set
vr . [f,vq] is set
Re [**qh,0**] is complex real ext-real Element of REAL
Im [**qh,0**] is complex real ext-real Element of REAL
[**qh,0**] * (A * (vr . (vq,f))) is complex Element of the carrier of F_Complex
the multF of F_Complex . ([**qh,0**],(A * (vr . (vq,f)))) is complex Element of the carrier of F_Complex
[[**qh,0**],(A * (vr . (vq,f)))] is set
{[**qh,0**],(A * (vr . (vq,f)))} is non empty V175() set
{{[**qh,0**],(A * (vr . (vq,f)))},{[**qh,0**]}} is non empty set
the multF of F_Complex . [[**qh,0**],(A * (vr . (vq,f)))] is set
K137([**qh,0**],(A * (vr . (vq,f)))) is complex Element of COMPLEX
Re ([**qh,0**] * (A * (vr . (vq,f)))) is complex real ext-real Element of REAL
qh * |.(vr . (vq,f)).| is complex real ext-real Element of REAL
A *' is complex Element of the carrier of F_Complex
(Im A) * <i> is complex set
(Re A) - ((Im A) * <i>) is complex set
(A *') * (vr . (f,vq)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((A *'),(vr . (f,vq))) is complex Element of the carrier of F_Complex
[(A *'),(vr . (f,vq))] is set
{(A *'),(vr . (f,vq))} is non empty V175() set
{(A *')} is non empty V175() set
{{(A *'),(vr . (f,vq))},{(A *')}} is non empty set
the multF of F_Complex . [(A *'),(vr . (f,vq))] is set
K137((A *'),(vr . (f,vq))) is complex Element of COMPLEX
((A *') * (vr . (f,vq))) *' is complex Element of the carrier of F_Complex
Re ((A *') * (vr . (f,vq))) is complex real ext-real Element of REAL
Im ((A *') * (vr . (f,vq))) is complex real ext-real Element of REAL
(Im ((A *') * (vr . (f,vq)))) * <i> is complex set
(Re ((A *') * (vr . (f,vq)))) - ((Im ((A *') * (vr . (f,vq)))) * <i>) is complex set
(((A *') * (vr . (f,vq))) *') *' is complex Element of the carrier of F_Complex
Re (((A *') * (vr . (f,vq))) *') is complex real ext-real Element of REAL
Im (((A *') * (vr . (f,vq))) *') is complex real ext-real Element of REAL
(Im (((A *') * (vr . (f,vq))) *')) * <i> is complex set
(Re (((A *') * (vr . (f,vq))) *')) - ((Im (((A *') * (vr . (f,vq))) *')) * <i>) is complex set
(A *') *' is complex Element of the carrier of F_Complex
Re (A *') is complex real ext-real Element of REAL
Im (A *') is complex real ext-real Element of REAL
(Im (A *')) * <i> is complex set
(Re (A *')) - ((Im (A *')) * <i>) is complex set
(vr . (f,vq)) *' is complex Element of the carrier of F_Complex
Re (vr . (f,vq)) is complex real ext-real Element of REAL
Im (vr . (f,vq)) is complex real ext-real Element of REAL
(Im (vr . (f,vq))) * <i> is complex set
(Re (vr . (f,vq))) - ((Im (vr . (f,vq))) * <i>) is complex set
((A *') *') * ((vr . (f,vq)) *') is complex Element of the carrier of F_Complex
the multF of F_Complex . (((A *') *'),((vr . (f,vq)) *')) is complex Element of the carrier of F_Complex
[((A *') *'),((vr . (f,vq)) *')] is set
{((A *') *'),((vr . (f,vq)) *')} is non empty V175() set
{((A *') *')} is non empty V175() set
{{((A *') *'),((vr . (f,vq)) *')},{((A *') *')}} is non empty set
the multF of F_Complex . [((A *') *'),((vr . (f,vq)) *')] is set
K137(((A *') *'),((vr . (f,vq)) *')) is complex Element of COMPLEX
(((A *') *') * ((vr . (f,vq)) *')) *' is complex Element of the carrier of F_Complex
Re (((A *') *') * ((vr . (f,vq)) *')) is complex real ext-real Element of REAL
Im (((A *') *') * ((vr . (f,vq)) *')) is complex real ext-real Element of REAL
(Im (((A *') *') * ((vr . (f,vq)) *'))) * <i> is complex set
(Re (((A *') *') * ((vr . (f,vq)) *'))) - ((Im (((A *') *') * ((vr . (f,vq)) *'))) * <i>) is complex set
(A * (vr . (vq,f))) *' is complex Element of the carrier of F_Complex
Im (A * (vr . (vq,f))) is complex real ext-real Element of REAL
(Im (A * (vr . (vq,f)))) * <i> is complex set
(Re (A * (vr . (vq,f)))) - ((Im (A * (vr . (vq,f)))) * <i>) is complex set
[**qh,0**] * ((A *') * (vr . (f,vq))) is complex Element of the carrier of F_Complex
the multF of F_Complex . ([**qh,0**],((A *') * (vr . (f,vq)))) is complex Element of the carrier of F_Complex
[[**qh,0**],((A *') * (vr . (f,vq)))] is set
{[**qh,0**],((A *') * (vr . (f,vq)))} is non empty V175() set
{{[**qh,0**],((A *') * (vr . (f,vq)))},{[**qh,0**]}} is non empty set
the multF of F_Complex . [[**qh,0**],((A *') * (vr . (f,vq)))] is set
K137([**qh,0**],((A *') * (vr . (f,vq)))) is complex Element of COMPLEX
Re ([**qh,0**] * ((A *') * (vr . (f,vq)))) is complex real ext-real Element of REAL
Re ((A * (vr . (vq,f))) *') is complex real ext-real Element of REAL
qh * (Re ((A * (vr . (vq,f))) *')) is complex real ext-real Element of REAL
[**(qh ^2),0**] is complex Element of the carrier of F_Complex
(qh ^2) + (0 * <i>) is complex set
Re [**(qh ^2),0**] is complex real ext-real Element of REAL
Im [**(qh ^2),0**] is complex real ext-real Element of REAL
[**(qh ^2),0**] * (vr . (vq,vq)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ([**(qh ^2),0**],(vr . (vq,vq))) is complex Element of the carrier of F_Complex
[[**(qh ^2),0**],(vr . (vq,vq))] is set
{[**(qh ^2),0**],(vr . (vq,vq))} is non empty V175() set
{[**(qh ^2),0**]} is non empty V175() set
{{[**(qh ^2),0**],(vr . (vq,vq))},{[**(qh ^2),0**]}} is non empty set
the multF of F_Complex . [[**(qh ^2),0**],(vr . (vq,vq))] is set
K137([**(qh ^2),0**],(vr . (vq,vq))) is complex Element of COMPLEX
Re ([**(qh ^2),0**] * (vr . (vq,vq))) is complex real ext-real Element of REAL
(qh ^2) * (V,vr,vq) is complex real ext-real set
(vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f)))) is complex Element of the carrier of F_Complex
- ([**qh,0**] * (A * (vr . (vq,f)))) is complex Element of the carrier of F_Complex
(vr . (f,f)) + (- ([**qh,0**] * (A * (vr . (vq,f))))) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . ((vr . (f,f)),(- ([**qh,0**] * (A * (vr . (vq,f)))))) is complex Element of the carrier of F_Complex
[(vr . (f,f)),(- ([**qh,0**] * (A * (vr . (vq,f)))))] is set
{(vr . (f,f)),(- ([**qh,0**] * (A * (vr . (vq,f)))))} is non empty V175() set
{(vr . (f,f))} is non empty V175() set
{{(vr . (f,f)),(- ([**qh,0**] * (A * (vr . (vq,f)))))},{(vr . (f,f))}} is non empty set
the addF of F_Complex . [(vr . (f,f)),(- ([**qh,0**] * (A * (vr . (vq,f)))))] is set
K135((vr . (f,f)),(- ([**qh,0**] * (A * (vr . (vq,f)))))) is complex Element of COMPLEX
((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq)))) is complex Element of the carrier of F_Complex
- ([**qh,0**] * ((A *') * (vr . (f,vq)))) is complex Element of the carrier of F_Complex
((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) + (- ([**qh,0**] * ((A *') * (vr . (f,vq))))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))),(- ([**qh,0**] * ((A *') * (vr . (f,vq)))))) is complex Element of the carrier of F_Complex
[((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))),(- ([**qh,0**] * ((A *') * (vr . (f,vq)))))] is set
{((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))),(- ([**qh,0**] * ((A *') * (vr . (f,vq)))))} is non empty V175() set
{((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f)))))} is non empty V175() set
{{((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))),(- ([**qh,0**] * ((A *') * (vr . (f,vq)))))},{((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f)))))}} is non empty set
the addF of F_Complex . [((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))),(- ([**qh,0**] * ((A *') * (vr . (f,vq)))))] is set
K135(((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))),(- ([**qh,0**] * ((A *') * (vr . (f,vq)))))) is complex Element of COMPLEX
(((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq))))) + ([**(qh ^2),0**] * (vr . (vq,vq))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),([**(qh ^2),0**] * (vr . (vq,vq)))) is complex Element of the carrier of F_Complex
[(((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),([**(qh ^2),0**] * (vr . (vq,vq)))] is set
{(((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),([**(qh ^2),0**] * (vr . (vq,vq)))} is non empty V175() set
{(((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq)))))} is non empty V175() set
{{(((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),([**(qh ^2),0**] * (vr . (vq,vq)))},{(((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq)))))}} is non empty set
the addF of F_Complex . [(((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),([**(qh ^2),0**] * (vr . (vq,vq)))] is set
K135((((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq))))),([**(qh ^2),0**] * (vr . (vq,vq)))) is complex Element of COMPLEX
Re (((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq))))) is complex real ext-real Element of REAL
(Re (((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) - ([**qh,0**] * ((A *') * (vr . (f,vq)))))) + ((V,vr,vq) * (qh ^2)) is complex real ext-real Element of REAL
Re ((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f))))) is complex real ext-real Element of REAL
(Re ((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f)))))) - (qh * |.(vr . (vq,f)).|) is complex real ext-real Element of REAL
((Re ((vr . (f,f)) - ([**qh,0**] * (A * (vr . (vq,f)))))) - (qh * |.(vr . (vq,f)).|)) + ((V,vr,vq) * (qh ^2)) is complex real ext-real Element of REAL
(V,vr,f) - (qh * |.(vr . (vq,f)).|) is complex real ext-real Element of REAL
((V,vr,f) - (qh * |.(vr . (vq,f)).|)) - (qh * |.(vr . (vq,f)).|) is complex real ext-real Element of REAL
(((V,vr,f) - (qh * |.(vr . (vq,f)).|)) - (qh * |.(vr . (vq,f)).|)) + ((V,vr,vq) * (qh ^2)) is complex real ext-real Element of REAL
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
vq is Element of the carrier of V
f is Element of the carrier of V
vr is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,V) (V) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
(V,vr,vq) is complex real ext-real set
vr . (vq,vq) is complex Element of the carrier of F_Complex
[vq,vq] is set
{vq,vq} is non empty set
{vq} is non empty set
{{vq,vq},{vq}} is non empty set
vr . [vq,vq] is set
Re (vr . (vq,vq)) is complex real ext-real Element of REAL
vr . (vq,f) is complex Element of the carrier of F_Complex
[vq,f] is set
{vq,f} is non empty set
{{vq,f},{vq}} is non empty set
vr . [vq,f] is set
|.(vr . (vq,f)).| is complex real ext-real Element of REAL
Re (vr . (vq,f)) is complex real ext-real Element of REAL
(Re (vr . (vq,f))) ^2 is complex real ext-real Element of REAL
(Re (vr . (vq,f))) * (Re (vr . (vq,f))) is complex real ext-real set
Im (vr . (vq,f)) is complex real ext-real Element of REAL
(Im (vr . (vq,f))) ^2 is complex real ext-real Element of REAL
(Im (vr . (vq,f))) * (Im (vr . (vq,f))) is complex real ext-real set
((Re (vr . (vq,f))) ^2) + ((Im (vr . (vq,f))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (vr . (vq,f))) ^2) + ((Im (vr . (vq,f))) ^2)) is complex real ext-real Element of REAL
(V,vr,f) is complex real ext-real set
vr . (f,f) is complex Element of the carrier of F_Complex
[f,f] is set
{f,f} is non empty set
{f} is non empty set
{{f,f},{f}} is non empty set
vr . [f,f] is set
Re (vr . (f,f)) is complex real ext-real Element of REAL
A is complex real ext-real Element of REAL
2 * |.(vr . (vq,f)).| is complex real ext-real Element of REAL
A / |.(vr . (vq,f)).| is complex real ext-real Element of COMPLEX
(2 * |.(vr . (vq,f)).|) * (A / |.(vr . (vq,f)).|) is complex real ext-real Element of REAL
A - ((2 * |.(vr . (vq,f)).|) * (A / |.(vr . (vq,f)).|)) is complex real ext-real Element of REAL
(A / |.(vr . (vq,f)).|) ^2 is complex real ext-real Element of COMPLEX
(A / |.(vr . (vq,f)).|) * (A / |.(vr . (vq,f)).|) is complex real ext-real set
(V,vr,vq) * ((A / |.(vr . (vq,f)).|) ^2) is complex real ext-real set
(A - ((2 * |.(vr . (vq,f)).|) * (A / |.(vr . (vq,f)).|))) + ((V,vr,vq) * ((A / |.(vr . (vq,f)).|) ^2)) is complex real ext-real Element of REAL
A * (2 * |.(vr . (vq,f)).|) is complex real ext-real Element of REAL
(A * (2 * |.(vr . (vq,f)).|)) / |.(vr . (vq,f)).| is complex real ext-real Element of COMPLEX
A - ((A * (2 * |.(vr . (vq,f)).|)) / |.(vr . (vq,f)).|) is complex real ext-real Element of REAL
A * 2 is complex real ext-real Element of REAL
(A * 2) * |.(vr . (vq,f)).| is complex real ext-real Element of REAL
((A * 2) * |.(vr . (vq,f)).|) / |.(vr . (vq,f)).| is complex real ext-real Element of COMPLEX
A - (((A * 2) * |.(vr . (vq,f)).|) / |.(vr . (vq,f)).|) is complex real ext-real Element of REAL
A + A is complex real ext-real Element of REAL
A - (A + A) is complex real ext-real Element of REAL
- A is complex real ext-real Element of REAL
B is complex Element of the carrier of F_Complex
|.B.| is complex real ext-real Element of REAL
Re B is complex real ext-real Element of REAL
(Re B) ^2 is complex real ext-real Element of REAL
(Re B) * (Re B) is complex real ext-real set
Im B is complex real ext-real Element of REAL
(Im B) ^2 is complex real ext-real Element of REAL
(Im B) * (Im B) is complex real ext-real set
((Re B) ^2) + ((Im B) ^2) is complex real ext-real Element of REAL
sqrt (((Re B) ^2) + ((Im B) ^2)) is complex real ext-real Element of REAL
B * (vr . (vq,f)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (B,(vr . (vq,f))) is complex Element of the carrier of F_Complex
[B,(vr . (vq,f))] is set
{B,(vr . (vq,f))} is non empty V175() set
{B} is non empty V175() set
{{B,(vr . (vq,f))},{B}} is non empty set
the multF of F_Complex . [B,(vr . (vq,f))] is set
K137(B,(vr . (vq,f))) is complex Element of COMPLEX
Re (B * (vr . (vq,f))) is complex real ext-real Element of REAL
Im (B * (vr . (vq,f))) is complex real ext-real Element of REAL
(2 * |.(vr . (vq,f)).|) * 0 is complex real ext-real Element of REAL
A - ((2 * |.(vr . (vq,f)).|) * 0) is complex real ext-real Element of REAL
0 ^2 is complex real ext-real Element of REAL
0 * 0 is empty complex real ext-real non positive non negative V175() V176() V177() V178() V179() V180() V181() set
(V,vr,vq) * (0 ^2) is complex real ext-real Element of REAL
(A - ((2 * |.(vr . (vq,f)).|) * 0)) + ((V,vr,vq) * (0 ^2)) is complex real ext-real Element of REAL
B is complex Element of the carrier of F_Complex
|.B.| is complex real ext-real Element of REAL
Re B is complex real ext-real Element of REAL
(Re B) ^2 is complex real ext-real Element of REAL
(Re B) * (Re B) is complex real ext-real set
Im B is complex real ext-real Element of REAL
(Im B) ^2 is complex real ext-real Element of REAL
(Im B) * (Im B) is complex real ext-real set
((Re B) ^2) + ((Im B) ^2) is complex real ext-real Element of REAL
sqrt (((Re B) ^2) + ((Im B) ^2)) is complex real ext-real Element of REAL
B * (vr . (vq,f)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (B,(vr . (vq,f))) is complex Element of the carrier of F_Complex
[B,(vr . (vq,f))] is set
{B,(vr . (vq,f))} is non empty V175() set
{B} is non empty V175() set
{{B,(vr . (vq,f))},{B}} is non empty set
the multF of F_Complex . [B,(vr . (vq,f))] is set
K137(B,(vr . (vq,f))) is complex Element of COMPLEX
Re (B * (vr . (vq,f))) is complex real ext-real Element of REAL
Im (B * (vr . (vq,f))) is complex real ext-real Element of REAL
(2 * |.(vr . (vq,f)).|) * 1 is complex real ext-real Element of REAL
A - ((2 * |.(vr . (vq,f)).|) * 1) is complex real ext-real Element of REAL
1 ^2 is complex real ext-real Element of REAL
1 * 1 is non empty complex real ext-real positive non negative set
(V,vr,vq) * (1 ^2) is complex real ext-real Element of REAL
(A - ((2 * |.(vr . (vq,f)).|) * 1)) + ((V,vr,vq) * (1 ^2)) is complex real ext-real Element of REAL
B is complex Element of the carrier of F_Complex
|.B.| is complex real ext-real Element of REAL
Re B is complex real ext-real Element of REAL
(Re B) ^2 is complex real ext-real Element of REAL
(Re B) * (Re B) is complex real ext-real set
Im B is complex real ext-real Element of REAL
(Im B) ^2 is complex real ext-real Element of REAL
(Im B) * (Im B) is complex real ext-real set
((Re B) ^2) + ((Im B) ^2) is complex real ext-real Element of REAL
sqrt (((Re B) ^2) + ((Im B) ^2)) is complex real ext-real Element of REAL
B * (vr . (vq,f)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (B,(vr . (vq,f))) is complex Element of the carrier of F_Complex
[B,(vr . (vq,f))] is set
{B,(vr . (vq,f))} is non empty V175() set
{B} is non empty V175() set
{{B,(vr . (vq,f))},{B}} is non empty set
the multF of F_Complex . [B,(vr . (vq,f))] is set
K137(B,(vr . (vq,f))) is complex Element of COMPLEX
Re (B * (vr . (vq,f))) is complex real ext-real Element of REAL
Im (B * (vr . (vq,f))) is complex real ext-real Element of REAL
- 1 is non empty complex real ext-real non positive negative Element of REAL
(2 * |.(vr . (vq,f)).|) * (- 1) is complex real ext-real Element of REAL
A - ((2 * |.(vr . (vq,f)).|) * (- 1)) is complex real ext-real Element of REAL
(- 1) ^2 is complex real ext-real Element of REAL
(- 1) * (- 1) is non empty complex real ext-real positive non negative set
(V,vr,vq) * ((- 1) ^2) is complex real ext-real Element of REAL
(A - ((2 * |.(vr . (vq,f)).|) * (- 1))) + ((V,vr,vq) * ((- 1) ^2)) is complex real ext-real Element of REAL
B is complex Element of the carrier of F_Complex
|.B.| is complex real ext-real Element of REAL
Re B is complex real ext-real Element of REAL
(Re B) ^2 is complex real ext-real Element of REAL
(Re B) * (Re B) is complex real ext-real set
Im B is complex real ext-real Element of REAL
(Im B) ^2 is complex real ext-real Element of REAL
(Im B) * (Im B) is complex real ext-real set
((Re B) ^2) + ((Im B) ^2) is complex real ext-real Element of REAL
sqrt (((Re B) ^2) + ((Im B) ^2)) is complex real ext-real Element of REAL
B * (vr . (vq,f)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (B,(vr . (vq,f))) is complex Element of the carrier of F_Complex
[B,(vr . (vq,f))] is set
{B,(vr . (vq,f))} is non empty V175() set
{B} is non empty V175() set
{{B,(vr . (vq,f))},{B}} is non empty set
the multF of F_Complex . [B,(vr . (vq,f))] is set
K137(B,(vr . (vq,f))) is complex Element of COMPLEX
Re (B * (vr . (vq,f))) is complex real ext-real Element of REAL
Im (B * (vr . (vq,f))) is complex real ext-real Element of REAL
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is Element of the carrier of V
vq is Element of the carrier of V
vr is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,V) (V) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
vr . (f,vq) is complex Element of the carrier of F_Complex
[f,vq] is set
{f,vq} is non empty set
{f} is non empty set
{{f,vq},{f}} is non empty set
vr . [f,vq] is set
|.(vr . (f,vq)).| is complex real ext-real Element of REAL
Re (vr . (f,vq)) is complex real ext-real Element of REAL
(Re (vr . (f,vq))) ^2 is complex real ext-real Element of REAL
(Re (vr . (f,vq))) * (Re (vr . (f,vq))) is complex real ext-real set
Im (vr . (f,vq)) is complex real ext-real Element of REAL
(Im (vr . (f,vq))) ^2 is complex real ext-real Element of REAL
(Im (vr . (f,vq))) * (Im (vr . (f,vq))) is complex real ext-real set
((Re (vr . (f,vq))) ^2) + ((Im (vr . (f,vq))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (vr . (f,vq))) ^2) + ((Im (vr . (f,vq))) ^2)) is complex real ext-real Element of REAL
|.(vr . (f,vq)).| ^2 is complex real ext-real Element of REAL
|.(vr . (f,vq)).| * |.(vr . (f,vq)).| is complex real ext-real set
(V,vr,f) is complex real ext-real set
vr . (f,f) is complex Element of the carrier of F_Complex
[f,f] is set
{f,f} is non empty set
{{f,f},{f}} is non empty set
vr . [f,f] is set
Re (vr . (f,f)) is complex real ext-real Element of REAL
(V,vr,vq) is complex real ext-real set
vr . (vq,vq) is complex Element of the carrier of F_Complex
[vq,vq] is set
{vq,vq} is non empty set
{vq} is non empty set
{{vq,vq},{vq}} is non empty set
vr . [vq,vq] is set
Re (vr . (vq,vq)) is complex real ext-real Element of REAL
(V,vr,f) * (V,vr,vq) is complex real ext-real set
vr . (vq,f) is complex Element of the carrier of F_Complex
[vq,f] is set
{vq,f} is non empty set
{{vq,f},{vq}} is non empty set
vr . [vq,f] is set
|.(vr . (vq,f)).| is complex real ext-real Element of REAL
Re (vr . (vq,f)) is complex real ext-real Element of REAL
(Re (vr . (vq,f))) ^2 is complex real ext-real Element of REAL
(Re (vr . (vq,f))) * (Re (vr . (vq,f))) is complex real ext-real set
Im (vr . (vq,f)) is complex real ext-real Element of REAL
(Im (vr . (vq,f))) ^2 is complex real ext-real Element of REAL
(Im (vr . (vq,f))) * (Im (vr . (vq,f))) is complex real ext-real set
((Re (vr . (vq,f))) ^2) + ((Im (vr . (vq,f))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (vr . (vq,f))) ^2) + ((Im (vr . (vq,f))) ^2)) is complex real ext-real Element of REAL
A is complex real ext-real Element of REAL
0 ^2 is complex real ext-real Element of REAL
0 * 0 is empty complex real ext-real non positive non negative V175() V176() V177() V178() V179() V180() V181() set
w is complex real ext-real Element of REAL
w ^2 is complex real ext-real Element of REAL
w * w is complex real ext-real set
B is complex real ext-real Element of REAL
B * A is complex real ext-real Element of REAL
2 * w is complex real ext-real Element of REAL
w / A is complex real ext-real Element of COMPLEX
(2 * w) * (w / A) is complex real ext-real Element of REAL
B - ((2 * w) * (w / A)) is complex real ext-real Element of REAL
(w / A) ^2 is complex real ext-real Element of COMPLEX
(w / A) * (w / A) is complex real ext-real set
A * ((w / A) ^2) is complex real ext-real Element of REAL
(B - ((2 * w) * (w / A))) + (A * ((w / A) ^2)) is complex real ext-real Element of REAL
w * (2 * w) is complex real ext-real Element of REAL
(w * (2 * w)) / A is complex real ext-real Element of COMPLEX
B - ((w * (2 * w)) / A) is complex real ext-real Element of REAL
(B - ((w * (2 * w)) / A)) + (A * ((w / A) ^2)) is complex real ext-real Element of REAL
(w ^2) * 2 is complex real ext-real Element of REAL
((w ^2) * 2) / A is complex real ext-real Element of COMPLEX
B - (((w ^2) * 2) / A) is complex real ext-real Element of REAL
(B - (((w ^2) * 2) / A)) + (A * ((w / A) ^2)) is complex real ext-real Element of REAL
(w ^2) / A is complex real ext-real Element of COMPLEX
2 * ((w ^2) / A) is complex real ext-real Element of REAL
B - (2 * ((w ^2) / A)) is complex real ext-real Element of REAL
(B - (2 * ((w ^2) / A))) + (A * ((w / A) ^2)) is complex real ext-real Element of REAL
A * A is complex real ext-real Element of REAL
(w ^2) / (A * A) is complex real ext-real Element of COMPLEX
A * ((w ^2) / (A * A)) is complex real ext-real Element of REAL
(B - (2 * ((w ^2) / A))) + (A * ((w ^2) / (A * A))) is complex real ext-real Element of REAL
A * (w ^2) is complex real ext-real Element of REAL
(A * (w ^2)) / (A * A) is complex real ext-real Element of COMPLEX
(B - (2 * ((w ^2) / A))) + ((A * (w ^2)) / (A * A)) is complex real ext-real Element of REAL
(B - (2 * ((w ^2) / A))) + ((w ^2) / A) is complex real ext-real Element of REAL
B - ((w ^2) / A) is complex real ext-real Element of REAL
(B * A) - (w ^2) is complex real ext-real Element of REAL
((B * A) - (w ^2)) / A is complex real ext-real Element of COMPLEX
wa is complex Element of the carrier of F_Complex
|.wa.| is complex real ext-real Element of REAL
Re wa is complex real ext-real Element of REAL
(Re wa) ^2 is complex real ext-real Element of REAL
(Re wa) * (Re wa) is complex real ext-real set
Im wa is complex real ext-real Element of REAL
(Im wa) ^2 is complex real ext-real Element of REAL
(Im wa) * (Im wa) is complex real ext-real set
((Re wa) ^2) + ((Im wa) ^2) is complex real ext-real Element of REAL
sqrt (((Re wa) ^2) + ((Im wa) ^2)) is complex real ext-real Element of REAL
wa * (vr . (vq,f)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (wa,(vr . (vq,f))) is complex Element of the carrier of F_Complex
[wa,(vr . (vq,f))] is set
{wa,(vr . (vq,f))} is non empty V175() set
{wa} is non empty V175() set
{{wa,(vr . (vq,f))},{wa}} is non empty set
the multF of F_Complex . [wa,(vr . (vq,f))] is set
K137(wa,(vr . (vq,f))) is complex Element of COMPLEX
Re (wa * (vr . (vq,f))) is complex real ext-real Element of REAL
Im (wa * (vr . (vq,f))) is complex real ext-real Element of REAL
0 + (w ^2) is complex real ext-real Element of REAL
((B * A) - (w ^2)) + (w ^2) is complex real ext-real Element of REAL
(vr . (f,vq)) *' is complex Element of the carrier of F_Complex
(Im (vr . (f,vq))) * <i> is complex set
(Re (vr . (f,vq))) - ((Im (vr . (f,vq))) * <i>) is complex set
|.((vr . (f,vq)) *').| is complex real ext-real Element of REAL
Re ((vr . (f,vq)) *') is complex real ext-real Element of REAL
(Re ((vr . (f,vq)) *')) ^2 is complex real ext-real Element of REAL
(Re ((vr . (f,vq)) *')) * (Re ((vr . (f,vq)) *')) is complex real ext-real set
Im ((vr . (f,vq)) *') is complex real ext-real Element of REAL
(Im ((vr . (f,vq)) *')) ^2 is complex real ext-real Element of REAL
(Im ((vr . (f,vq)) *')) * (Im ((vr . (f,vq)) *')) is complex real ext-real set
((Re ((vr . (f,vq)) *')) ^2) + ((Im ((vr . (f,vq)) *')) ^2) is complex real ext-real Element of REAL
sqrt (((Re ((vr . (f,vq)) *')) ^2) + ((Im ((vr . (f,vq)) *')) ^2)) is complex real ext-real Element of REAL
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,V) (V) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
vq is Element of the carrier of V
vr is Element of the carrier of V
f . (vq,vr) is complex Element of the carrier of F_Complex
[vq,vr] is set
{vq,vr} is non empty set
{vq} is non empty set
{{vq,vr},{vq}} is non empty set
f . [vq,vr] is set
|.(f . (vq,vr)).| is complex real ext-real Element of REAL
Re (f . (vq,vr)) is complex real ext-real Element of REAL
(Re (f . (vq,vr))) ^2 is complex real ext-real Element of REAL
(Re (f . (vq,vr))) * (Re (f . (vq,vr))) is complex real ext-real set
Im (f . (vq,vr)) is complex real ext-real Element of REAL
(Im (f . (vq,vr))) ^2 is complex real ext-real Element of REAL
(Im (f . (vq,vr))) * (Im (f . (vq,vr))) is complex real ext-real set
((Re (f . (vq,vr))) ^2) + ((Im (f . (vq,vr))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (f . (vq,vr))) ^2) + ((Im (f . (vq,vr))) ^2)) is complex real ext-real Element of REAL
|.(f . (vq,vr)).| ^2 is complex real ext-real Element of REAL
|.(f . (vq,vr)).| * |.(f . (vq,vr)).| is complex real ext-real set
f . (vq,vq) is complex Element of the carrier of F_Complex
[vq,vq] is set
{vq,vq} is non empty set
{{vq,vq},{vq}} is non empty set
f . [vq,vq] is set
|.(f . (vq,vq)).| is complex real ext-real Element of REAL
Re (f . (vq,vq)) is complex real ext-real Element of REAL
(Re (f . (vq,vq))) ^2 is complex real ext-real Element of REAL
(Re (f . (vq,vq))) * (Re (f . (vq,vq))) is complex real ext-real set
Im (f . (vq,vq)) is complex real ext-real Element of REAL
(Im (f . (vq,vq))) ^2 is complex real ext-real Element of REAL
(Im (f . (vq,vq))) * (Im (f . (vq,vq))) is complex real ext-real set
((Re (f . (vq,vq))) ^2) + ((Im (f . (vq,vq))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (f . (vq,vq))) ^2) + ((Im (f . (vq,vq))) ^2)) is complex real ext-real Element of REAL
f . (vr,vr) is complex Element of the carrier of F_Complex
[vr,vr] is set
{vr,vr} is non empty set
{vr} is non empty set
{{vr,vr},{vr}} is non empty set
f . [vr,vr] is set
|.(f . (vr,vr)).| is complex real ext-real Element of REAL
Re (f . (vr,vr)) is complex real ext-real Element of REAL
(Re (f . (vr,vr))) ^2 is complex real ext-real Element of REAL
(Re (f . (vr,vr))) * (Re (f . (vr,vr))) is complex real ext-real set
Im (f . (vr,vr)) is complex real ext-real Element of REAL
(Im (f . (vr,vr))) ^2 is complex real ext-real Element of REAL
(Im (f . (vr,vr))) * (Im (f . (vr,vr))) is complex real ext-real set
((Re (f . (vr,vr))) ^2) + ((Im (f . (vr,vr))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (f . (vr,vr))) ^2) + ((Im (f . (vr,vr))) ^2)) is complex real ext-real Element of REAL
|.(f . (vq,vq)).| * |.(f . (vr,vr)).| is complex real ext-real Element of REAL
(V,f,vq) is complex real ext-real set
(V,f,vr) is complex real ext-real set
(V,f,vq) * (V,f,vr) is complex real ext-real set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,V) (V) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
vq is Element of the carrier of V
vr is Element of the carrier of V
vq + vr is Element of the carrier of V
the addF of V is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[:[: the carrier of V, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is set
the addF of V . (vq,vr) is Element of the carrier of V
[vq,vr] is set
{vq,vr} is non empty set
{vq} is non empty set
{{vq,vr},{vq}} is non empty set
the addF of V . [vq,vr] is set
(V,f,(vq + vr)) is complex real ext-real set
f . ((vq + vr),(vq + vr)) is complex Element of the carrier of F_Complex
[(vq + vr),(vq + vr)] is set
{(vq + vr),(vq + vr)} is non empty set
{(vq + vr)} is non empty set
{{(vq + vr),(vq + vr)},{(vq + vr)}} is non empty set
f . [(vq + vr),(vq + vr)] is set
Re (f . ((vq + vr),(vq + vr))) is complex real ext-real Element of REAL
(V,f,vq) is complex real ext-real set
f . (vq,vq) is complex Element of the carrier of F_Complex
[vq,vq] is set
{vq,vq} is non empty set
{{vq,vq},{vq}} is non empty set
f . [vq,vq] is set
Re (f . (vq,vq)) is complex real ext-real Element of REAL
sqrt (V,f,vq) is complex real ext-real set
(V,f,vr) is complex real ext-real set
f . (vr,vr) is complex Element of the carrier of F_Complex
[vr,vr] is set
{vr,vr} is non empty set
{vr} is non empty set
{{vr,vr},{vr}} is non empty set
f . [vr,vr] is set
Re (f . (vr,vr)) is complex real ext-real Element of REAL
sqrt (V,f,vr) is complex real ext-real set
(sqrt (V,f,vq)) + (sqrt (V,f,vr)) is complex real ext-real set
((sqrt (V,f,vq)) + (sqrt (V,f,vr))) ^2 is complex real ext-real set
((sqrt (V,f,vq)) + (sqrt (V,f,vr))) * ((sqrt (V,f,vq)) + (sqrt (V,f,vr))) is complex real ext-real set
f . (vq,vr) is complex Element of the carrier of F_Complex
f . [vq,vr] is set
f . (vr,vq) is complex Element of the carrier of F_Complex
[vr,vq] is set
{vr,vq} is non empty set
{{vr,vq},{vr}} is non empty set
f . [vr,vq] is set
(f . (vq,vq)) + (f . (vq,vr)) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . ((f . (vq,vq)),(f . (vq,vr))) is complex Element of the carrier of F_Complex
[(f . (vq,vq)),(f . (vq,vr))] is set
{(f . (vq,vq)),(f . (vq,vr))} is non empty V175() set
{(f . (vq,vq))} is non empty V175() set
{{(f . (vq,vq)),(f . (vq,vr))},{(f . (vq,vq))}} is non empty set
the addF of F_Complex . [(f . (vq,vq)),(f . (vq,vr))] is set
K135((f . (vq,vq)),(f . (vq,vr))) is complex Element of COMPLEX
(f . (vr,vq)) + (f . (vr,vr)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((f . (vr,vq)),(f . (vr,vr))) is complex Element of the carrier of F_Complex
[(f . (vr,vq)),(f . (vr,vr))] is set
{(f . (vr,vq)),(f . (vr,vr))} is non empty V175() set
{(f . (vr,vq))} is non empty V175() set
{{(f . (vr,vq)),(f . (vr,vr))},{(f . (vr,vq))}} is non empty set
the addF of F_Complex . [(f . (vr,vq)),(f . (vr,vr))] is set
K135((f . (vr,vq)),(f . (vr,vr))) is complex Element of COMPLEX
((f . (vq,vq)) + (f . (vq,vr))) + ((f . (vr,vq)) + (f . (vr,vr))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((f . (vq,vq)) + (f . (vq,vr))),((f . (vr,vq)) + (f . (vr,vr)))) is complex Element of the carrier of F_Complex
[((f . (vq,vq)) + (f . (vq,vr))),((f . (vr,vq)) + (f . (vr,vr)))] is set
{((f . (vq,vq)) + (f . (vq,vr))),((f . (vr,vq)) + (f . (vr,vr)))} is non empty V175() set
{((f . (vq,vq)) + (f . (vq,vr)))} is non empty V175() set
{{((f . (vq,vq)) + (f . (vq,vr))),((f . (vr,vq)) + (f . (vr,vr)))},{((f . (vq,vq)) + (f . (vq,vr)))}} is non empty set
the addF of F_Complex . [((f . (vq,vq)) + (f . (vq,vr))),((f . (vr,vq)) + (f . (vr,vr)))] is set
K135(((f . (vq,vq)) + (f . (vq,vr))),((f . (vr,vq)) + (f . (vr,vr)))) is complex Element of COMPLEX
Re (((f . (vq,vq)) + (f . (vq,vr))) + ((f . (vr,vq)) + (f . (vr,vr)))) is complex real ext-real Element of REAL
Re ((f . (vq,vq)) + (f . (vq,vr))) is complex real ext-real Element of REAL
Re ((f . (vr,vq)) + (f . (vr,vr))) is complex real ext-real Element of REAL
(Re ((f . (vq,vq)) + (f . (vq,vr)))) + (Re ((f . (vr,vq)) + (f . (vr,vr)))) is complex real ext-real Element of REAL
Re (f . (vq,vr)) is complex real ext-real Element of REAL
(Re (f . (vq,vq))) + (Re (f . (vq,vr))) is complex real ext-real Element of REAL
((Re (f . (vq,vq))) + (Re (f . (vq,vr)))) + (Re ((f . (vr,vq)) + (f . (vr,vr)))) is complex real ext-real Element of REAL
Re (f . (vr,vq)) is complex real ext-real Element of REAL
(Re (f . (vr,vq))) + (Re (f . (vr,vr))) is complex real ext-real Element of REAL
((Re (f . (vq,vq))) + (Re (f . (vq,vr)))) + ((Re (f . (vr,vq))) + (Re (f . (vr,vr)))) is complex real ext-real Element of REAL
(Re (f . (vq,vr))) + (Re (f . (vr,vq))) is complex real ext-real Element of REAL
(V,f,vq) + ((Re (f . (vq,vr))) + (Re (f . (vr,vq)))) is complex real ext-real Element of REAL
((V,f,vq) + ((Re (f . (vq,vr))) + (Re (f . (vr,vq))))) + (V,f,vr) is complex real ext-real Element of REAL
(f . (vq,vr)) *' is complex Element of the carrier of F_Complex
Im (f . (vq,vr)) is complex real ext-real Element of REAL
(Im (f . (vq,vr))) * <i> is complex set
(Re (f . (vq,vr))) - ((Im (f . (vq,vr))) * <i>) is complex set
Re ((f . (vq,vr)) *') is complex real ext-real Element of REAL
(Re (f . (vq,vr))) + (Re ((f . (vq,vr)) *')) is complex real ext-real Element of REAL
(V,f,vq) + ((Re (f . (vq,vr))) + (Re ((f . (vq,vr)) *'))) is complex real ext-real Element of REAL
((V,f,vq) + ((Re (f . (vq,vr))) + (Re ((f . (vq,vr)) *')))) + (V,f,vr) is complex real ext-real Element of REAL
2 * (Re (f . (vq,vr))) is complex real ext-real Element of REAL
(V,f,vq) + (2 * (Re (f . (vq,vr)))) is complex real ext-real Element of REAL
((V,f,vq) + (2 * (Re (f . (vq,vr))))) + (V,f,vr) is complex real ext-real Element of REAL
(V,f,vq) + (V,f,vr) is complex real ext-real set
((V,f,vq) + (V,f,vr)) + (2 * (Re (f . (vq,vr)))) is complex real ext-real Element of REAL
|.(f . (vq,vr)).| is complex real ext-real Element of REAL
(Re (f . (vq,vr))) ^2 is complex real ext-real Element of REAL
(Re (f . (vq,vr))) * (Re (f . (vq,vr))) is complex real ext-real set
(Im (f . (vq,vr))) ^2 is complex real ext-real Element of REAL
(Im (f . (vq,vr))) * (Im (f . (vq,vr))) is complex real ext-real set
((Re (f . (vq,vr))) ^2) + ((Im (f . (vq,vr))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (f . (vq,vr))) ^2) + ((Im (f . (vq,vr))) ^2)) is complex real ext-real Element of REAL
|.(f . (vq,vr)).| ^2 is complex real ext-real Element of REAL
|.(f . (vq,vr)).| * |.(f . (vq,vr)).| is complex real ext-real set
sqrt (|.(f . (vq,vr)).| ^2) is complex real ext-real Element of REAL
(V,f,vq) * (V,f,vr) is complex real ext-real set
sqrt ((V,f,vq) * (V,f,vr)) is complex real ext-real set
(sqrt (V,f,vq)) * (sqrt (V,f,vr)) is complex real ext-real set
2 * ((sqrt (V,f,vq)) * (sqrt (V,f,vr))) is complex real ext-real Element of REAL
((V,f,vq) + (V,f,vr)) + (2 * ((sqrt (V,f,vq)) * (sqrt (V,f,vr)))) is complex real ext-real Element of REAL
(sqrt (V,f,vq)) ^2 is complex real ext-real set
(sqrt (V,f,vq)) * (sqrt (V,f,vq)) is complex real ext-real set
((sqrt (V,f,vq)) ^2) + (V,f,vr) is complex real ext-real set
(((sqrt (V,f,vq)) ^2) + (V,f,vr)) + (2 * ((sqrt (V,f,vq)) * (sqrt (V,f,vr)))) is complex real ext-real Element of REAL
(sqrt (V,f,vr)) ^2 is complex real ext-real set
(sqrt (V,f,vr)) * (sqrt (V,f,vr)) is complex real ext-real set
((sqrt (V,f,vq)) ^2) + ((sqrt (V,f,vr)) ^2) is complex real ext-real set
(((sqrt (V,f,vq)) ^2) + ((sqrt (V,f,vr)) ^2)) + (2 * ((sqrt (V,f,vq)) * (sqrt (V,f,vr)))) is complex real ext-real Element of REAL
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,V) (V) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
vq is Element of the carrier of V
vr is Element of the carrier of V
vq + vr is Element of the carrier of V
the addF of V is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[:[: the carrier of V, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is set
the addF of V . (vq,vr) is Element of the carrier of V
[vq,vr] is set
{vq,vr} is non empty set
{vq} is non empty set
{{vq,vr},{vq}} is non empty set
the addF of V . [vq,vr] is set
f . ((vq + vr),(vq + vr)) is complex Element of the carrier of F_Complex
[(vq + vr),(vq + vr)] is set
{(vq + vr),(vq + vr)} is non empty set
{(vq + vr)} is non empty set
{{(vq + vr),(vq + vr)},{(vq + vr)}} is non empty set
f . [(vq + vr),(vq + vr)] is set
|.(f . ((vq + vr),(vq + vr))).| is complex real ext-real Element of REAL
Re (f . ((vq + vr),(vq + vr))) is complex real ext-real Element of REAL
(Re (f . ((vq + vr),(vq + vr)))) ^2 is complex real ext-real Element of REAL
(Re (f . ((vq + vr),(vq + vr)))) * (Re (f . ((vq + vr),(vq + vr)))) is complex real ext-real set
Im (f . ((vq + vr),(vq + vr))) is complex real ext-real Element of REAL
(Im (f . ((vq + vr),(vq + vr)))) ^2 is complex real ext-real Element of REAL
(Im (f . ((vq + vr),(vq + vr)))) * (Im (f . ((vq + vr),(vq + vr)))) is complex real ext-real set
((Re (f . ((vq + vr),(vq + vr)))) ^2) + ((Im (f . ((vq + vr),(vq + vr)))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (f . ((vq + vr),(vq + vr)))) ^2) + ((Im (f . ((vq + vr),(vq + vr)))) ^2)) is complex real ext-real Element of REAL
f . (vq,vq) is complex Element of the carrier of F_Complex
[vq,vq] is set
{vq,vq} is non empty set
{{vq,vq},{vq}} is non empty set
f . [vq,vq] is set
|.(f . (vq,vq)).| is complex real ext-real Element of REAL
Re (f . (vq,vq)) is complex real ext-real Element of REAL
(Re (f . (vq,vq))) ^2 is complex real ext-real Element of REAL
(Re (f . (vq,vq))) * (Re (f . (vq,vq))) is complex real ext-real set
Im (f . (vq,vq)) is complex real ext-real Element of REAL
(Im (f . (vq,vq))) ^2 is complex real ext-real Element of REAL
(Im (f . (vq,vq))) * (Im (f . (vq,vq))) is complex real ext-real set
((Re (f . (vq,vq))) ^2) + ((Im (f . (vq,vq))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (f . (vq,vq))) ^2) + ((Im (f . (vq,vq))) ^2)) is complex real ext-real Element of REAL
sqrt |.(f . (vq,vq)).| is complex real ext-real Element of REAL
f . (vr,vr) is complex Element of the carrier of F_Complex
[vr,vr] is set
{vr,vr} is non empty set
{vr} is non empty set
{{vr,vr},{vr}} is non empty set
f . [vr,vr] is set
|.(f . (vr,vr)).| is complex real ext-real Element of REAL
Re (f . (vr,vr)) is complex real ext-real Element of REAL
(Re (f . (vr,vr))) ^2 is complex real ext-real Element of REAL
(Re (f . (vr,vr))) * (Re (f . (vr,vr))) is complex real ext-real set
Im (f . (vr,vr)) is complex real ext-real Element of REAL
(Im (f . (vr,vr))) ^2 is complex real ext-real Element of REAL
(Im (f . (vr,vr))) * (Im (f . (vr,vr))) is complex real ext-real set
((Re (f . (vr,vr))) ^2) + ((Im (f . (vr,vr))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (f . (vr,vr))) ^2) + ((Im (f . (vr,vr))) ^2)) is complex real ext-real Element of REAL
sqrt |.(f . (vr,vr)).| is complex real ext-real Element of REAL
(sqrt |.(f . (vq,vq)).|) + (sqrt |.(f . (vr,vr)).|) is complex real ext-real Element of REAL
((sqrt |.(f . (vq,vq)).|) + (sqrt |.(f . (vr,vr)).|)) ^2 is complex real ext-real Element of REAL
((sqrt |.(f . (vq,vq)).|) + (sqrt |.(f . (vr,vr)).|)) * ((sqrt |.(f . (vq,vq)).|) + (sqrt |.(f . (vr,vr)).|)) is complex real ext-real set
(V,f,vq) is complex real ext-real set
(V,f,vr) is complex real ext-real set
(V,f,(vq + vr)) is complex real ext-real set
sqrt (V,f,vq) is complex real ext-real set
sqrt (V,f,vr) is complex real ext-real set
(sqrt (V,f,vq)) + (sqrt (V,f,vr)) is complex real ext-real set
((sqrt (V,f,vq)) + (sqrt (V,f,vr))) ^2 is complex real ext-real set
((sqrt (V,f,vq)) + (sqrt (V,f,vr))) * ((sqrt (V,f,vq)) + (sqrt (V,f,vr))) is complex real ext-real set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,V) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
vq is Element of the carrier of V
vr is Element of the carrier of V
vq + vr is Element of the carrier of V
the addF of V is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[:[: the carrier of V, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is set
the addF of V . (vq,vr) is Element of the carrier of V
[vq,vr] is set
{vq,vr} is non empty set
{vq} is non empty set
{{vq,vr},{vq}} is non empty set
the addF of V . [vq,vr] is set
(V,f,(vq + vr)) is complex real ext-real set
f . ((vq + vr),(vq + vr)) is complex Element of the carrier of F_Complex
[(vq + vr),(vq + vr)] is set
{(vq + vr),(vq + vr)} is non empty set
{(vq + vr)} is non empty set
{{(vq + vr),(vq + vr)},{(vq + vr)}} is non empty set
f . [(vq + vr),(vq + vr)] is set
Re (f . ((vq + vr),(vq + vr))) is complex real ext-real Element of REAL
vq - vr is Element of the carrier of V
- vr is Element of the carrier of V
vq + (- vr) is Element of the carrier of V
the addF of V . (vq,(- vr)) is Element of the carrier of V
[vq,(- vr)] is set
{vq,(- vr)} is non empty set
{{vq,(- vr)},{vq}} is non empty set
the addF of V . [vq,(- vr)] is set
(V,f,(vq - vr)) is complex real ext-real set
f . ((vq - vr),(vq - vr)) is complex Element of the carrier of F_Complex
[(vq - vr),(vq - vr)] is set
{(vq - vr),(vq - vr)} is non empty set
{(vq - vr)} is non empty set
{{(vq - vr),(vq - vr)},{(vq - vr)}} is non empty set
f . [(vq - vr),(vq - vr)] is set
Re (f . ((vq - vr),(vq - vr))) is complex real ext-real Element of REAL
(V,f,(vq + vr)) + (V,f,(vq - vr)) is complex real ext-real set
(V,f,vq) is complex real ext-real set
f . (vq,vq) is complex Element of the carrier of F_Complex
[vq,vq] is set
{vq,vq} is non empty set
{{vq,vq},{vq}} is non empty set
f . [vq,vq] is set
Re (f . (vq,vq)) is complex real ext-real Element of REAL
2 * (V,f,vq) is complex real ext-real Element of REAL
(V,f,vr) is complex real ext-real set
f . (vr,vr) is complex Element of the carrier of F_Complex
[vr,vr] is set
{vr,vr} is non empty set
{vr} is non empty set
{{vr,vr},{vr}} is non empty set
f . [vr,vr] is set
Re (f . (vr,vr)) is complex real ext-real Element of REAL
2 * (V,f,vr) is complex real ext-real Element of REAL
(2 * (V,f,vq)) + (2 * (V,f,vr)) is complex real ext-real Element of REAL
f . (vq,vr) is complex Element of the carrier of F_Complex
f . [vq,vr] is set
f . (vr,vq) is complex Element of the carrier of F_Complex
[vr,vq] is set
{vr,vq} is non empty set
{{vr,vq},{vr}} is non empty set
f . [vr,vq] is set
(f . (vq,vq)) + (f . (vq,vr)) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . ((f . (vq,vq)),(f . (vq,vr))) is complex Element of the carrier of F_Complex
[(f . (vq,vq)),(f . (vq,vr))] is set
{(f . (vq,vq)),(f . (vq,vr))} is non empty V175() set
{(f . (vq,vq))} is non empty V175() set
{{(f . (vq,vq)),(f . (vq,vr))},{(f . (vq,vq))}} is non empty set
the addF of F_Complex . [(f . (vq,vq)),(f . (vq,vr))] is set
K135((f . (vq,vq)),(f . (vq,vr))) is complex Element of COMPLEX
(f . (vr,vq)) + (f . (vr,vr)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((f . (vr,vq)),(f . (vr,vr))) is complex Element of the carrier of F_Complex
[(f . (vr,vq)),(f . (vr,vr))] is set
{(f . (vr,vq)),(f . (vr,vr))} is non empty V175() set
{(f . (vr,vq))} is non empty V175() set
{{(f . (vr,vq)),(f . (vr,vr))},{(f . (vr,vq))}} is non empty set
the addF of F_Complex . [(f . (vr,vq)),(f . (vr,vr))] is set
K135((f . (vr,vq)),(f . (vr,vr))) is complex Element of COMPLEX
((f . (vq,vq)) + (f . (vq,vr))) + ((f . (vr,vq)) + (f . (vr,vr))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((f . (vq,vq)) + (f . (vq,vr))),((f . (vr,vq)) + (f . (vr,vr)))) is complex Element of the carrier of F_Complex
[((f . (vq,vq)) + (f . (vq,vr))),((f . (vr,vq)) + (f . (vr,vr)))] is set
{((f . (vq,vq)) + (f . (vq,vr))),((f . (vr,vq)) + (f . (vr,vr)))} is non empty V175() set
{((f . (vq,vq)) + (f . (vq,vr)))} is non empty V175() set
{{((f . (vq,vq)) + (f . (vq,vr))),((f . (vr,vq)) + (f . (vr,vr)))},{((f . (vq,vq)) + (f . (vq,vr)))}} is non empty set
the addF of F_Complex . [((f . (vq,vq)) + (f . (vq,vr))),((f . (vr,vq)) + (f . (vr,vr)))] is set
K135(((f . (vq,vq)) + (f . (vq,vr))),((f . (vr,vq)) + (f . (vr,vr)))) is complex Element of COMPLEX
(f . ((vq + vr),(vq + vr))) + (f . ((vq - vr),(vq - vr))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((f . ((vq + vr),(vq + vr))),(f . ((vq - vr),(vq - vr)))) is complex Element of the carrier of F_Complex
[(f . ((vq + vr),(vq + vr))),(f . ((vq - vr),(vq - vr)))] is set
{(f . ((vq + vr),(vq + vr))),(f . ((vq - vr),(vq - vr)))} is non empty V175() set
{(f . ((vq + vr),(vq + vr)))} is non empty V175() set
{{(f . ((vq + vr),(vq + vr))),(f . ((vq - vr),(vq - vr)))},{(f . ((vq + vr),(vq + vr)))}} is non empty set
the addF of F_Complex . [(f . ((vq + vr),(vq + vr))),(f . ((vq - vr),(vq - vr)))] is set
K135((f . ((vq + vr),(vq + vr))),(f . ((vq - vr),(vq - vr)))) is complex Element of COMPLEX
(f . (vq,vq)) - (f . (vq,vr)) is complex Element of the carrier of F_Complex
- (f . (vq,vr)) is complex Element of the carrier of F_Complex
(f . (vq,vq)) + (- (f . (vq,vr))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((f . (vq,vq)),(- (f . (vq,vr)))) is complex Element of the carrier of F_Complex
[(f . (vq,vq)),(- (f . (vq,vr)))] is set
{(f . (vq,vq)),(- (f . (vq,vr)))} is non empty V175() set
{{(f . (vq,vq)),(- (f . (vq,vr)))},{(f . (vq,vq))}} is non empty set
the addF of F_Complex . [(f . (vq,vq)),(- (f . (vq,vr)))] is set
K135((f . (vq,vq)),(- (f . (vq,vr)))) is complex Element of COMPLEX
(f . (vr,vq)) - (f . (vr,vr)) is complex Element of the carrier of F_Complex
- (f . (vr,vr)) is complex Element of the carrier of F_Complex
(f . (vr,vq)) + (- (f . (vr,vr))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((f . (vr,vq)),(- (f . (vr,vr)))) is complex Element of the carrier of F_Complex
[(f . (vr,vq)),(- (f . (vr,vr)))] is set
{(f . (vr,vq)),(- (f . (vr,vr)))} is non empty V175() set
{{(f . (vr,vq)),(- (f . (vr,vr)))},{(f . (vr,vq))}} is non empty set
the addF of F_Complex . [(f . (vr,vq)),(- (f . (vr,vr)))] is set
K135((f . (vr,vq)),(- (f . (vr,vr)))) is complex Element of COMPLEX
((f . (vq,vq)) - (f . (vq,vr))) - ((f . (vr,vq)) - (f . (vr,vr))) is complex Element of the carrier of F_Complex
- ((f . (vr,vq)) - (f . (vr,vr))) is complex Element of the carrier of F_Complex
((f . (vq,vq)) - (f . (vq,vr))) + (- ((f . (vr,vq)) - (f . (vr,vr)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((f . (vq,vq)) - (f . (vq,vr))),(- ((f . (vr,vq)) - (f . (vr,vr))))) is complex Element of the carrier of F_Complex
[((f . (vq,vq)) - (f . (vq,vr))),(- ((f . (vr,vq)) - (f . (vr,vr))))] is set
{((f . (vq,vq)) - (f . (vq,vr))),(- ((f . (vr,vq)) - (f . (vr,vr))))} is non empty V175() set
{((f . (vq,vq)) - (f . (vq,vr)))} is non empty V175() set
{{((f . (vq,vq)) - (f . (vq,vr))),(- ((f . (vr,vq)) - (f . (vr,vr))))},{((f . (vq,vq)) - (f . (vq,vr)))}} is non empty set
the addF of F_Complex . [((f . (vq,vq)) - (f . (vq,vr))),(- ((f . (vr,vq)) - (f . (vr,vr))))] is set
K135(((f . (vq,vq)) - (f . (vq,vr))),(- ((f . (vr,vq)) - (f . (vr,vr))))) is complex Element of COMPLEX
(((f . (vq,vq)) + (f . (vq,vr))) + ((f . (vr,vq)) + (f . (vr,vr)))) + (((f . (vq,vq)) - (f . (vq,vr))) - ((f . (vr,vq)) - (f . (vr,vr)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((f . (vq,vq)) + (f . (vq,vr))) + ((f . (vr,vq)) + (f . (vr,vr)))),(((f . (vq,vq)) - (f . (vq,vr))) - ((f . (vr,vq)) - (f . (vr,vr))))) is complex Element of the carrier of F_Complex
[(((f . (vq,vq)) + (f . (vq,vr))) + ((f . (vr,vq)) + (f . (vr,vr)))),(((f . (vq,vq)) - (f . (vq,vr))) - ((f . (vr,vq)) - (f . (vr,vr))))] is set
{(((f . (vq,vq)) + (f . (vq,vr))) + ((f . (vr,vq)) + (f . (vr,vr)))),(((f . (vq,vq)) - (f . (vq,vr))) - ((f . (vr,vq)) - (f . (vr,vr))))} is non empty V175() set
{(((f . (vq,vq)) + (f . (vq,vr))) + ((f . (vr,vq)) + (f . (vr,vr))))} is non empty V175() set
{{(((f . (vq,vq)) + (f . (vq,vr))) + ((f . (vr,vq)) + (f . (vr,vr)))),(((f . (vq,vq)) - (f . (vq,vr))) - ((f . (vr,vq)) - (f . (vr,vr))))},{(((f . (vq,vq)) + (f . (vq,vr))) + ((f . (vr,vq)) + (f . (vr,vr))))}} is non empty set
the addF of F_Complex . [(((f . (vq,vq)) + (f . (vq,vr))) + ((f . (vr,vq)) + (f . (vr,vr)))),(((f . (vq,vq)) - (f . (vq,vr))) - ((f . (vr,vq)) - (f . (vr,vr))))] is set
K135((((f . (vq,vq)) + (f . (vq,vr))) + ((f . (vr,vq)) + (f . (vr,vr)))),(((f . (vq,vq)) - (f . (vq,vr))) - ((f . (vr,vq)) - (f . (vr,vr))))) is complex Element of COMPLEX
(f . (vq,vr)) + (f . (vq,vq)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((f . (vq,vr)),(f . (vq,vq))) is complex Element of the carrier of F_Complex
[(f . (vq,vr)),(f . (vq,vq))] is set
{(f . (vq,vr)),(f . (vq,vq))} is non empty V175() set
{(f . (vq,vr))} is non empty V175() set
{{(f . (vq,vr)),(f . (vq,vq))},{(f . (vq,vr))}} is non empty set
the addF of F_Complex . [(f . (vq,vr)),(f . (vq,vq))] is set
K135((f . (vq,vr)),(f . (vq,vq))) is complex Element of COMPLEX
((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)) is complex Element of the carrier of F_Complex
((f . (vq,vr)) + (f . (vq,vq))) + (- (f . (vq,vr))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((f . (vq,vr)) + (f . (vq,vq))),(- (f . (vq,vr)))) is complex Element of the carrier of F_Complex
[((f . (vq,vr)) + (f . (vq,vq))),(- (f . (vq,vr)))] is set
{((f . (vq,vr)) + (f . (vq,vq))),(- (f . (vq,vr)))} is non empty V175() set
{((f . (vq,vr)) + (f . (vq,vq)))} is non empty V175() set
{{((f . (vq,vr)) + (f . (vq,vq))),(- (f . (vq,vr)))},{((f . (vq,vr)) + (f . (vq,vq)))}} is non empty set
the addF of F_Complex . [((f . (vq,vr)) + (f . (vq,vq))),(- (f . (vq,vr)))] is set
K135(((f . (vq,vr)) + (f . (vq,vq))),(- (f . (vq,vr)))) is complex Element of COMPLEX
(f . (vq,vq)) + (((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((f . (vq,vq)),(((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)))) is complex Element of the carrier of F_Complex
[(f . (vq,vq)),(((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)))] is set
{(f . (vq,vq)),(((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)))} is non empty V175() set
{{(f . (vq,vq)),(((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)))},{(f . (vq,vq))}} is non empty set
the addF of F_Complex . [(f . (vq,vq)),(((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)))] is set
K135((f . (vq,vq)),(((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)))) is complex Element of COMPLEX
((f . (vq,vq)) + (((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)))) + ((f . (vr,vq)) + (f . (vr,vr))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((f . (vq,vq)) + (((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)))),((f . (vr,vq)) + (f . (vr,vr)))) is complex Element of the carrier of F_Complex
[((f . (vq,vq)) + (((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)))),((f . (vr,vq)) + (f . (vr,vr)))] is set
{((f . (vq,vq)) + (((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)))),((f . (vr,vq)) + (f . (vr,vr)))} is non empty V175() set
{((f . (vq,vq)) + (((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr))))} is non empty V175() set
{{((f . (vq,vq)) + (((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)))),((f . (vr,vq)) + (f . (vr,vr)))},{((f . (vq,vq)) + (((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr))))}} is non empty set
the addF of F_Complex . [((f . (vq,vq)) + (((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)))),((f . (vr,vq)) + (f . (vr,vr)))] is set
K135(((f . (vq,vq)) + (((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)))),((f . (vr,vq)) + (f . (vr,vr)))) is complex Element of COMPLEX
(((f . (vq,vq)) + (((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)))) + ((f . (vr,vq)) + (f . (vr,vr)))) - ((f . (vr,vq)) - (f . (vr,vr))) is complex Element of the carrier of F_Complex
(((f . (vq,vq)) + (((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)))) + ((f . (vr,vq)) + (f . (vr,vr)))) + (- ((f . (vr,vq)) - (f . (vr,vr)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((f . (vq,vq)) + (((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)))) + ((f . (vr,vq)) + (f . (vr,vr)))),(- ((f . (vr,vq)) - (f . (vr,vr))))) is complex Element of the carrier of F_Complex
[(((f . (vq,vq)) + (((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)))) + ((f . (vr,vq)) + (f . (vr,vr)))),(- ((f . (vr,vq)) - (f . (vr,vr))))] is set
{(((f . (vq,vq)) + (((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)))) + ((f . (vr,vq)) + (f . (vr,vr)))),(- ((f . (vr,vq)) - (f . (vr,vr))))} is non empty V175() set
{(((f . (vq,vq)) + (((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)))) + ((f . (vr,vq)) + (f . (vr,vr))))} is non empty V175() set
{{(((f . (vq,vq)) + (((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)))) + ((f . (vr,vq)) + (f . (vr,vr)))),(- ((f . (vr,vq)) - (f . (vr,vr))))},{(((f . (vq,vq)) + (((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)))) + ((f . (vr,vq)) + (f . (vr,vr))))}} is non empty set
the addF of F_Complex . [(((f . (vq,vq)) + (((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)))) + ((f . (vr,vq)) + (f . (vr,vr)))),(- ((f . (vr,vq)) - (f . (vr,vr))))] is set
K135((((f . (vq,vq)) + (((f . (vq,vr)) + (f . (vq,vq))) - (f . (vq,vr)))) + ((f . (vr,vq)) + (f . (vr,vr)))),(- ((f . (vr,vq)) - (f . (vr,vr))))) is complex Element of COMPLEX
(f . (vq,vq)) + (f . (vq,vq)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((f . (vq,vq)),(f . (vq,vq))) is complex Element of the carrier of F_Complex
[(f . (vq,vq)),(f . (vq,vq))] is set
{(f . (vq,vq)),(f . (vq,vq))} is non empty V175() set
{{(f . (vq,vq)),(f . (vq,vq))},{(f . (vq,vq))}} is non empty set
the addF of F_Complex . [(f . (vq,vq)),(f . (vq,vq))] is set
K135((f . (vq,vq)),(f . (vq,vq))) is complex Element of COMPLEX
((f . (vq,vq)) + (f . (vq,vq))) + ((f . (vr,vq)) + (f . (vr,vr))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((f . (vq,vq)) + (f . (vq,vq))),((f . (vr,vq)) + (f . (vr,vr)))) is complex Element of the carrier of F_Complex
[((f . (vq,vq)) + (f . (vq,vq))),((f . (vr,vq)) + (f . (vr,vr)))] is set
{((f . (vq,vq)) + (f . (vq,vq))),((f . (vr,vq)) + (f . (vr,vr)))} is non empty V175() set
{((f . (vq,vq)) + (f . (vq,vq)))} is non empty V175() set
{{((f . (vq,vq)) + (f . (vq,vq))),((f . (vr,vq)) + (f . (vr,vr)))},{((f . (vq,vq)) + (f . (vq,vq)))}} is non empty set
the addF of F_Complex . [((f . (vq,vq)) + (f . (vq,vq))),((f . (vr,vq)) + (f . (vr,vr)))] is set
K135(((f . (vq,vq)) + (f . (vq,vq))),((f . (vr,vq)) + (f . (vr,vr)))) is complex Element of COMPLEX
(((f . (vq,vq)) + (f . (vq,vq))) + ((f . (vr,vq)) + (f . (vr,vr)))) - ((f . (vr,vq)) - (f . (vr,vr))) is complex Element of the carrier of F_Complex
(((f . (vq,vq)) + (f . (vq,vq))) + ((f . (vr,vq)) + (f . (vr,vr)))) + (- ((f . (vr,vq)) - (f . (vr,vr)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((f . (vq,vq)) + (f . (vq,vq))) + ((f . (vr,vq)) + (f . (vr,vr)))),(- ((f . (vr,vq)) - (f . (vr,vr))))) is complex Element of the carrier of F_Complex
[(((f . (vq,vq)) + (f . (vq,vq))) + ((f . (vr,vq)) + (f . (vr,vr)))),(- ((f . (vr,vq)) - (f . (vr,vr))))] is set
{(((f . (vq,vq)) + (f . (vq,vq))) + ((f . (vr,vq)) + (f . (vr,vr)))),(- ((f . (vr,vq)) - (f . (vr,vr))))} is non empty V175() set
{(((f . (vq,vq)) + (f . (vq,vq))) + ((f . (vr,vq)) + (f . (vr,vr))))} is non empty V175() set
{{(((f . (vq,vq)) + (f . (vq,vq))) + ((f . (vr,vq)) + (f . (vr,vr)))),(- ((f . (vr,vq)) - (f . (vr,vr))))},{(((f . (vq,vq)) + (f . (vq,vq))) + ((f . (vr,vq)) + (f . (vr,vr))))}} is non empty set
the addF of F_Complex . [(((f . (vq,vq)) + (f . (vq,vq))) + ((f . (vr,vq)) + (f . (vr,vr)))),(- ((f . (vr,vq)) - (f . (vr,vr))))] is set
K135((((f . (vq,vq)) + (f . (vq,vq))) + ((f . (vr,vq)) + (f . (vr,vr)))),(- ((f . (vr,vq)) - (f . (vr,vr))))) is complex Element of COMPLEX
((f . (vr,vq)) + (f . (vr,vr))) - ((f . (vr,vq)) - (f . (vr,vr))) is complex Element of the carrier of F_Complex
((f . (vr,vq)) + (f . (vr,vr))) + (- ((f . (vr,vq)) - (f . (vr,vr)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((f . (vr,vq)) + (f . (vr,vr))),(- ((f . (vr,vq)) - (f . (vr,vr))))) is complex Element of the carrier of F_Complex
[((f . (vr,vq)) + (f . (vr,vr))),(- ((f . (vr,vq)) - (f . (vr,vr))))] is set
{((f . (vr,vq)) + (f . (vr,vr))),(- ((f . (vr,vq)) - (f . (vr,vr))))} is non empty V175() set
{((f . (vr,vq)) + (f . (vr,vr)))} is non empty V175() set
{{((f . (vr,vq)) + (f . (vr,vr))),(- ((f . (vr,vq)) - (f . (vr,vr))))},{((f . (vr,vq)) + (f . (vr,vr)))}} is non empty set
the addF of F_Complex . [((f . (vr,vq)) + (f . (vr,vr))),(- ((f . (vr,vq)) - (f . (vr,vr))))] is set
K135(((f . (vr,vq)) + (f . (vr,vr))),(- ((f . (vr,vq)) - (f . (vr,vr))))) is complex Element of COMPLEX
((f . (vq,vq)) + (f . (vq,vq))) + (((f . (vr,vq)) + (f . (vr,vr))) - ((f . (vr,vq)) - (f . (vr,vr)))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((f . (vq,vq)) + (f . (vq,vq))),(((f . (vr,vq)) + (f . (vr,vr))) - ((f . (vr,vq)) - (f . (vr,vr))))) is complex Element of the carrier of F_Complex
[((f . (vq,vq)) + (f . (vq,vq))),(((f . (vr,vq)) + (f . (vr,vr))) - ((f . (vr,vq)) - (f . (vr,vr))))] is set
{((f . (vq,vq)) + (f . (vq,vq))),(((f . (vr,vq)) + (f . (vr,vr))) - ((f . (vr,vq)) - (f . (vr,vr))))} is non empty V175() set
{{((f . (vq,vq)) + (f . (vq,vq))),(((f . (vr,vq)) + (f . (vr,vr))) - ((f . (vr,vq)) - (f . (vr,vr))))},{((f . (vq,vq)) + (f . (vq,vq)))}} is non empty set
the addF of F_Complex . [((f . (vq,vq)) + (f . (vq,vq))),(((f . (vr,vq)) + (f . (vr,vr))) - ((f . (vr,vq)) - (f . (vr,vr))))] is set
K135(((f . (vq,vq)) + (f . (vq,vq))),(((f . (vr,vq)) + (f . (vr,vr))) - ((f . (vr,vq)) - (f . (vr,vr))))) is complex Element of COMPLEX
((f . (vr,vq)) + (f . (vr,vr))) - (f . (vr,vq)) is complex Element of the carrier of F_Complex
- (f . (vr,vq)) is complex Element of the carrier of F_Complex
((f . (vr,vq)) + (f . (vr,vr))) + (- (f . (vr,vq))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((f . (vr,vq)) + (f . (vr,vr))),(- (f . (vr,vq)))) is complex Element of the carrier of F_Complex
[((f . (vr,vq)) + (f . (vr,vr))),(- (f . (vr,vq)))] is set
{((f . (vr,vq)) + (f . (vr,vr))),(- (f . (vr,vq)))} is non empty V175() set
{{((f . (vr,vq)) + (f . (vr,vr))),(- (f . (vr,vq)))},{((f . (vr,vq)) + (f . (vr,vr)))}} is non empty set
the addF of F_Complex . [((f . (vr,vq)) + (f . (vr,vr))),(- (f . (vr,vq)))] is set
K135(((f . (vr,vq)) + (f . (vr,vr))),(- (f . (vr,vq)))) is complex Element of COMPLEX
(((f . (vr,vq)) + (f . (vr,vr))) - (f . (vr,vq))) + (f . (vr,vr)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((f . (vr,vq)) + (f . (vr,vr))) - (f . (vr,vq))),(f . (vr,vr))) is complex Element of the carrier of F_Complex
[(((f . (vr,vq)) + (f . (vr,vr))) - (f . (vr,vq))),(f . (vr,vr))] is set
{(((f . (vr,vq)) + (f . (vr,vr))) - (f . (vr,vq))),(f . (vr,vr))} is non empty V175() set
{(((f . (vr,vq)) + (f . (vr,vr))) - (f . (vr,vq)))} is non empty V175() set
{{(((f . (vr,vq)) + (f . (vr,vr))) - (f . (vr,vq))),(f . (vr,vr))},{(((f . (vr,vq)) + (f . (vr,vr))) - (f . (vr,vq)))}} is non empty set
the addF of F_Complex . [(((f . (vr,vq)) + (f . (vr,vr))) - (f . (vr,vq))),(f . (vr,vr))] is set
K135((((f . (vr,vq)) + (f . (vr,vr))) - (f . (vr,vq))),(f . (vr,vr))) is complex Element of COMPLEX
((f . (vq,vq)) + (f . (vq,vq))) + ((((f . (vr,vq)) + (f . (vr,vr))) - (f . (vr,vq))) + (f . (vr,vr))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((f . (vq,vq)) + (f . (vq,vq))),((((f . (vr,vq)) + (f . (vr,vr))) - (f . (vr,vq))) + (f . (vr,vr)))) is complex Element of the carrier of F_Complex
[((f . (vq,vq)) + (f . (vq,vq))),((((f . (vr,vq)) + (f . (vr,vr))) - (f . (vr,vq))) + (f . (vr,vr)))] is set
{((f . (vq,vq)) + (f . (vq,vq))),((((f . (vr,vq)) + (f . (vr,vr))) - (f . (vr,vq))) + (f . (vr,vr)))} is non empty V175() set
{{((f . (vq,vq)) + (f . (vq,vq))),((((f . (vr,vq)) + (f . (vr,vr))) - (f . (vr,vq))) + (f . (vr,vr)))},{((f . (vq,vq)) + (f . (vq,vq)))}} is non empty set
the addF of F_Complex . [((f . (vq,vq)) + (f . (vq,vq))),((((f . (vr,vq)) + (f . (vr,vr))) - (f . (vr,vq))) + (f . (vr,vr)))] is set
K135(((f . (vq,vq)) + (f . (vq,vq))),((((f . (vr,vq)) + (f . (vr,vr))) - (f . (vr,vq))) + (f . (vr,vr)))) is complex Element of COMPLEX
(f . (vr,vr)) + (f . (vr,vr)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((f . (vr,vr)),(f . (vr,vr))) is complex Element of the carrier of F_Complex
[(f . (vr,vr)),(f . (vr,vr))] is set
{(f . (vr,vr)),(f . (vr,vr))} is non empty V175() set
{(f . (vr,vr))} is non empty V175() set
{{(f . (vr,vr)),(f . (vr,vr))},{(f . (vr,vr))}} is non empty set
the addF of F_Complex . [(f . (vr,vr)),(f . (vr,vr))] is set
K135((f . (vr,vr)),(f . (vr,vr))) is complex Element of COMPLEX
((f . (vq,vq)) + (f . (vq,vq))) + ((f . (vr,vr)) + (f . (vr,vr))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((f . (vq,vq)) + (f . (vq,vq))),((f . (vr,vr)) + (f . (vr,vr)))) is complex Element of the carrier of F_Complex
[((f . (vq,vq)) + (f . (vq,vq))),((f . (vr,vr)) + (f . (vr,vr)))] is set
{((f . (vq,vq)) + (f . (vq,vq))),((f . (vr,vr)) + (f . (vr,vr)))} is non empty V175() set
{{((f . (vq,vq)) + (f . (vq,vq))),((f . (vr,vr)) + (f . (vr,vr)))},{((f . (vq,vq)) + (f . (vq,vq)))}} is non empty set
the addF of F_Complex . [((f . (vq,vq)) + (f . (vq,vq))),((f . (vr,vr)) + (f . (vr,vr)))] is set
K135(((f . (vq,vq)) + (f . (vq,vq))),((f . (vr,vr)) + (f . (vr,vr)))) is complex Element of COMPLEX
Re ((f . ((vq + vr),(vq + vr))) + (f . ((vq - vr),(vq - vr)))) is complex real ext-real Element of REAL
Re ((f . (vq,vq)) + (f . (vq,vq))) is complex real ext-real Element of REAL
Re ((f . (vr,vr)) + (f . (vr,vr))) is complex real ext-real Element of REAL
(Re ((f . (vq,vq)) + (f . (vq,vq)))) + (Re ((f . (vr,vr)) + (f . (vr,vr)))) is complex real ext-real Element of REAL
(Re (f . (vq,vq))) + (Re (f . (vq,vq))) is complex real ext-real Element of REAL
((Re (f . (vq,vq))) + (Re (f . (vq,vq)))) + (Re ((f . (vr,vr)) + (f . (vr,vr)))) is complex real ext-real Element of REAL
2 * (Re (f . (vq,vq))) is complex real ext-real Element of REAL
(Re (f . (vr,vr))) + (Re (f . (vr,vr))) is complex real ext-real Element of REAL
(2 * (Re (f . (vq,vq)))) + ((Re (f . (vr,vr))) + (Re (f . (vr,vr)))) is complex real ext-real Element of REAL
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,V) (V) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
vq is Element of the carrier of V
vr is Element of the carrier of V
vq + vr is Element of the carrier of V
the addF of V is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[:[: the carrier of V, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is set
the addF of V . (vq,vr) is Element of the carrier of V
[vq,vr] is set
{vq,vr} is non empty set
{vq} is non empty set
{{vq,vr},{vq}} is non empty set
the addF of V . [vq,vr] is set
f . ((vq + vr),(vq + vr)) is complex Element of the carrier of F_Complex
[(vq + vr),(vq + vr)] is set
{(vq + vr),(vq + vr)} is non empty set
{(vq + vr)} is non empty set
{{(vq + vr),(vq + vr)},{(vq + vr)}} is non empty set
f . [(vq + vr),(vq + vr)] is set
|.(f . ((vq + vr),(vq + vr))).| is complex real ext-real Element of REAL
Re (f . ((vq + vr),(vq + vr))) is complex real ext-real Element of REAL
(Re (f . ((vq + vr),(vq + vr)))) ^2 is complex real ext-real Element of REAL
(Re (f . ((vq + vr),(vq + vr)))) * (Re (f . ((vq + vr),(vq + vr)))) is complex real ext-real set
Im (f . ((vq + vr),(vq + vr))) is complex real ext-real Element of REAL
(Im (f . ((vq + vr),(vq + vr)))) ^2 is complex real ext-real Element of REAL
(Im (f . ((vq + vr),(vq + vr)))) * (Im (f . ((vq + vr),(vq + vr)))) is complex real ext-real set
((Re (f . ((vq + vr),(vq + vr)))) ^2) + ((Im (f . ((vq + vr),(vq + vr)))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (f . ((vq + vr),(vq + vr)))) ^2) + ((Im (f . ((vq + vr),(vq + vr)))) ^2)) is complex real ext-real Element of REAL
vq - vr is Element of the carrier of V
- vr is Element of the carrier of V
vq + (- vr) is Element of the carrier of V
the addF of V . (vq,(- vr)) is Element of the carrier of V
[vq,(- vr)] is set
{vq,(- vr)} is non empty set
{{vq,(- vr)},{vq}} is non empty set
the addF of V . [vq,(- vr)] is set
f . ((vq - vr),(vq - vr)) is complex Element of the carrier of F_Complex
[(vq - vr),(vq - vr)] is set
{(vq - vr),(vq - vr)} is non empty set
{(vq - vr)} is non empty set
{{(vq - vr),(vq - vr)},{(vq - vr)}} is non empty set
f . [(vq - vr),(vq - vr)] is set
|.(f . ((vq - vr),(vq - vr))).| is complex real ext-real Element of REAL
Re (f . ((vq - vr),(vq - vr))) is complex real ext-real Element of REAL
(Re (f . ((vq - vr),(vq - vr)))) ^2 is complex real ext-real Element of REAL
(Re (f . ((vq - vr),(vq - vr)))) * (Re (f . ((vq - vr),(vq - vr)))) is complex real ext-real set
Im (f . ((vq - vr),(vq - vr))) is complex real ext-real Element of REAL
(Im (f . ((vq - vr),(vq - vr)))) ^2 is complex real ext-real Element of REAL
(Im (f . ((vq - vr),(vq - vr)))) * (Im (f . ((vq - vr),(vq - vr)))) is complex real ext-real set
((Re (f . ((vq - vr),(vq - vr)))) ^2) + ((Im (f . ((vq - vr),(vq - vr)))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (f . ((vq - vr),(vq - vr)))) ^2) + ((Im (f . ((vq - vr),(vq - vr)))) ^2)) is complex real ext-real Element of REAL
|.(f . ((vq + vr),(vq + vr))).| + |.(f . ((vq - vr),(vq - vr))).| is complex real ext-real Element of REAL
f . (vq,vq) is complex Element of the carrier of F_Complex
[vq,vq] is set
{vq,vq} is non empty set
{{vq,vq},{vq}} is non empty set
f . [vq,vq] is set
|.(f . (vq,vq)).| is complex real ext-real Element of REAL
Re (f . (vq,vq)) is complex real ext-real Element of REAL
(Re (f . (vq,vq))) ^2 is complex real ext-real Element of REAL
(Re (f . (vq,vq))) * (Re (f . (vq,vq))) is complex real ext-real set
Im (f . (vq,vq)) is complex real ext-real Element of REAL
(Im (f . (vq,vq))) ^2 is complex real ext-real Element of REAL
(Im (f . (vq,vq))) * (Im (f . (vq,vq))) is complex real ext-real set
((Re (f . (vq,vq))) ^2) + ((Im (f . (vq,vq))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (f . (vq,vq))) ^2) + ((Im (f . (vq,vq))) ^2)) is complex real ext-real Element of REAL
2 * |.(f . (vq,vq)).| is complex real ext-real Element of REAL
f . (vr,vr) is complex Element of the carrier of F_Complex
[vr,vr] is set
{vr,vr} is non empty set
{vr} is non empty set
{{vr,vr},{vr}} is non empty set
f . [vr,vr] is set
|.(f . (vr,vr)).| is complex real ext-real Element of REAL
Re (f . (vr,vr)) is complex real ext-real Element of REAL
(Re (f . (vr,vr))) ^2 is complex real ext-real Element of REAL
(Re (f . (vr,vr))) * (Re (f . (vr,vr))) is complex real ext-real set
Im (f . (vr,vr)) is complex real ext-real Element of REAL
(Im (f . (vr,vr))) ^2 is complex real ext-real Element of REAL
(Im (f . (vr,vr))) * (Im (f . (vr,vr))) is complex real ext-real set
((Re (f . (vr,vr))) ^2) + ((Im (f . (vr,vr))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (f . (vr,vr))) ^2) + ((Im (f . (vr,vr))) ^2)) is complex real ext-real Element of REAL
2 * |.(f . (vr,vr)).| is complex real ext-real Element of REAL
(2 * |.(f . (vq,vq)).|) + (2 * |.(f . (vr,vr)).|) is complex real ext-real Element of REAL
(V,f,vq) is complex real ext-real set
(V,f,vr) is complex real ext-real set
(V,f,(vq + vr)) is complex real ext-real set
(V,f,(vq - vr)) is complex real ext-real set
(V,f,(vq + vr)) + (V,f,(vq - vr)) is complex real ext-real set
2 * (V,f,vq) is complex real ext-real Element of REAL
2 * (V,f,vr) is complex real ext-real Element of REAL
(2 * (V,f,vq)) + (2 * (V,f,vr)) is complex real ext-real Element of REAL
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
[: the carrier of V,REAL:] is set
bool [: the carrier of V,REAL:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
vr is Element of the carrier of V
(V,f,vr) is complex real ext-real set
f . (vr,vr) is complex Element of the carrier of F_Complex
[vr,vr] is set
{vr,vr} is non empty set
{vr} is non empty set
{{vr,vr},{vr}} is non empty set
f . [vr,vr] is set
Re (f . (vr,vr)) is complex real ext-real Element of REAL
sqrt (V,f,vr) is complex real ext-real set
qh is complex real ext-real Element of REAL
A is complex real ext-real Element of REAL
vr is V16() V19( the carrier of V) V20( REAL ) Function-like V30( the carrier of V, REAL ) Element of bool [: the carrier of V,REAL:]
qh is V16() V19( the carrier of V) V20( REAL ) Function-like V30( the carrier of V, REAL ) Element of bool [: the carrier of V,REAL:]
A is Element of the carrier of V
qh . A is complex real ext-real Element of REAL
(V,f,A) is complex real ext-real set
f . (A,A) is complex Element of the carrier of F_Complex
[A,A] is set
{A,A} is non empty set
{A} is non empty set
{{A,A},{A}} is non empty set
f . [A,A] is set
Re (f . (A,A)) is complex real ext-real Element of REAL
sqrt (V,f,A) is complex real ext-real set
vq is V16() V19( the carrier of V) V20( REAL ) Function-like V30( the carrier of V, REAL ) Element of bool [: the carrier of V,REAL:]
vr is V16() V19( the carrier of V) V20( REAL ) Function-like V30( the carrier of V, REAL ) Element of bool [: the carrier of V,REAL:]
qh is Element of the carrier of V
vq . qh is complex real ext-real Element of REAL
(V,f,qh) is complex real ext-real set
f . (qh,qh) is complex Element of the carrier of F_Complex
[qh,qh] is set
{qh,qh} is non empty set
{qh} is non empty set
{{qh,qh},{qh}} is non empty set
f . [qh,qh] is set
Re (f . (qh,qh)) is complex real ext-real Element of REAL
sqrt (V,f,qh) is complex real ext-real set
vr . qh is complex real ext-real Element of REAL
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,V) (V) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
(V,f) is V16() V19( the carrier of V) V20( REAL ) Function-like V30( the carrier of V, REAL ) Element of bool [: the carrier of V,REAL:]
[: the carrier of V,REAL:] is set
bool [: the carrier of V,REAL:] is set
vr is Element of the carrier of V
qh is Element of the carrier of V
vr + qh is Element of the carrier of V
the addF of V is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[:[: the carrier of V, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is set
the addF of V . (vr,qh) is Element of the carrier of V
[vr,qh] is set
{vr,qh} is non empty set
{vr} is non empty set
{{vr,qh},{vr}} is non empty set
the addF of V . [vr,qh] is set
(V,f) . (vr + qh) is complex real ext-real Element of REAL
(V,f) . vr is complex real ext-real Element of REAL
(V,f) . qh is complex real ext-real Element of REAL
((V,f) . vr) + ((V,f) . qh) is complex real ext-real Element of REAL
vr + qh is Element of the carrier of V
(V,f,(vr + qh)) is complex real ext-real set
f . ((vr + qh),(vr + qh)) is complex Element of the carrier of F_Complex
[(vr + qh),(vr + qh)] is set
{(vr + qh),(vr + qh)} is non empty set
{(vr + qh)} is non empty set
{{(vr + qh),(vr + qh)},{(vr + qh)}} is non empty set
f . [(vr + qh),(vr + qh)] is set
Re (f . ((vr + qh),(vr + qh))) is complex real ext-real Element of REAL
(V,f,vr) is complex real ext-real set
f . (vr,vr) is complex Element of the carrier of F_Complex
[vr,vr] is set
{vr,vr} is non empty set
{{vr,vr},{vr}} is non empty set
f . [vr,vr] is set
Re (f . (vr,vr)) is complex real ext-real Element of REAL
(V,f,qh) is complex real ext-real set
f . (qh,qh) is complex Element of the carrier of F_Complex
[qh,qh] is set
{qh,qh} is non empty set
{qh} is non empty set
{{qh,qh},{qh}} is non empty set
f . [qh,qh] is set
Re (f . (qh,qh)) is complex real ext-real Element of REAL
sqrt (V,f,vr) is complex real ext-real set
sqrt (V,f,qh) is complex real ext-real set
(V,f) . (vr + qh) is complex real ext-real Element of REAL
sqrt (V,f,(vr + qh)) is complex real ext-real set
(((V,f) . vr) + ((V,f) . qh)) ^2 is complex real ext-real Element of REAL
(((V,f) . vr) + ((V,f) . qh)) * (((V,f) . vr) + ((V,f) . qh)) is complex real ext-real set
sqrt ((((V,f) . vr) + ((V,f) . qh)) ^2) is complex real ext-real Element of REAL
vr is Element of the carrier of V
(V,f) . vr is complex real ext-real Element of REAL
qh is complex Element of the carrier of F_Complex
qh * vr is Element of the carrier of V
the lmult of V is V16() V19([: the carrier of F_Complex, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of F_Complex, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:]
[: the carrier of F_Complex, the carrier of V:] is set
[:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
the lmult of V . (qh,vr) is Element of the carrier of V
[qh,vr] is set
{qh,vr} is non empty set
{qh} is non empty V175() set
{{qh,vr},{qh}} is non empty set
the lmult of V . [qh,vr] is set
(V,f) . (qh * vr) is complex real ext-real Element of REAL
|.qh.| is complex real ext-real Element of REAL
Re qh is complex real ext-real Element of REAL
(Re qh) ^2 is complex real ext-real Element of REAL
(Re qh) * (Re qh) is complex real ext-real set
Im qh is complex real ext-real Element of REAL
(Im qh) ^2 is complex real ext-real Element of REAL
(Im qh) * (Im qh) is complex real ext-real set
((Re qh) ^2) + ((Im qh) ^2) is complex real ext-real Element of REAL
sqrt (((Re qh) ^2) + ((Im qh) ^2)) is complex real ext-real Element of REAL
|.qh.| * ((V,f) . vr) is complex real ext-real Element of REAL
|.qh.| ^2 is complex real ext-real Element of REAL
|.qh.| * |.qh.| is complex real ext-real set
f . (vr,vr) is complex Element of the carrier of F_Complex
[vr,vr] is set
{vr,vr} is non empty set
{vr} is non empty set
{{vr,vr},{vr}} is non empty set
f . [vr,vr] is set
Re (f . (vr,vr)) is complex real ext-real Element of REAL
f . ((qh * vr),(qh * vr)) is complex Element of the carrier of F_Complex
[(qh * vr),(qh * vr)] is set
{(qh * vr),(qh * vr)} is non empty set
{(qh * vr)} is non empty set
{{(qh * vr),(qh * vr)},{(qh * vr)}} is non empty set
f . [(qh * vr),(qh * vr)] is set
f . (vr,(qh * vr)) is complex Element of the carrier of F_Complex
[vr,(qh * vr)] is set
{vr,(qh * vr)} is non empty set
{{vr,(qh * vr)},{vr}} is non empty set
f . [vr,(qh * vr)] is set
qh * (f . (vr,(qh * vr))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (qh,(f . (vr,(qh * vr)))) is complex Element of the carrier of F_Complex
[qh,(f . (vr,(qh * vr)))] is set
{qh,(f . (vr,(qh * vr)))} is non empty V175() set
{{qh,(f . (vr,(qh * vr)))},{qh}} is non empty set
the multF of F_Complex . [qh,(f . (vr,(qh * vr)))] is set
K137(qh,(f . (vr,(qh * vr)))) is complex Element of COMPLEX
qh *' is complex Element of the carrier of F_Complex
(Im qh) * <i> is complex set
(Re qh) - ((Im qh) * <i>) is complex set
(qh *') * (f . (vr,vr)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((qh *'),(f . (vr,vr))) is complex Element of the carrier of F_Complex
[(qh *'),(f . (vr,vr))] is set
{(qh *'),(f . (vr,vr))} is non empty V175() set
{(qh *')} is non empty V175() set
{{(qh *'),(f . (vr,vr))},{(qh *')}} is non empty set
the multF of F_Complex . [(qh *'),(f . (vr,vr))] is set
K137((qh *'),(f . (vr,vr))) is complex Element of COMPLEX
qh * ((qh *') * (f . (vr,vr))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (qh,((qh *') * (f . (vr,vr)))) is complex Element of the carrier of F_Complex
[qh,((qh *') * (f . (vr,vr)))] is set
{qh,((qh *') * (f . (vr,vr)))} is non empty V175() set
{{qh,((qh *') * (f . (vr,vr)))},{qh}} is non empty set
the multF of F_Complex . [qh,((qh *') * (f . (vr,vr)))] is set
K137(qh,((qh *') * (f . (vr,vr)))) is complex Element of COMPLEX
qh * (qh *') is complex Element of the carrier of F_Complex
the multF of F_Complex . (qh,(qh *')) is complex Element of the carrier of F_Complex
[qh,(qh *')] is set
{qh,(qh *')} is non empty V175() set
{{qh,(qh *')},{qh}} is non empty set
the multF of F_Complex . [qh,(qh *')] is set
K137(qh,(qh *')) is complex Element of COMPLEX
(qh * (qh *')) * (f . (vr,vr)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((qh * (qh *')),(f . (vr,vr))) is complex Element of the carrier of F_Complex
[(qh * (qh *')),(f . (vr,vr))] is set
{(qh * (qh *')),(f . (vr,vr))} is non empty V175() set
{(qh * (qh *'))} is non empty V175() set
{{(qh * (qh *')),(f . (vr,vr))},{(qh * (qh *'))}} is non empty set
the multF of F_Complex . [(qh * (qh *')),(f . (vr,vr))] is set
K137((qh * (qh *')),(f . (vr,vr))) is complex Element of COMPLEX
[**(|.qh.| ^2),0**] is complex Element of the carrier of F_Complex
(|.qh.| ^2) + (0 * <i>) is complex set
[**(|.qh.| ^2),0**] * (f . (vr,vr)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ([**(|.qh.| ^2),0**],(f . (vr,vr))) is complex Element of the carrier of F_Complex
[[**(|.qh.| ^2),0**],(f . (vr,vr))] is set
{[**(|.qh.| ^2),0**],(f . (vr,vr))} is non empty V175() set
{[**(|.qh.| ^2),0**]} is non empty V175() set
{{[**(|.qh.| ^2),0**],(f . (vr,vr))},{[**(|.qh.| ^2),0**]}} is non empty set
the multF of F_Complex . [[**(|.qh.| ^2),0**],(f . (vr,vr))] is set
K137([**(|.qh.| ^2),0**],(f . (vr,vr))) is complex Element of COMPLEX
Im (f . (vr,vr)) is complex real ext-real Element of REAL
[**(Re (f . (vr,vr))),(Im (f . (vr,vr)))**] is complex Element of the carrier of F_Complex
(Im (f . (vr,vr))) * <i> is complex set
(Re (f . (vr,vr))) + ((Im (f . (vr,vr))) * <i>) is complex set
[**(|.qh.| ^2),0**] * [**(Re (f . (vr,vr))),(Im (f . (vr,vr)))**] is complex Element of the carrier of F_Complex
the multF of F_Complex . ([**(|.qh.| ^2),0**],[**(Re (f . (vr,vr))),(Im (f . (vr,vr)))**]) is complex Element of the carrier of F_Complex
[[**(|.qh.| ^2),0**],[**(Re (f . (vr,vr))),(Im (f . (vr,vr)))**]] is set
{[**(|.qh.| ^2),0**],[**(Re (f . (vr,vr))),(Im (f . (vr,vr)))**]} is non empty V175() set
{{[**(|.qh.| ^2),0**],[**(Re (f . (vr,vr))),(Im (f . (vr,vr)))**]},{[**(|.qh.| ^2),0**]}} is non empty set
the multF of F_Complex . [[**(|.qh.| ^2),0**],[**(Re (f . (vr,vr))),(Im (f . (vr,vr)))**]] is set
K137([**(|.qh.| ^2),0**],[**(Re (f . (vr,vr))),(Im (f . (vr,vr)))**]) is complex Element of COMPLEX
[**(Re (f . (vr,vr))),0**] is complex Element of the carrier of F_Complex
(Re (f . (vr,vr))) + (0 * <i>) is complex set
[**(|.qh.| ^2),0**] * [**(Re (f . (vr,vr))),0**] is complex Element of the carrier of F_Complex
the multF of F_Complex . ([**(|.qh.| ^2),0**],[**(Re (f . (vr,vr))),0**]) is complex Element of the carrier of F_Complex
[[**(|.qh.| ^2),0**],[**(Re (f . (vr,vr))),0**]] is set
{[**(|.qh.| ^2),0**],[**(Re (f . (vr,vr))),0**]} is non empty V175() set
{{[**(|.qh.| ^2),0**],[**(Re (f . (vr,vr))),0**]},{[**(|.qh.| ^2),0**]}} is non empty set
the multF of F_Complex . [[**(|.qh.| ^2),0**],[**(Re (f . (vr,vr))),0**]] is set
K137([**(|.qh.| ^2),0**],[**(Re (f . (vr,vr))),0**]) is complex Element of COMPLEX
(|.qh.| ^2) * (Re (f . (vr,vr))) is complex real ext-real Element of REAL
[**((|.qh.| ^2) * (Re (f . (vr,vr)))),0**] is complex Element of the carrier of F_Complex
((|.qh.| ^2) * (Re (f . (vr,vr)))) + (0 * <i>) is complex set
(V,f,(qh * vr)) is complex real ext-real set
Re (f . ((qh * vr),(qh * vr))) is complex real ext-real Element of REAL
sqrt (V,f,(qh * vr)) is complex real ext-real set
sqrt ((|.qh.| ^2) * (Re (f . (vr,vr)))) is complex real ext-real Element of REAL
sqrt (|.qh.| ^2) is complex real ext-real Element of REAL
sqrt (Re (f . (vr,vr))) is complex real ext-real Element of REAL
(sqrt (|.qh.| ^2)) * (sqrt (Re (f . (vr,vr)))) is complex real ext-real Element of REAL
(V,f,vr) is complex real ext-real set
sqrt (V,f,vr) is complex real ext-real set
|.qh.| * (sqrt (V,f,vr)) is complex real ext-real Element of REAL
V is non empty right_complementable add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) (V,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
diagker f is Element of bool the carrier of V
bool the carrier of V is set
{ b₁ where b₁ is Element of the carrier of V : f . (b₁,b₁) = 0. F_Complex } is set
0. V is zero Element of the carrier of V
f . ((0. V),(0. V)) is complex Element of the carrier of F_Complex
[(0. V),(0. V)] is set
{(0. V),(0. V)} is non empty set
{(0. V)} is non empty set
{{(0. V),(0. V)},{(0. V)}} is non empty set
f . [(0. V),(0. V)] is set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,V) (V) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
diagker f is non empty Element of bool the carrier of V
bool the carrier of V is set
{ b₁ where b₁ is Element of the carrier of V : f . (b₁,b₁) = 0. F_Complex } is set
vr is Element of the carrier of V
qh is Element of the carrier of V
vr + qh is Element of the carrier of V
the addF of V is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[:[: the carrier of V, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is set
the addF of V . (vr,qh) is Element of the carrier of V
[vr,qh] is set
{vr,qh} is non empty set
{vr} is non empty set
{{vr,qh},{vr}} is non empty set
the addF of V . [vr,qh] is set
f . (vr,qh) is complex Element of the carrier of F_Complex
f . [vr,qh] is set
|.(f . (vr,qh)).| is complex real ext-real Element of REAL
Re (f . (vr,qh)) is complex real ext-real Element of REAL
(Re (f . (vr,qh))) ^2 is complex real ext-real Element of REAL
(Re (f . (vr,qh))) * (Re (f . (vr,qh))) is complex real ext-real set
Im (f . (vr,qh)) is complex real ext-real Element of REAL
(Im (f . (vr,qh))) ^2 is complex real ext-real Element of REAL
(Im (f . (vr,qh))) * (Im (f . (vr,qh))) is complex real ext-real set
((Re (f . (vr,qh))) ^2) + ((Im (f . (vr,qh))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (f . (vr,qh))) ^2) + ((Im (f . (vr,qh))) ^2)) is complex real ext-real Element of REAL
|.(f . (vr,qh)).| ^2 is complex real ext-real Element of REAL
|.(f . (vr,qh)).| * |.(f . (vr,qh)).| is complex real ext-real set
f . (vr,vr) is complex Element of the carrier of F_Complex
[vr,vr] is set
{vr,vr} is non empty set
{{vr,vr},{vr}} is non empty set
f . [vr,vr] is set
|.(f . (vr,vr)).| is complex real ext-real Element of REAL
Re (f . (vr,vr)) is complex real ext-real Element of REAL
(Re (f . (vr,vr))) ^2 is complex real ext-real Element of REAL
(Re (f . (vr,vr))) * (Re (f . (vr,vr))) is complex real ext-real set
Im (f . (vr,vr)) is complex real ext-real Element of REAL
(Im (f . (vr,vr))) ^2 is complex real ext-real Element of REAL
(Im (f . (vr,vr))) * (Im (f . (vr,vr))) is complex real ext-real set
((Re (f . (vr,vr))) ^2) + ((Im (f . (vr,vr))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (f . (vr,vr))) ^2) + ((Im (f . (vr,vr))) ^2)) is complex real ext-real Element of REAL
|.(f . (vr,vr)).| * 0 is complex real ext-real Element of REAL
A is Element of the carrier of V
f . (A,A) is complex Element of the carrier of F_Complex
[A,A] is set
{A,A} is non empty set
{A} is non empty set
{{A,A},{A}} is non empty set
f . [A,A] is set
(f . (vr,qh)) *' is complex Element of the carrier of F_Complex
(Im (f . (vr,qh))) * <i> is complex set
(Re (f . (vr,qh))) - ((Im (f . (vr,qh))) * <i>) is complex set
|.((f . (vr,qh)) *').| is complex real ext-real Element of REAL
Re ((f . (vr,qh)) *') is complex real ext-real Element of REAL
(Re ((f . (vr,qh)) *')) ^2 is complex real ext-real Element of REAL
(Re ((f . (vr,qh)) *')) * (Re ((f . (vr,qh)) *')) is complex real ext-real set
Im ((f . (vr,qh)) *') is complex real ext-real Element of REAL
(Im ((f . (vr,qh)) *')) ^2 is complex real ext-real Element of REAL
(Im ((f . (vr,qh)) *')) * (Im ((f . (vr,qh)) *')) is complex real ext-real set
((Re ((f . (vr,qh)) *')) ^2) + ((Im ((f . (vr,qh)) *')) ^2) is complex real ext-real Element of REAL
sqrt (((Re ((f . (vr,qh)) *')) ^2) + ((Im ((f . (vr,qh)) *')) ^2)) is complex real ext-real Element of REAL
f . (qh,vr) is complex Element of the carrier of F_Complex
[qh,vr] is set
{qh,vr} is non empty set
{qh} is non empty set
{{qh,vr},{qh}} is non empty set
f . [qh,vr] is set
|.(f . (qh,vr)).| is complex real ext-real Element of REAL
Re (f . (qh,vr)) is complex real ext-real Element of REAL
(Re (f . (qh,vr))) ^2 is complex real ext-real Element of REAL
(Re (f . (qh,vr))) * (Re (f . (qh,vr))) is complex real ext-real set
Im (f . (qh,vr)) is complex real ext-real Element of REAL
(Im (f . (qh,vr))) ^2 is complex real ext-real Element of REAL
(Im (f . (qh,vr))) * (Im (f . (qh,vr))) is complex real ext-real set
((Re (f . (qh,vr))) ^2) + ((Im (f . (qh,vr))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (f . (qh,vr))) ^2) + ((Im (f . (qh,vr))) ^2)) is complex real ext-real Element of REAL
f . ((vr + qh),(vr + qh)) is complex Element of the carrier of F_Complex
[(vr + qh),(vr + qh)] is set
{(vr + qh),(vr + qh)} is non empty set
{(vr + qh)} is non empty set
{{(vr + qh),(vr + qh)},{(vr + qh)}} is non empty set
f . [(vr + qh),(vr + qh)] is set
(0. F_Complex) + (f . (vr,qh)) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . ((0. F_Complex),(f . (vr,qh))) is complex Element of the carrier of F_Complex
[(0. F_Complex),(f . (vr,qh))] is set
{(0. F_Complex),(f . (vr,qh))} is non empty V175() set
{(0. F_Complex)} is non empty V175() set
{{(0. F_Complex),(f . (vr,qh))},{(0. F_Complex)}} is non empty set
the addF of F_Complex . [(0. F_Complex),(f . (vr,qh))] is set
K135((0. F_Complex),(f . (vr,qh))) is complex Element of COMPLEX
(f . (qh,vr)) + (0. F_Complex) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((f . (qh,vr)),(0. F_Complex)) is complex Element of the carrier of F_Complex
[(f . (qh,vr)),(0. F_Complex)] is set
{(f . (qh,vr)),(0. F_Complex)} is non empty V175() set
{(f . (qh,vr))} is non empty V175() set
{{(f . (qh,vr)),(0. F_Complex)},{(f . (qh,vr))}} is non empty set
the addF of F_Complex . [(f . (qh,vr)),(0. F_Complex)] is set
K135((f . (qh,vr)),(0. F_Complex)) is complex Element of COMPLEX
((0. F_Complex) + (f . (vr,qh))) + ((f . (qh,vr)) + (0. F_Complex)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((0. F_Complex) + (f . (vr,qh))),((f . (qh,vr)) + (0. F_Complex))) is complex Element of the carrier of F_Complex
[((0. F_Complex) + (f . (vr,qh))),((f . (qh,vr)) + (0. F_Complex))] is set
{((0. F_Complex) + (f . (vr,qh))),((f . (qh,vr)) + (0. F_Complex))} is non empty V175() set
{((0. F_Complex) + (f . (vr,qh)))} is non empty V175() set
{{((0. F_Complex) + (f . (vr,qh))),((f . (qh,vr)) + (0. F_Complex))},{((0. F_Complex) + (f . (vr,qh)))}} is non empty set
the addF of F_Complex . [((0. F_Complex) + (f . (vr,qh))),((f . (qh,vr)) + (0. F_Complex))] is set
K135(((0. F_Complex) + (f . (vr,qh))),((f . (qh,vr)) + (0. F_Complex))) is complex Element of COMPLEX
(f . (vr,qh)) + ((f . (qh,vr)) + (0. F_Complex)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((f . (vr,qh)),((f . (qh,vr)) + (0. F_Complex))) is complex Element of the carrier of F_Complex
[(f . (vr,qh)),((f . (qh,vr)) + (0. F_Complex))] is set
{(f . (vr,qh)),((f . (qh,vr)) + (0. F_Complex))} is non empty V175() set
{(f . (vr,qh))} is non empty V175() set
{{(f . (vr,qh)),((f . (qh,vr)) + (0. F_Complex))},{(f . (vr,qh))}} is non empty set
the addF of F_Complex . [(f . (vr,qh)),((f . (qh,vr)) + (0. F_Complex))] is set
K135((f . (vr,qh)),((f . (qh,vr)) + (0. F_Complex))) is complex Element of COMPLEX
(f . (vr,qh)) + (f . (qh,vr)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((f . (vr,qh)),(f . (qh,vr))) is complex Element of the carrier of F_Complex
[(f . (vr,qh)),(f . (qh,vr))] is set
{(f . (vr,qh)),(f . (qh,vr))} is non empty V175() set
{{(f . (vr,qh)),(f . (qh,vr))},{(f . (vr,qh))}} is non empty set
the addF of F_Complex . [(f . (vr,qh)),(f . (qh,vr))] is set
K135((f . (vr,qh)),(f . (qh,vr))) is complex Element of COMPLEX
A is Element of the carrier of V
f . (A,A) is complex Element of the carrier of F_Complex
[A,A] is set
{A,A} is non empty set
{A} is non empty set
{{A,A},{A}} is non empty set
f . [A,A] is set
K is Element of the carrier of V
f . (K,K) is complex Element of the carrier of F_Complex
[K,K] is set
{K,K} is non empty set
{K} is non empty set
{{K,K},{K}} is non empty set
f . [K,K] is set
vr is complex Element of the carrier of F_Complex
qh is Element of the carrier of V
vr * qh is Element of the carrier of V
the lmult of V is V16() V19([: the carrier of F_Complex, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of F_Complex, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:]
[: the carrier of F_Complex, the carrier of V:] is set
[:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
the lmult of V . (vr,qh) is Element of the carrier of V
[vr,qh] is set
{vr,qh} is non empty set
{vr} is non empty V175() set
{{vr,qh},{vr}} is non empty set
the lmult of V . [vr,qh] is set
f . ((vr * qh),(vr * qh)) is complex Element of the carrier of F_Complex
[(vr * qh),(vr * qh)] is set
{(vr * qh),(vr * qh)} is non empty set
{(vr * qh)} is non empty set
{{(vr * qh),(vr * qh)},{(vr * qh)}} is non empty set
f . [(vr * qh),(vr * qh)] is set
f . (qh,(vr * qh)) is complex Element of the carrier of F_Complex
[qh,(vr * qh)] is set
{qh,(vr * qh)} is non empty set
{qh} is non empty set
{{qh,(vr * qh)},{qh}} is non empty set
f . [qh,(vr * qh)] is set
vr * (f . (qh,(vr * qh))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (vr,(f . (qh,(vr * qh)))) is complex Element of the carrier of F_Complex
[vr,(f . (qh,(vr * qh)))] is set
{vr,(f . (qh,(vr * qh)))} is non empty V175() set
{{vr,(f . (qh,(vr * qh)))},{vr}} is non empty set
the multF of F_Complex . [vr,(f . (qh,(vr * qh)))] is set
K137(vr,(f . (qh,(vr * qh)))) is complex Element of COMPLEX
vr *' is complex Element of the carrier of F_Complex
Re vr is complex real ext-real Element of REAL
Im vr is complex real ext-real Element of REAL
(Im vr) * <i> is complex set
(Re vr) - ((Im vr) * <i>) is complex set
(vr *') * (0. F_Complex) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((vr *'),(0. F_Complex)) is complex Element of the carrier of F_Complex
[(vr *'),(0. F_Complex)] is set
{(vr *'),(0. F_Complex)} is non empty V175() set
{(vr *')} is non empty V175() set
{{(vr *'),(0. F_Complex)},{(vr *')}} is non empty set
the multF of F_Complex . [(vr *'),(0. F_Complex)] is set
K137((vr *'),(0. F_Complex)) is complex Element of COMPLEX
vr * ((vr *') * (0. F_Complex)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (vr,((vr *') * (0. F_Complex))) is complex Element of the carrier of F_Complex
[vr,((vr *') * (0. F_Complex))] is set
{vr,((vr *') * (0. F_Complex))} is non empty V175() set
{{vr,((vr *') * (0. F_Complex))},{vr}} is non empty set
the multF of F_Complex . [vr,((vr *') * (0. F_Complex))] is set
K137(vr,((vr *') * (0. F_Complex))) is complex Element of COMPLEX
vr * (0. F_Complex) is complex Element of the carrier of F_Complex
the multF of F_Complex . (vr,(0. F_Complex)) is complex Element of the carrier of F_Complex
[vr,(0. F_Complex)] is set
{vr,(0. F_Complex)} is non empty V175() set
{{vr,(0. F_Complex)},{vr}} is non empty set
the multF of F_Complex . [vr,(0. F_Complex)] is set
K137(vr,(0. F_Complex)) is complex Element of COMPLEX
A is Element of the carrier of V
f . (A,A) is complex Element of the carrier of F_Complex
[A,A] is set
{A,A} is non empty set
{A} is non empty set
{{A,A},{A}} is non empty set
f . [A,A] is set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,V) (V) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
diagker f is non empty Element of bool the carrier of V
bool the carrier of V is set
{ b₁ where b₁ is Element of the carrier of V : f . (b₁,b₁) = 0. F_Complex } is set
leftker f is non empty Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of V holds f . (b₁,b₂) = 0. F_Complex } is set
vq is set
vr is Element of the carrier of V
f . (vr,vr) is complex Element of the carrier of F_Complex
[vr,vr] is set
{vr,vr} is non empty set
{vr} is non empty set
{{vr,vr},{vr}} is non empty set
f . [vr,vr] is set
qh is Element of the carrier of V
f . (vr,qh) is complex Element of the carrier of F_Complex
[vr,qh] is set
{vr,qh} is non empty set
{{vr,qh},{vr}} is non empty set
f . [vr,qh] is set
|.(f . (vr,qh)).| is complex real ext-real Element of REAL
Re (f . (vr,qh)) is complex real ext-real Element of REAL
(Re (f . (vr,qh))) ^2 is complex real ext-real Element of REAL
(Re (f . (vr,qh))) * (Re (f . (vr,qh))) is complex real ext-real set
Im (f . (vr,qh)) is complex real ext-real Element of REAL
(Im (f . (vr,qh))) ^2 is complex real ext-real Element of REAL
(Im (f . (vr,qh))) * (Im (f . (vr,qh))) is complex real ext-real set
((Re (f . (vr,qh))) ^2) + ((Im (f . (vr,qh))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (f . (vr,qh))) ^2) + ((Im (f . (vr,qh))) ^2)) is complex real ext-real Element of REAL
|.(f . (vr,qh)).| ^2 is complex real ext-real Element of REAL
|.(f . (vr,qh)).| * |.(f . (vr,qh)).| is complex real ext-real set
f . (qh,qh) is complex Element of the carrier of F_Complex
[qh,qh] is set
{qh,qh} is non empty set
{qh} is non empty set
{{qh,qh},{qh}} is non empty set
f . [qh,qh] is set
|.(f . (qh,qh)).| is complex real ext-real Element of REAL
Re (f . (qh,qh)) is complex real ext-real Element of REAL
(Re (f . (qh,qh))) ^2 is complex real ext-real Element of REAL
(Re (f . (qh,qh))) * (Re (f . (qh,qh))) is complex real ext-real set
Im (f . (qh,qh)) is complex real ext-real Element of REAL
(Im (f . (qh,qh))) ^2 is complex real ext-real Element of REAL
(Im (f . (qh,qh))) * (Im (f . (qh,qh))) is complex real ext-real set
((Re (f . (qh,qh))) ^2) + ((Im (f . (qh,qh))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (f . (qh,qh))) ^2) + ((Im (f . (qh,qh))) ^2)) is complex real ext-real Element of REAL
0 * |.(f . (qh,qh)).| is complex real ext-real Element of REAL
vq is set
vr is Element of the carrier of V
f . (vr,vr) is complex Element of the carrier of F_Complex
[vr,vr] is set
{vr,vr} is non empty set
{vr} is non empty set
{{vr,vr},{vr}} is non empty set
f . [vr,vr] is set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,V) (V) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
diagker f is non empty Element of bool the carrier of V
bool the carrier of V is set
{ b₁ where b₁ is Element of the carrier of V : f . (b₁,b₁) = 0. F_Complex } is set
rightker f is non empty Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of V holds f . (b₂,b₁) = 0. F_Complex } is set
vq is set
vr is Element of the carrier of V
f . (vr,vr) is complex Element of the carrier of F_Complex
[vr,vr] is set
{vr,vr} is non empty set
{vr} is non empty set
{{vr,vr},{vr}} is non empty set
f . [vr,vr] is set
qh is Element of the carrier of V
f . (qh,vr) is complex Element of the carrier of F_Complex
[qh,vr] is set
{qh,vr} is non empty set
{qh} is non empty set
{{qh,vr},{qh}} is non empty set
f . [qh,vr] is set
|.(f . (qh,vr)).| is complex real ext-real Element of REAL
Re (f . (qh,vr)) is complex real ext-real Element of REAL
(Re (f . (qh,vr))) ^2 is complex real ext-real Element of REAL
(Re (f . (qh,vr))) * (Re (f . (qh,vr))) is complex real ext-real set
Im (f . (qh,vr)) is complex real ext-real Element of REAL
(Im (f . (qh,vr))) ^2 is complex real ext-real Element of REAL
(Im (f . (qh,vr))) * (Im (f . (qh,vr))) is complex real ext-real set
((Re (f . (qh,vr))) ^2) + ((Im (f . (qh,vr))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (f . (qh,vr))) ^2) + ((Im (f . (qh,vr))) ^2)) is complex real ext-real Element of REAL
|.(f . (qh,vr)).| ^2 is complex real ext-real Element of REAL
|.(f . (qh,vr)).| * |.(f . (qh,vr)).| is complex real ext-real set
f . (qh,qh) is complex Element of the carrier of F_Complex
[qh,qh] is set
{qh,qh} is non empty set
{{qh,qh},{qh}} is non empty set
f . [qh,qh] is set
|.(f . (qh,qh)).| is complex real ext-real Element of REAL
Re (f . (qh,qh)) is complex real ext-real Element of REAL
(Re (f . (qh,qh))) ^2 is complex real ext-real Element of REAL
(Re (f . (qh,qh))) * (Re (f . (qh,qh))) is complex real ext-real set
Im (f . (qh,qh)) is complex real ext-real Element of REAL
(Im (f . (qh,qh))) ^2 is complex real ext-real Element of REAL
(Im (f . (qh,qh))) * (Im (f . (qh,qh))) is complex real ext-real set
((Re (f . (qh,qh))) ^2) + ((Im (f . (qh,qh))) ^2) is complex real ext-real Element of REAL
sqrt (((Re (f . (qh,qh))) ^2) + ((Im (f . (qh,qh))) ^2)) is complex real ext-real Element of REAL
|.(f . (qh,qh)).| * 0 is complex real ext-real Element of REAL
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
diagker f is Element of bool the carrier of V
bool the carrier of V is set
{ b₁ where b₁ is Element of the carrier of V : f . (b₁,b₁) = 0. F_Complex } is set
(V,V,f) is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
diagker (V,V,f) is Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : (V,V,f) . (b₁,b₁) = 0. F_Complex } is set
vr is set
qh is Element of the carrier of V
f . (qh,qh) is complex Element of the carrier of F_Complex
[qh,qh] is set
{qh,qh} is non empty set
{qh} is non empty set
{{qh,qh},{qh}} is non empty set
f . [qh,qh] is set
(V,V,f) . (qh,qh) is complex Element of the carrier of F_Complex
(V,V,f) . [qh,qh] is set
vr is set
qh is Element of the carrier of V
(V,V,f) . (qh,qh) is complex Element of the carrier of F_Complex
[qh,qh] is set
{qh,qh} is non empty set
{qh} is non empty set
{{qh,qh},{qh}} is non empty set
(V,V,f) . [qh,qh] is set
f . (qh,qh) is complex Element of the carrier of F_Complex
f . [qh,qh] is set
(f . (qh,qh)) *' is complex Element of the carrier of F_Complex
Re (f . (qh,qh)) is complex real ext-real Element of REAL
Im (f . (qh,qh)) is complex real ext-real Element of REAL
(Im (f . (qh,qh))) * <i> is complex set
(Re (f . (qh,qh))) - ((Im (f . (qh,qh))) * <i>) is complex set
((f . (qh,qh)) *') *' is complex Element of the carrier of F_Complex
Re ((f . (qh,qh)) *') is complex real ext-real Element of REAL
Im ((f . (qh,qh)) *') is complex real ext-real Element of REAL
(Im ((f . (qh,qh)) *')) * <i> is complex set
(Re ((f . (qh,qh)) *')) - ((Im ((f . (qh,qh)) *')) * <i>) is complex set
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
leftker vq is Element of bool the carrier of V
bool the carrier of V is set
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of f holds vq . (b₁,b₂) = 0. F_Complex } is set
(V,f,vq) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
leftker (V,f,vq) is Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of f holds (V,f,vq) . (b₁,b₂) = 0. F_Complex } is set
rightker vq is Element of bool the carrier of f
bool the carrier of f is set
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of V holds vq . (b₂,b₁) = 0. F_Complex } is set
rightker (V,f,vq) is Element of bool the carrier of f
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of V holds (V,f,vq) . (b₂,b₁) = 0. F_Complex } is set
qh is set
A is Element of the carrier of V
K is Element of the carrier of f
vq . (A,K) is complex Element of the carrier of F_Complex
[A,K] is set
{A,K} is non empty set
{A} is non empty set
{{A,K},{A}} is non empty set
vq . [A,K] is set
(vq . (A,K)) *' is complex Element of the carrier of F_Complex
Re (vq . (A,K)) is complex real ext-real Element of REAL
Im (vq . (A,K)) is complex real ext-real Element of REAL
(Im (vq . (A,K))) * <i> is complex set
(Re (vq . (A,K))) - ((Im (vq . (A,K))) * <i>) is complex set
(V,f,vq) . (A,K) is complex Element of the carrier of F_Complex
(V,f,vq) . [A,K] is set
qh is set
A is Element of the carrier of V
K is Element of the carrier of f
(V,f,vq) . (A,K) is complex Element of the carrier of F_Complex
[A,K] is set
{A,K} is non empty set
{A} is non empty set
{{A,K},{A}} is non empty set
(V,f,vq) . [A,K] is set
((V,f,vq) . (A,K)) *' is complex Element of the carrier of F_Complex
Re ((V,f,vq) . (A,K)) is complex real ext-real Element of REAL
Im ((V,f,vq) . (A,K)) is complex real ext-real Element of REAL
(Im ((V,f,vq) . (A,K))) * <i> is complex set
(Re ((V,f,vq) . (A,K))) - ((Im ((V,f,vq) . (A,K))) * <i>) is complex set
vq . (A,K) is complex Element of the carrier of F_Complex
vq . [A,K] is set
(vq . (A,K)) *' is complex Element of the carrier of F_Complex
Re (vq . (A,K)) is complex real ext-real Element of REAL
Im (vq . (A,K)) is complex real ext-real Element of REAL
(Im (vq . (A,K))) * <i> is complex set
(Re (vq . (A,K))) - ((Im (vq . (A,K))) * <i>) is complex set
((vq . (A,K)) *') *' is complex Element of the carrier of F_Complex
Re ((vq . (A,K)) *') is complex real ext-real Element of REAL
Im ((vq . (A,K)) *') is complex real ext-real Element of REAL
(Im ((vq . (A,K)) *')) * <i> is complex set
(Re ((vq . (A,K)) *')) - ((Im ((vq . (A,K)) *')) * <i>) is complex set
qh is set
A is Element of the carrier of f
K is Element of the carrier of V
vq . (K,A) is complex Element of the carrier of F_Complex
[K,A] is set
{K,A} is non empty set
{K} is non empty set
{{K,A},{K}} is non empty set
vq . [K,A] is set
(vq . (K,A)) *' is complex Element of the carrier of F_Complex
Re (vq . (K,A)) is complex real ext-real Element of REAL
Im (vq . (K,A)) is complex real ext-real Element of REAL
(Im (vq . (K,A))) * <i> is complex set
(Re (vq . (K,A))) - ((Im (vq . (K,A))) * <i>) is complex set
(V,f,vq) . (K,A) is complex Element of the carrier of F_Complex
(V,f,vq) . [K,A] is set
qh is set
A is Element of the carrier of f
K is Element of the carrier of V
(V,f,vq) . (K,A) is complex Element of the carrier of F_Complex
[K,A] is set
{K,A} is non empty set
{K} is non empty set
{{K,A},{K}} is non empty set
(V,f,vq) . [K,A] is set
((V,f,vq) . (K,A)) *' is complex Element of the carrier of F_Complex
Re ((V,f,vq) . (K,A)) is complex real ext-real Element of REAL
Im ((V,f,vq) . (K,A)) is complex real ext-real Element of REAL
(Im ((V,f,vq) . (K,A))) * <i> is complex set
(Re ((V,f,vq) . (K,A))) - ((Im ((V,f,vq) . (K,A))) * <i>) is complex set
vq . (K,A) is complex Element of the carrier of F_Complex
vq . [K,A] is set
(vq . (K,A)) *' is complex Element of the carrier of F_Complex
Re (vq . (K,A)) is complex real ext-real Element of REAL
Im (vq . (K,A)) is complex real ext-real Element of REAL
(Im (vq . (K,A))) * <i> is complex set
(Re (vq . (K,A))) - ((Im (vq . (K,A))) * <i>) is complex set
((vq . (K,A)) *') *' is complex Element of the carrier of F_Complex
Re ((vq . (K,A)) *') is complex real ext-real Element of REAL
Im ((vq . (K,A)) *') is complex real ext-real Element of REAL
(Im ((vq . (K,A)) *')) * <i> is complex set
(Re ((vq . (K,A)) *')) - ((Im ((vq . (K,A)) *')) * <i>) is complex set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,V) (V) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
LKer f is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
(V,V,f) is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
RKer (V,V,f) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
the carrier of (LKer f) is non empty set
leftker f is non empty Element of bool the carrier of V
bool the carrier of V is set
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of V holds f . (b₁,b₂) = 0. F_Complex } is set
diagker f is non empty Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : f . (b₁,b₁) = 0. F_Complex } is set
rightker f is non empty Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of V holds f . (b₂,b₁) = 0. F_Complex } is set
rightker (V,V,f) is non empty Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of V holds (V,V,f) . (b₂,b₁) = 0. F_Complex } is set
the carrier of (RKer (V,V,f)) is non empty set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
vq is Element of the carrier of V
f . (vq,vq) is complex Element of the carrier of F_Complex
[vq,vq] is set
{vq,vq} is non empty set
{vq} is non empty set
{{vq,vq},{vq}} is non empty set
f . [vq,vq] is set
Re (f . (vq,vq)) is complex real ext-real Element of REAL
Im (f . (vq,vq)) is complex real ext-real Element of REAL
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
0. V is zero Element of the carrier of V
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,V) (V) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
vq is Element of the carrier of V
f . (vq,vq) is complex Element of the carrier of F_Complex
[vq,vq] is set
{vq,vq} is non empty set
{vq} is non empty set
{{vq,vq},{vq}} is non empty set
f . [vq,vq] is set
Re (f . (vq,vq)) is complex real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of V : f . (b₁,b₁) = 0. F_Complex } is set
{(0. V)} is non empty set
leftker f is non empty Element of bool the carrier of V
bool the carrier of V is set
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of V holds f . (b₁,b₂) = 0. F_Complex } is set
diagker f is non empty Element of bool the carrier of V
{(0. V)} is non empty set
rightker f is non empty Element of bool the carrier of V
bool the carrier of V is set
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of V holds f . (b₂,b₁) = 0. F_Complex } is set
diagker f is non empty Element of bool the carrier of V
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,vq) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF homogeneousFAF Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
RKer (V,f,vq) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(RKer (V,f,vq))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
RQForm (V,f,vq) is V16() V19([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF homogeneousFAF Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
the carrier of (VectQuot (f,(RKer (V,f,vq)))) is non empty set
[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):] is set
[:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:] is set
(V,(VectQuot (f,(RKer (V,f,vq)))),(RQForm (V,f,vq))) is V16() V19([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF (V, VectQuot (f,(RKer (V,f,vq)))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,vq) is V16() V19([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF (V, VectQuot (f,(RKer (V,f,vq)))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
(V,f,vq) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF homogeneousFAF Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
RKer (V,f,vq) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(RKer (V,f,vq))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of (VectQuot (f,(RKer (V,f,vq)))) is non empty set
[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):] is set
[:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:] is set
RQForm (V,f,vq) is V16() V19([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF homogeneousFAF Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
(V,(VectQuot (f,(RKer (V,f,vq)))),(RQForm (V,f,vq))) is V16() V19([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF (V, VectQuot (f,(RKer (V,f,vq)))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
vr is Element of the carrier of V
qh is Element of the carrier of f
qh + (RKer (V,f,vq)) is Element of bool the carrier of f
bool the carrier of f is set
{ (qh + b₁) where b₁ is Element of the carrier of f : b₁ in RKer (V,f,vq) } is set
(V,f,vq) . (vr,(qh + (RKer (V,f,vq)))) is set
[vr,(qh + (RKer (V,f,vq)))] is set
{vr,(qh + (RKer (V,f,vq)))} is non empty set
{vr} is non empty set
{{vr,(qh + (RKer (V,f,vq)))},{vr}} is non empty set
(V,f,vq) . [vr,(qh + (RKer (V,f,vq)))] is set
vq . (vr,qh) is complex Element of the carrier of F_Complex
[vr,qh] is set
{vr,qh} is non empty set
{{vr,qh},{vr}} is non empty set
vq . [vr,qh] is set
A is Element of the carrier of (VectQuot (f,(RKer (V,f,vq))))
(RQForm (V,f,vq)) . (vr,A) is complex Element of the carrier of F_Complex
[vr,A] is set
{vr,A} is non empty set
{{vr,A},{vr}} is non empty set
(RQForm (V,f,vq)) . [vr,A] is set
((RQForm (V,f,vq)) . (vr,A)) *' is complex Element of the carrier of F_Complex
Re ((RQForm (V,f,vq)) . (vr,A)) is complex real ext-real Element of REAL
Im ((RQForm (V,f,vq)) . (vr,A)) is complex real ext-real Element of REAL
(Im ((RQForm (V,f,vq)) . (vr,A))) * <i> is complex set
(Re ((RQForm (V,f,vq)) . (vr,A))) - ((Im ((RQForm (V,f,vq)) . (vr,A))) * <i>) is complex set
(V,f,vq) . (vr,qh) is complex Element of the carrier of F_Complex
(V,f,vq) . [vr,qh] is set
((V,f,vq) . (vr,qh)) *' is complex Element of the carrier of F_Complex
Re ((V,f,vq) . (vr,qh)) is complex real ext-real Element of REAL
Im ((V,f,vq) . (vr,qh)) is complex real ext-real Element of REAL
(Im ((V,f,vq) . (vr,qh))) * <i> is complex set
(Re ((V,f,vq) . (vr,qh))) - ((Im ((V,f,vq) . (vr,qh))) * <i>) is complex set
(vq . (vr,qh)) *' is complex Element of the carrier of F_Complex
Re (vq . (vr,qh)) is complex real ext-real Element of REAL
Im (vq . (vr,qh)) is complex real ext-real Element of REAL
(Im (vq . (vr,qh))) * <i> is complex set
(Re (vq . (vr,qh))) - ((Im (vq . (vr,qh))) * <i>) is complex set
((vq . (vr,qh)) *') *' is complex Element of the carrier of F_Complex
Re ((vq . (vr,qh)) *') is complex real ext-real Element of REAL
Im ((vq . (vr,qh)) *') is complex real ext-real Element of REAL
(Im ((vq . (vr,qh)) *')) * <i> is complex set
(Re ((vq . (vr,qh)) *')) - ((Im ((vq . (vr,qh)) *')) * <i>) is complex set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
LKer vq is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(LKer vq)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
LQForm vq is V16() V19([: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:], the carrier of F_Complex) additiveSAF homogeneousSAF non degenerated-on-left Element of bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:], the carrier of F_Complex:]
the carrier of (VectQuot (V,(LKer vq))) is non empty set
[: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:] is set
[:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:], the carrier of F_Complex:] is set
qh is Element of the carrier of (VectQuot (V,(LKer vq)))
FunctionalFAF ((LQForm vq),qh) is V16() V19( the carrier of f) V20( the carrier of F_Complex) Function-like V30( the carrier of f, the carrier of F_Complex) Element of bool [: the carrier of f, the carrier of F_Complex:]
[: the carrier of f, the carrier of F_Complex:] is set
bool [: the carrier of f, the carrier of F_Complex:] is set
K is Element of the carrier of V
K + (LKer vq) is Element of bool the carrier of V
bool the carrier of V is set
{ (K + b₁) where b₁ is Element of the carrier of V : b₁ in LKer vq } is set
x is Element of the carrier of f
A is Element of the carrier of f
x + A is Element of the carrier of f
the addF of f is V16() V19([: the carrier of f, the carrier of f:]) V20( the carrier of f) Function-like V30([: the carrier of f, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of f, the carrier of f:], the carrier of f:]
[: the carrier of f, the carrier of f:] is set
[:[: the carrier of f, the carrier of f:], the carrier of f:] is set
bool [:[: the carrier of f, the carrier of f:], the carrier of f:] is set
the addF of f . (x,A) is Element of the carrier of f
[x,A] is set
{x,A} is non empty set
{x} is non empty set
{{x,A},{x}} is non empty set
the addF of f . [x,A] is set
(FunctionalFAF ((LQForm vq),qh)) . (x + A) is complex Element of the carrier of F_Complex
(FunctionalFAF ((LQForm vq),qh)) . x is complex Element of the carrier of F_Complex
(FunctionalFAF ((LQForm vq),qh)) . A is complex Element of the carrier of F_Complex
((FunctionalFAF ((LQForm vq),qh)) . x) + ((FunctionalFAF ((LQForm vq),qh)) . A) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . (((FunctionalFAF ((LQForm vq),qh)) . x),((FunctionalFAF ((LQForm vq),qh)) . A)) is complex Element of the carrier of F_Complex
[((FunctionalFAF ((LQForm vq),qh)) . x),((FunctionalFAF ((LQForm vq),qh)) . A)] is set
{((FunctionalFAF ((LQForm vq),qh)) . x),((FunctionalFAF ((LQForm vq),qh)) . A)} is non empty V175() set
{((FunctionalFAF ((LQForm vq),qh)) . x)} is non empty V175() set
{{((FunctionalFAF ((LQForm vq),qh)) . x),((FunctionalFAF ((LQForm vq),qh)) . A)},{((FunctionalFAF ((LQForm vq),qh)) . x)}} is non empty set
the addF of F_Complex . [((FunctionalFAF ((LQForm vq),qh)) . x),((FunctionalFAF ((LQForm vq),qh)) . A)] is set
K135(((FunctionalFAF ((LQForm vq),qh)) . x),((FunctionalFAF ((LQForm vq),qh)) . A)) is complex Element of COMPLEX
x + A is Element of the carrier of f
(FunctionalFAF ((LQForm vq),qh)) . (x + A) is complex Element of the carrier of F_Complex
(LQForm vq) . (qh,(x + A)) is complex Element of the carrier of F_Complex
[qh,(x + A)] is set
{qh,(x + A)} is non empty set
{qh} is non empty set
{{qh,(x + A)},{qh}} is non empty set
(LQForm vq) . [qh,(x + A)] is set
vq . (K,(x + A)) is complex Element of the carrier of F_Complex
[K,(x + A)] is set
{K,(x + A)} is non empty set
{K} is non empty set
{{K,(x + A)},{K}} is non empty set
vq . [K,(x + A)] is set
vq . (K,x) is complex Element of the carrier of F_Complex
[K,x] is set
{K,x} is non empty set
{{K,x},{K}} is non empty set
vq . [K,x] is set
vq . (K,A) is complex Element of the carrier of F_Complex
[K,A] is set
{K,A} is non empty set
{{K,A},{K}} is non empty set
vq . [K,A] is set
(vq . (K,x)) + (vq . (K,A)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vq . (K,x)),(vq . (K,A))) is complex Element of the carrier of F_Complex
[(vq . (K,x)),(vq . (K,A))] is set
{(vq . (K,x)),(vq . (K,A))} is non empty V175() set
{(vq . (K,x))} is non empty V175() set
{{(vq . (K,x)),(vq . (K,A))},{(vq . (K,x))}} is non empty set
the addF of F_Complex . [(vq . (K,x)),(vq . (K,A))] is set
K135((vq . (K,x)),(vq . (K,A))) is complex Element of COMPLEX
(LQForm vq) . (qh,x) is complex Element of the carrier of F_Complex
[qh,x] is set
{qh,x} is non empty set
{{qh,x},{qh}} is non empty set
(LQForm vq) . [qh,x] is set
((LQForm vq) . (qh,x)) + (vq . (K,A)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((LQForm vq) . (qh,x)),(vq . (K,A))) is complex Element of the carrier of F_Complex
[((LQForm vq) . (qh,x)),(vq . (K,A))] is set
{((LQForm vq) . (qh,x)),(vq . (K,A))} is non empty V175() set
{((LQForm vq) . (qh,x))} is non empty V175() set
{{((LQForm vq) . (qh,x)),(vq . (K,A))},{((LQForm vq) . (qh,x))}} is non empty set
the addF of F_Complex . [((LQForm vq) . (qh,x)),(vq . (K,A))] is set
K135(((LQForm vq) . (qh,x)),(vq . (K,A))) is complex Element of COMPLEX
(LQForm vq) . (qh,A) is complex Element of the carrier of F_Complex
[qh,A] is set
{qh,A} is non empty set
{{qh,A},{qh}} is non empty set
(LQForm vq) . [qh,A] is set
((LQForm vq) . (qh,x)) + ((LQForm vq) . (qh,A)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((LQForm vq) . (qh,x)),((LQForm vq) . (qh,A))) is complex Element of the carrier of F_Complex
[((LQForm vq) . (qh,x)),((LQForm vq) . (qh,A))] is set
{((LQForm vq) . (qh,x)),((LQForm vq) . (qh,A))} is non empty V175() set
{{((LQForm vq) . (qh,x)),((LQForm vq) . (qh,A))},{((LQForm vq) . (qh,x))}} is non empty set
the addF of F_Complex . [((LQForm vq) . (qh,x)),((LQForm vq) . (qh,A))] is set
K135(((LQForm vq) . (qh,x)),((LQForm vq) . (qh,A))) is complex Element of COMPLEX
((FunctionalFAF ((LQForm vq),qh)) . x) + ((LQForm vq) . (qh,A)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((FunctionalFAF ((LQForm vq),qh)) . x),((LQForm vq) . (qh,A))) is complex Element of the carrier of F_Complex
[((FunctionalFAF ((LQForm vq),qh)) . x),((LQForm vq) . (qh,A))] is set
{((FunctionalFAF ((LQForm vq),qh)) . x),((LQForm vq) . (qh,A))} is non empty V175() set
{{((FunctionalFAF ((LQForm vq),qh)) . x),((LQForm vq) . (qh,A))},{((FunctionalFAF ((LQForm vq),qh)) . x)}} is non empty set
the addF of F_Complex . [((FunctionalFAF ((LQForm vq),qh)) . x),((LQForm vq) . (qh,A))] is set
K135(((FunctionalFAF ((LQForm vq),qh)) . x),((LQForm vq) . (qh,A))) is complex Element of COMPLEX
((FunctionalFAF ((LQForm vq),qh)) . x) + ((FunctionalFAF ((LQForm vq),qh)) . A) is complex Element of the carrier of F_Complex
qh is Element of the carrier of (VectQuot (V,(LKer vq)))
FunctionalFAF ((LQForm vq),qh) is V16() V19( the carrier of f) V20( the carrier of F_Complex) Function-like V30( the carrier of f, the carrier of F_Complex) Element of bool [: the carrier of f, the carrier of F_Complex:]
[: the carrier of f, the carrier of F_Complex:] is set
bool [: the carrier of f, the carrier of F_Complex:] is set
K is Element of the carrier of V
K + (LKer vq) is Element of bool the carrier of V
bool the carrier of V is set
{ (K + b₁) where b₁ is Element of the carrier of V : b₁ in LKer vq } is set
x is Element of the carrier of f
(FunctionalFAF ((LQForm vq),qh)) . x is complex Element of the carrier of F_Complex
A is complex Element of the carrier of F_Complex
A * x is Element of the carrier of f
the lmult of f is V16() V19([: the carrier of F_Complex, the carrier of f:]) V20( the carrier of f) Function-like V30([: the carrier of F_Complex, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of F_Complex, the carrier of f:], the carrier of f:]
[: the carrier of F_Complex, the carrier of f:] is set
[:[: the carrier of F_Complex, the carrier of f:], the carrier of f:] is set
bool [:[: the carrier of F_Complex, the carrier of f:], the carrier of f:] is set
the lmult of f . (A,x) is Element of the carrier of f
[A,x] is set
{A,x} is non empty set
{A} is non empty V175() set
{{A,x},{A}} is non empty set
the lmult of f . [A,x] is set
(FunctionalFAF ((LQForm vq),qh)) . (A * x) is complex Element of the carrier of F_Complex
A *' is complex Element of the carrier of F_Complex
Re A is complex real ext-real Element of REAL
Im A is complex real ext-real Element of REAL
(Im A) * <i> is complex set
(Re A) - ((Im A) * <i>) is complex set
(A *') * ((FunctionalFAF ((LQForm vq),qh)) . x) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((A *'),((FunctionalFAF ((LQForm vq),qh)) . x)) is complex Element of the carrier of F_Complex
[(A *'),((FunctionalFAF ((LQForm vq),qh)) . x)] is set
{(A *'),((FunctionalFAF ((LQForm vq),qh)) . x)} is non empty V175() set
{(A *')} is non empty V175() set
{{(A *'),((FunctionalFAF ((LQForm vq),qh)) . x)},{(A *')}} is non empty set
the multF of F_Complex . [(A *'),((FunctionalFAF ((LQForm vq),qh)) . x)] is set
K137((A *'),((FunctionalFAF ((LQForm vq),qh)) . x)) is complex Element of COMPLEX
(LQForm vq) . (qh,(A * x)) is complex Element of the carrier of F_Complex
[qh,(A * x)] is set
{qh,(A * x)} is non empty set
{qh} is non empty set
{{qh,(A * x)},{qh}} is non empty set
(LQForm vq) . [qh,(A * x)] is set
vq . (K,(A * x)) is complex Element of the carrier of F_Complex
[K,(A * x)] is set
{K,(A * x)} is non empty set
{K} is non empty set
{{K,(A * x)},{K}} is non empty set
vq . [K,(A * x)] is set
vq . (K,x) is complex Element of the carrier of F_Complex
[K,x] is set
{K,x} is non empty set
{{K,x},{K}} is non empty set
vq . [K,x] is set
(A *') * (vq . (K,x)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((A *'),(vq . (K,x))) is complex Element of the carrier of F_Complex
[(A *'),(vq . (K,x))] is set
{(A *'),(vq . (K,x))} is non empty V175() set
{{(A *'),(vq . (K,x))},{(A *')}} is non empty set
the multF of F_Complex . [(A *'),(vq . (K,x))] is set
K137((A *'),(vq . (K,x))) is complex Element of COMPLEX
(LQForm vq) . (qh,x) is complex Element of the carrier of F_Complex
[qh,x] is set
{qh,x} is non empty set
{{qh,x},{qh}} is non empty set
(LQForm vq) . [qh,x] is set
(A *') * ((LQForm vq) . (qh,x)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((A *'),((LQForm vq) . (qh,x))) is complex Element of the carrier of F_Complex
[(A *'),((LQForm vq) . (qh,x))] is set
{(A *'),((LQForm vq) . (qh,x))} is non empty V175() set
{{(A *'),((LQForm vq) . (qh,x))},{(A *')}} is non empty set
the multF of F_Complex . [(A *'),((LQForm vq) . (qh,x))] is set
K137((A *'),((LQForm vq) . (qh,x))) is complex Element of COMPLEX
(V,f,vq) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
RKer (V,f,vq) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(RKer (V,f,vq))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
(V,f,vq) is V16() V19([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF (V, VectQuot (f,(RKer (V,f,vq)))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
the carrier of (VectQuot (f,(RKer (V,f,vq)))) is non empty set
[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):] is set
[:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:] is set
RQForm (V,f,vq) is V16() V19([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF homogeneousFAF non degenerated-on-right Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
(V,(VectQuot (f,(RKer (V,f,vq)))),(RQForm (V,f,vq))) is V16() V19([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF (V, VectQuot (f,(RKer (V,f,vq)))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
qh is Element of the carrier of (VectQuot (f,(RKer (V,f,vq))))
FunctionalSAF ((V,f,vq),qh) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
K is Element of the carrier of f
K + (RKer (V,f,vq)) is Element of bool the carrier of f
bool the carrier of f is set
{ (K + b₁) where b₁ is Element of the carrier of f : b₁ in RKer (V,f,vq) } is set
x is Element of the carrier of V
A is Element of the carrier of V
x + A is Element of the carrier of V
the addF of V is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is set
the addF of V . (x,A) is Element of the carrier of V
[x,A] is set
{x,A} is non empty set
{x} is non empty set
{{x,A},{x}} is non empty set
the addF of V . [x,A] is set
(FunctionalSAF ((V,f,vq),qh)) . (x + A) is complex Element of the carrier of F_Complex
(FunctionalSAF ((V,f,vq),qh)) . x is complex Element of the carrier of F_Complex
(FunctionalSAF ((V,f,vq),qh)) . A is complex Element of the carrier of F_Complex
((FunctionalSAF ((V,f,vq),qh)) . x) + ((FunctionalSAF ((V,f,vq),qh)) . A) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . (((FunctionalSAF ((V,f,vq),qh)) . x),((FunctionalSAF ((V,f,vq),qh)) . A)) is complex Element of the carrier of F_Complex
[((FunctionalSAF ((V,f,vq),qh)) . x),((FunctionalSAF ((V,f,vq),qh)) . A)] is set
{((FunctionalSAF ((V,f,vq),qh)) . x),((FunctionalSAF ((V,f,vq),qh)) . A)} is non empty V175() set
{((FunctionalSAF ((V,f,vq),qh)) . x)} is non empty V175() set
{{((FunctionalSAF ((V,f,vq),qh)) . x),((FunctionalSAF ((V,f,vq),qh)) . A)},{((FunctionalSAF ((V,f,vq),qh)) . x)}} is non empty set
the addF of F_Complex . [((FunctionalSAF ((V,f,vq),qh)) . x),((FunctionalSAF ((V,f,vq),qh)) . A)] is set
K135(((FunctionalSAF ((V,f,vq),qh)) . x),((FunctionalSAF ((V,f,vq),qh)) . A)) is complex Element of COMPLEX
x + A is Element of the carrier of V
(FunctionalSAF ((V,f,vq),qh)) . (x + A) is complex Element of the carrier of F_Complex
(V,f,vq) . ((x + A),qh) is complex Element of the carrier of F_Complex
[(x + A),qh] is set
{(x + A),qh} is non empty set
{(x + A)} is non empty set
{{(x + A),qh},{(x + A)}} is non empty set
(V,f,vq) . [(x + A),qh] is set
vq . ((x + A),K) is complex Element of the carrier of F_Complex
[(x + A),K] is set
{(x + A),K} is non empty set
{{(x + A),K},{(x + A)}} is non empty set
vq . [(x + A),K] is set
vq . (x,K) is complex Element of the carrier of F_Complex
[x,K] is set
{x,K} is non empty set
{{x,K},{x}} is non empty set
vq . [x,K] is set
vq . (A,K) is complex Element of the carrier of F_Complex
[A,K] is set
{A,K} is non empty set
{A} is non empty set
{{A,K},{A}} is non empty set
vq . [A,K] is set
(vq . (x,K)) + (vq . (A,K)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vq . (x,K)),(vq . (A,K))) is complex Element of the carrier of F_Complex
[(vq . (x,K)),(vq . (A,K))] is set
{(vq . (x,K)),(vq . (A,K))} is non empty V175() set
{(vq . (x,K))} is non empty V175() set
{{(vq . (x,K)),(vq . (A,K))},{(vq . (x,K))}} is non empty set
the addF of F_Complex . [(vq . (x,K)),(vq . (A,K))] is set
K135((vq . (x,K)),(vq . (A,K))) is complex Element of COMPLEX
(V,f,vq) . (x,qh) is complex Element of the carrier of F_Complex
[x,qh] is set
{x,qh} is non empty set
{{x,qh},{x}} is non empty set
(V,f,vq) . [x,qh] is set
((V,f,vq) . (x,qh)) + (vq . (A,K)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((V,f,vq) . (x,qh)),(vq . (A,K))) is complex Element of the carrier of F_Complex
[((V,f,vq) . (x,qh)),(vq . (A,K))] is set
{((V,f,vq) . (x,qh)),(vq . (A,K))} is non empty V175() set
{((V,f,vq) . (x,qh))} is non empty V175() set
{{((V,f,vq) . (x,qh)),(vq . (A,K))},{((V,f,vq) . (x,qh))}} is non empty set
the addF of F_Complex . [((V,f,vq) . (x,qh)),(vq . (A,K))] is set
K135(((V,f,vq) . (x,qh)),(vq . (A,K))) is complex Element of COMPLEX
(V,f,vq) . (A,qh) is complex Element of the carrier of F_Complex
[A,qh] is set
{A,qh} is non empty set
{{A,qh},{A}} is non empty set
(V,f,vq) . [A,qh] is set
((V,f,vq) . (x,qh)) + ((V,f,vq) . (A,qh)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((V,f,vq) . (x,qh)),((V,f,vq) . (A,qh))) is complex Element of the carrier of F_Complex
[((V,f,vq) . (x,qh)),((V,f,vq) . (A,qh))] is set
{((V,f,vq) . (x,qh)),((V,f,vq) . (A,qh))} is non empty V175() set
{{((V,f,vq) . (x,qh)),((V,f,vq) . (A,qh))},{((V,f,vq) . (x,qh))}} is non empty set
the addF of F_Complex . [((V,f,vq) . (x,qh)),((V,f,vq) . (A,qh))] is set
K135(((V,f,vq) . (x,qh)),((V,f,vq) . (A,qh))) is complex Element of COMPLEX
((FunctionalSAF ((V,f,vq),qh)) . x) + ((V,f,vq) . (A,qh)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((FunctionalSAF ((V,f,vq),qh)) . x),((V,f,vq) . (A,qh))) is complex Element of the carrier of F_Complex
[((FunctionalSAF ((V,f,vq),qh)) . x),((V,f,vq) . (A,qh))] is set
{((FunctionalSAF ((V,f,vq),qh)) . x),((V,f,vq) . (A,qh))} is non empty V175() set
{{((FunctionalSAF ((V,f,vq),qh)) . x),((V,f,vq) . (A,qh))},{((FunctionalSAF ((V,f,vq),qh)) . x)}} is non empty set
the addF of F_Complex . [((FunctionalSAF ((V,f,vq),qh)) . x),((V,f,vq) . (A,qh))] is set
K135(((FunctionalSAF ((V,f,vq),qh)) . x),((V,f,vq) . (A,qh))) is complex Element of COMPLEX
((FunctionalSAF ((V,f,vq),qh)) . x) + ((FunctionalSAF ((V,f,vq),qh)) . A) is complex Element of the carrier of F_Complex
qh is Element of the carrier of (VectQuot (f,(RKer (V,f,vq))))
FunctionalSAF ((V,f,vq),qh) is V16() V19( the carrier of V) V20( the carrier of F_Complex) Function-like V30( the carrier of V, the carrier of F_Complex) Element of bool [: the carrier of V, the carrier of F_Complex:]
[: the carrier of V, the carrier of F_Complex:] is set
bool [: the carrier of V, the carrier of F_Complex:] is set
K is Element of the carrier of f
K + (RKer (V,f,vq)) is Element of bool the carrier of f
bool the carrier of f is set
{ (K + b₁) where b₁ is Element of the carrier of f : b₁ in RKer (V,f,vq) } is set
x is Element of the carrier of V
(FunctionalSAF ((V,f,vq),qh)) . x is complex Element of the carrier of F_Complex
A is complex Element of the carrier of F_Complex
A * x is Element of the carrier of V
the lmult of V is V16() V19([: the carrier of F_Complex, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of F_Complex, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:]
[: the carrier of F_Complex, the carrier of V:] is set
[:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
the lmult of V . (A,x) is Element of the carrier of V
[A,x] is set
{A,x} is non empty set
{A} is non empty V175() set
{{A,x},{A}} is non empty set
the lmult of V . [A,x] is set
(FunctionalSAF ((V,f,vq),qh)) . (A * x) is complex Element of the carrier of F_Complex
A * ((FunctionalSAF ((V,f,vq),qh)) . x) is complex Element of the carrier of F_Complex
the multF of F_Complex . (A,((FunctionalSAF ((V,f,vq),qh)) . x)) is complex Element of the carrier of F_Complex
[A,((FunctionalSAF ((V,f,vq),qh)) . x)] is set
{A,((FunctionalSAF ((V,f,vq),qh)) . x)} is non empty V175() set
{{A,((FunctionalSAF ((V,f,vq),qh)) . x)},{A}} is non empty set
the multF of F_Complex . [A,((FunctionalSAF ((V,f,vq),qh)) . x)] is set
K137(A,((FunctionalSAF ((V,f,vq),qh)) . x)) is complex Element of COMPLEX
(V,f,vq) . ((A * x),qh) is complex Element of the carrier of F_Complex
[(A * x),qh] is set
{(A * x),qh} is non empty set
{(A * x)} is non empty set
{{(A * x),qh},{(A * x)}} is non empty set
(V,f,vq) . [(A * x),qh] is set
vq . ((A * x),K) is complex Element of the carrier of F_Complex
[(A * x),K] is set
{(A * x),K} is non empty set
{{(A * x),K},{(A * x)}} is non empty set
vq . [(A * x),K] is set
vq . (x,K) is complex Element of the carrier of F_Complex
[x,K] is set
{x,K} is non empty set
{x} is non empty set
{{x,K},{x}} is non empty set
vq . [x,K] is set
A * (vq . (x,K)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (A,(vq . (x,K))) is complex Element of the carrier of F_Complex
[A,(vq . (x,K))] is set
{A,(vq . (x,K))} is non empty V175() set
{{A,(vq . (x,K))},{A}} is non empty set
the multF of F_Complex . [A,(vq . (x,K))] is set
K137(A,(vq . (x,K))) is complex Element of COMPLEX
(V,f,vq) . (x,qh) is complex Element of the carrier of F_Complex
[x,qh] is set
{x,qh} is non empty set
{{x,qh},{x}} is non empty set
(V,f,vq) . [x,qh] is set
A * ((V,f,vq) . (x,qh)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (A,((V,f,vq) . (x,qh))) is complex Element of the carrier of F_Complex
[A,((V,f,vq) . (x,qh))] is set
{A,((V,f,vq) . (x,qh))} is non empty V175() set
{{A,((V,f,vq) . (x,qh))},{A}} is non empty set
the multF of F_Complex . [A,((V,f,vq) . (x,qh))] is set
K137(A,((V,f,vq) . (x,qh))) is complex Element of COMPLEX
A * ((FunctionalSAF ((V,f,vq),qh)) . x) is complex Element of the carrier of F_Complex
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
LKer vq is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(LKer vq)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of (VectQuot (V,(LKer vq))) is non empty set
(V,f,vq) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
RKer (V,f,vq) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(RKer (V,f,vq))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of (VectQuot (f,(RKer (V,f,vq)))) is non empty set
[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):] is set
[:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:] is set
CosetSet (V,(LKer vq)) is non empty Element of bool (bool the carrier of V)
bool the carrier of V is set
bool (bool the carrier of V) is set
{ b₁ where b₁ is Coset of LKer vq : verum } is set
addCoset (V,(LKer vq)) is V16() V19([:(CosetSet (V,(LKer vq))),(CosetSet (V,(LKer vq))):]) V20( CosetSet (V,(LKer vq))) Function-like V30([:(CosetSet (V,(LKer vq))),(CosetSet (V,(LKer vq))):], CosetSet (V,(LKer vq))) Element of bool [:[:(CosetSet (V,(LKer vq))),(CosetSet (V,(LKer vq))):],(CosetSet (V,(LKer vq))):]
[:(CosetSet (V,(LKer vq))),(CosetSet (V,(LKer vq))):] is set
[:[:(CosetSet (V,(LKer vq))),(CosetSet (V,(LKer vq))):],(CosetSet (V,(LKer vq))):] is set
bool [:[:(CosetSet (V,(LKer vq))),(CosetSet (V,(LKer vq))):],(CosetSet (V,(LKer vq))):] is set
lmultCoset (V,(LKer vq)) is V16() V19([: the carrier of F_Complex,(CosetSet (V,(LKer vq))):]) V20( CosetSet (V,(LKer vq))) Function-like V30([: the carrier of F_Complex,(CosetSet (V,(LKer vq))):], CosetSet (V,(LKer vq))) Element of bool [:[: the carrier of F_Complex,(CosetSet (V,(LKer vq))):],(CosetSet (V,(LKer vq))):]
[: the carrier of F_Complex,(CosetSet (V,(LKer vq))):] is set
[:[: the carrier of F_Complex,(CosetSet (V,(LKer vq))):],(CosetSet (V,(LKer vq))):] is set
bool [:[: the carrier of F_Complex,(CosetSet (V,(LKer vq))):],(CosetSet (V,(LKer vq))):] is set
CosetSet (f,(RKer (V,f,vq))) is non empty Element of bool (bool the carrier of f)
bool the carrier of f is set
bool (bool the carrier of f) is set
{ b₁ where b₁ is Coset of RKer (V,f,vq) : verum } is set
addCoset (f,(RKer (V,f,vq))) is V16() V19([:(CosetSet (f,(RKer (V,f,vq)))),(CosetSet (f,(RKer (V,f,vq)))):]) V20( CosetSet (f,(RKer (V,f,vq)))) Function-like V30([:(CosetSet (f,(RKer (V,f,vq)))),(CosetSet (f,(RKer (V,f,vq)))):], CosetSet (f,(RKer (V,f,vq)))) Element of bool [:[:(CosetSet (f,(RKer (V,f,vq)))),(CosetSet (f,(RKer (V,f,vq)))):],(CosetSet (f,(RKer (V,f,vq)))):]
[:(CosetSet (f,(RKer (V,f,vq)))),(CosetSet (f,(RKer (V,f,vq)))):] is set
[:[:(CosetSet (f,(RKer (V,f,vq)))),(CosetSet (f,(RKer (V,f,vq)))):],(CosetSet (f,(RKer (V,f,vq)))):] is set
bool [:[:(CosetSet (f,(RKer (V,f,vq)))),(CosetSet (f,(RKer (V,f,vq)))):],(CosetSet (f,(RKer (V,f,vq)))):] is set
lmultCoset (f,(RKer (V,f,vq))) is V16() V19([: the carrier of F_Complex,(CosetSet (f,(RKer (V,f,vq)))):]) V20( CosetSet (f,(RKer (V,f,vq)))) Function-like V30([: the carrier of F_Complex,(CosetSet (f,(RKer (V,f,vq)))):], CosetSet (f,(RKer (V,f,vq)))) Element of bool [:[: the carrier of F_Complex,(CosetSet (f,(RKer (V,f,vq)))):],(CosetSet (f,(RKer (V,f,vq)))):]
[: the carrier of F_Complex,(CosetSet (f,(RKer (V,f,vq)))):] is set
[:[: the carrier of F_Complex,(CosetSet (f,(RKer (V,f,vq)))):],(CosetSet (f,(RKer (V,f,vq)))):] is set
bool [:[: the carrier of F_Complex,(CosetSet (f,(RKer (V,f,vq)))):],(CosetSet (f,(RKer (V,f,vq)))):] is set
rightker vq is non empty Element of bool the carrier of f
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of V holds vq . (b₂,b₁) = 0. F_Complex } is set
rightker (V,f,vq) is non empty Element of bool the carrier of f
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of V holds (V,f,vq) . (b₂,b₁) = 0. F_Complex } is set
v is Element of the carrier of (VectQuot (V,(LKer vq)))
v is Element of the carrier of V
v + (LKer vq) is Element of bool the carrier of V
{ (v + b₁) where b₁ is Element of the carrier of V : b₁ in LKer vq } is set
A is Element of the carrier of (VectQuot (f,(RKer (V,f,vq))))
B is Element of the carrier of f
B + (RKer (V,f,vq)) is Element of bool the carrier of f
{ (B + b₁) where b₁ is Element of the carrier of f : b₁ in RKer (V,f,vq) } is set
vq . (v,B) is complex Element of the carrier of F_Complex
[v,B] is set
{v,B} is non empty set
{v} is non empty set
{{v,B},{v}} is non empty set
vq . [v,B] is set
A is Element of the carrier of V
A + (LKer vq) is Element of bool the carrier of V
{ (A + b₁) where b₁ is Element of the carrier of V : b₁ in LKer vq } is set
a is Element of the carrier of V
A + a is Element of the carrier of V
the addF of V is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is set
the addF of V . (A,a) is Element of the carrier of V
[A,a] is set
{A,a} is non empty set
{A} is non empty set
{{A,a},{A}} is non empty set
the addF of V . [A,a] is set
the carrier of (LKer vq) is non empty set
leftker vq is non empty Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of f holds vq . (b₁,b₂) = 0. F_Complex } is set
B is Element of the carrier of f
B + (RKer (V,f,vq)) is Element of bool the carrier of f
{ (B + b₁) where b₁ is Element of the carrier of f : b₁ in RKer (V,f,vq) } is set
b is Element of the carrier of f
B + b is Element of the carrier of f
the addF of f is V16() V19([: the carrier of f, the carrier of f:]) V20( the carrier of f) Function-like V30([: the carrier of f, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of f, the carrier of f:], the carrier of f:]
[: the carrier of f, the carrier of f:] is set
[:[: the carrier of f, the carrier of f:], the carrier of f:] is set
bool [:[: the carrier of f, the carrier of f:], the carrier of f:] is set
the addF of f . (B,b) is Element of the carrier of f
[B,b] is set
{B,b} is non empty set
{B} is non empty set
{{B,b},{B}} is non empty set
the addF of f . [B,b] is set
the carrier of (RKer (V,f,vq)) is non empty set
w is complex Element of the carrier of F_Complex
vq . (A,B) is complex Element of the carrier of F_Complex
[A,B] is set
{A,B} is non empty set
{{A,B},{A}} is non empty set
vq . [A,B] is set
vq . (A,b) is complex Element of the carrier of F_Complex
[A,b] is set
{A,b} is non empty set
{{A,b},{A}} is non empty set
vq . [A,b] is set
(vq . (A,B)) + (vq . (A,b)) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . ((vq . (A,B)),(vq . (A,b))) is complex Element of the carrier of F_Complex
[(vq . (A,B)),(vq . (A,b))] is set
{(vq . (A,B)),(vq . (A,b))} is non empty V175() set
{(vq . (A,B))} is non empty V175() set
{{(vq . (A,B)),(vq . (A,b))},{(vq . (A,B))}} is non empty set
the addF of F_Complex . [(vq . (A,B)),(vq . (A,b))] is set
K135((vq . (A,B)),(vq . (A,b))) is complex Element of COMPLEX
vq . (a,B) is complex Element of the carrier of F_Complex
[a,B] is set
{a,B} is non empty set
{a} is non empty set
{{a,B},{a}} is non empty set
vq . [a,B] is set
vq . (a,b) is complex Element of the carrier of F_Complex
[a,b] is set
{a,b} is non empty set
{{a,b},{a}} is non empty set
vq . [a,b] is set
(vq . (a,B)) + (vq . (a,b)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vq . (a,B)),(vq . (a,b))) is complex Element of the carrier of F_Complex
[(vq . (a,B)),(vq . (a,b))] is set
{(vq . (a,B)),(vq . (a,b))} is non empty V175() set
{(vq . (a,B))} is non empty V175() set
{{(vq . (a,B)),(vq . (a,b))},{(vq . (a,B))}} is non empty set
the addF of F_Complex . [(vq . (a,B)),(vq . (a,b))] is set
K135((vq . (a,B)),(vq . (a,b))) is complex Element of COMPLEX
((vq . (A,B)) + (vq . (A,b))) + ((vq . (a,B)) + (vq . (a,b))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vq . (A,B)) + (vq . (A,b))),((vq . (a,B)) + (vq . (a,b)))) is complex Element of the carrier of F_Complex
[((vq . (A,B)) + (vq . (A,b))),((vq . (a,B)) + (vq . (a,b)))] is set
{((vq . (A,B)) + (vq . (A,b))),((vq . (a,B)) + (vq . (a,b)))} is non empty V175() set
{((vq . (A,B)) + (vq . (A,b)))} is non empty V175() set
{{((vq . (A,B)) + (vq . (A,b))),((vq . (a,B)) + (vq . (a,b)))},{((vq . (A,B)) + (vq . (A,b)))}} is non empty set
the addF of F_Complex . [((vq . (A,B)) + (vq . (A,b))),((vq . (a,B)) + (vq . (a,b)))] is set
K135(((vq . (A,B)) + (vq . (A,b))),((vq . (a,B)) + (vq . (a,b)))) is complex Element of COMPLEX
(vq . (A,B)) + (0. F_Complex) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vq . (A,B)),(0. F_Complex)) is complex Element of the carrier of F_Complex
[(vq . (A,B)),(0. F_Complex)] is set
{(vq . (A,B)),(0. F_Complex)} is non empty V175() set
{{(vq . (A,B)),(0. F_Complex)},{(vq . (A,B))}} is non empty set
the addF of F_Complex . [(vq . (A,B)),(0. F_Complex)] is set
K135((vq . (A,B)),(0. F_Complex)) is complex Element of COMPLEX
((vq . (A,B)) + (0. F_Complex)) + ((vq . (a,B)) + (vq . (a,b))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vq . (A,B)) + (0. F_Complex)),((vq . (a,B)) + (vq . (a,b)))) is complex Element of the carrier of F_Complex
[((vq . (A,B)) + (0. F_Complex)),((vq . (a,B)) + (vq . (a,b)))] is set
{((vq . (A,B)) + (0. F_Complex)),((vq . (a,B)) + (vq . (a,b)))} is non empty V175() set
{((vq . (A,B)) + (0. F_Complex))} is non empty V175() set
{{((vq . (A,B)) + (0. F_Complex)),((vq . (a,B)) + (vq . (a,b)))},{((vq . (A,B)) + (0. F_Complex))}} is non empty set
the addF of F_Complex . [((vq . (A,B)) + (0. F_Complex)),((vq . (a,B)) + (vq . (a,b)))] is set
K135(((vq . (A,B)) + (0. F_Complex)),((vq . (a,B)) + (vq . (a,b)))) is complex Element of COMPLEX
(0. F_Complex) + (vq . (a,b)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((0. F_Complex),(vq . (a,b))) is complex Element of the carrier of F_Complex
[(0. F_Complex),(vq . (a,b))] is set
{(0. F_Complex),(vq . (a,b))} is non empty V175() set
{(0. F_Complex)} is non empty V175() set
{{(0. F_Complex),(vq . (a,b))},{(0. F_Complex)}} is non empty set
the addF of F_Complex . [(0. F_Complex),(vq . (a,b))] is set
K135((0. F_Complex),(vq . (a,b))) is complex Element of COMPLEX
((vq . (A,B)) + (0. F_Complex)) + ((0. F_Complex) + (vq . (a,b))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((vq . (A,B)) + (0. F_Complex)),((0. F_Complex) + (vq . (a,b)))) is complex Element of the carrier of F_Complex
[((vq . (A,B)) + (0. F_Complex)),((0. F_Complex) + (vq . (a,b)))] is set
{((vq . (A,B)) + (0. F_Complex)),((0. F_Complex) + (vq . (a,b)))} is non empty V175() set
{{((vq . (A,B)) + (0. F_Complex)),((0. F_Complex) + (vq . (a,b)))},{((vq . (A,B)) + (0. F_Complex))}} is non empty set
the addF of F_Complex . [((vq . (A,B)) + (0. F_Complex)),((0. F_Complex) + (vq . (a,b)))] is set
K135(((vq . (A,B)) + (0. F_Complex)),((0. F_Complex) + (vq . (a,b)))) is complex Element of COMPLEX
(vq . (A,B)) + ((0. F_Complex) + (vq . (a,b))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vq . (A,B)),((0. F_Complex) + (vq . (a,b)))) is complex Element of the carrier of F_Complex
[(vq . (A,B)),((0. F_Complex) + (vq . (a,b)))] is set
{(vq . (A,B)),((0. F_Complex) + (vq . (a,b)))} is non empty V175() set
{{(vq . (A,B)),((0. F_Complex) + (vq . (a,b)))},{(vq . (A,B))}} is non empty set
the addF of F_Complex . [(vq . (A,B)),((0. F_Complex) + (vq . (a,b)))] is set
K135((vq . (A,B)),((0. F_Complex) + (vq . (a,b)))) is complex Element of COMPLEX
(vq . (A,B)) + (vq . (a,b)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vq . (A,B)),(vq . (a,b))) is complex Element of the carrier of F_Complex
[(vq . (A,B)),(vq . (a,b))] is set
{(vq . (A,B)),(vq . (a,b))} is non empty V175() set
{{(vq . (A,B)),(vq . (a,b))},{(vq . (A,B))}} is non empty set
the addF of F_Complex . [(vq . (A,B)),(vq . (a,b))] is set
K135((vq . (A,B)),(vq . (a,b))) is complex Element of COMPLEX
c₂₄ is Element of the carrier of f
c₂₄ is Element of the carrier of V
c₂₄ is Element of the carrier of V
A is Element of the carrier of V
A + (LKer vq) is Element of bool the carrier of V
{ (A + b₁) where b₁ is Element of the carrier of V : b₁ in LKer vq } is set
B is Element of the carrier of f
B + (RKer (V,f,vq)) is Element of bool the carrier of f
{ (B + b₁) where b₁ is Element of the carrier of f : b₁ in RKer (V,f,vq) } is set
vq . (A,B) is complex Element of the carrier of F_Complex
[A,B] is set
{A,B} is non empty set
{A} is non empty set
{{A,B},{A}} is non empty set
vq . [A,B] is set
v is V16() V19([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) Element of bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
v is Element of the carrier of (VectQuot (f,(RKer (V,f,vq))))
B is Element of the carrier of f
B + (RKer (V,f,vq)) is Element of bool the carrier of f
{ (B + b₁) where b₁ is Element of the carrier of f : b₁ in RKer (V,f,vq) } is set
A is V16() V19([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) Element of bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
FunctionalSAF (A,v) is V16() V19( the carrier of (VectQuot (V,(LKer vq)))) V20( the carrier of F_Complex) Function-like V30( the carrier of (VectQuot (V,(LKer vq))), the carrier of F_Complex) Element of bool [: the carrier of (VectQuot (V,(LKer vq))), the carrier of F_Complex:]
[: the carrier of (VectQuot (V,(LKer vq))), the carrier of F_Complex:] is set
bool [: the carrier of (VectQuot (V,(LKer vq))), the carrier of F_Complex:] is set
A is Element of the carrier of (VectQuot (V,(LKer vq)))
a is Element of the carrier of V
a + (LKer vq) is Element of bool the carrier of V
{ (a + b₁) where b₁ is Element of the carrier of V : b₁ in LKer vq } is set
[: the carrier of F_Complex, the carrier of (VectQuot (V,(LKer vq))):] is set
the lmult of (VectQuot (V,(LKer vq))) is V16() V19([: the carrier of F_Complex, the carrier of (VectQuot (V,(LKer vq))):]) V20( the carrier of (VectQuot (V,(LKer vq)))) Function-like V30([: the carrier of F_Complex, the carrier of (VectQuot (V,(LKer vq))):], the carrier of (VectQuot (V,(LKer vq)))) Element of bool [:[: the carrier of F_Complex, the carrier of (VectQuot (V,(LKer vq))):], the carrier of (VectQuot (V,(LKer vq))):]
[:[: the carrier of F_Complex, the carrier of (VectQuot (V,(LKer vq))):], the carrier of (VectQuot (V,(LKer vq))):] is set
bool [:[: the carrier of F_Complex, the carrier of (VectQuot (V,(LKer vq))):], the carrier of (VectQuot (V,(LKer vq))):] is set
B is complex Element of the carrier of F_Complex
(lmultCoset (V,(LKer vq))) . (B,A) is set
[B,A] is set
{B,A} is non empty set
{B} is non empty V175() set
{{B,A},{B}} is non empty set
(lmultCoset (V,(LKer vq))) . [B,A] is set
B * a is Element of the carrier of V
the lmult of V is V16() V19([: the carrier of F_Complex, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of F_Complex, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:]
[: the carrier of F_Complex, the carrier of V:] is set
[:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
the lmult of V . (B,a) is Element of the carrier of V
[B,a] is set
{B,a} is non empty set
{{B,a},{B}} is non empty set
the lmult of V . [B,a] is set
(B * a) + (LKer vq) is Element of bool the carrier of V
{ ((B * a) + b₁) where b₁ is Element of the carrier of V : b₁ in LKer vq } is set
B * A is Element of the carrier of (VectQuot (V,(LKer vq)))
the lmult of (VectQuot (V,(LKer vq))) . (B,A) is Element of the carrier of (VectQuot (V,(LKer vq)))
the lmult of (VectQuot (V,(LKer vq))) . [B,A] is set
(FunctionalSAF (A,v)) . (B * A) is complex Element of the carrier of F_Complex
A . (( the lmult of (VectQuot (V,(LKer vq))) . (B,A)),v) is complex Element of the carrier of F_Complex
[( the lmult of (VectQuot (V,(LKer vq))) . (B,A)),v] is set
{( the lmult of (VectQuot (V,(LKer vq))) . (B,A)),v} is non empty set
{( the lmult of (VectQuot (V,(LKer vq))) . (B,A))} is non empty set
{{( the lmult of (VectQuot (V,(LKer vq))) . (B,A)),v},{( the lmult of (VectQuot (V,(LKer vq))) . (B,A))}} is non empty set
A . [( the lmult of (VectQuot (V,(LKer vq))) . (B,A)),v] is set
vq . ((B * a),B) is complex Element of the carrier of F_Complex
[(B * a),B] is set
{(B * a),B} is non empty set
{(B * a)} is non empty set
{{(B * a),B},{(B * a)}} is non empty set
vq . [(B * a),B] is set
vq . (a,B) is complex Element of the carrier of F_Complex
[a,B] is set
{a,B} is non empty set
{a} is non empty set
{{a,B},{a}} is non empty set
vq . [a,B] is set
B * (vq . (a,B)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (B,(vq . (a,B))) is complex Element of the carrier of F_Complex
[B,(vq . (a,B))] is set
{B,(vq . (a,B))} is non empty V175() set
{{B,(vq . (a,B))},{B}} is non empty set
the multF of F_Complex . [B,(vq . (a,B))] is set
K137(B,(vq . (a,B))) is complex Element of COMPLEX
A . (A,v) is complex Element of the carrier of F_Complex
[A,v] is set
{A,v} is non empty set
{A} is non empty set
{{A,v},{A}} is non empty set
A . [A,v] is set
B * (A . (A,v)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (B,(A . (A,v))) is complex Element of the carrier of F_Complex
[B,(A . (A,v))] is set
{B,(A . (A,v))} is non empty V175() set
{{B,(A . (A,v))},{B}} is non empty set
the multF of F_Complex . [B,(A . (A,v))] is set
K137(B,(A . (A,v))) is complex Element of COMPLEX
(FunctionalSAF (A,v)) . A is complex Element of the carrier of F_Complex
B * ((FunctionalSAF (A,v)) . A) is complex Element of the carrier of F_Complex
the multF of F_Complex . (B,((FunctionalSAF (A,v)) . A)) is complex Element of the carrier of F_Complex
[B,((FunctionalSAF (A,v)) . A)] is set
{B,((FunctionalSAF (A,v)) . A)} is non empty V175() set
{{B,((FunctionalSAF (A,v)) . A)},{B}} is non empty set
the multF of F_Complex . [B,((FunctionalSAF (A,v)) . A)] is set
K137(B,((FunctionalSAF (A,v)) . A)) is complex Element of COMPLEX
v is Element of the carrier of (VectQuot (V,(LKer vq)))
B is Element of the carrier of V
B + (LKer vq) is Element of bool the carrier of V
{ (B + b₁) where b₁ is Element of the carrier of V : b₁ in LKer vq } is set
FunctionalFAF (A,v) is V16() V19( the carrier of (VectQuot (f,(RKer (V,f,vq))))) V20( the carrier of F_Complex) Function-like V30( the carrier of (VectQuot (f,(RKer (V,f,vq)))), the carrier of F_Complex) Element of bool [: the carrier of (VectQuot (f,(RKer (V,f,vq)))), the carrier of F_Complex:]
[: the carrier of (VectQuot (f,(RKer (V,f,vq)))), the carrier of F_Complex:] is set
bool [: the carrier of (VectQuot (f,(RKer (V,f,vq)))), the carrier of F_Complex:] is set
A is Element of the carrier of (VectQuot (f,(RKer (V,f,vq))))
a is Element of the carrier of f
a + (RKer (V,f,vq)) is Element of bool the carrier of f
{ (a + b₁) where b₁ is Element of the carrier of f : b₁ in RKer (V,f,vq) } is set
[: the carrier of F_Complex, the carrier of (VectQuot (f,(RKer (V,f,vq)))):] is set
the lmult of (VectQuot (f,(RKer (V,f,vq)))) is V16() V19([: the carrier of F_Complex, the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of (VectQuot (f,(RKer (V,f,vq))))) Function-like V30([: the carrier of F_Complex, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of (VectQuot (f,(RKer (V,f,vq))))) Element of bool [:[: the carrier of F_Complex, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of (VectQuot (f,(RKer (V,f,vq)))):]
[:[: the carrier of F_Complex, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of (VectQuot (f,(RKer (V,f,vq)))):] is set
bool [:[: the carrier of F_Complex, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of (VectQuot (f,(RKer (V,f,vq)))):] is set
B is complex Element of the carrier of F_Complex
(lmultCoset (f,(RKer (V,f,vq)))) . (B,A) is set
[B,A] is set
{B,A} is non empty set
{B} is non empty V175() set
{{B,A},{B}} is non empty set
(lmultCoset (f,(RKer (V,f,vq)))) . [B,A] is set
B * a is Element of the carrier of f
the lmult of f is V16() V19([: the carrier of F_Complex, the carrier of f:]) V20( the carrier of f) Function-like V30([: the carrier of F_Complex, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of F_Complex, the carrier of f:], the carrier of f:]
[: the carrier of F_Complex, the carrier of f:] is set
[:[: the carrier of F_Complex, the carrier of f:], the carrier of f:] is set
bool [:[: the carrier of F_Complex, the carrier of f:], the carrier of f:] is set
the lmult of f . (B,a) is Element of the carrier of f
[B,a] is set
{B,a} is non empty set
{{B,a},{B}} is non empty set
the lmult of f . [B,a] is set
(B * a) + (RKer (V,f,vq)) is Element of bool the carrier of f
{ ((B * a) + b₁) where b₁ is Element of the carrier of f : b₁ in RKer (V,f,vq) } is set
B * A is Element of the carrier of (VectQuot (f,(RKer (V,f,vq))))
the lmult of (VectQuot (f,(RKer (V,f,vq)))) . (B,A) is Element of the carrier of (VectQuot (f,(RKer (V,f,vq))))
the lmult of (VectQuot (f,(RKer (V,f,vq)))) . [B,A] is set
(FunctionalFAF (A,v)) . (B * A) is complex Element of the carrier of F_Complex
A . (v,( the lmult of (VectQuot (f,(RKer (V,f,vq)))) . (B,A))) is complex Element of the carrier of F_Complex
[v,( the lmult of (VectQuot (f,(RKer (V,f,vq)))) . (B,A))] is set
{v,( the lmult of (VectQuot (f,(RKer (V,f,vq)))) . (B,A))} is non empty set
{v} is non empty set
{{v,( the lmult of (VectQuot (f,(RKer (V,f,vq)))) . (B,A))},{v}} is non empty set
A . [v,( the lmult of (VectQuot (f,(RKer (V,f,vq)))) . (B,A))] is set
vq . (B,(B * a)) is complex Element of the carrier of F_Complex
[B,(B * a)] is set
{B,(B * a)} is non empty set
{B} is non empty set
{{B,(B * a)},{B}} is non empty set
vq . [B,(B * a)] is set
B *' is complex Element of the carrier of F_Complex
Re B is complex real ext-real Element of REAL
Im B is complex real ext-real Element of REAL
(Im B) * <i> is complex set
(Re B) - ((Im B) * <i>) is complex set
vq . (B,a) is complex Element of the carrier of F_Complex
[B,a] is set
{B,a} is non empty set
{{B,a},{B}} is non empty set
vq . [B,a] is set
(B *') * (vq . (B,a)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((B *'),(vq . (B,a))) is complex Element of the carrier of F_Complex
[(B *'),(vq . (B,a))] is set
{(B *'),(vq . (B,a))} is non empty V175() set
{(B *')} is non empty V175() set
{{(B *'),(vq . (B,a))},{(B *')}} is non empty set
the multF of F_Complex . [(B *'),(vq . (B,a))] is set
K137((B *'),(vq . (B,a))) is complex Element of COMPLEX
A . (v,A) is complex Element of the carrier of F_Complex
[v,A] is set
{v,A} is non empty set
{{v,A},{v}} is non empty set
A . [v,A] is set
(B *') * (A . (v,A)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((B *'),(A . (v,A))) is complex Element of the carrier of F_Complex
[(B *'),(A . (v,A))] is set
{(B *'),(A . (v,A))} is non empty V175() set
{{(B *'),(A . (v,A))},{(B *')}} is non empty set
the multF of F_Complex . [(B *'),(A . (v,A))] is set
K137((B *'),(A . (v,A))) is complex Element of COMPLEX
(FunctionalFAF (A,v)) . A is complex Element of the carrier of F_Complex
(B *') * ((FunctionalFAF (A,v)) . A) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((B *'),((FunctionalFAF (A,v)) . A)) is complex Element of the carrier of F_Complex
[(B *'),((FunctionalFAF (A,v)) . A)] is set
{(B *'),((FunctionalFAF (A,v)) . A)} is non empty V175() set
{{(B *'),((FunctionalFAF (A,v)) . A)},{(B *')}} is non empty set
the multF of F_Complex . [(B *'),((FunctionalFAF (A,v)) . A)] is set
K137((B *'),((FunctionalFAF (A,v)) . A)) is complex Element of COMPLEX
v is Element of the carrier of (VectQuot (f,(RKer (V,f,vq))))
B is Element of the carrier of f
B + (RKer (V,f,vq)) is Element of bool the carrier of f
{ (B + b₁) where b₁ is Element of the carrier of f : b₁ in RKer (V,f,vq) } is set
FunctionalSAF (A,v) is V16() V19( the carrier of (VectQuot (V,(LKer vq)))) V20( the carrier of F_Complex) Function-like V30( the carrier of (VectQuot (V,(LKer vq))), the carrier of F_Complex) Element of bool [: the carrier of (VectQuot (V,(LKer vq))), the carrier of F_Complex:]
A is Element of the carrier of (VectQuot (V,(LKer vq)))
a is Element of the carrier of V
a + (LKer vq) is Element of bool the carrier of V
{ (a + b₁) where b₁ is Element of the carrier of V : b₁ in LKer vq } is set
B is Element of the carrier of (VectQuot (V,(LKer vq)))
b is Element of the carrier of V
b + (LKer vq) is Element of bool the carrier of V
{ (b + b₁) where b₁ is Element of the carrier of V : b₁ in LKer vq } is set
[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (V,(LKer vq))):] is set
the addF of (VectQuot (V,(LKer vq))) is V16() V19([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (V,(LKer vq))):]) V20( the carrier of (VectQuot (V,(LKer vq)))) Function-like V30([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (V,(LKer vq))):], the carrier of (VectQuot (V,(LKer vq)))) Element of bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (V,(LKer vq))):], the carrier of (VectQuot (V,(LKer vq))):]
[:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (V,(LKer vq))):], the carrier of (VectQuot (V,(LKer vq))):] is set
bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (V,(LKer vq))):], the carrier of (VectQuot (V,(LKer vq))):] is set
(addCoset (V,(LKer vq))) . (A,B) is set
[A,B] is set
{A,B} is non empty set
{A} is non empty set
{{A,B},{A}} is non empty set
(addCoset (V,(LKer vq))) . [A,B] is set
a + b is Element of the carrier of V
the addF of V . (a,b) is Element of the carrier of V
[a,b] is set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the addF of V . [a,b] is set
(a + b) + (LKer vq) is Element of bool the carrier of V
{ ((a + b) + b₁) where b₁ is Element of the carrier of V : b₁ in LKer vq } is set
A + B is Element of the carrier of (VectQuot (V,(LKer vq)))
the addF of (VectQuot (V,(LKer vq))) . (A,B) is Element of the carrier of (VectQuot (V,(LKer vq)))
the addF of (VectQuot (V,(LKer vq))) . [A,B] is set
(FunctionalSAF (A,v)) . (A + B) is complex Element of the carrier of F_Complex
A . (( the addF of (VectQuot (V,(LKer vq))) . (A,B)),v) is complex Element of the carrier of F_Complex
[( the addF of (VectQuot (V,(LKer vq))) . (A,B)),v] is set
{( the addF of (VectQuot (V,(LKer vq))) . (A,B)),v} is non empty set
{( the addF of (VectQuot (V,(LKer vq))) . (A,B))} is non empty set
{{( the addF of (VectQuot (V,(LKer vq))) . (A,B)),v},{( the addF of (VectQuot (V,(LKer vq))) . (A,B))}} is non empty set
A . [( the addF of (VectQuot (V,(LKer vq))) . (A,B)),v] is set
vq . ((a + b),B) is complex Element of the carrier of F_Complex
[(a + b),B] is set
{(a + b),B} is non empty set
{(a + b)} is non empty set
{{(a + b),B},{(a + b)}} is non empty set
vq . [(a + b),B] is set
vq . (a,B) is complex Element of the carrier of F_Complex
[a,B] is set
{a,B} is non empty set
{{a,B},{a}} is non empty set
vq . [a,B] is set
vq . (b,B) is complex Element of the carrier of F_Complex
[b,B] is set
{b,B} is non empty set
{b} is non empty set
{{b,B},{b}} is non empty set
vq . [b,B] is set
(vq . (a,B)) + (vq . (b,B)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vq . (a,B)),(vq . (b,B))) is complex Element of the carrier of F_Complex
[(vq . (a,B)),(vq . (b,B))] is set
{(vq . (a,B)),(vq . (b,B))} is non empty V175() set
{(vq . (a,B))} is non empty V175() set
{{(vq . (a,B)),(vq . (b,B))},{(vq . (a,B))}} is non empty set
the addF of F_Complex . [(vq . (a,B)),(vq . (b,B))] is set
K135((vq . (a,B)),(vq . (b,B))) is complex Element of COMPLEX
A . (A,v) is complex Element of the carrier of F_Complex
[A,v] is set
{A,v} is non empty set
{{A,v},{A}} is non empty set
A . [A,v] is set
(A . (A,v)) + (vq . (b,B)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((A . (A,v)),(vq . (b,B))) is complex Element of the carrier of F_Complex
[(A . (A,v)),(vq . (b,B))] is set
{(A . (A,v)),(vq . (b,B))} is non empty V175() set
{(A . (A,v))} is non empty V175() set
{{(A . (A,v)),(vq . (b,B))},{(A . (A,v))}} is non empty set
the addF of F_Complex . [(A . (A,v)),(vq . (b,B))] is set
K135((A . (A,v)),(vq . (b,B))) is complex Element of COMPLEX
A . (B,v) is complex Element of the carrier of F_Complex
[B,v] is set
{B,v} is non empty set
{B} is non empty set
{{B,v},{B}} is non empty set
A . [B,v] is set
(A . (A,v)) + (A . (B,v)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((A . (A,v)),(A . (B,v))) is complex Element of the carrier of F_Complex
[(A . (A,v)),(A . (B,v))] is set
{(A . (A,v)),(A . (B,v))} is non empty V175() set
{{(A . (A,v)),(A . (B,v))},{(A . (A,v))}} is non empty set
the addF of F_Complex . [(A . (A,v)),(A . (B,v))] is set
K135((A . (A,v)),(A . (B,v))) is complex Element of COMPLEX
(FunctionalSAF (A,v)) . A is complex Element of the carrier of F_Complex
((FunctionalSAF (A,v)) . A) + (A . (B,v)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((FunctionalSAF (A,v)) . A),(A . (B,v))) is complex Element of the carrier of F_Complex
[((FunctionalSAF (A,v)) . A),(A . (B,v))] is set
{((FunctionalSAF (A,v)) . A),(A . (B,v))} is non empty V175() set
{((FunctionalSAF (A,v)) . A)} is non empty V175() set
{{((FunctionalSAF (A,v)) . A),(A . (B,v))},{((FunctionalSAF (A,v)) . A)}} is non empty set
the addF of F_Complex . [((FunctionalSAF (A,v)) . A),(A . (B,v))] is set
K135(((FunctionalSAF (A,v)) . A),(A . (B,v))) is complex Element of COMPLEX
(FunctionalSAF (A,v)) . B is complex Element of the carrier of F_Complex
((FunctionalSAF (A,v)) . A) + ((FunctionalSAF (A,v)) . B) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((FunctionalSAF (A,v)) . A),((FunctionalSAF (A,v)) . B)) is complex Element of the carrier of F_Complex
[((FunctionalSAF (A,v)) . A),((FunctionalSAF (A,v)) . B)] is set
{((FunctionalSAF (A,v)) . A),((FunctionalSAF (A,v)) . B)} is non empty V175() set
{{((FunctionalSAF (A,v)) . A),((FunctionalSAF (A,v)) . B)},{((FunctionalSAF (A,v)) . A)}} is non empty set
the addF of F_Complex . [((FunctionalSAF (A,v)) . A),((FunctionalSAF (A,v)) . B)] is set
K135(((FunctionalSAF (A,v)) . A),((FunctionalSAF (A,v)) . B)) is complex Element of COMPLEX
v is Element of the carrier of (VectQuot (V,(LKer vq)))
B is Element of the carrier of V
B + (LKer vq) is Element of bool the carrier of V
{ (B + b₁) where b₁ is Element of the carrier of V : b₁ in LKer vq } is set
FunctionalFAF (A,v) is V16() V19( the carrier of (VectQuot (f,(RKer (V,f,vq))))) V20( the carrier of F_Complex) Function-like V30( the carrier of (VectQuot (f,(RKer (V,f,vq)))), the carrier of F_Complex) Element of bool [: the carrier of (VectQuot (f,(RKer (V,f,vq)))), the carrier of F_Complex:]
A is Element of the carrier of (VectQuot (f,(RKer (V,f,vq))))
a is Element of the carrier of f
a + (RKer (V,f,vq)) is Element of bool the carrier of f
{ (a + b₁) where b₁ is Element of the carrier of f : b₁ in RKer (V,f,vq) } is set
B is Element of the carrier of (VectQuot (f,(RKer (V,f,vq))))
b is Element of the carrier of f
b + (RKer (V,f,vq)) is Element of bool the carrier of f
{ (b + b₁) where b₁ is Element of the carrier of f : b₁ in RKer (V,f,vq) } is set
[: the carrier of (VectQuot (f,(RKer (V,f,vq)))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):] is set
the addF of (VectQuot (f,(RKer (V,f,vq)))) is V16() V19([: the carrier of (VectQuot (f,(RKer (V,f,vq)))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of (VectQuot (f,(RKer (V,f,vq))))) Function-like V30([: the carrier of (VectQuot (f,(RKer (V,f,vq)))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of (VectQuot (f,(RKer (V,f,vq))))) Element of bool [:[: the carrier of (VectQuot (f,(RKer (V,f,vq)))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of (VectQuot (f,(RKer (V,f,vq)))):]
[:[: the carrier of (VectQuot (f,(RKer (V,f,vq)))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of (VectQuot (f,(RKer (V,f,vq)))):] is set
bool [:[: the carrier of (VectQuot (f,(RKer (V,f,vq)))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of (VectQuot (f,(RKer (V,f,vq)))):] is set
(addCoset (f,(RKer (V,f,vq)))) . (A,B) is set
[A,B] is set
{A,B} is non empty set
{A} is non empty set
{{A,B},{A}} is non empty set
(addCoset (f,(RKer (V,f,vq)))) . [A,B] is set
a + b is Element of the carrier of f
the addF of f . (a,b) is Element of the carrier of f
[a,b] is set
{a,b} is non empty set
{a} is non empty set
{{a,b},{a}} is non empty set
the addF of f . [a,b] is set
(a + b) + (RKer (V,f,vq)) is Element of bool the carrier of f
{ ((a + b) + b₁) where b₁ is Element of the carrier of f : b₁ in RKer (V,f,vq) } is set
A + B is Element of the carrier of (VectQuot (f,(RKer (V,f,vq))))
the addF of (VectQuot (f,(RKer (V,f,vq)))) . (A,B) is Element of the carrier of (VectQuot (f,(RKer (V,f,vq))))
the addF of (VectQuot (f,(RKer (V,f,vq)))) . [A,B] is set
(FunctionalFAF (A,v)) . (A + B) is complex Element of the carrier of F_Complex
A . (v,( the addF of (VectQuot (f,(RKer (V,f,vq)))) . (A,B))) is complex Element of the carrier of F_Complex
[v,( the addF of (VectQuot (f,(RKer (V,f,vq)))) . (A,B))] is set
{v,( the addF of (VectQuot (f,(RKer (V,f,vq)))) . (A,B))} is non empty set
{v} is non empty set
{{v,( the addF of (VectQuot (f,(RKer (V,f,vq)))) . (A,B))},{v}} is non empty set
A . [v,( the addF of (VectQuot (f,(RKer (V,f,vq)))) . (A,B))] is set
vq . (B,(a + b)) is complex Element of the carrier of F_Complex
[B,(a + b)] is set
{B,(a + b)} is non empty set
{B} is non empty set
{{B,(a + b)},{B}} is non empty set
vq . [B,(a + b)] is set
vq . (B,a) is complex Element of the carrier of F_Complex
[B,a] is set
{B,a} is non empty set
{{B,a},{B}} is non empty set
vq . [B,a] is set
vq . (B,b) is complex Element of the carrier of F_Complex
[B,b] is set
{B,b} is non empty set
{{B,b},{B}} is non empty set
vq . [B,b] is set
(vq . (B,a)) + (vq . (B,b)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((vq . (B,a)),(vq . (B,b))) is complex Element of the carrier of F_Complex
[(vq . (B,a)),(vq . (B,b))] is set
{(vq . (B,a)),(vq . (B,b))} is non empty V175() set
{(vq . (B,a))} is non empty V175() set
{{(vq . (B,a)),(vq . (B,b))},{(vq . (B,a))}} is non empty set
the addF of F_Complex . [(vq . (B,a)),(vq . (B,b))] is set
K135((vq . (B,a)),(vq . (B,b))) is complex Element of COMPLEX
A . (v,A) is complex Element of the carrier of F_Complex
[v,A] is set
{v,A} is non empty set
{{v,A},{v}} is non empty set
A . [v,A] is set
(A . (v,A)) + (vq . (B,b)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((A . (v,A)),(vq . (B,b))) is complex Element of the carrier of F_Complex
[(A . (v,A)),(vq . (B,b))] is set
{(A . (v,A)),(vq . (B,b))} is non empty V175() set
{(A . (v,A))} is non empty V175() set
{{(A . (v,A)),(vq . (B,b))},{(A . (v,A))}} is non empty set
the addF of F_Complex . [(A . (v,A)),(vq . (B,b))] is set
K135((A . (v,A)),(vq . (B,b))) is complex Element of COMPLEX
A . (v,B) is complex Element of the carrier of F_Complex
[v,B] is set
{v,B} is non empty set
{{v,B},{v}} is non empty set
A . [v,B] is set
(A . (v,A)) + (A . (v,B)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((A . (v,A)),(A . (v,B))) is complex Element of the carrier of F_Complex
[(A . (v,A)),(A . (v,B))] is set
{(A . (v,A)),(A . (v,B))} is non empty V175() set
{{(A . (v,A)),(A . (v,B))},{(A . (v,A))}} is non empty set
the addF of F_Complex . [(A . (v,A)),(A . (v,B))] is set
K135((A . (v,A)),(A . (v,B))) is complex Element of COMPLEX
(FunctionalFAF (A,v)) . A is complex Element of the carrier of F_Complex
((FunctionalFAF (A,v)) . A) + (A . (v,B)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((FunctionalFAF (A,v)) . A),(A . (v,B))) is complex Element of the carrier of F_Complex
[((FunctionalFAF (A,v)) . A),(A . (v,B))] is set
{((FunctionalFAF (A,v)) . A),(A . (v,B))} is non empty V175() set
{((FunctionalFAF (A,v)) . A)} is non empty V175() set
{{((FunctionalFAF (A,v)) . A),(A . (v,B))},{((FunctionalFAF (A,v)) . A)}} is non empty set
the addF of F_Complex . [((FunctionalFAF (A,v)) . A),(A . (v,B))] is set
K135(((FunctionalFAF (A,v)) . A),(A . (v,B))) is complex Element of COMPLEX
(FunctionalFAF (A,v)) . B is complex Element of the carrier of F_Complex
((FunctionalFAF (A,v)) . A) + ((FunctionalFAF (A,v)) . B) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((FunctionalFAF (A,v)) . A),((FunctionalFAF (A,v)) . B)) is complex Element of the carrier of F_Complex
[((FunctionalFAF (A,v)) . A),((FunctionalFAF (A,v)) . B)] is set
{((FunctionalFAF (A,v)) . A),((FunctionalFAF (A,v)) . B)} is non empty V175() set
{{((FunctionalFAF (A,v)) . A),((FunctionalFAF (A,v)) . B)},{((FunctionalFAF (A,v)) . A)}} is non empty set
the addF of F_Complex . [((FunctionalFAF (A,v)) . A),((FunctionalFAF (A,v)) . B)] is set
K135(((FunctionalFAF (A,v)) . A),((FunctionalFAF (A,v)) . B)) is complex Element of COMPLEX
v is V16() V19([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF ( VectQuot (V,(LKer vq)), VectQuot (f,(RKer (V,f,vq)))) Element of bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
B is Element of the carrier of (VectQuot (V,(LKer vq)))
A is Element of the carrier of V
A + (LKer vq) is Element of bool the carrier of V
{ (A + b₁) where b₁ is Element of the carrier of V : b₁ in LKer vq } is set
w is Element of the carrier of (VectQuot (f,(RKer (V,f,vq))))
B is Element of the carrier of f
B + (RKer (V,f,vq)) is Element of bool the carrier of f
{ (B + b₁) where b₁ is Element of the carrier of f : b₁ in RKer (V,f,vq) } is set
v . (B,w) is complex Element of the carrier of F_Complex
[B,w] is set
{B,w} is non empty set
{B} is non empty set
{{B,w},{B}} is non empty set
v . [B,w] is set
vq . (A,B) is complex Element of the carrier of F_Complex
[A,B] is set
{A,B} is non empty set
{A} is non empty set
{{A,B},{A}} is non empty set
vq . [A,B] is set
x is V16() V19([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF ( VectQuot (V,(LKer vq)), VectQuot (f,(RKer (V,f,vq)))) Element of bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
A is V16() V19([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF ( VectQuot (V,(LKer vq)), VectQuot (f,(RKer (V,f,vq)))) Element of bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
B is Element of the carrier of (VectQuot (V,(LKer vq)))
A is Element of the carrier of V
A + (LKer vq) is Element of bool the carrier of V
bool the carrier of V is set
{ (A + b₁) where b₁ is Element of the carrier of V : b₁ in LKer vq } is set
w is Element of the carrier of (VectQuot (f,(RKer (V,f,vq))))
wa is Element of the carrier of f
wa + (RKer (V,f,vq)) is Element of bool the carrier of f
bool the carrier of f is set
{ (wa + b₁) where b₁ is Element of the carrier of f : b₁ in RKer (V,f,vq) } is set
x . (B,w) is complex Element of the carrier of F_Complex
[B,w] is set
{B,w} is non empty set
{B} is non empty set
{{B,w},{B}} is non empty set
x . [B,w] is set
vq . (A,wa) is complex Element of the carrier of F_Complex
[A,wa] is set
{A,wa} is non empty set
{A} is non empty set
{{A,wa},{A}} is non empty set
vq . [A,wa] is set
A . (B,w) is complex Element of the carrier of F_Complex
A . [B,w] is set
V is non empty non trivial right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty non trivial set
f is non empty non trivial right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of f is non empty non trivial set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like non constant V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,vq) is V16() V19([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF ( VectQuot (V,(LKer vq)), VectQuot (f,(RKer (V,f,vq)))) Element of bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
LKer vq is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(LKer vq)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of (VectQuot (V,(LKer vq))) is non empty set
(V,f,vq) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like non constant V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
RKer (V,f,vq) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(RKer (V,f,vq))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of (VectQuot (f,(RKer (V,f,vq)))) is non empty set
[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):] is set
[:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:] is set
qh is Element of the carrier of V
A is Element of the carrier of f
vq . (qh,A) is complex Element of the carrier of F_Complex
[qh,A] is set
{qh,A} is non empty set
{qh} is non empty set
{{qh,A},{qh}} is non empty set
vq . [qh,A] is set
A + (RKer (V,f,vq)) is Element of bool the carrier of f
bool the carrier of f is set
{ (A + b₁) where b₁ is Element of the carrier of f : b₁ in RKer (V,f,vq) } is set
qh + (LKer vq) is Element of bool the carrier of V
bool the carrier of V is set
{ (qh + b₁) where b₁ is Element of the carrier of V : b₁ in LKer vq } is set
x is Element of the carrier of (VectQuot (V,(LKer vq)))
K is Element of the carrier of (VectQuot (f,(RKer (V,f,vq))))
(V,f,vq) . (x,K) is complex Element of the carrier of F_Complex
[x,K] is set
{x,K} is non empty set
{x} is non empty set
{{x,K},{x}} is non empty set
(V,f,vq) . [x,K] is set
V is non empty right_zeroed VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
(V,f,vq) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF homogeneousFAF Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
RKer (V,f,vq) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(RKer (V,f,vq))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
(V,f,vq) is V16() V19([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF (V, VectQuot (f,(RKer (V,f,vq)))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
the carrier of (VectQuot (f,(RKer (V,f,vq)))) is non empty set
[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):] is set
[:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:] is set
RQForm (V,f,vq) is V16() V19([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF homogeneousFAF non degenerated-on-right Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
(V,(VectQuot (f,(RKer (V,f,vq)))),(RQForm (V,f,vq))) is V16() V19([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF (V, VectQuot (f,(RKer (V,f,vq)))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
rightker vq is non empty Element of bool the carrier of f
bool the carrier of f is set
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of V holds vq . (b₂,b₁) = 0. F_Complex } is set
rightker (V,f,vq) is non empty Element of bool the carrier of f
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of V holds (V,f,vq) . (b₂,b₁) = 0. F_Complex } is set
rightker (V,f,vq) is non empty Element of bool the carrier of (VectQuot (f,(RKer (V,f,vq))))
bool the carrier of (VectQuot (f,(RKer (V,f,vq)))) is set
{ b₁ where b₁ is Element of the carrier of (VectQuot (f,(RKer (V,f,vq)))) : for b₂ being Element of the carrier of V holds (V,f,vq) . (b₂,b₁) = 0. F_Complex } is set
0. (VectQuot (f,(RKer (V,f,vq)))) is zero Element of the carrier of (VectQuot (f,(RKer (V,f,vq))))
{(0. (VectQuot (f,(RKer (V,f,vq)))))} is non empty set
x is set
A is Element of the carrier of (VectQuot (f,(RKer (V,f,vq))))
B is Element of the carrier of f
B + (RKer (V,f,vq)) is Element of bool the carrier of f
{ (B + b₁) where b₁ is Element of the carrier of f : b₁ in RKer (V,f,vq) } is set
w is Element of the carrier of V
vq . (w,B) is complex Element of the carrier of F_Complex
[w,B] is set
{w,B} is non empty set
{w} is non empty set
{{w,B},{w}} is non empty set
vq . [w,B] is set
(V,f,vq) . (w,A) is complex Element of the carrier of F_Complex
[w,A] is set
{w,A} is non empty set
{{w,A},{w}} is non empty set
(V,f,vq) . [w,A] is set
the carrier of (RKer (V,f,vq)) is non empty set
zeroCoset (f,(RKer (V,f,vq))) is Element of CosetSet (f,(RKer (V,f,vq)))
CosetSet (f,(RKer (V,f,vq))) is non empty Element of bool (bool the carrier of f)
bool (bool the carrier of f) is set
{ b₁ where b₁ is Coset of RKer (V,f,vq) : verum } is set
K203( the carrier of (VectQuot (f,(RKer (V,f,vq)))),(0. (VectQuot (f,(RKer (V,f,vq)))))) is non empty Element of bool the carrier of (VectQuot (f,(RKer (V,f,vq))))
x is set
A is Element of the carrier of V
(V,f,vq) . (A,(0. (VectQuot (f,(RKer (V,f,vq)))))) is complex Element of the carrier of F_Complex
[A,(0. (VectQuot (f,(RKer (V,f,vq)))))] is set
{A,(0. (VectQuot (f,(RKer (V,f,vq)))))} is non empty set
{A} is non empty set
{{A,(0. (VectQuot (f,(RKer (V,f,vq)))))},{A}} is non empty set
(V,f,vq) . [A,(0. (VectQuot (f,(RKer (V,f,vq)))))] is set
f is non empty VectSpStr over F_Complex
the carrier of f is non empty set
vq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of vq is non empty set
[: the carrier of f, the carrier of vq:] is set
[:[: the carrier of f, the carrier of vq:], the carrier of F_Complex:] is set
bool [:[: the carrier of f, the carrier of vq:], the carrier of F_Complex:] is set
vr is V16() V19([: the carrier of f, the carrier of vq:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of f, the carrier of vq:], the carrier of F_Complex) additiveFAF (f,vq) Element of bool [:[: the carrier of f, the carrier of vq:], the carrier of F_Complex:]
leftker vr is Element of bool the carrier of f
bool the carrier of f is set
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of vq holds vr . (b₁,b₂) = 0. F_Complex } is set
(f,vq,vr) is V16() V19([: the carrier of f, the carrier of vq:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of f, the carrier of vq:], the carrier of F_Complex) additiveFAF homogeneousFAF Element of bool [:[: the carrier of f, the carrier of vq:], the carrier of F_Complex:]
RKer (f,vq,vr) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of vq
VectQuot (vq,(RKer (f,vq,vr))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
(f,vq,vr) is V16() V19([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex) additiveFAF (f, VectQuot (vq,(RKer (f,vq,vr)))) Element of bool [:[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:]
the carrier of (VectQuot (vq,(RKer (f,vq,vr)))) is non empty set
[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):] is set
[:[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:] is set
RQForm (f,vq,vr) is V16() V19([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex) additiveFAF homogeneousFAF Element of bool [:[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:]
(f,(VectQuot (vq,(RKer (f,vq,vr)))),(RQForm (f,vq,vr))) is V16() V19([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex) additiveFAF (f, VectQuot (vq,(RKer (f,vq,vr)))) Element of bool [:[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:]
leftker (f,vq,vr) is Element of bool the carrier of f
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of (VectQuot (vq,(RKer (f,vq,vr)))) holds (f,vq,vr) . (b₁,b₂) = 0. F_Complex } is set
K is set
x is Element of the carrier of f
A is Element of the carrier of (VectQuot (vq,(RKer (f,vq,vr))))
B is Element of the carrier of vq
B + (RKer (f,vq,vr)) is Element of bool the carrier of vq
bool the carrier of vq is set
{ (B + b₁) where b₁ is Element of the carrier of vq : b₁ in RKer (f,vq,vr) } is set
(f,vq,vr) . (x,A) is complex Element of the carrier of F_Complex
[x,A] is set
{x,A} is non empty set
{x} is non empty set
{{x,A},{x}} is non empty set
(f,vq,vr) . [x,A] is set
vr . (x,B) is complex Element of the carrier of F_Complex
[x,B] is set
{x,B} is non empty set
{{x,B},{x}} is non empty set
vr . [x,B] is set
K is set
x is Element of the carrier of f
A is Element of the carrier of vq
A + (RKer (f,vq,vr)) is Element of bool the carrier of vq
bool the carrier of vq is set
{ (A + b₁) where b₁ is Element of the carrier of vq : b₁ in RKer (f,vq,vr) } is set
vr . (x,A) is complex Element of the carrier of F_Complex
[x,A] is set
{x,A} is non empty set
{x} is non empty set
{{x,A},{x}} is non empty set
vr . [x,A] is set
B is Element of the carrier of (VectQuot (vq,(RKer (f,vq,vr))))
(f,vq,vr) . (x,B) is complex Element of the carrier of F_Complex
[x,B] is set
{x,B} is non empty set
{{x,B},{x}} is non empty set
(f,vq,vr) . [x,B] is set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of f is non empty set
vq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of vq is non empty set
[: the carrier of f, the carrier of vq:] is set
[:[: the carrier of f, the carrier of vq:], the carrier of F_Complex:] is set
bool [:[: the carrier of f, the carrier of vq:], the carrier of F_Complex:] is set
vr is V16() V19([: the carrier of f, the carrier of vq:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of f, the carrier of vq:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (f,vq) Element of bool [:[: the carrier of f, the carrier of vq:], the carrier of F_Complex:]
(f,vq,vr) is V16() V19([: the carrier of f, the carrier of vq:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of f, the carrier of vq:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF Element of bool [:[: the carrier of f, the carrier of vq:], the carrier of F_Complex:]
RKer (f,vq,vr) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of vq
LKer vr is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(LKer vr)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
LQForm vr is V16() V19([: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:]) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:], the carrier of F_Complex) V30([: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF non degenerated-on-left ( VectQuot (f,(LKer vr)),vq) Element of bool [:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:], the carrier of F_Complex:]
the carrier of (VectQuot (f,(LKer vr))) is non empty set
[: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:] is set
[:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:], the carrier of F_Complex:] is set
((VectQuot (f,(LKer vr))),vq,(LQForm vr)) is V16() V19([: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF Element of bool [:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:], the carrier of F_Complex:]
RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of vq
the carrier of (RKer (f,vq,vr)) is non empty set
rightker (f,vq,vr) is non empty Element of bool the carrier of vq
bool the carrier of vq is set
{ b₁ where b₁ is Element of the carrier of vq : for b₂ being Element of the carrier of f holds (f,vq,vr) . (b₂,b₁) = 0. F_Complex } is set
rightker vr is non empty Element of bool the carrier of vq
{ b₁ where b₁ is Element of the carrier of vq : for b₂ being Element of the carrier of f holds vr . (b₂,b₁) = 0. F_Complex } is set
rightker (LQForm vr) is non empty Element of bool the carrier of vq
{ b₁ where b₁ is Element of the carrier of vq : for b₂ being Element of the carrier of (VectQuot (f,(LKer vr))) holds (LQForm vr) . (b₂,b₁) = 0. F_Complex } is set
rightker ((VectQuot (f,(LKer vr))),vq,(LQForm vr)) is non empty Element of bool the carrier of vq
{ b₁ where b₁ is Element of the carrier of vq : for b₂ being Element of the carrier of (VectQuot (f,(LKer vr))) holds ((VectQuot (f,(LKer vr))),vq,(LQForm vr)) . (b₂,b₁) = 0. F_Complex } is set
the carrier of (RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))) is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of f is non empty set
vq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of vq is non empty set
[: the carrier of f, the carrier of vq:] is set
[:[: the carrier of f, the carrier of vq:], the carrier of F_Complex:] is set
bool [:[: the carrier of f, the carrier of vq:], the carrier of F_Complex:] is set
vr is V16() V19([: the carrier of f, the carrier of vq:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of f, the carrier of vq:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (f,vq) Element of bool [:[: the carrier of f, the carrier of vq:], the carrier of F_Complex:]
LKer vr is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
(f,vq,vr) is V16() V19([: the carrier of f, the carrier of vq:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of f, the carrier of vq:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF Element of bool [:[: the carrier of f, the carrier of vq:], the carrier of F_Complex:]
RKer (f,vq,vr) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of vq
VectQuot (vq,(RKer (f,vq,vr))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
(f,vq,vr) is V16() V19([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF non degenerated-on-right (f, VectQuot (vq,(RKer (f,vq,vr)))) Element of bool [:[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:]
the carrier of (VectQuot (vq,(RKer (f,vq,vr)))) is non empty set
[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):] is set
[:[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:] is set
RQForm (f,vq,vr) is V16() V19([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex) additiveFAF homogeneousFAF non degenerated-on-right Element of bool [:[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:]
(f,(VectQuot (vq,(RKer (f,vq,vr)))),(RQForm (f,vq,vr))) is V16() V19([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex) additiveFAF (f, VectQuot (vq,(RKer (f,vq,vr)))) Element of bool [:[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:]
LKer (f,vq,vr) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
the carrier of (LKer vr) is non empty set
leftker vr is non empty Element of bool the carrier of f
bool the carrier of f is set
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of vq holds vr . (b₁,b₂) = 0. F_Complex } is set
leftker (f,vq,vr) is non empty Element of bool the carrier of f
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of (VectQuot (vq,(RKer (f,vq,vr)))) holds (f,vq,vr) . (b₁,b₂) = 0. F_Complex } is set
the carrier of (LKer (f,vq,vr)) is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of f is non empty set
vq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of vq is non empty set
[: the carrier of f, the carrier of vq:] is set
[:[: the carrier of f, the carrier of vq:], the carrier of F_Complex:] is set
bool [:[: the carrier of f, the carrier of vq:], the carrier of F_Complex:] is set
vr is V16() V19([: the carrier of f, the carrier of vq:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of f, the carrier of vq:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (f,vq) Element of bool [:[: the carrier of f, the carrier of vq:], the carrier of F_Complex:]
LKer vr is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(LKer vr)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of (VectQuot (f,(LKer vr))) is non empty set
(f,vq,vr) is V16() V19([: the carrier of f, the carrier of vq:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of f, the carrier of vq:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF Element of bool [:[: the carrier of f, the carrier of vq:], the carrier of F_Complex:]
RKer (f,vq,vr) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of vq
VectQuot (vq,(RKer (f,vq,vr))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of (VectQuot (vq,(RKer (f,vq,vr)))) is non empty set
[: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):] is set
LQForm vr is V16() V19([: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:]) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:], the carrier of F_Complex) V30([: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF non degenerated-on-left ( VectQuot (f,(LKer vr)),vq) Element of bool [:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:], the carrier of F_Complex:]
[: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:] is set
[:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:], the carrier of F_Complex:] is set
((VectQuot (f,(LKer vr))),vq,(LQForm vr)) is V16() V19([: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF Element of bool [:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:], the carrier of F_Complex:]
RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of vq
VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr)))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))) is non empty set
[: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):] is set
(f,vq,vr) is V16() V19([: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF ( VectQuot (f,(LKer vr)), VectQuot (vq,(RKer (f,vq,vr)))) Element of bool [:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:]
[:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:] is set
((VectQuot (f,(LKer vr))),vq,(LQForm vr)) is V16() V19([: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF non degenerated-on-right ( VectQuot (f,(LKer vr)), VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))) Element of bool [:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):], the carrier of F_Complex:]
[:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):], the carrier of F_Complex:] is set
RQForm ((VectQuot (f,(LKer vr))),vq,(LQForm vr)) is V16() V19([: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):], the carrier of F_Complex) additiveFAF homogeneousFAF non degenerated-on-right Element of bool [:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):], the carrier of F_Complex:]
((VectQuot (f,(LKer vr))),(VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))),(RQForm ((VectQuot (f,(LKer vr))),vq,(LQForm vr)))) is V16() V19([: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):], the carrier of F_Complex) additiveFAF ( VectQuot (f,(LKer vr)), VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))) Element of bool [:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):], the carrier of F_Complex:]
(f,vq,vr) is V16() V19([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF non degenerated-on-right (f, VectQuot (vq,(RKer (f,vq,vr)))) Element of bool [:[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:]
[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):] is set
[:[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:] is set
RQForm (f,vq,vr) is V16() V19([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex) additiveFAF homogeneousFAF non degenerated-on-right Element of bool [:[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:]
(f,(VectQuot (vq,(RKer (f,vq,vr)))),(RQForm (f,vq,vr))) is V16() V19([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex) additiveFAF (f, VectQuot (vq,(RKer (f,vq,vr)))) Element of bool [:[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:]
LKer (f,vq,vr) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(LKer (f,vq,vr))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of (VectQuot (f,(LKer (f,vq,vr)))) is non empty set
[: the carrier of (VectQuot (f,(LKer (f,vq,vr)))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):] is set
LQForm (f,vq,vr) is V16() V19([: the carrier of (VectQuot (f,(LKer (f,vq,vr)))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):]) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (f,(LKer (f,vq,vr)))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex) V30([: the carrier of (VectQuot (f,(LKer (f,vq,vr)))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF non degenerated-on-left ( VectQuot (f,(LKer (f,vq,vr))), VectQuot (vq,(RKer (f,vq,vr)))) Element of bool [:[: the carrier of (VectQuot (f,(LKer (f,vq,vr)))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:]
[:[: the carrier of (VectQuot (f,(LKer (f,vq,vr)))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (f,(LKer (f,vq,vr)))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:] is set
dom (f,vq,vr) is V16() V19( the carrier of (VectQuot (f,(LKer vr)))) V20( the carrier of (VectQuot (vq,(RKer (f,vq,vr))))) Element of bool [: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):]
bool [: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):] is set
wa is set
vv is set
v is set
[vv,v] is set
{vv,v} is non empty set
{vv} is non empty set
{{vv,v},{vv}} is non empty set
A is Element of the carrier of (VectQuot (f,(LKer vr)))
v is Element of the carrier of f
v + (LKer vr) is Element of bool the carrier of f
bool the carrier of f is set
{ (v + b₁) where b₁ is Element of the carrier of f : b₁ in LKer vr } is set
B is Element of the carrier of (VectQuot (vq,(RKer (f,vq,vr))))
w is Element of the carrier of vq
w + (RKer (f,vq,vr)) is Element of bool the carrier of vq
bool the carrier of vq is set
{ (w + b₁) where b₁ is Element of the carrier of vq : b₁ in RKer (f,vq,vr) } is set
(f,vq,vr) . wa is set
(f,vq,vr) . (A,B) is complex Element of the carrier of F_Complex
[A,B] is set
{A,B} is non empty set
{A} is non empty set
{{A,B},{A}} is non empty set
(f,vq,vr) . [A,B] is set
vr . (v,w) is complex Element of the carrier of F_Complex
[v,w] is set
{v,w} is non empty set
{v} is non empty set
{{v,w},{v}} is non empty set
vr . [v,w] is set
(LQForm vr) . (A,w) is complex Element of the carrier of F_Complex
[A,w] is set
{A,w} is non empty set
{{A,w},{A}} is non empty set
(LQForm vr) . [A,w] is set
((VectQuot (f,(LKer vr))),vq,(LQForm vr)) . (A,B) is set
((VectQuot (f,(LKer vr))),vq,(LQForm vr)) . [A,B] is set
((VectQuot (f,(LKer vr))),vq,(LQForm vr)) . wa is set
dom ((VectQuot (f,(LKer vr))),vq,(LQForm vr)) is V16() V19( the carrier of (VectQuot (f,(LKer vr)))) V20( the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr)))))) Element of bool [: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):]
bool [: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):] is set
wa is set
vv is set
v is set
[vv,v] is set
{vv,v} is non empty set
{vv} is non empty set
{{vv,v},{vv}} is non empty set
A is Element of the carrier of (VectQuot (f,(LKer vr)))
v is Element of the carrier of f
v + (LKer vr) is Element of bool the carrier of f
{ (v + b₁) where b₁ is Element of the carrier of f : b₁ in LKer vr } is set
B is Element of the carrier of (VectQuot (vq,(RKer (f,vq,vr))))
w is Element of the carrier of vq
w + (RKer (f,vq,vr)) is Element of bool the carrier of vq
{ (w + b₁) where b₁ is Element of the carrier of vq : b₁ in RKer (f,vq,vr) } is set
(f,vq,vr) . wa is set
(f,vq,vr) . (A,B) is complex Element of the carrier of F_Complex
[A,B] is set
{A,B} is non empty set
{A} is non empty set
{{A,B},{A}} is non empty set
(f,vq,vr) . [A,B] is set
vr . (v,w) is complex Element of the carrier of F_Complex
[v,w] is set
{v,w} is non empty set
{v} is non empty set
{{v,w},{v}} is non empty set
vr . [v,w] is set
(f,vq,vr) . (v,B) is complex Element of the carrier of F_Complex
[v,B] is set
{v,B} is non empty set
{{v,B},{v}} is non empty set
(f,vq,vr) . [v,B] is set
(LQForm (f,vq,vr)) . (A,B) is set
(LQForm (f,vq,vr)) . [A,B] is set
(LQForm (f,vq,vr)) . wa is set
dom (LQForm (f,vq,vr)) is V16() V19( the carrier of (VectQuot (f,(LKer (f,vq,vr))))) V20( the carrier of (VectQuot (vq,(RKer (f,vq,vr))))) Element of bool [: the carrier of (VectQuot (f,(LKer (f,vq,vr)))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):]
bool [: the carrier of (VectQuot (f,(LKer (f,vq,vr)))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):] is set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of f is non empty set
vq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of vq is non empty set
[: the carrier of f, the carrier of vq:] is set
[:[: the carrier of f, the carrier of vq:], the carrier of F_Complex:] is set
bool [:[: the carrier of f, the carrier of vq:], the carrier of F_Complex:] is set
vr is V16() V19([: the carrier of f, the carrier of vq:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of f, the carrier of vq:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (f,vq) Element of bool [:[: the carrier of f, the carrier of vq:], the carrier of F_Complex:]
LKer vr is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(LKer vr)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
(f,vq,vr) is V16() V19([: the carrier of f, the carrier of vq:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of f, the carrier of vq:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF Element of bool [:[: the carrier of f, the carrier of vq:], the carrier of F_Complex:]
RKer (f,vq,vr) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of vq
VectQuot (vq,(RKer (f,vq,vr))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
(f,vq,vr) is V16() V19([: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF ( VectQuot (f,(LKer vr)), VectQuot (vq,(RKer (f,vq,vr)))) Element of bool [:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:]
the carrier of (VectQuot (f,(LKer vr))) is non empty set
the carrier of (VectQuot (vq,(RKer (f,vq,vr)))) is non empty set
[: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):] is set
[:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:] is set
leftker (f,vq,vr) is non empty Element of bool the carrier of (VectQuot (f,(LKer vr)))
bool the carrier of (VectQuot (f,(LKer vr))) is set
{ b₁ where b₁ is Element of the carrier of (VectQuot (f,(LKer vr))) : for b₂ being Element of the carrier of (VectQuot (vq,(RKer (f,vq,vr)))) holds (f,vq,vr) . (b₁,b₂) = 0. F_Complex } is set
LQForm vr is V16() V19([: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:]) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:], the carrier of F_Complex) V30([: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF non degenerated-on-left ( VectQuot (f,(LKer vr)),vq) Element of bool [:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:], the carrier of F_Complex:]
[: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:] is set
[:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:], the carrier of F_Complex:] is set
((VectQuot (f,(LKer vr))),vq,(LQForm vr)) is V16() V19([: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF Element of bool [:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of vq:], the carrier of F_Complex:]
RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of vq
VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr)))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
((VectQuot (f,(LKer vr))),vq,(LQForm vr)) is V16() V19([: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF non degenerated-on-right ( VectQuot (f,(LKer vr)), VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))) Element of bool [:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):], the carrier of F_Complex:]
the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))) is non empty set
[: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):] is set
[:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):], the carrier of F_Complex:] is set
RQForm ((VectQuot (f,(LKer vr))),vq,(LQForm vr)) is V16() V19([: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):], the carrier of F_Complex) additiveFAF homogeneousFAF non degenerated-on-right Element of bool [:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):], the carrier of F_Complex:]
((VectQuot (f,(LKer vr))),(VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))),(RQForm ((VectQuot (f,(LKer vr))),vq,(LQForm vr)))) is V16() V19([: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):], the carrier of F_Complex) additiveFAF ( VectQuot (f,(LKer vr)), VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))) Element of bool [:[: the carrier of (VectQuot (f,(LKer vr))), the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))):], the carrier of F_Complex:]
leftker ((VectQuot (f,(LKer vr))),vq,(LQForm vr)) is non empty Element of bool the carrier of (VectQuot (f,(LKer vr)))
{ b₁ where b₁ is Element of the carrier of (VectQuot (f,(LKer vr))) : for b₂ being Element of the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))) holds ((VectQuot (f,(LKer vr))),vq,(LQForm vr)) . (b₁,b₂) = 0. F_Complex } is set
rightker (f,vq,vr) is non empty Element of bool the carrier of (VectQuot (vq,(RKer (f,vq,vr))))
bool the carrier of (VectQuot (vq,(RKer (f,vq,vr)))) is set
{ b₁ where b₁ is Element of the carrier of (VectQuot (vq,(RKer (f,vq,vr)))) : for b₂ being Element of the carrier of (VectQuot (f,(LKer vr))) holds (f,vq,vr) . (b₂,b₁) = 0. F_Complex } is set
rightker ((VectQuot (f,(LKer vr))),vq,(LQForm vr)) is non empty Element of bool the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr)))))
bool the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))) is set
{ b₁ where b₁ is Element of the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr))))) : for b₂ being Element of the carrier of (VectQuot (f,(LKer vr))) holds ((VectQuot (f,(LKer vr))),vq,(LQForm vr)) . (b₂,b₁) = 0. F_Complex } is set
(f,vq,vr) is V16() V19([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF non degenerated-on-right (f, VectQuot (vq,(RKer (f,vq,vr)))) Element of bool [:[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:]
[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):] is set
[:[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:] is set
RQForm (f,vq,vr) is V16() V19([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex) additiveFAF homogeneousFAF non degenerated-on-right Element of bool [:[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:]
(f,(VectQuot (vq,(RKer (f,vq,vr)))),(RQForm (f,vq,vr))) is V16() V19([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex) additiveFAF (f, VectQuot (vq,(RKer (f,vq,vr)))) Element of bool [:[: the carrier of f, the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:]
LKer (f,vq,vr) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(LKer (f,vq,vr))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
LQForm (f,vq,vr) is V16() V19([: the carrier of (VectQuot (f,(LKer (f,vq,vr)))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):]) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (f,(LKer (f,vq,vr)))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex) V30([: the carrier of (VectQuot (f,(LKer (f,vq,vr)))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF non degenerated-on-left ( VectQuot (f,(LKer (f,vq,vr))), VectQuot (vq,(RKer (f,vq,vr)))) Element of bool [:[: the carrier of (VectQuot (f,(LKer (f,vq,vr)))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:]
the carrier of (VectQuot (f,(LKer (f,vq,vr)))) is non empty set
[: the carrier of (VectQuot (f,(LKer (f,vq,vr)))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):] is set
[:[: the carrier of (VectQuot (f,(LKer (f,vq,vr)))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (f,(LKer (f,vq,vr)))), the carrier of (VectQuot (vq,(RKer (f,vq,vr)))):], the carrier of F_Complex:] is set
leftker (LQForm (f,vq,vr)) is non empty Element of bool the carrier of (VectQuot (f,(LKer (f,vq,vr))))
bool the carrier of (VectQuot (f,(LKer (f,vq,vr)))) is set
{ b₁ where b₁ is Element of the carrier of (VectQuot (f,(LKer (f,vq,vr)))) : for b₂ being Element of the carrier of (VectQuot (vq,(RKer (f,vq,vr)))) holds (LQForm (f,vq,vr)) . (b₁,b₂) = 0. F_Complex } is set
rightker (LQForm (f,vq,vr)) is non empty Element of bool the carrier of (VectQuot (vq,(RKer (f,vq,vr))))
{ b₁ where b₁ is Element of the carrier of (VectQuot (vq,(RKer (f,vq,vr)))) : for b₂ being Element of the carrier of (VectQuot (f,(LKer (f,vq,vr)))) holds (LQForm (f,vq,vr)) . (b₂,b₁) = 0. F_Complex } is set
A is set
wa is Element of the carrier of (VectQuot (f,(LKer vr)))
vv is Element of the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr)))))
((VectQuot (f,(LKer vr))),vq,(LQForm vr)) . (wa,vv) is complex Element of the carrier of F_Complex
[wa,vv] is set
{wa,vv} is non empty set
{wa} is non empty set
{{wa,vv},{wa}} is non empty set
((VectQuot (f,(LKer vr))),vq,(LQForm vr)) . [wa,vv] is set
v is Element of the carrier of (VectQuot (vq,(RKer (f,vq,vr))))
(f,vq,vr) . (wa,v) is complex Element of the carrier of F_Complex
[wa,v] is set
{wa,v} is non empty set
{{wa,v},{wa}} is non empty set
(f,vq,vr) . [wa,v] is set
A is set
wa is Element of the carrier of (VectQuot (f,(LKer vr)))
vv is Element of the carrier of (VectQuot (vq,(RKer (f,vq,vr))))
(f,vq,vr) . (wa,vv) is complex Element of the carrier of F_Complex
[wa,vv] is set
{wa,vv} is non empty set
{wa} is non empty set
{{wa,vv},{wa}} is non empty set
(f,vq,vr) . [wa,vv] is set
v is Element of the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr)))))
((VectQuot (f,(LKer vr))),vq,(LQForm vr)) . (wa,v) is complex Element of the carrier of F_Complex
[wa,v] is set
{wa,v} is non empty set
{{wa,v},{wa}} is non empty set
((VectQuot (f,(LKer vr))),vq,(LQForm vr)) . [wa,v] is set
A is set
wa is Element of the carrier of (VectQuot (vq,(RKer (f,vq,vr))))
v is Element of the carrier of (VectQuot (f,(LKer vr)))
vv is Element of the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr)))))
((VectQuot (f,(LKer vr))),vq,(LQForm vr)) . (v,vv) is complex Element of the carrier of F_Complex
[v,vv] is set
{v,vv} is non empty set
{v} is non empty set
{{v,vv},{v}} is non empty set
((VectQuot (f,(LKer vr))),vq,(LQForm vr)) . [v,vv] is set
(f,vq,vr) . (v,wa) is complex Element of the carrier of F_Complex
[v,wa] is set
{v,wa} is non empty set
{{v,wa},{v}} is non empty set
(f,vq,vr) . [v,wa] is set
A is set
wa is Element of the carrier of (VectQuot (vq,(RKer ((VectQuot (f,(LKer vr))),vq,(LQForm vr)))))
v is Element of the carrier of (VectQuot (f,(LKer vr)))
vv is Element of the carrier of (VectQuot (vq,(RKer (f,vq,vr))))
(f,vq,vr) . (v,vv) is complex Element of the carrier of F_Complex
[v,vv] is set
{v,vv} is non empty set
{v} is non empty set
{{v,vv},{v}} is non empty set
(f,vq,vr) . [v,vv] is set
((VectQuot (f,(LKer vr))),vq,(LQForm vr)) . (v,wa) is complex Element of the carrier of F_Complex
[v,wa] is set
{v,wa} is non empty set
{{v,wa},{v}} is non empty set
((VectQuot (f,(LKer vr))),vq,(LQForm vr)) . [v,wa] is set
A is set
wa is Element of the carrier of (VectQuot (f,(LKer vr)))
vv is Element of the carrier of (VectQuot (f,(LKer (f,vq,vr))))
v is Element of the carrier of (VectQuot (vq,(RKer (f,vq,vr))))
(LQForm (f,vq,vr)) . (vv,v) is complex Element of the carrier of F_Complex
[vv,v] is set
{vv,v} is non empty set
{vv} is non empty set
{{vv,v},{vv}} is non empty set
(LQForm (f,vq,vr)) . [vv,v] is set
(f,vq,vr) . (wa,v) is complex Element of the carrier of F_Complex
[wa,v] is set
{wa,v} is non empty set
{wa} is non empty set
{{wa,v},{wa}} is non empty set
(f,vq,vr) . [wa,v] is set
A is set
wa is Element of the carrier of (VectQuot (f,(LKer (f,vq,vr))))
vv is Element of the carrier of (VectQuot (f,(LKer vr)))
v is Element of the carrier of (VectQuot (vq,(RKer (f,vq,vr))))
(f,vq,vr) . (vv,v) is complex Element of the carrier of F_Complex
[vv,v] is set
{vv,v} is non empty set
{vv} is non empty set
{{vv,v},{vv}} is non empty set
(f,vq,vr) . [vv,v] is set
(LQForm (f,vq,vr)) . (wa,v) is complex Element of the carrier of F_Complex
[wa,v] is set
{wa,v} is non empty set
{wa} is non empty set
{{wa,v},{wa}} is non empty set
(LQForm (f,vq,vr)) . [wa,v] is set
A is set
wa is Element of the carrier of (VectQuot (vq,(RKer (f,vq,vr))))
vv is Element of the carrier of (VectQuot (f,(LKer (f,vq,vr))))
(LQForm (f,vq,vr)) . (vv,wa) is complex Element of the carrier of F_Complex
[vv,wa] is set
{vv,wa} is non empty set
{vv} is non empty set
{{vv,wa},{vv}} is non empty set
(LQForm (f,vq,vr)) . [vv,wa] is set
v is Element of the carrier of (VectQuot (f,(LKer vr)))
(f,vq,vr) . (v,wa) is complex Element of the carrier of F_Complex
[v,wa] is set
{v,wa} is non empty set
{v} is non empty set
{{v,wa},{v}} is non empty set
(f,vq,vr) . [v,wa] is set
A is set
wa is Element of the carrier of (VectQuot (vq,(RKer (f,vq,vr))))
vv is Element of the carrier of (VectQuot (f,(LKer vr)))
(f,vq,vr) . (vv,wa) is complex Element of the carrier of F_Complex
[vv,wa] is set
{vv,wa} is non empty set
{vv} is non empty set
{{vv,wa},{vv}} is non empty set
(f,vq,vr) . [vv,wa] is set
v is Element of the carrier of (VectQuot (f,(LKer (f,vq,vr))))
(LQForm (f,vq,vr)) . (v,wa) is complex Element of the carrier of F_Complex
[v,wa] is set
{v,wa} is non empty set
{v} is non empty set
{{v,wa},{v}} is non empty set
(LQForm (f,vq,vr)) . [v,wa] is set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
LKer vq is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(LKer vq)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
LQForm vq is V16() V19([: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:]) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:], the carrier of F_Complex) V30([: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF non degenerated-on-left ( VectQuot (V,(LKer vq)),f) Element of bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:], the carrier of F_Complex:]
the carrier of (VectQuot (V,(LKer vq))) is non empty set
[: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:] is set
[:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:], the carrier of F_Complex:] is set
((VectQuot (V,(LKer vq))),f,(LQForm vq)) is V16() V19([: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF Element of bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:], the carrier of F_Complex:]
RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq)))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
((VectQuot (V,(LKer vq))),f,(LQForm vq)) is V16() V19([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF non degenerated-on-right ( VectQuot (V,(LKer vq)), VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))) Element of bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):], the carrier of F_Complex:]
the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))) is non empty set
[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):] is set
[:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):], the carrier of F_Complex:] is set
RQForm ((VectQuot (V,(LKer vq))),f,(LQForm vq)) is V16() V19([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):], the carrier of F_Complex) additiveFAF homogeneousFAF non degenerated-on-right Element of bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):], the carrier of F_Complex:]
((VectQuot (V,(LKer vq))),(VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))),(RQForm ((VectQuot (V,(LKer vq))),f,(LQForm vq)))) is V16() V19([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):], the carrier of F_Complex) additiveFAF ( VectQuot (V,(LKer vq)), VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))) Element of bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):], the carrier of F_Complex:]
leftker (LQForm vq) is non empty Element of bool the carrier of (VectQuot (V,(LKer vq)))
bool the carrier of (VectQuot (V,(LKer vq))) is set
{ b₁ where b₁ is Element of the carrier of (VectQuot (V,(LKer vq))) : for b₂ being Element of the carrier of f holds (LQForm vq) . (b₁,b₂) = 0. F_Complex } is set
0. (VectQuot (V,(LKer vq))) is zero Element of the carrier of (VectQuot (V,(LKer vq)))
{(0. (VectQuot (V,(LKer vq))))} is non empty set
leftker ((VectQuot (V,(LKer vq))),f,(LQForm vq)) is non empty Element of bool the carrier of (VectQuot (V,(LKer vq)))
{ b₁ where b₁ is Element of the carrier of (VectQuot (V,(LKer vq))) : for b₂ being Element of the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))) holds ((VectQuot (V,(LKer vq))),f,(LQForm vq)) . (b₁,b₂) = 0. F_Complex } is set
(V,f,vq) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
RKer (V,f,vq) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(RKer (V,f,vq))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
(V,f,vq) is V16() V19([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF non degenerated-on-right (V, VectQuot (f,(RKer (V,f,vq)))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
the carrier of (VectQuot (f,(RKer (V,f,vq)))) is non empty set
[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):] is set
[:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:] is set
RQForm (V,f,vq) is V16() V19([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF homogeneousFAF non degenerated-on-right Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
(V,(VectQuot (f,(RKer (V,f,vq)))),(RQForm (V,f,vq))) is V16() V19([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF (V, VectQuot (f,(RKer (V,f,vq)))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
LKer (V,f,vq) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(LKer (V,f,vq))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
LQForm (V,f,vq) is V16() V19([: the carrier of (VectQuot (V,(LKer (V,f,vq)))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer (V,f,vq)))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) V30([: the carrier of (VectQuot (V,(LKer (V,f,vq)))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF non degenerated-on-left ( VectQuot (V,(LKer (V,f,vq))), VectQuot (f,(RKer (V,f,vq)))) Element of bool [:[: the carrier of (VectQuot (V,(LKer (V,f,vq)))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
the carrier of (VectQuot (V,(LKer (V,f,vq)))) is non empty set
[: the carrier of (VectQuot (V,(LKer (V,f,vq)))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):] is set
[:[: the carrier of (VectQuot (V,(LKer (V,f,vq)))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (V,(LKer (V,f,vq)))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:] is set
rightker (V,f,vq) is non empty Element of bool the carrier of (VectQuot (f,(RKer (V,f,vq))))
bool the carrier of (VectQuot (f,(RKer (V,f,vq)))) is set
{ b₁ where b₁ is Element of the carrier of (VectQuot (f,(RKer (V,f,vq)))) : for b₂ being Element of the carrier of V holds (V,f,vq) . (b₂,b₁) = 0. F_Complex } is set
0. (VectQuot (f,(RKer (V,f,vq)))) is zero Element of the carrier of (VectQuot (f,(RKer (V,f,vq))))
{(0. (VectQuot (f,(RKer (V,f,vq)))))} is non empty set
rightker (LQForm (V,f,vq)) is non empty Element of bool the carrier of (VectQuot (f,(RKer (V,f,vq))))
{ b₁ where b₁ is Element of the carrier of (VectQuot (f,(RKer (V,f,vq)))) : for b₂ being Element of the carrier of (VectQuot (V,(LKer (V,f,vq)))) holds (LQForm (V,f,vq)) . (b₂,b₁) = 0. F_Complex } is set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is set
[:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:] is set
vq is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
LKer vq is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(LKer vq)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
(V,f,vq) is V16() V19([: the carrier of V, the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of f:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF Element of bool [:[: the carrier of V, the carrier of f:], the carrier of F_Complex:]
RKer (V,f,vq) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(RKer (V,f,vq))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
(V,f,vq) is V16() V19([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF ( VectQuot (V,(LKer vq)), VectQuot (f,(RKer (V,f,vq)))) Element of bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
the carrier of (VectQuot (V,(LKer vq))) is non empty set
the carrier of (VectQuot (f,(RKer (V,f,vq)))) is non empty set
[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):] is set
[:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:] is set
LQForm vq is V16() V19([: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:]) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:], the carrier of F_Complex) V30([: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF non degenerated-on-left ( VectQuot (V,(LKer vq)),f) Element of bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:], the carrier of F_Complex:]
[: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:] is set
[:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:], the carrier of F_Complex:] is set
((VectQuot (V,(LKer vq))),f,(LQForm vq)) is V16() V19([: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF Element of bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of f:], the carrier of F_Complex:]
RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq)))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
((VectQuot (V,(LKer vq))),f,(LQForm vq)) is V16() V19([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):]) V19([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):], the carrier of F_Complex) V30([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):], the carrier of F_Complex) additiveFAF additiveFAF additiveSAF additiveSAF homogeneousSAF homogeneousSAF non degenerated-on-left non degenerated-on-right non degenerated-on-right ( VectQuot (V,(LKer vq)), VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))) ( VectQuot (V,(LKer vq)), VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))) Element of bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):], the carrier of F_Complex:]
the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))) is non empty set
[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):] is set
[:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):], the carrier of F_Complex:] is set
RQForm ((VectQuot (V,(LKer vq))),f,(LQForm vq)) is V16() V19([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):], the carrier of F_Complex) additiveFAF homogeneousFAF non degenerated-on-right Element of bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):], the carrier of F_Complex:]
((VectQuot (V,(LKer vq))),(VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))),(RQForm ((VectQuot (V,(LKer vq))),f,(LQForm vq)))) is V16() V19([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):], the carrier of F_Complex) additiveFAF ( VectQuot (V,(LKer vq)), VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))) Element of bool [:[: the carrier of (VectQuot (V,(LKer vq))), the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))):], the carrier of F_Complex:]
leftker ((VectQuot (V,(LKer vq))),f,(LQForm vq)) is non empty Element of bool the carrier of (VectQuot (V,(LKer vq)))
bool the carrier of (VectQuot (V,(LKer vq))) is set
{ b₁ where b₁ is Element of the carrier of (VectQuot (V,(LKer vq))) : for b₂ being Element of the carrier of (VectQuot (f,(RKer ((VectQuot (V,(LKer vq))),f,(LQForm vq))))) holds ((VectQuot (V,(LKer vq))),f,(LQForm vq)) . (b₁,b₂) = 0. F_Complex } is set
0. (VectQuot (V,(LKer vq))) is zero Element of the carrier of (VectQuot (V,(LKer vq)))
{(0. (VectQuot (V,(LKer vq))))} is non empty set
(V,f,vq) is V16() V19([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF non degenerated-on-right (V, VectQuot (f,(RKer (V,f,vq)))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):] is set
[:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:] is set
RQForm (V,f,vq) is V16() V19([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF homogeneousFAF non degenerated-on-right Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
(V,(VectQuot (f,(RKer (V,f,vq)))),(RQForm (V,f,vq))) is V16() V19([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF (V, VectQuot (f,(RKer (V,f,vq)))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
LKer (V,f,vq) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(LKer (V,f,vq))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
LQForm (V,f,vq) is V16() V19([: the carrier of (VectQuot (V,(LKer (V,f,vq)))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V19([: the carrier of (VectQuot (V,(LKer (V,f,vq)))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):]) V20( the carrier of F_Complex) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer (V,f,vq)))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) V30([: the carrier of (VectQuot (V,(LKer (V,f,vq)))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) V30([: the carrier of (VectQuot (V,(LKer (V,f,vq)))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex) additiveFAF additiveFAF additiveSAF additiveSAF homogeneousSAF homogeneousSAF non degenerated-on-left non degenerated-on-left non degenerated-on-right ( VectQuot (V,(LKer (V,f,vq))), VectQuot (f,(RKer (V,f,vq)))) ( VectQuot (V,(LKer (V,f,vq))), VectQuot (f,(RKer (V,f,vq)))) Element of bool [:[: the carrier of (VectQuot (V,(LKer (V,f,vq)))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:]
the carrier of (VectQuot (V,(LKer (V,f,vq)))) is non empty set
[: the carrier of (VectQuot (V,(LKer (V,f,vq)))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):] is set
[:[: the carrier of (VectQuot (V,(LKer (V,f,vq)))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (V,(LKer (V,f,vq)))), the carrier of (VectQuot (f,(RKer (V,f,vq)))):], the carrier of F_Complex:] is set
rightker (LQForm (V,f,vq)) is non empty Element of bool the carrier of (VectQuot (f,(RKer (V,f,vq))))
bool the carrier of (VectQuot (f,(RKer (V,f,vq)))) is set
{ b₁ where b₁ is Element of the carrier of (VectQuot (f,(RKer (V,f,vq)))) : for b₂ being Element of the carrier of (VectQuot (V,(LKer (V,f,vq)))) holds (LQForm (V,f,vq)) . (b₂,b₁) = 0. F_Complex } is set
0. (VectQuot (f,(RKer (V,f,vq)))) is zero Element of the carrier of (VectQuot (f,(RKer (V,f,vq))))
{(0. (VectQuot (f,(RKer (V,f,vq)))))} is non empty set
leftker (V,f,vq) is non empty Element of bool the carrier of (VectQuot (V,(LKer vq)))
{ b₁ where b₁ is Element of the carrier of (VectQuot (V,(LKer vq))) : for b₂ being Element of the carrier of (VectQuot (f,(RKer (V,f,vq)))) holds (V,f,vq) . (b₁,b₂) = 0. F_Complex } is set
rightker (V,f,vq) is non empty Element of bool the carrier of (VectQuot (f,(RKer (V,f,vq))))
{ b₁ where b₁ is Element of the carrier of (VectQuot (f,(RKer (V,f,vq)))) : for b₂ being Element of the carrier of (VectQuot (V,(LKer vq))) holds (V,f,vq) . (b₂,b₁) = 0. F_Complex } is set
V is non empty VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
V is non empty right_zeroed VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
vq is Element of the carrier of V
f . (vq,vq) is complex Element of the carrier of F_Complex
[vq,vq] is set
{vq,vq} is non empty set
{vq} is non empty set
{{vq,vq},{vq}} is non empty set
f . [vq,vq] is set
Re (f . (vq,vq)) is complex real ext-real Element of REAL
0. V is zero Element of the carrier of V
[**(Re (0. F_Complex)),(Im (0. F_Complex))**] is complex Element of the carrier of F_Complex
(Re (0. F_Complex)) + ((Im (0. F_Complex)) * <i>) is complex set
[**0,0**] is complex Element of the carrier of F_Complex
0. V is zero Element of the carrier of V
0. V is zero Element of the carrier of V
V is non empty right_zeroed VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
vq is Element of the carrier of V
f . (vq,vq) is complex Element of the carrier of F_Complex
[vq,vq] is set
{vq,vq} is non empty set
{vq} is non empty set
{{vq,vq},{vq}} is non empty set
f . [vq,vq] is set
Re (f . (vq,vq)) is complex real ext-real Element of REAL
0. V is zero Element of the carrier of V
[**(Re (0. F_Complex)),(Im (0. F_Complex))**] is complex Element of the carrier of F_Complex
(Re (0. F_Complex)) + ((Im (0. F_Complex)) * <i>) is complex set
[**0,0**] is complex Element of the carrier of F_Complex
0. V is zero Element of the carrier of V
0. V is zero Element of the carrier of V
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,V) (V) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
(V,V,f) is V16() V19([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF non degenerated-on-left non degenerated-on-right ( VectQuot (V,(LKer f)), VectQuot (V,(RKer (V,V,f)))) Element of bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex:]
LKer f is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(LKer f)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of (VectQuot (V,(LKer f))) is non empty set
(V,V,f) is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
RKer (V,V,f) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(RKer (V,V,f))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of (VectQuot (V,(RKer (V,V,f)))) is non empty set
[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):] is set
[:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex:] is set
[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):] is set
[:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex:] is set
qh is V16() V19([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex) Element of bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex:]
A is Element of the carrier of (VectQuot (V,(LKer f)))
FunctionalSAF (qh,A) is V16() V19( the carrier of (VectQuot (V,(LKer f)))) V20( the carrier of F_Complex) Function-like V30( the carrier of (VectQuot (V,(LKer f))), the carrier of F_Complex) Element of bool [: the carrier of (VectQuot (V,(LKer f))), the carrier of F_Complex:]
[: the carrier of (VectQuot (V,(LKer f))), the carrier of F_Complex:] is set
bool [: the carrier of (VectQuot (V,(LKer f))), the carrier of F_Complex:] is set
x is Element of the carrier of (VectQuot (V,(LKer f)))
(FunctionalSAF (qh,A)) . x is complex Element of the carrier of F_Complex
A is complex Element of the carrier of F_Complex
A * x is Element of the carrier of (VectQuot (V,(LKer f)))
the lmult of (VectQuot (V,(LKer f))) is V16() V19([: the carrier of F_Complex, the carrier of (VectQuot (V,(LKer f))):]) V20( the carrier of (VectQuot (V,(LKer f)))) Function-like V30([: the carrier of F_Complex, the carrier of (VectQuot (V,(LKer f))):], the carrier of (VectQuot (V,(LKer f)))) Element of bool [:[: the carrier of F_Complex, the carrier of (VectQuot (V,(LKer f))):], the carrier of (VectQuot (V,(LKer f))):]
[: the carrier of F_Complex, the carrier of (VectQuot (V,(LKer f))):] is set
[:[: the carrier of F_Complex, the carrier of (VectQuot (V,(LKer f))):], the carrier of (VectQuot (V,(LKer f))):] is set
bool [:[: the carrier of F_Complex, the carrier of (VectQuot (V,(LKer f))):], the carrier of (VectQuot (V,(LKer f))):] is set
the lmult of (VectQuot (V,(LKer f))) . (A,x) is Element of the carrier of (VectQuot (V,(LKer f)))
[A,x] is set
{A,x} is non empty set
{A} is non empty V175() set
{{A,x},{A}} is non empty set
the lmult of (VectQuot (V,(LKer f))) . [A,x] is set
(FunctionalSAF (qh,A)) . (A * x) is complex Element of the carrier of F_Complex
A * ((FunctionalSAF (qh,A)) . x) is complex Element of the carrier of F_Complex
the multF of F_Complex . (A,((FunctionalSAF (qh,A)) . x)) is complex Element of the carrier of F_Complex
[A,((FunctionalSAF (qh,A)) . x)] is set
{A,((FunctionalSAF (qh,A)) . x)} is non empty V175() set
{{A,((FunctionalSAF (qh,A)) . x)},{A}} is non empty set
the multF of F_Complex . [A,((FunctionalSAF (qh,A)) . x)] is set
K137(A,((FunctionalSAF (qh,A)) . x)) is complex Element of COMPLEX
B is Element of the carrier of V
B + (LKer f) is Element of bool the carrier of V
bool the carrier of V is set
{ (B + b₁) where b₁ is Element of the carrier of V : b₁ in LKer f } is set
A * B is Element of the carrier of V
the lmult of V is V16() V19([: the carrier of F_Complex, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of F_Complex, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:]
[: the carrier of F_Complex, the carrier of V:] is set
[:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of F_Complex, the carrier of V:], the carrier of V:] is set
the lmult of V . (A,B) is Element of the carrier of V
[A,B] is set
{A,B} is non empty set
{{A,B},{A}} is non empty set
the lmult of V . [A,B] is set
(A * B) + (LKer f) is Element of bool the carrier of V
{ ((A * B) + b₁) where b₁ is Element of the carrier of V : b₁ in LKer f } is set
w is Element of the carrier of (VectQuot (V,(RKer (V,V,f))))
A is Element of the carrier of V
A + (RKer (V,V,f)) is Element of bool the carrier of V
{ (A + b₁) where b₁ is Element of the carrier of V : b₁ in RKer (V,V,f) } is set
(V,V,f) . ((A * x),A) is set
[(A * x),A] is set
{(A * x),A} is non empty set
{(A * x)} is non empty set
{{(A * x),A},{(A * x)}} is non empty set
(V,V,f) . [(A * x),A] is set
f . ((A * B),A) is complex Element of the carrier of F_Complex
[(A * B),A] is set
{(A * B),A} is non empty set
{(A * B)} is non empty set
{{(A * B),A},{(A * B)}} is non empty set
f . [(A * B),A] is set
f . (B,A) is complex Element of the carrier of F_Complex
[B,A] is set
{B,A} is non empty set
{B} is non empty set
{{B,A},{B}} is non empty set
f . [B,A] is set
A * (f . (B,A)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (A,(f . (B,A))) is complex Element of the carrier of F_Complex
[A,(f . (B,A))] is set
{A,(f . (B,A))} is non empty V175() set
{{A,(f . (B,A))},{A}} is non empty set
the multF of F_Complex . [A,(f . (B,A))] is set
K137(A,(f . (B,A))) is complex Element of COMPLEX
qh . (x,A) is complex Element of the carrier of F_Complex
[x,A] is set
{x,A} is non empty set
{x} is non empty set
{{x,A},{x}} is non empty set
qh . [x,A] is set
A * (qh . (x,A)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (A,(qh . (x,A))) is complex Element of the carrier of F_Complex
[A,(qh . (x,A))] is set
{A,(qh . (x,A))} is non empty V175() set
{{A,(qh . (x,A))},{A}} is non empty set
the multF of F_Complex . [A,(qh . (x,A))] is set
K137(A,(qh . (x,A))) is complex Element of COMPLEX
A * ((FunctionalSAF (qh,A)) . x) is complex Element of the carrier of F_Complex
A is Element of the carrier of (VectQuot (V,(LKer f)))
FunctionalSAF (qh,A) is V16() V19( the carrier of (VectQuot (V,(LKer f)))) V20( the carrier of F_Complex) Function-like V30( the carrier of (VectQuot (V,(LKer f))), the carrier of F_Complex) Element of bool [: the carrier of (VectQuot (V,(LKer f))), the carrier of F_Complex:]
[: the carrier of (VectQuot (V,(LKer f))), the carrier of F_Complex:] is set
bool [: the carrier of (VectQuot (V,(LKer f))), the carrier of F_Complex:] is set
x is Element of the carrier of (VectQuot (V,(LKer f)))
A is Element of the carrier of (VectQuot (V,(LKer f)))
x + A is Element of the carrier of (VectQuot (V,(LKer f)))
the addF of (VectQuot (V,(LKer f))) is V16() V19([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):]) V20( the carrier of (VectQuot (V,(LKer f)))) Function-like V30([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of (VectQuot (V,(LKer f)))) Element of bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of (VectQuot (V,(LKer f))):]
[:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of (VectQuot (V,(LKer f))):] is set
bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of (VectQuot (V,(LKer f))):] is set
the addF of (VectQuot (V,(LKer f))) . (x,A) is Element of the carrier of (VectQuot (V,(LKer f)))
[x,A] is set
{x,A} is non empty set
{x} is non empty set
{{x,A},{x}} is non empty set
the addF of (VectQuot (V,(LKer f))) . [x,A] is set
(FunctionalSAF (qh,A)) . (x + A) is complex Element of the carrier of F_Complex
(FunctionalSAF (qh,A)) . x is complex Element of the carrier of F_Complex
(FunctionalSAF (qh,A)) . A is complex Element of the carrier of F_Complex
((FunctionalSAF (qh,A)) . x) + ((FunctionalSAF (qh,A)) . A) is complex Element of the carrier of F_Complex
the addF of F_Complex is V16() V19([: the carrier of F_Complex, the carrier of F_Complex:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex) Element of bool [:[: the carrier of F_Complex, the carrier of F_Complex:], the carrier of F_Complex:]
the addF of F_Complex . (((FunctionalSAF (qh,A)) . x),((FunctionalSAF (qh,A)) . A)) is complex Element of the carrier of F_Complex
[((FunctionalSAF (qh,A)) . x),((FunctionalSAF (qh,A)) . A)] is set
{((FunctionalSAF (qh,A)) . x),((FunctionalSAF (qh,A)) . A)} is non empty V175() set
{((FunctionalSAF (qh,A)) . x)} is non empty V175() set
{{((FunctionalSAF (qh,A)) . x),((FunctionalSAF (qh,A)) . A)},{((FunctionalSAF (qh,A)) . x)}} is non empty set
the addF of F_Complex . [((FunctionalSAF (qh,A)) . x),((FunctionalSAF (qh,A)) . A)] is set
K135(((FunctionalSAF (qh,A)) . x),((FunctionalSAF (qh,A)) . A)) is complex Element of COMPLEX
B is Element of the carrier of V
B + (LKer f) is Element of bool the carrier of V
bool the carrier of V is set
{ (B + b₁) where b₁ is Element of the carrier of V : b₁ in LKer f } is set
w is Element of the carrier of V
w + (LKer f) is Element of bool the carrier of V
{ (w + b₁) where b₁ is Element of the carrier of V : b₁ in LKer f } is set
A is Element of the carrier of (VectQuot (V,(RKer (V,V,f))))
wa is Element of the carrier of V
wa + (RKer (V,V,f)) is Element of bool the carrier of V
{ (wa + b₁) where b₁ is Element of the carrier of V : b₁ in RKer (V,V,f) } is set
x + A is Element of the carrier of (VectQuot (V,(LKer f)))
B + w is Element of the carrier of V
the addF of V is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of V) Function-like V30([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[:[: the carrier of V, the carrier of V:], the carrier of V:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is set
the addF of V . (B,w) is Element of the carrier of V
[B,w] is set
{B,w} is non empty set
{B} is non empty set
{{B,w},{B}} is non empty set
the addF of V . [B,w] is set
(B + w) + (LKer f) is Element of bool the carrier of V
{ ((B + w) + b₁) where b₁ is Element of the carrier of V : b₁ in LKer f } is set
(FunctionalSAF (qh,A)) . (x + A) is complex Element of the carrier of F_Complex
(V,V,f) . ((x + A),A) is set
[(x + A),A] is set
{(x + A),A} is non empty set
{(x + A)} is non empty set
{{(x + A),A},{(x + A)}} is non empty set
(V,V,f) . [(x + A),A] is set
f . ((B + w),wa) is complex Element of the carrier of F_Complex
[(B + w),wa] is set
{(B + w),wa} is non empty set
{(B + w)} is non empty set
{{(B + w),wa},{(B + w)}} is non empty set
f . [(B + w),wa] is set
f . (B,wa) is complex Element of the carrier of F_Complex
[B,wa] is set
{B,wa} is non empty set
{{B,wa},{B}} is non empty set
f . [B,wa] is set
f . (w,wa) is complex Element of the carrier of F_Complex
[w,wa] is set
{w,wa} is non empty set
{w} is non empty set
{{w,wa},{w}} is non empty set
f . [w,wa] is set
(f . (B,wa)) + (f . (w,wa)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((f . (B,wa)),(f . (w,wa))) is complex Element of the carrier of F_Complex
[(f . (B,wa)),(f . (w,wa))] is set
{(f . (B,wa)),(f . (w,wa))} is non empty V175() set
{(f . (B,wa))} is non empty V175() set
{{(f . (B,wa)),(f . (w,wa))},{(f . (B,wa))}} is non empty set
the addF of F_Complex . [(f . (B,wa)),(f . (w,wa))] is set
K135((f . (B,wa)),(f . (w,wa))) is complex Element of COMPLEX
qh . (x,A) is complex Element of the carrier of F_Complex
[x,A] is set
{x,A} is non empty set
{{x,A},{x}} is non empty set
qh . [x,A] is set
(qh . (x,A)) + (f . (w,wa)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((qh . (x,A)),(f . (w,wa))) is complex Element of the carrier of F_Complex
[(qh . (x,A)),(f . (w,wa))] is set
{(qh . (x,A)),(f . (w,wa))} is non empty V175() set
{(qh . (x,A))} is non empty V175() set
{{(qh . (x,A)),(f . (w,wa))},{(qh . (x,A))}} is non empty set
the addF of F_Complex . [(qh . (x,A)),(f . (w,wa))] is set
K135((qh . (x,A)),(f . (w,wa))) is complex Element of COMPLEX
qh . (A,A) is complex Element of the carrier of F_Complex
[A,A] is set
{A,A} is non empty set
{A} is non empty set
{{A,A},{A}} is non empty set
qh . [A,A] is set
(qh . (x,A)) + (qh . (A,A)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((qh . (x,A)),(qh . (A,A))) is complex Element of the carrier of F_Complex
[(qh . (x,A)),(qh . (A,A))] is set
{(qh . (x,A)),(qh . (A,A))} is non empty V175() set
{{(qh . (x,A)),(qh . (A,A))},{(qh . (x,A))}} is non empty set
the addF of F_Complex . [(qh . (x,A)),(qh . (A,A))] is set
K135((qh . (x,A)),(qh . (A,A))) is complex Element of COMPLEX
((FunctionalSAF (qh,A)) . x) + (qh . (A,A)) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((FunctionalSAF (qh,A)) . x),(qh . (A,A))) is complex Element of the carrier of F_Complex
[((FunctionalSAF (qh,A)) . x),(qh . (A,A))] is set
{((FunctionalSAF (qh,A)) . x),(qh . (A,A))} is non empty V175() set
{{((FunctionalSAF (qh,A)) . x),(qh . (A,A))},{((FunctionalSAF (qh,A)) . x)}} is non empty set
the addF of F_Complex . [((FunctionalSAF (qh,A)) . x),(qh . (A,A))] is set
K135(((FunctionalSAF (qh,A)) . x),(qh . (A,A))) is complex Element of COMPLEX
((FunctionalSAF (qh,A)) . x) + ((FunctionalSAF (qh,A)) . A) is complex Element of the carrier of F_Complex
A is Element of the carrier of (VectQuot (V,(LKer f)))
K is Element of the carrier of (VectQuot (V,(LKer f)))
qh . (A,K) is complex Element of the carrier of F_Complex
[A,K] is set
{A,K} is non empty set
{A} is non empty set
{{A,K},{A}} is non empty set
qh . [A,K] is set
qh . (K,A) is complex Element of the carrier of F_Complex
[K,A] is set
{K,A} is non empty set
{K} is non empty set
{{K,A},{K}} is non empty set
qh . [K,A] is set
(qh . (K,A)) *' is complex Element of the carrier of F_Complex
Re (qh . (K,A)) is complex real ext-real Element of REAL
Im (qh . (K,A)) is complex real ext-real Element of REAL
(Im (qh . (K,A))) * <i> is complex set
(Re (qh . (K,A))) - ((Im (qh . (K,A))) * <i>) is complex set
x is Element of the carrier of (VectQuot (V,(RKer (V,V,f))))
A is Element of the carrier of V
A + (RKer (V,V,f)) is Element of bool the carrier of V
bool the carrier of V is set
{ (A + b₁) where b₁ is Element of the carrier of V : b₁ in RKer (V,V,f) } is set
A + (LKer f) is Element of bool the carrier of V
{ (A + b₁) where b₁ is Element of the carrier of V : b₁ in LKer f } is set
w is Element of the carrier of V
w + (LKer f) is Element of bool the carrier of V
{ (w + b₁) where b₁ is Element of the carrier of V : b₁ in LKer f } is set
B is Element of the carrier of (VectQuot (V,(RKer (V,V,f))))
w + (RKer (V,V,f)) is Element of bool the carrier of V
{ (w + b₁) where b₁ is Element of the carrier of V : b₁ in RKer (V,V,f) } is set
f . (w,A) is complex Element of the carrier of F_Complex
[w,A] is set
{w,A} is non empty set
{w} is non empty set
{{w,A},{w}} is non empty set
f . [w,A] is set
f . (A,w) is complex Element of the carrier of F_Complex
[A,w] is set
{A,w} is non empty set
{A} is non empty set
{{A,w},{A}} is non empty set
f . [A,w] is set
(f . (A,w)) *' is complex Element of the carrier of F_Complex
Re (f . (A,w)) is complex real ext-real Element of REAL
Im (f . (A,w)) is complex real ext-real Element of REAL
(Im (f . (A,w))) * <i> is complex set
(Re (f . (A,w))) - ((Im (f . (A,w))) * <i>) is complex set
A is Element of the carrier of (VectQuot (V,(LKer f)))
qh . (A,A) is complex Element of the carrier of F_Complex
[A,A] is set
{A,A} is non empty set
{A} is non empty set
{{A,A},{A}} is non empty set
qh . [A,A] is set
Re (qh . (A,A)) is complex real ext-real Element of REAL
x is Element of the carrier of V
x + (LKer f) is Element of bool the carrier of V
bool the carrier of V is set
{ (x + b₁) where b₁ is Element of the carrier of V : b₁ in LKer f } is set
K is Element of the carrier of (VectQuot (V,(RKer (V,V,f))))
x + (RKer (V,V,f)) is Element of bool the carrier of V
{ (x + b₁) where b₁ is Element of the carrier of V : b₁ in RKer (V,V,f) } is set
f . (x,x) is complex Element of the carrier of F_Complex
[x,x] is set
{x,x} is non empty set
{x} is non empty set
{{x,x},{x}} is non empty set
f . [x,x] is set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,V) (V) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
LKer f is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(LKer f)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of (VectQuot (V,(LKer f))) is non empty set
(V,f) is V16() V19([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF ( VectQuot (V,(LKer f)), VectQuot (V,(LKer f))) ( VectQuot (V,(LKer f))) ( VectQuot (V,(LKer f))) ( VectQuot (V,(LKer f))) Element of bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex:]
[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):] is set
[:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex:] is set
(V,V,f) is V16() V19([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF non degenerated-on-left non degenerated-on-right ( VectQuot (V,(LKer f)), VectQuot (V,(RKer (V,V,f)))) Element of bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex:]
(V,V,f) is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
RKer (V,V,f) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(RKer (V,V,f))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of (VectQuot (V,(RKer (V,V,f)))) is non empty set
[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):] is set
[:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex:] is set
qh is Element of the carrier of (VectQuot (V,(LKer f)))
A is Element of the carrier of (VectQuot (V,(LKer f)))
(V,f) . (qh,A) is complex Element of the carrier of F_Complex
[qh,A] is set
{qh,A} is non empty set
{qh} is non empty set
{{qh,A},{qh}} is non empty set
(V,f) . [qh,A] is set
K is Element of the carrier of V
K + (LKer f) is Element of bool the carrier of V
bool the carrier of V is set
{ (K + b₁) where b₁ is Element of the carrier of V : b₁ in LKer f } is set
x is Element of the carrier of V
x + (LKer f) is Element of bool the carrier of V
{ (x + b₁) where b₁ is Element of the carrier of V : b₁ in LKer f } is set
f . (K,x) is complex Element of the carrier of F_Complex
[K,x] is set
{K,x} is non empty set
{K} is non empty set
{{K,x},{K}} is non empty set
f . [K,x] is set
A is Element of the carrier of (VectQuot (V,(RKer (V,V,f))))
x + (RKer (V,V,f)) is Element of bool the carrier of V
{ (x + b₁) where b₁ is Element of the carrier of V : b₁ in RKer (V,V,f) } is set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,V) (V) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
LKer f is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(LKer f)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
(V,f) is V16() V19([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF ( VectQuot (V,(LKer f)), VectQuot (V,(LKer f))) ( VectQuot (V,(LKer f))) ( VectQuot (V,(LKer f))) ( VectQuot (V,(LKer f))) Element of bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex:]
the carrier of (VectQuot (V,(LKer f))) is non empty set
[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):] is set
[:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex:] is set
(V,V,f) is V16() V19([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF non degenerated-on-left non degenerated-on-right ( VectQuot (V,(LKer f)), VectQuot (V,(RKer (V,V,f)))) Element of bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex:]
(V,V,f) is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
RKer (V,V,f) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(RKer (V,V,f))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of (VectQuot (V,(RKer (V,V,f)))) is non empty set
[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):] is set
[:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex:] is set
leftker (V,f) is non empty Element of bool the carrier of (VectQuot (V,(LKer f)))
bool the carrier of (VectQuot (V,(LKer f))) is set
{ b₁ where b₁ is Element of the carrier of (VectQuot (V,(LKer f))) : for b₂ being Element of the carrier of (VectQuot (V,(LKer f))) holds (V,f) . (b₁,b₂) = 0. F_Complex } is set
leftker (V,V,f) is non empty Element of bool the carrier of (VectQuot (V,(LKer f)))
{ b₁ where b₁ is Element of the carrier of (VectQuot (V,(LKer f))) : for b₂ being Element of the carrier of (VectQuot (V,(RKer (V,V,f)))) holds (V,V,f) . (b₁,b₂) = 0. F_Complex } is set
x is set
A is Element of the carrier of (VectQuot (V,(LKer f)))
B is Element of the carrier of (VectQuot (V,(RKer (V,V,f))))
(V,V,f) . (A,B) is complex Element of the carrier of F_Complex
[A,B] is set
{A,B} is non empty set
{A} is non empty set
{{A,B},{A}} is non empty set
(V,V,f) . [A,B] is set
w is Element of the carrier of (VectQuot (V,(LKer f)))
(V,f) . (A,w) is complex Element of the carrier of F_Complex
[A,w] is set
{A,w} is non empty set
{{A,w},{A}} is non empty set
(V,f) . [A,w] is set
x is set
A is Element of the carrier of (VectQuot (V,(LKer f)))
B is Element of the carrier of (VectQuot (V,(LKer f)))
(V,f) . (A,B) is complex Element of the carrier of F_Complex
[A,B] is set
{A,B} is non empty set
{A} is non empty set
{{A,B},{A}} is non empty set
(V,f) . [A,B] is set
w is Element of the carrier of (VectQuot (V,(RKer (V,V,f))))
(V,V,f) . (A,w) is complex Element of the carrier of F_Complex
[A,w] is set
{A,w} is non empty set
{{A,w},{A}} is non empty set
(V,V,f) . [A,w] is set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,V) (V) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
LKer f is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(LKer f)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
(V,f) is V16() V19([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF ( VectQuot (V,(LKer f)), VectQuot (V,(LKer f))) ( VectQuot (V,(LKer f))) ( VectQuot (V,(LKer f))) ( VectQuot (V,(LKer f))) Element of bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex:]
the carrier of (VectQuot (V,(LKer f))) is non empty set
[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):] is set
[:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex:] is set
(V,V,f) is V16() V19([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF non degenerated-on-left non degenerated-on-right ( VectQuot (V,(LKer f)), VectQuot (V,(RKer (V,V,f)))) Element of bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex:]
(V,V,f) is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
RKer (V,V,f) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(RKer (V,V,f))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of (VectQuot (V,(RKer (V,V,f)))) is non empty set
[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):] is set
[:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex:] is set
rightker (V,f) is non empty Element of bool the carrier of (VectQuot (V,(LKer f)))
bool the carrier of (VectQuot (V,(LKer f))) is set
{ b₁ where b₁ is Element of the carrier of (VectQuot (V,(LKer f))) : for b₂ being Element of the carrier of (VectQuot (V,(LKer f))) holds (V,f) . (b₂,b₁) = 0. F_Complex } is set
rightker (V,V,f) is non empty Element of bool the carrier of (VectQuot (V,(RKer (V,V,f))))
bool the carrier of (VectQuot (V,(RKer (V,V,f)))) is set
{ b₁ where b₁ is Element of the carrier of (VectQuot (V,(RKer (V,V,f)))) : for b₂ being Element of the carrier of (VectQuot (V,(LKer f))) holds (V,V,f) . (b₂,b₁) = 0. F_Complex } is set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,V) (V) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
LKer f is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(LKer f)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
(V,f) is V16() V19([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF ( VectQuot (V,(LKer f)), VectQuot (V,(LKer f))) ( VectQuot (V,(LKer f))) ( VectQuot (V,(LKer f))) ( VectQuot (V,(LKer f))) Element of bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex:]
the carrier of (VectQuot (V,(LKer f))) is non empty set
[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):] is set
[:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex:] is set
(V,V,f) is V16() V19([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF non degenerated-on-left non degenerated-on-right ( VectQuot (V,(LKer f)), VectQuot (V,(RKer (V,V,f)))) Element of bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex:]
(V,V,f) is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
RKer (V,V,f) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(RKer (V,V,f))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of (VectQuot (V,(RKer (V,V,f)))) is non empty set
[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):] is set
[:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex:] is set
leftker (V,f) is non empty Element of bool the carrier of (VectQuot (V,(LKer f)))
bool the carrier of (VectQuot (V,(LKer f))) is set
{ b₁ where b₁ is Element of the carrier of (VectQuot (V,(LKer f))) : for b₂ being Element of the carrier of (VectQuot (V,(LKer f))) holds (V,f) . (b₁,b₂) = 0. F_Complex } is set
leftker (V,V,f) is non empty Element of bool the carrier of (VectQuot (V,(LKer f)))
{ b₁ where b₁ is Element of the carrier of (VectQuot (V,(LKer f))) : for b₂ being Element of the carrier of (VectQuot (V,(RKer (V,V,f)))) holds (V,V,f) . (b₁,b₂) = 0. F_Complex } is set
0. (VectQuot (V,(LKer f))) is zero Element of the carrier of (VectQuot (V,(LKer f)))
{(0. (VectQuot (V,(LKer f))))} is non empty set
rightker (V,f) is non empty Element of bool the carrier of (VectQuot (V,(LKer f)))
{ b₁ where b₁ is Element of the carrier of (VectQuot (V,(LKer f))) : for b₂ being Element of the carrier of (VectQuot (V,(LKer f))) holds (V,f) . (b₂,b₁) = 0. F_Complex } is set
rightker (V,V,f) is non empty Element of bool the carrier of (VectQuot (V,(RKer (V,V,f))))
bool the carrier of (VectQuot (V,(RKer (V,V,f)))) is set
{ b₁ where b₁ is Element of the carrier of (VectQuot (V,(RKer (V,V,f)))) : for b₂ being Element of the carrier of (VectQuot (V,(LKer f))) holds (V,V,f) . (b₂,b₁) = 0. F_Complex } is set
0. (VectQuot (V,(RKer (V,V,f)))) is zero Element of the carrier of (VectQuot (V,(RKer (V,V,f))))
{(0. (VectQuot (V,(RKer (V,V,f)))))} is non empty set
A is Element of the carrier of (VectQuot (V,(LKer f)))
(V,f) . (A,A) is complex Element of the carrier of F_Complex
[A,A] is set
{A,A} is non empty set
{A} is non empty set
{{A,A},{A}} is non empty set
(V,f) . [A,A] is set
Re ((V,f) . (A,A)) is complex real ext-real Element of REAL
V is non empty non trivial right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of V is non empty non trivial set
[: the carrier of V, the carrier of V:] is set
[:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:] is set
f is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like non constant V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF (V,V) (V) (V) (V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
(V,f) is V16() V19([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):]) V20( the carrier of F_Complex) Function-like V30([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF non degenerated-on-left non degenerated-on-right ( VectQuot (V,(LKer f)), VectQuot (V,(LKer f))) ( VectQuot (V,(LKer f))) ( VectQuot (V,(LKer f))) ( VectQuot (V,(LKer f))) ( VectQuot (V,(LKer f))) Element of bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex:]
LKer f is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(LKer f)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of (VectQuot (V,(LKer f))) is non empty set
[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):] is set
[:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(LKer f))):], the carrier of F_Complex:] is set
(V,V,f) is V16() V19([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):]) V20( the carrier of F_Complex) Function-like non constant V30([: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex) additiveFAF additiveSAF homogeneousSAF non degenerated-on-left non degenerated-on-right ( VectQuot (V,(LKer f)), VectQuot (V,(RKer (V,V,f)))) Element of bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex:]
(V,V,f) is V16() V19([: the carrier of V, the carrier of V:]) V20( the carrier of F_Complex) Function-like non constant V30([: the carrier of V, the carrier of V:], the carrier of F_Complex) additiveFAF additiveSAF homogeneousFAF Element of bool [:[: the carrier of V, the carrier of V:], the carrier of F_Complex:]
RKer (V,V,f) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(RKer (V,V,f))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over F_Complex
the carrier of (VectQuot (V,(RKer (V,V,f)))) is non empty set
[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):] is set
[:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex:] is set
bool [:[: the carrier of (VectQuot (V,(LKer f))), the carrier of (VectQuot (V,(RKer (V,V,f)))):], the carrier of F_Complex:] is set