:: HURWITZ semantic presentation

REAL is set
NAT is non empty V24() V25() V26() V40() V45() V46() Element of K19(REAL)
K19(REAL) is set
F_Complex is non empty non degenerated V72() left_add-cancelable right_add-cancelable right_complementable almost_left_invertible strict unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like V150() V151() V152() V153() algebraic-closed doubleLoopStr
the carrier of F_Complex is non empty V12() set
COMPLEX is set
NAT is non empty V24() V25() V26() V40() V45() V46() set
K19(NAT) is V40() set
K19(NAT) is V40() set
K141(NAT) is V39() set
RAT is set
INT is set
K20(COMPLEX,COMPLEX) is set
K19(K20(COMPLEX,COMPLEX)) is set
K20(K20(COMPLEX,COMPLEX),COMPLEX) is set
K19(K20(K20(COMPLEX,COMPLEX),COMPLEX)) is set
K20(REAL,REAL) is set
K19(K20(REAL,REAL)) is set
K20(K20(REAL,REAL),REAL) is set
K19(K20(K20(REAL,REAL),REAL)) is set
K20(RAT,RAT) is set
K19(K20(RAT,RAT)) is set
K20(K20(RAT,RAT),RAT) is set
K19(K20(K20(RAT,RAT),RAT)) is set
K20(INT,INT) is set
K19(K20(INT,INT)) is set
K20(K20(INT,INT),INT) is set
K19(K20(K20(INT,INT),INT)) is set
K20(NAT,NAT) is V40() set
K20(K20(NAT,NAT),NAT) is V40() set
K19(K20(K20(NAT,NAT),NAT)) is V40() set
K280() is set
1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
{} is functional empty V24() V25() V26() V28() V29() V30() complex V32() ext-real non positive non negative V40() V45() V47( {} ) FinSequence-membered integer set
2 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
K20(NAT,REAL) is set
K19(K20(NAT,REAL)) is set
K271(1,NAT) is M8( NAT )
3 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
0 is functional empty V24() V25() V26() V28() V29() V30() complex V32() ext-real non positive non negative V40() V45() V47( {} ) FinSequence-membered integer Element of NAT
Seg 1 is non empty V12() V40() V47(1) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= 1 ) } is set
{1} is non empty V12() V47(1) set
Seg 2 is non empty V40() V47(2) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= 2 ) } is set
{1,2} is non empty set
K204() is Relation-like K20(COMPLEX,COMPLEX) -defined COMPLEX -valued Function-like V18(K20(COMPLEX,COMPLEX), COMPLEX ) Element of K19(K20(K20(COMPLEX,COMPLEX),COMPLEX))
K206() is Relation-like K20(COMPLEX,COMPLEX) -defined COMPLEX -valued Function-like V18(K20(COMPLEX,COMPLEX), COMPLEX ) Element of K19(K20(K20(COMPLEX,COMPLEX),COMPLEX))
1r is complex Element of COMPLEX
0c is functional empty V24() V25() V26() V28() V29() V30() complex V32() ext-real non positive non negative V40() V45() V47( {} ) FinSequence-membered integer 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 V32() ext-real Element of REAL
Im (0. F_Complex) is complex V32() ext-real Element of REAL
<i> is complex Element of COMPLEX
(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 V32() ext-real Element of REAL
Im (1. F_Complex) is complex V32() 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
K20(NAT, the carrier of F_Complex) is V40() set
K19(K20(NAT, the carrier of F_Complex)) is V40() set
Re 0 is complex V32() ext-real Element of REAL
Im 0 is complex V32() ext-real Element of REAL
Re 1r is complex V32() ext-real Element of REAL
Im 1r is complex V32() ext-real Element of REAL
0 *' is complex Element of COMPLEX
(Im 0) * <i> is complex set
(Re 0) - ((Im 0) * <i>) is complex set
f is non empty left_add-cancelable right_add-cancelable right_complementable add-associative right_zeroed V150() V151() V152() V153() addLoopStr
the carrier of f is non empty set
rho is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
dom rho is Element of K19(NAT)
ef is Relation-like NAT -defined Function-like V40() FinSequence-like FinSubsequence-like set
dom ef is Element of K19(NAT)
len ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
Seg ef1 is V40() V47(ef1) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= ef1 ) } is set
rho | (Seg ef1) is Relation-like NAT -defined the carrier of f -valued Function-like FinSubsequence-like Element of K19(K20(NAT, the carrier of f))
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
ef1 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
rho /. (ef1 + 1) is Element of the carrier of f
<*(rho /. (ef1 + 1))*> is Relation-like NAT -defined the carrier of f -valued Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of f
[1,(rho /. (ef1 + 1))] is set
{[1,(rho /. (ef1 + 1))]} is non empty V12() V47(1) set
ef ^ <*(rho /. (ef1 + 1))*> is Relation-like NAT -defined Function-like non empty V40() FinSequence-like FinSubsequence-like set
t is Relation-like NAT -defined Function-like V40() FinSequence-like FinSubsequence-like set
len t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
b9 is set
rng t is set
dom t is Element of K19(NAT)
zz is set
t . zz is set
a1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
rho . zz is set
rho /. zz is Element of the carrier of f
b9 is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
b9 ^ <*(rho /. (ef1 + 1))*> is Relation-like NAT -defined the carrier of f -valued Function-like non empty V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
dom (b9 ^ <*(rho /. (ef1 + 1))*>) is Element of K19(NAT)
len b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
len <*(rho /. (ef1 + 1))*> is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(len b9) + (len <*(rho /. (ef1 + 1))*>) is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
Seg ((len b9) + (len <*(rho /. (ef1 + 1))*>)) is non empty V40() V47((len b9) + (len <*(rho /. (ef1 + 1))*>)) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= (len b9) + (len <*(rho /. (ef1 + 1))*>) ) } is set
Seg (ef1 + 1) is non empty V40() V47(ef1 + 1) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= ef1 + 1 ) } is set
zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
dom b9 is Element of K19(NAT)
rho . zz is set
b9 . zz is set
(b9 ^ <*(rho /. (ef1 + 1))*>) . zz is set
dom b9 is Element of K19(NAT)
Seg (len rho) is V40() V47( len rho) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len rho ) } is set
dom <*(rho /. (ef1 + 1))*> is non empty V12() V47(1) Element of K19(NAT)
(b9 ^ <*(rho /. (ef1 + 1))*>) . zz is set
<*(rho /. (ef1 + 1))*> . 1 is set
rho . zz is set
dom b9 is Element of K19(NAT)
f is non empty left_add-cancelable right_add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty set
0. f is zero Element of the carrier of f
rho is Element of the carrier of f
rho " is Element of the carrier of f
- (rho ") is Element of the carrier of f
- rho is Element of the carrier of f
(- rho) " is Element of the carrier of f
- (- rho) is Element of the carrier of f
(- rho) * (- (rho ")) is Element of the carrier of f
(- rho) * (rho ") is Element of the carrier of f
- ((- rho) * (rho ")) is Element of the carrier of f
rho * (rho ") is Element of the carrier of f
- (rho * (rho ")) is Element of the carrier of f
- (- (rho * (rho "))) is Element of the carrier of f
1_ f is Element of the carrier of f
1. f is Element of the carrier of f
- (1_ f) is Element of the carrier of f
- (- (1_ f)) is Element of the carrier of f
f is non empty non degenerated V72() left_add-cancelable right_add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty V12() set
power f is Relation-like K20( the carrier of f,NAT) -defined the carrier of f -valued Function-like total V18(K20( the carrier of f,NAT), the carrier of f) Element of K19(K20(K20( the carrier of f,NAT), the carrier of f))
K20( the carrier of f,NAT) is V40() set
K20(K20( the carrier of f,NAT), the carrier of f) is V40() set
K19(K20(K20( the carrier of f,NAT), the carrier of f)) is V40() set
1_ f is Element of the carrier of f
1. f is non zero Element of the carrier of f
- (1_ f) is Element of the carrier of f
0. f is zero Element of the carrier of f
rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power f) . ((- (1_ f)),rho) is Element of the carrier of f
(1_ f) * (1_ f) is Element of the carrier of f
(- (1_ f)) * (- (1_ f)) is Element of the carrier of f
ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(power f) . ((- (1_ f)),(ef + 1)) is Element of the carrier of f
(power f) . ((- (1_ f)),ef) is Element of the carrier of f
((power f) . ((- (1_ f)),ef)) * (- (1_ f)) is Element of the carrier of f
(power f) . ((- (1_ f)),ef) is set
(power f) . ((- (1_ f)),(ef + 1)) is set
(power f) . ((- (1_ f)),0) is set
f is non empty unital associative right_unital well-unital left_unital multLoopStr
the carrier of f is non empty set
power f is Relation-like K20( the carrier of f,NAT) -defined the carrier of f -valued Function-like total V18(K20( the carrier of f,NAT), the carrier of f) Element of K19(K20(K20( the carrier of f,NAT), the carrier of f))
K20( the carrier of f,NAT) is V40() set
K20(K20( the carrier of f,NAT), the carrier of f) is V40() set
K19(K20(K20( the carrier of f,NAT), the carrier of f)) is V40() set
rho is Element of the carrier of f
ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power f) . (rho,ef) is Element of the carrier of f
ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power f) . (rho,ef1) is Element of the carrier of f
((power f) . (rho,ef)) * ((power f) . (rho,ef1)) is Element of the carrier of f
ef + ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power f) . (rho,(ef + ef1)) is Element of the carrier of f
t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
t + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(power f) . (rho,(t + 1)) is Element of the carrier of f
((power f) . (rho,ef)) * ((power f) . (rho,(t + 1))) is Element of the carrier of f
(power f) . (rho,t) is Element of the carrier of f
((power f) . (rho,t)) * rho is Element of the carrier of f
((power f) . (rho,ef)) * (((power f) . (rho,t)) * rho) is Element of the carrier of f
((power f) . (rho,ef)) * ((power f) . (rho,t)) is Element of the carrier of f
(((power f) . (rho,ef)) * ((power f) . (rho,t))) * rho is Element of the carrier of f
ef + t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(ef + t) + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(power f) . (rho,((ef + t) + 1)) is Element of the carrier of f
ef + (t + 1) is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(power f) . (rho,(ef + (t + 1))) is Element of the carrier of f
b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power f) . (rho,b9) is Element of the carrier of f
((power f) . (rho,ef)) * ((power f) . (rho,b9)) is Element of the carrier of f
ef + b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power f) . (rho,(ef + b9)) is Element of the carrier of f
1_ f is Element of the carrier of f
1. f is Element of the carrier of f
(power f) . (rho,0) is Element of the carrier of f
((power f) . (rho,ef)) * ((power f) . (rho,0)) is Element of the carrier of f
((power f) . (rho,ef)) * (1. f) is Element of the carrier of f
ef + 0 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power f) . (rho,(ef + 0)) is Element of the carrier of f
t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power f) . (rho,t) is Element of the carrier of f
((power f) . (rho,ef)) * ((power f) . (rho,t)) is Element of the carrier of f
ef + t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power f) . (rho,(ef + t)) is Element of the carrier of f
Im (1_ F_Complex) is complex V32() ext-real Element of REAL
- (1_ F_Complex) is complex Element of the carrier of F_Complex
Im (- (1_ F_Complex)) is complex V32() ext-real Element of REAL
- 1r is complex Element of COMPLEX
- 0 is functional empty V24() V25() V26() V28() V29() V30() complex V32() ext-real non positive non negative V40() V45() V47( {} ) FinSequence-membered integer set
f is non empty left_add-cancelable right_add-cancelable right_complementable unital right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty set
power f is Relation-like K20( the carrier of f,NAT) -defined the carrier of f -valued Function-like total V18(K20( the carrier of f,NAT), the carrier of f) Element of K19(K20(K20( the carrier of f,NAT), the carrier of f))
K20( the carrier of f,NAT) is V40() set
K20(K20( the carrier of f,NAT), the carrier of f) is V40() set
K19(K20(K20( the carrier of f,NAT), the carrier of f)) is V40() set
1_ f is Element of the carrier of f
1. f is Element of the carrier of f
- (1_ f) is Element of the carrier of f
rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
2 * rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power f) . ((- (1_ f)),(2 * rho)) is Element of the carrier of f
(2 * rho) + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(power f) . ((- (1_ f)),((2 * rho) + 1)) is Element of the carrier of f
ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
2 * ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power f) . ((- (1_ f)),(2 * ef)) is Element of the carrier of f
(2 * ef) + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(power f) . ((- (1_ f)),((2 * ef) + 1)) is Element of the carrier of f
ef + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
2 * (ef + 1) is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(power f) . ((- (1_ f)),(2 * (ef + 1))) is Element of the carrier of f
((2 * ef) + 1) + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(power f) . ((- (1_ f)),(((2 * ef) + 1) + 1)) is Element of the carrier of f
((power f) . ((- (1_ f)),((2 * ef) + 1))) * (- (1_ f)) is Element of the carrier of f
(1_ f) * (- (1_ f)) is Element of the carrier of f
- ((1_ f) * (- (1_ f))) is Element of the carrier of f
- (- (1_ f)) is Element of the carrier of f
(2 * (ef + 1)) + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(power f) . ((- (1_ f)),((2 * (ef + 1)) + 1)) is Element of the carrier of f
((power f) . ((- (1_ f)),(2 * (ef + 1)))) * (- (1_ f)) is Element of the carrier of f
2 * 0 is functional empty V24() V25() V26() V28() V29() V30() complex V32() ext-real non positive non negative V40() V45() V47( {} ) FinSequence-membered integer Element of NAT
(2 * 0) + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(power f) . ((- (1_ f)),((2 * 0) + 1)) is Element of the carrier of f
(power f) . ((- (1_ f)),0) is Element of the carrier of f
((power f) . ((- (1_ f)),0)) * (- (1_ f)) is Element of the carrier of f
(power f) . ((- (1_ f)),(2 * 0)) is Element of the carrier of f
power F_Complex is Relation-like K20( the carrier of F_Complex,NAT) -defined the carrier of F_Complex -valued Function-like total V18(K20( the carrier of F_Complex,NAT), the carrier of F_Complex) Element of K19(K20(K20( the carrier of F_Complex,NAT), the carrier of F_Complex))
K20( the carrier of F_Complex,NAT) is V40() set
K20(K20( the carrier of F_Complex,NAT), the carrier of F_Complex) is V40() set
K19(K20(K20( the carrier of F_Complex,NAT), the carrier of F_Complex)) is V40() set
f is complex Element of the carrier of F_Complex
f *' is complex Element of the carrier of F_Complex
Re f is complex V32() ext-real Element of REAL
Im f is complex V32() ext-real Element of REAL
(Im f) * <i> is complex set
(Re f) - ((Im f) * <i>) is complex set
rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power F_Complex) . (f,rho) is complex Element of the carrier of F_Complex
((power F_Complex) . (f,rho)) *' is complex Element of the carrier of F_Complex
Re ((power F_Complex) . (f,rho)) is complex V32() ext-real Element of REAL
Im ((power F_Complex) . (f,rho)) is complex V32() ext-real Element of REAL
(Im ((power F_Complex) . (f,rho))) * <i> is complex set
(Re ((power F_Complex) . (f,rho))) - ((Im ((power F_Complex) . (f,rho))) * <i>) is complex set
(power F_Complex) . ((f *'),rho) is complex Element of the carrier of F_Complex
ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(power F_Complex) . (f,(ef + 1)) is complex Element of the carrier of F_Complex
((power F_Complex) . (f,(ef + 1))) *' is complex Element of the carrier of F_Complex
Re ((power F_Complex) . (f,(ef + 1))) is complex V32() ext-real Element of REAL
Im ((power F_Complex) . (f,(ef + 1))) is complex V32() ext-real Element of REAL
(Im ((power F_Complex) . (f,(ef + 1)))) * <i> is complex set
(Re ((power F_Complex) . (f,(ef + 1)))) - ((Im ((power F_Complex) . (f,(ef + 1)))) * <i>) is complex set
(power F_Complex) . (f,ef) is complex Element of the carrier of F_Complex
((power F_Complex) . (f,ef)) * f is complex Element of the carrier of F_Complex
K182(((power F_Complex) . (f,ef)),f) is complex Element of COMPLEX
(((power F_Complex) . (f,ef)) * f) *' is complex Element of the carrier of F_Complex
Re (((power F_Complex) . (f,ef)) * f) is complex V32() ext-real Element of REAL
Im (((power F_Complex) . (f,ef)) * f) is complex V32() ext-real Element of REAL
(Im (((power F_Complex) . (f,ef)) * f)) * <i> is complex set
(Re (((power F_Complex) . (f,ef)) * f)) - ((Im (((power F_Complex) . (f,ef)) * f)) * <i>) is complex set
(power F_Complex) . ((f *'),ef) is complex Element of the carrier of F_Complex
((power F_Complex) . ((f *'),ef)) * (f *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((f *'),ef)),(f *')) is complex Element of COMPLEX
(power F_Complex) . ((f *'),(ef + 1)) is complex Element of the carrier of F_Complex
ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power F_Complex) . (f,ef1) is complex Element of the carrier of F_Complex
((power F_Complex) . (f,ef1)) *' is complex Element of the carrier of F_Complex
Re ((power F_Complex) . (f,ef1)) is complex V32() ext-real Element of REAL
Im ((power F_Complex) . (f,ef1)) is complex V32() ext-real Element of REAL
(Im ((power F_Complex) . (f,ef1))) * <i> is complex set
(Re ((power F_Complex) . (f,ef1))) - ((Im ((power F_Complex) . (f,ef1))) * <i>) is complex set
(power F_Complex) . ((f *'),ef1) is complex Element of the carrier of F_Complex
(power F_Complex) . (f,0) is complex Element of the carrier of F_Complex
((power F_Complex) . (f,0)) *' is complex Element of the carrier of F_Complex
Re ((power F_Complex) . (f,0)) is complex V32() ext-real Element of REAL
Im ((power F_Complex) . (f,0)) is complex V32() ext-real Element of REAL
(Im ((power F_Complex) . (f,0))) * <i> is complex set
(Re ((power F_Complex) . (f,0))) - ((Im ((power F_Complex) . (f,0))) * <i>) is complex set
(1_ F_Complex) *' is complex Element of the carrier of F_Complex
Re (1_ F_Complex) is complex V32() 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
(power F_Complex) . ((f *'),0) is complex Element of the carrier of F_Complex
ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power F_Complex) . (f,ef) is complex Element of the carrier of F_Complex
((power F_Complex) . (f,ef)) *' is complex Element of the carrier of F_Complex
Re ((power F_Complex) . (f,ef)) is complex V32() ext-real Element of REAL
Im ((power F_Complex) . (f,ef)) is complex V32() ext-real Element of REAL
(Im ((power F_Complex) . (f,ef))) * <i> is complex set
(Re ((power F_Complex) . (f,ef))) - ((Im ((power F_Complex) . (f,ef))) * <i>) is complex set
(power F_Complex) . ((f *'),ef) is complex Element of the carrier of F_Complex
rho is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
len rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
len f is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
dom rho is Element of K19(NAT)
Sum rho is complex Element of the carrier of F_Complex
Sum f is complex Element of the carrier of F_Complex
(Sum f) *' is complex Element of the carrier of F_Complex
Re (Sum f) is complex V32() ext-real Element of REAL
Im (Sum f) is complex V32() ext-real Element of REAL
(Im (Sum f)) * <i> is complex set
(Re (Sum f)) - ((Im (Sum f)) * <i>) is complex set
ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef1 is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
len ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
t is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
len t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
dom t is Element of K19(NAT)
Seg ef is V40() V47(ef) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= ef ) } is set
t | (Seg ef) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like FinSubsequence-like Element of K19(K20(NAT, the carrier of F_Complex))
zz is Relation-like NAT -defined Function-like V40() FinSequence-like FinSubsequence-like set
a1 is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
t /. (ef + 1) is complex Element of the carrier of F_Complex
<*(t /. (ef + 1))*> is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
[1,(t /. (ef + 1))] is set
{[1,(t /. (ef + 1))]} is non empty V12() V47(1) set
a1 ^ <*(t /. (ef + 1))*> is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
ef1 | (Seg ef) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like FinSubsequence-like Element of K19(K20(NAT, the carrier of F_Complex))
a19 is Relation-like NAT -defined Function-like V40() FinSequence-like FinSubsequence-like set
b19 is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
len b19 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
len a1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
dom a1 is Element of K19(NAT)
Seg (len b19) is V40() V47( len b19) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len b19 ) } is set
dom b19 is Element of K19(NAT)
ef1 /. (ef + 1) is complex Element of the carrier of F_Complex
<*(ef1 /. (ef + 1))*> is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
[1,(ef1 /. (ef + 1))] is set
{[1,(ef1 /. (ef + 1))]} is non empty V12() V47(1) set
b19 ^ <*(ef1 /. (ef + 1))*> is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
Seg (len ef1) is V40() V47( len ef1) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len ef1 ) } is set
dom ef1 is Element of K19(NAT)
z is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef1 /. z is complex Element of the carrier of F_Complex
ef1 . z is set
b19 . z is set
b19 /. z is complex Element of the carrier of F_Complex
a1 /. z is complex Element of the carrier of F_Complex
a1 . z is set
t . z is set
t /. z is complex Element of the carrier of F_Complex
(b19 /. z) *' is complex Element of the carrier of F_Complex
Re (b19 /. z) is complex V32() ext-real Element of REAL
Im (b19 /. z) is complex V32() ext-real Element of REAL
(Im (b19 /. z)) * <i> is complex set
(Re (b19 /. z)) - ((Im (b19 /. z)) * <i>) is complex set
Sum ef1 is complex Element of the carrier of F_Complex
(Sum ef1) *' is complex Element of the carrier of F_Complex
Re (Sum ef1) is complex V32() ext-real Element of REAL
Im (Sum ef1) is complex V32() ext-real Element of REAL
(Im (Sum ef1)) * <i> is complex set
(Re (Sum ef1)) - ((Im (Sum ef1)) * <i>) is complex set
Sum b19 is complex Element of the carrier of F_Complex
Sum <*(ef1 /. (ef + 1))*> is complex Element of the carrier of F_Complex
(Sum b19) + (Sum <*(ef1 /. (ef + 1))*>) is complex Element of the carrier of F_Complex
K180((Sum b19),(Sum <*(ef1 /. (ef + 1))*>)) is complex Element of COMPLEX
((Sum b19) + (Sum <*(ef1 /. (ef + 1))*>)) *' is complex Element of the carrier of F_Complex
Re ((Sum b19) + (Sum <*(ef1 /. (ef + 1))*>)) is complex V32() ext-real Element of REAL
Im ((Sum b19) + (Sum <*(ef1 /. (ef + 1))*>)) is complex V32() ext-real Element of REAL
(Im ((Sum b19) + (Sum <*(ef1 /. (ef + 1))*>))) * <i> is complex set
(Re ((Sum b19) + (Sum <*(ef1 /. (ef + 1))*>))) - ((Im ((Sum b19) + (Sum <*(ef1 /. (ef + 1))*>))) * <i>) is complex set
(Sum b19) *' is complex Element of the carrier of F_Complex
Re (Sum b19) is complex V32() ext-real Element of REAL
Im (Sum b19) is complex V32() ext-real Element of REAL
(Im (Sum b19)) * <i> is complex set
(Re (Sum b19)) - ((Im (Sum b19)) * <i>) is complex set
(Sum <*(ef1 /. (ef + 1))*>) *' is complex Element of the carrier of F_Complex
Re (Sum <*(ef1 /. (ef + 1))*>) is complex V32() ext-real Element of REAL
Im (Sum <*(ef1 /. (ef + 1))*>) is complex V32() ext-real Element of REAL
(Im (Sum <*(ef1 /. (ef + 1))*>)) * <i> is complex set
(Re (Sum <*(ef1 /. (ef + 1))*>)) - ((Im (Sum <*(ef1 /. (ef + 1))*>)) * <i>) is complex set
((Sum b19) *') + ((Sum <*(ef1 /. (ef + 1))*>) *') is complex Element of the carrier of F_Complex
K180(((Sum b19) *'),((Sum <*(ef1 /. (ef + 1))*>) *')) is complex Element of COMPLEX
Sum a1 is complex Element of the carrier of F_Complex
(Sum a1) + ((Sum <*(ef1 /. (ef + 1))*>) *') is complex Element of the carrier of F_Complex
K180((Sum a1),((Sum <*(ef1 /. (ef + 1))*>) *')) is complex Element of COMPLEX
(ef1 /. (ef + 1)) *' is complex Element of the carrier of F_Complex
Re (ef1 /. (ef + 1)) is complex V32() ext-real Element of REAL
Im (ef1 /. (ef + 1)) is complex V32() ext-real Element of REAL
(Im (ef1 /. (ef + 1))) * <i> is complex set
(Re (ef1 /. (ef + 1))) - ((Im (ef1 /. (ef + 1))) * <i>) is complex set
(Sum a1) + ((ef1 /. (ef + 1)) *') is complex Element of the carrier of F_Complex
K180((Sum a1),((ef1 /. (ef + 1)) *')) is complex Element of COMPLEX
(Sum a1) + (t /. (ef + 1)) is complex Element of the carrier of F_Complex
K180((Sum a1),(t /. (ef + 1))) is complex Element of COMPLEX
Sum <*(t /. (ef + 1))*> is complex Element of the carrier of F_Complex
(Sum a1) + (Sum <*(t /. (ef + 1))*>) is complex Element of the carrier of F_Complex
K180((Sum a1),(Sum <*(t /. (ef + 1))*>)) is complex Element of COMPLEX
Sum t is complex Element of the carrier of F_Complex
t is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
len t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef1 is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
len ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
dom t is Element of K19(NAT)
Sum t is complex Element of the carrier of F_Complex
Sum ef1 is complex Element of the carrier of F_Complex
(Sum ef1) *' is complex Element of the carrier of F_Complex
Re (Sum ef1) is complex V32() ext-real Element of REAL
Im (Sum ef1) is complex V32() ext-real Element of REAL
(Im (Sum ef1)) * <i> is complex set
(Re (Sum ef1)) - ((Im (Sum ef1)) * <i>) is complex set
ef is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
len ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef1 is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
len ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
dom ef1 is Element of K19(NAT)
<*> the carrier of F_Complex is Relation-like NAT -defined the carrier of F_Complex -valued Function-like functional empty V24() V25() V26() V28() V29() V30() complex V32() ext-real non positive non negative V40() V45() V47( {} ) FinSequence-like FinSubsequence-like FinSequence-membered integer Function-yielding V54() FinSequence of the carrier of F_Complex
Sum ef is complex Element of the carrier of F_Complex
Sum ef1 is complex Element of the carrier of F_Complex
(Sum ef) *' is complex Element of the carrier of F_Complex
Re (Sum ef) is complex V32() ext-real Element of REAL
Im (Sum ef) is complex V32() ext-real Element of REAL
(Im (Sum ef)) * <i> is complex set
(Re (Sum ef)) - ((Im (Sum ef)) * <i>) is complex set
ef1 is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
len ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
len ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
dom ef1 is Element of K19(NAT)
Sum ef1 is complex Element of the carrier of F_Complex
Sum ef is complex Element of the carrier of F_Complex
(Sum ef) *' is complex Element of the carrier of F_Complex
Re (Sum ef) is complex V32() ext-real Element of REAL
Im (Sum ef) is complex V32() ext-real Element of REAL
(Im (Sum ef)) * <i> is complex set
(Re (Sum ef)) - ((Im (Sum ef)) * <i>) is complex set
f is non empty left_add-cancelable right_add-cancelable right_complementable Abelian add-associative right_zeroed V150() V151() V152() V153() addLoopStr
the carrier of f is non empty set
rho is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
dom rho is Element of K19(NAT)
Sum rho is Element of the carrier of f
Sum ef is Element of the carrier of f
- (Sum ef) is Element of the carrier of f
ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
t is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef1 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
b9 is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
dom t is Element of K19(NAT)
Seg ef1 is V40() V47(ef1) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= ef1 ) } is set
t | (Seg ef1) is Relation-like NAT -defined the carrier of f -valued Function-like FinSubsequence-like Element of K19(K20(NAT, the carrier of f))
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
b9 | (Seg ef1) is Relation-like NAT -defined the carrier of f -valued Function-like FinSubsequence-like Element of K19(K20(NAT, the carrier of f))
b1 is Relation-like NAT -defined Function-like V40() FinSequence-like FinSubsequence-like set
a19 is Relation-like NAT -defined Function-like V40() FinSequence-like FinSubsequence-like set
b19 is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len b19 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
z is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len z is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
dom b19 is Element of K19(NAT)
Seg (len z) is V40() V47( len z) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len z ) } is set
dom z is Element of K19(NAT)
t /. (ef1 + 1) is Element of the carrier of f
<*(t /. (ef1 + 1))*> is Relation-like NAT -defined the carrier of f -valued Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of f
[1,(t /. (ef1 + 1))] is set
{[1,(t /. (ef1 + 1))]} is non empty V12() V47(1) set
b19 ^ <*(t /. (ef1 + 1))*> is Relation-like NAT -defined the carrier of f -valued Function-like non empty V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
b9 /. (ef1 + 1) is Element of the carrier of f
<*(b9 /. (ef1 + 1))*> is Relation-like NAT -defined the carrier of f -valued Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of f
[1,(b9 /. (ef1 + 1))] is set
{[1,(b9 /. (ef1 + 1))]} is non empty V12() V47(1) set
z ^ <*(b9 /. (ef1 + 1))*> is Relation-like NAT -defined the carrier of f -valued Function-like non empty V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
g1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
dom b9 is Element of K19(NAT)
b9 /. g1 is Element of the carrier of f
b9 . g1 is set
z . g1 is set
z /. g1 is Element of the carrier of f
b19 /. g1 is Element of the carrier of f
b19 . g1 is set
t . g1 is set
t /. g1 is Element of the carrier of f
- (z /. g1) is Element of the carrier of f
Sum t is Element of the carrier of f
Sum b19 is Element of the carrier of f
Sum <*(t /. (ef1 + 1))*> is Element of the carrier of f
(Sum b19) + (Sum <*(t /. (ef1 + 1))*>) is Element of the carrier of f
Sum z is Element of the carrier of f
- (Sum z) is Element of the carrier of f
(- (Sum z)) + (Sum <*(t /. (ef1 + 1))*>) is Element of the carrier of f
(- (Sum z)) + (t /. (ef1 + 1)) is Element of the carrier of f
- (b9 /. (ef1 + 1)) is Element of the carrier of f
(- (Sum z)) + (- (b9 /. (ef1 + 1))) is Element of the carrier of f
(Sum z) + (b9 /. (ef1 + 1)) is Element of the carrier of f
- ((Sum z) + (b9 /. (ef1 + 1))) is Element of the carrier of f
Sum <*(b9 /. (ef1 + 1))*> is Element of the carrier of f
(Sum z) + (Sum <*(b9 /. (ef1 + 1))*>) is Element of the carrier of f
- ((Sum z) + (Sum <*(b9 /. (ef1 + 1))*>)) is Element of the carrier of f
Sum b9 is Element of the carrier of f
- (Sum b9) is Element of the carrier of f
t is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
b9 is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
dom t is Element of K19(NAT)
Sum t is Element of the carrier of f
Sum b9 is Element of the carrier of f
- (Sum b9) is Element of the carrier of f
ef1 is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
t is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
dom ef1 is Element of K19(NAT)
<*> the carrier of f is Relation-like NAT -defined the carrier of f -valued Function-like functional empty V24() V25() V26() V28() V29() V30() complex V32() ext-real non positive non negative V40() V45() V47( {} ) FinSequence-like FinSubsequence-like FinSequence-membered integer Function-yielding V54() FinSequence of the carrier of f
Sum ef1 is Element of the carrier of f
0. f is zero Element of the carrier of f
- (0. f) is Element of the carrier of f
Sum t is Element of the carrier of f
- (Sum t) is Element of the carrier of f
ef1 is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
t is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
dom ef1 is Element of K19(NAT)
Sum ef1 is Element of the carrier of f
Sum t is Element of the carrier of f
- (Sum t) is Element of the carrier of f
f is non empty left_add-cancelable right_add-cancelable right_complementable right-distributive left-distributive distributive add-associative right_zeroed V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty set
rho is Element of the carrier of f
ef is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
Sum ef is Element of the carrier of f
rho * (Sum ef) is Element of the carrier of f
rho * ef is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
Sum (rho * ef) is Element of the carrier of f
len ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
b9 is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
Seg ef1 is V40() V47(ef1) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= ef1 ) } is set
b9 | (Seg ef1) is Relation-like NAT -defined the carrier of f -valued Function-like FinSubsequence-like Element of K19(K20(NAT, the carrier of f))
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
len b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef1 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
a1 is Relation-like NAT -defined Function-like V40() FinSequence-like FinSubsequence-like set
b1 is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len b1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
b9 /. (ef1 + 1) is Element of the carrier of f
<*(b9 /. (ef1 + 1))*> is Relation-like NAT -defined the carrier of f -valued Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of f
[1,(b9 /. (ef1 + 1))] is set
{[1,(b9 /. (ef1 + 1))]} is non empty V12() V47(1) set
b1 ^ <*(b9 /. (ef1 + 1))*> is Relation-like NAT -defined the carrier of f -valued Function-like non empty V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
t is Element of the carrier of f
Sum b9 is Element of the carrier of f
t * (Sum b9) is Element of the carrier of f
Sum (b1 ^ <*(b9 /. (ef1 + 1))*>) is Element of the carrier of f
t * (Sum (b1 ^ <*(b9 /. (ef1 + 1))*>)) is Element of the carrier of f
Sum b1 is Element of the carrier of f
Sum <*(b9 /. (ef1 + 1))*> is Element of the carrier of f
(Sum b1) + (Sum <*(b9 /. (ef1 + 1))*>) is Element of the carrier of f
t * ((Sum b1) + (Sum <*(b9 /. (ef1 + 1))*>)) is Element of the carrier of f
t * (Sum b1) is Element of the carrier of f
t * (Sum <*(b9 /. (ef1 + 1))*>) is Element of the carrier of f
(t * (Sum b1)) + (t * (Sum <*(b9 /. (ef1 + 1))*>)) is Element of the carrier of f
t * b1 is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
Sum (t * b1) is Element of the carrier of f
(Sum (t * b1)) + (t * (Sum <*(b9 /. (ef1 + 1))*>)) is Element of the carrier of f
t * (b9 /. (ef1 + 1)) is Element of the carrier of f
(Sum (t * b1)) + (t * (b9 /. (ef1 + 1))) is Element of the carrier of f
<*(t * (b9 /. (ef1 + 1)))*> is Relation-like NAT -defined the carrier of f -valued Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of f
[1,(t * (b9 /. (ef1 + 1)))] is set
{[1,(t * (b9 /. (ef1 + 1)))]} is non empty V12() V47(1) set
Sum <*(t * (b9 /. (ef1 + 1)))*> is Element of the carrier of f
(Sum (t * b1)) + (Sum <*(t * (b9 /. (ef1 + 1)))*>) is Element of the carrier of f
t * <*(b9 /. (ef1 + 1))*> is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
Sum (t * <*(b9 /. (ef1 + 1))*>) is Element of the carrier of f
(Sum (t * b1)) + (Sum (t * <*(b9 /. (ef1 + 1))*>)) is Element of the carrier of f
(t * b1) ^ (t * <*(b9 /. (ef1 + 1))*>) is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
Sum ((t * b1) ^ (t * <*(b9 /. (ef1 + 1))*>)) is Element of the carrier of f
t * b9 is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
Sum (t * b9) is Element of the carrier of f
b9 is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
t is Element of the carrier of f
Sum b9 is Element of the carrier of f
t * (Sum b9) is Element of the carrier of f
t * b9 is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
Sum (t * b9) is Element of the carrier of f
t is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef1 is Element of the carrier of f
ef1 * t is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len (ef1 * t) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
Seg (len (ef1 * t)) is V40() V47( len (ef1 * t)) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len (ef1 * t) ) } is set
dom (ef1 * t) is Element of K19(NAT)
dom t is Element of K19(NAT)
Seg (len t) is V40() V47( len t) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len t ) } is set
<*> the carrier of f is Relation-like NAT -defined the carrier of f -valued Function-like functional empty V24() V25() V26() V28() V29() V30() complex V32() ext-real non positive non negative V40() V45() V47( {} ) FinSequence-like FinSubsequence-like FinSequence-membered integer Function-yielding V54() FinSequence of the carrier of f
Sum t is Element of the carrier of f
0. f is zero Element of the carrier of f
ef1 * (Sum t) is Element of the carrier of f
Sum (ef1 * t) is Element of the carrier of f
t is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef1 is Element of the carrier of f
Sum t is Element of the carrier of f
ef1 * (Sum t) is Element of the carrier of f
ef1 * t is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
Sum (ef1 * t) is Element of the carrier of f
ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
f is non empty left_add-cancelable right_add-cancelable right_complementable add-associative right_zeroed V150() V151() V152() V153() addLoopStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- (- rho) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
len rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
(- (- rho)) . ef is Element of the carrier of f
(- rho) . ef is Element of the carrier of f
- ((- rho) . ef) is Element of the carrier of f
rho . ef is Element of the carrier of f
- (rho . ef) is Element of the carrier of f
- (- (rho . ef)) is Element of the carrier of f
len (- rho) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
len (- (- rho)) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
f is non empty left_add-cancelable right_add-cancelable right_complementable add-associative right_zeroed V150() V151() V152() V153() addLoopStr
the carrier of f is non empty set
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
- (0_. f) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
len (0_. f) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
(0_. f) . ef1 is Element of the carrier of f
(- (0_. f)) . ef1 is Element of the carrier of f
len (- (0_. f)) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
f is non empty left_add-cancelable right_add-cancelable right_complementable right-distributive left-distributive distributive add-associative right_zeroed V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
Polynom-Ring f is non empty left_add-cancelable right_add-cancelable right_complementable strict add-associative right_zeroed V150() V151() V152() V153() doubleLoopStr
the carrier of (Polynom-Ring f) is non empty set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef is Element of the carrier of (Polynom-Ring f)
- ef is Element of the carrier of (Polynom-Ring f)
ef1 is Element of the carrier of (Polynom-Ring f)
t is Element of the carrier of (Polynom-Ring f)
ef + t is Element of the carrier of (Polynom-Ring f)
rho - rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho + (- rho) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
0. (Polynom-Ring f) is zero Element of the carrier of (Polynom-Ring f)
- t is Element of the carrier of (Polynom-Ring f)
f is non empty left_add-cancelable right_add-cancelable right_complementable add-associative right_zeroed V150() V151() V152() V153() addLoopStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- (- rho) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
f is non empty left_add-cancelable right_add-cancelable right_complementable right-distributive left-distributive distributive Abelian add-associative right_zeroed V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho + ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- (rho + ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(- rho) + (- ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
Polynom-Ring f is non empty left_add-cancelable right_add-cancelable right_complementable strict right-distributive left-distributive distributive Abelian add-associative right_zeroed V150() V151() V152() V153() doubleLoopStr
the carrier of (Polynom-Ring f) is non empty set
ef1 is Element of the carrier of (Polynom-Ring f)
t is Element of the carrier of (Polynom-Ring f)
ef1 + t is Element of the carrier of (Polynom-Ring f)
- (ef1 + t) is Element of the carrier of (Polynom-Ring f)
- ef1 is Element of the carrier of (Polynom-Ring f)
- t is Element of the carrier of (Polynom-Ring f)
(- ef1) + (- t) is Element of the carrier of (Polynom-Ring f)
f is non empty left_add-cancelable right_add-cancelable right_complementable right-distributive left-distributive distributive Abelian add-associative right_zeroed V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho *' ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- (rho *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(- rho) *' ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho *' (- ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
Polynom-Ring f is non empty left_add-cancelable right_add-cancelable right_complementable strict right-distributive left-distributive distributive Abelian add-associative right_zeroed V150() V151() V152() V153() doubleLoopStr
the carrier of (Polynom-Ring f) is non empty set
ef1 is Element of the carrier of (Polynom-Ring f)
t is Element of the carrier of (Polynom-Ring f)
ef1 * t is Element of the carrier of (Polynom-Ring f)
- (ef1 * t) is Element of the carrier of (Polynom-Ring f)
- ef1 is Element of the carrier of (Polynom-Ring f)
(- ef1) * t is Element of the carrier of (Polynom-Ring f)
- t is Element of the carrier of (Polynom-Ring f)
ef1 * (- t) is Element of the carrier of (Polynom-Ring f)
f is non empty left_add-cancelable right_add-cancelable right_complementable right-distributive left-distributive distributive add-associative right_zeroed V150() V151() V152() V153() doubleLoopStr
Polynom-Ring f is non empty left_add-cancelable right_add-cancelable right_complementable strict add-associative right_zeroed V150() V151() V152() V153() doubleLoopStr
the carrier of (Polynom-Ring f) is non empty set
the carrier of f is non empty set
rho is Relation-like NAT -defined the carrier of (Polynom-Ring f) -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring f)
len rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
Seg (len rho) is V40() V47( len rho) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len rho ) } is set
ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
rho . ef1 is set
rho /. ef1 is Element of the carrier of (Polynom-Ring f)
t is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
t . ef is Element of the carrier of f
dom rho is Element of K19(NAT)
ef1 is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
dom ef1 is Element of K19(NAT)
len ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
rho . t is set
ef1 . t is set
ef1 is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
dom ef1 is Element of K19(NAT)
t is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
dom t is Element of K19(NAT)
Seg (len rho) is V40() V47( len rho) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len rho ) } is set
b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
rho . b9 is set
ef1 . b9 is set
t . b9 is set
zz is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
zz . ef is Element of the carrier of f
a1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
a1 . ef is Element of the carrier of f
f is non empty left_add-cancelable right_add-cancelable right_complementable right-distributive left-distributive distributive add-associative right_zeroed V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
Polynom-Ring f is non empty left_add-cancelable right_add-cancelable right_complementable strict add-associative right_zeroed V150() V151() V152() V153() doubleLoopStr
the carrier of (Polynom-Ring f) is non empty set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef is Relation-like NAT -defined the carrier of (Polynom-Ring f) -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring f)
Sum ef is Element of the carrier of (Polynom-Ring f)
ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
rho . ef1 is Element of the carrier of f
(f,ef,ef1) is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
Sum (f,ef,ef1) is Element of the carrier of f
len ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
b9 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
zz is Relation-like NAT -defined the carrier of (Polynom-Ring f) -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring f)
Sum zz is Element of the carrier of (Polynom-Ring f)
len zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
t + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
zz /. (t + 1) is Element of the carrier of (Polynom-Ring f)
Seg t is V40() V47(t) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= t ) } is set
zz | (Seg t) is Relation-like NAT -defined the carrier of (Polynom-Ring f) -valued Function-like FinSubsequence-like Element of K19(K20(NAT, the carrier of (Polynom-Ring f)))
K20(NAT, the carrier of (Polynom-Ring f)) is V40() set
K19(K20(NAT, the carrier of (Polynom-Ring f))) is V40() set
b19 is Relation-like NAT -defined Function-like V40() FinSequence-like FinSubsequence-like set
z is Relation-like NAT -defined the carrier of (Polynom-Ring f) -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring f)
len z is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
b1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(f,z,b1) is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
dom (f,z,b1) is Element of K19(NAT)
len (f,z,b1) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
Seg (len (f,z,b1)) is V40() V47( len (f,z,b1)) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len (f,z,b1) ) } is set
Seg (len z) is V40() V47( len z) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len z ) } is set
dom z is Element of K19(NAT)
g1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
(f,zz,b1) is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
dom (f,zz,b1) is Element of K19(NAT)
a1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
a1 . b1 is Element of the carrier of f
<*(a1 . b1)*> is Relation-like NAT -defined the carrier of f -valued Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of f
[1,(a1 . b1)] is set
{[1,(a1 . b1)]} is non empty V12() V47(1) set
(f,z,b1) ^ <*(a1 . b1)*> is Relation-like NAT -defined the carrier of f -valued Function-like non empty V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
((f,z,b1) ^ <*(a1 . b1)*>) . g1 is set
(f,z,b1) . g1 is set
zz . g1 is set
(f,zz,b1) . g1 is set
z . g1 is set
s1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
s1 . b1 is Element of the carrier of f
i is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
i . b1 is Element of the carrier of f
len (f,zz,b1) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
Seg (len (f,zz,b1)) is V40() V47( len (f,zz,b1)) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len (f,zz,b1) ) } is set
Seg (len zz) is V40() V47( len zz) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len zz ) } is set
a1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
a1 . b1 is Element of the carrier of f
<*(a1 . b1)*> is Relation-like NAT -defined the carrier of f -valued Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of f
[1,(a1 . b1)] is set
{[1,(a1 . b1)]} is non empty V12() V47(1) set
dom <*(a1 . b1)*> is non empty V12() V47(1) Element of K19(NAT)
dom zz is Element of K19(NAT)
zz . g1 is set
(f,zz,b1) . g1 is set
(f,z,b1) ^ <*(a1 . b1)*> is Relation-like NAT -defined the carrier of f -valued Function-like non empty V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
((f,z,b1) ^ <*(a1 . b1)*>) . g1 is set
<*(a1 . b1)*> . 1 is set
s1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
s1 . b1 is Element of the carrier of f
a1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
a1 . b1 is Element of the carrier of f
<*(a1 . b1)*> is Relation-like NAT -defined the carrier of f -valued Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of f
[1,(a1 . b1)] is set
{[1,(a1 . b1)]} is non empty V12() V47(1) set
(f,z,b1) ^ <*(a1 . b1)*> is Relation-like NAT -defined the carrier of f -valued Function-like non empty V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
a1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
a1 . b1 is Element of the carrier of f
<*(a1 . b1)*> is Relation-like NAT -defined the carrier of f -valued Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of f
[1,(a1 . b1)] is set
{[1,(a1 . b1)]} is non empty V12() V47(1) set
(f,z,b1) ^ <*(a1 . b1)*> is Relation-like NAT -defined the carrier of f -valued Function-like non empty V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len ((f,z,b1) ^ <*(a1 . b1)*>) is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
len <*(a1 . b1)*> is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(len (f,z,b1)) + (len <*(a1 . b1)*>) is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(len (f,z,b1)) + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
len (f,zz,b1) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
Seg (len ((f,z,b1) ^ <*(a1 . b1)*>)) is non empty V40() V47( len ((f,z,b1) ^ <*(a1 . b1)*>)) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len ((f,z,b1) ^ <*(a1 . b1)*>) ) } is set
dom ((f,z,b1) ^ <*(a1 . b1)*>) is Element of K19(NAT)
Sum z is Element of the carrier of (Polynom-Ring f)
<*(zz /. (t + 1))*> is Relation-like NAT -defined the carrier of (Polynom-Ring f) -valued Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring f)
[1,(zz /. (t + 1))] is set
{[1,(zz /. (t + 1))]} is non empty V12() V47(1) set
z ^ <*(zz /. (t + 1))*> is Relation-like NAT -defined the carrier of (Polynom-Ring f) -valued Function-like non empty V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring f)
Sum <*(zz /. (t + 1))*> is Element of the carrier of (Polynom-Ring f)
(Sum z) + (Sum <*(zz /. (t + 1))*>) is Element of the carrier of (Polynom-Ring f)
(Sum z) + (zz /. (t + 1)) is Element of the carrier of (Polynom-Ring f)
g1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
g1 + a1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
b9 . b1 is Element of the carrier of f
g1 . b1 is Element of the carrier of f
(g1 . b1) + (a1 . b1) is Element of the carrier of f
Sum (f,z,b1) is Element of the carrier of f
(Sum (f,z,b1)) + (a1 . b1) is Element of the carrier of f
Sum <*(a1 . b1)*> is Element of the carrier of f
(Sum (f,z,b1)) + (Sum <*(a1 . b1)*>) is Element of the carrier of f
Sum (f,zz,b1) is Element of the carrier of f
b9 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
zz is Relation-like NAT -defined the carrier of (Polynom-Ring f) -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring f)
Sum zz is Element of the carrier of (Polynom-Ring f)
len zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
a1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
b9 . a1 is Element of the carrier of f
(f,zz,a1) is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
Sum (f,zz,a1) is Element of the carrier of f
t is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
b9 is Relation-like NAT -defined the carrier of (Polynom-Ring f) -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring f)
Sum b9 is Element of the carrier of (Polynom-Ring f)
len b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
<*> the carrier of (Polynom-Ring f) is Relation-like NAT -defined the carrier of (Polynom-Ring f) -valued Function-like functional empty V24() V25() V26() V28() V29() V30() complex V32() ext-real non positive non negative V40() V45() V47( {} ) FinSequence-like FinSubsequence-like FinSequence-membered integer Function-yielding V54() FinSequence of the carrier of (Polynom-Ring f)
0. (Polynom-Ring f) is zero Element of the carrier of (Polynom-Ring f)
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
t . zz is Element of the carrier of f
(f,b9,zz) is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len (f,b9,zz) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
<*> the carrier of f is Relation-like NAT -defined the carrier of f -valued Function-like functional empty V24() V25() V26() V28() V29() V30() complex V32() ext-real non positive non negative V40() V45() V47( {} ) FinSequence-like FinSubsequence-like FinSequence-membered integer Function-yielding V54() FinSequence of the carrier of f
Sum (f,b9,zz) is Element of the carrier of f
t is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
b9 is Relation-like NAT -defined the carrier of (Polynom-Ring f) -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring f)
Sum b9 is Element of the carrier of (Polynom-Ring f)
len b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
t . zz is Element of the carrier of f
(f,b9,zz) is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
Sum (f,b9,zz) is Element of the carrier of f
t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
f is non empty left_add-cancelable right_add-cancelable right_complementable right-distributive left-distributive distributive Abelian add-associative right_zeroed V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
Polynom-Ring f is non empty left_add-cancelable right_add-cancelable right_complementable strict right-distributive left-distributive distributive Abelian add-associative right_zeroed V150() V151() V152() V153() doubleLoopStr
the carrier of (Polynom-Ring f) is non empty set
ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef *' rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef1 is Element of the carrier of (Polynom-Ring f)
b9 is Relation-like NAT -defined the carrier of (Polynom-Ring f) -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring f)
Sum b9 is Element of the carrier of (Polynom-Ring f)
ef1 * b9 is Relation-like NAT -defined the carrier of (Polynom-Ring f) -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring f)
Sum (ef1 * b9) is Element of the carrier of (Polynom-Ring f)
t is Element of the carrier of (Polynom-Ring f)
ef1 * t is Element of the carrier of (Polynom-Ring f)
f is non empty associative doubleLoopStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef1 is Element of the carrier of f
ef1 * rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) Element of K19(K20(NAT, the carrier of f))
ef is Element of the carrier of f
ef * (ef1 * rho) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) Element of K19(K20(NAT, the carrier of f))
ef * ef1 is Element of the carrier of f
(ef * ef1) * rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) Element of K19(K20(NAT, the carrier of f))
zz is set
dom (ef * (ef1 * rho)) is Element of K19(NAT)
a1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(ef * (ef1 * rho)) . a1 is Element of the carrier of f
(ef1 * rho) . a1 is Element of the carrier of f
ef * ((ef1 * rho) . a1) is Element of the carrier of f
rho . a1 is Element of the carrier of f
ef1 * (rho . a1) is Element of the carrier of f
ef * (ef1 * (rho . a1)) is Element of the carrier of f
(ef * ef1) * (rho . a1) is Element of the carrier of f
((ef * ef1) * rho) . a1 is Element of the carrier of f
(ef * (ef1 * rho)) . zz is set
((ef * ef1) * rho) . zz is set
dom ((ef * ef1) * rho) is Element of K19(NAT)
f is non empty left_add-cancelable right_add-cancelable right_complementable left-distributive add-associative right_zeroed V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef is Element of the carrier of f
ef * rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) Element of K19(K20(NAT, the carrier of f))
- (ef * rho) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) Element of K19(K20(NAT, the carrier of f))
- ef is Element of the carrier of f
(- ef) * rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) Element of K19(K20(NAT, the carrier of f))
b9 is set
dom (- (ef * rho)) is Element of K19(NAT)
zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(- (ef * rho)) . zz is Element of the carrier of f
(ef * rho) . zz is Element of the carrier of f
- ((ef * rho) . zz) is Element of the carrier of f
rho . zz is Element of the carrier of f
ef * (rho . zz) is Element of the carrier of f
- (ef * (rho . zz)) is Element of the carrier of f
(- ef) * (rho . zz) is Element of the carrier of f
((- ef) * rho) . zz is Element of the carrier of f
(- (ef * rho)) . b9 is set
((- ef) * rho) . b9 is set
dom ((- ef) * rho) is Element of K19(NAT)
f is non empty left_add-cancelable right_add-cancelable right_complementable right-distributive add-associative right_zeroed V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef is Element of the carrier of f
ef * rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- (ef * rho) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef * (- rho) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
b9 is set
dom (- (ef * rho)) is Element of K19(NAT)
zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(- (ef * rho)) . zz is Element of the carrier of f
(ef * rho) . zz is Element of the carrier of f
- ((ef * rho) . zz) is Element of the carrier of f
rho . zz is Element of the carrier of f
ef * (rho . zz) is Element of the carrier of f
- (ef * (rho . zz)) is Element of the carrier of f
- (rho . zz) is Element of the carrier of f
ef * (- (rho . zz)) is Element of the carrier of f
(- rho) . zz is Element of the carrier of f
ef * ((- rho) . zz) is Element of the carrier of f
(ef * (- rho)) . zz is Element of the carrier of f
(- (ef * rho)) . b9 is set
(ef * (- rho)) . b9 is set
dom (ef * (- rho)) is Element of K19(NAT)
f is non empty left-distributive doubleLoopStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef is Element of the carrier of f
ef1 is Element of the carrier of f
ef + ef1 is Element of the carrier of f
(ef + ef1) * rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) Element of K19(K20(NAT, the carrier of f))
ef * rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) Element of K19(K20(NAT, the carrier of f))
ef1 * rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) Element of K19(K20(NAT, the carrier of f))
(ef * rho) + (ef1 * rho) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) Element of K19(K20(NAT, the carrier of f))
zz is set
dom ((ef + ef1) * rho) is Element of K19(NAT)
a1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
((ef + ef1) * rho) . a1 is Element of the carrier of f
rho . a1 is Element of the carrier of f
(ef + ef1) * (rho . a1) is Element of the carrier of f
ef * (rho . a1) is Element of the carrier of f
ef1 * (rho . a1) is Element of the carrier of f
(ef * (rho . a1)) + (ef1 * (rho . a1)) is Element of the carrier of f
(ef * rho) . a1 is Element of the carrier of f
((ef * rho) . a1) + (ef1 * (rho . a1)) is Element of the carrier of f
(ef1 * rho) . a1 is Element of the carrier of f
((ef * rho) . a1) + ((ef1 * rho) . a1) is Element of the carrier of f
((ef * rho) + (ef1 * rho)) . a1 is Element of the carrier of f
((ef + ef1) * rho) . zz is set
((ef * rho) + (ef1 * rho)) . zz is set
dom ((ef * rho) + (ef1 * rho)) is Element of K19(NAT)
f is non empty right-distributive doubleLoopStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho + ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) Element of K19(K20(NAT, the carrier of f))
ef1 is Element of the carrier of f
ef1 * (rho + ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) Element of K19(K20(NAT, the carrier of f))
ef1 * rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) Element of K19(K20(NAT, the carrier of f))
ef1 * ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) Element of K19(K20(NAT, the carrier of f))
(ef1 * rho) + (ef1 * ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) Element of K19(K20(NAT, the carrier of f))
zz is set
dom (ef1 * (rho + ef)) is Element of K19(NAT)
a1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(ef1 * (rho + ef)) . a1 is Element of the carrier of f
(rho + ef) . a1 is Element of the carrier of f
ef1 * ((rho + ef) . a1) is Element of the carrier of f
rho . a1 is Element of the carrier of f
ef . a1 is Element of the carrier of f
(rho . a1) + (ef . a1) is Element of the carrier of f
ef1 * ((rho . a1) + (ef . a1)) is Element of the carrier of f
ef1 * (rho . a1) is Element of the carrier of f
ef1 * (ef . a1) is Element of the carrier of f
(ef1 * (rho . a1)) + (ef1 * (ef . a1)) is Element of the carrier of f
(ef1 * rho) . a1 is Element of the carrier of f
((ef1 * rho) . a1) + (ef1 * (ef . a1)) is Element of the carrier of f
(ef1 * ef) . a1 is Element of the carrier of f
((ef1 * rho) . a1) + ((ef1 * ef) . a1) is Element of the carrier of f
((ef1 * rho) + (ef1 * ef)) . a1 is Element of the carrier of f
(ef1 * (rho + ef)) . zz is set
((ef1 * rho) + (ef1 * ef)) . zz is set
dom ((ef1 * rho) + (ef1 * ef)) is Element of K19(NAT)
f is non empty left_add-cancelable right_add-cancelable right_complementable associative commutative right-distributive left-distributive distributive add-associative right_zeroed V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho *' ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef1 is Element of the carrier of f
ef1 * ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho *' (ef1 * ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef1 * (rho *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
zz is set
dom (rho *' (ef1 * ef)) is Element of K19(NAT)
a1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
a1 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(rho *' (ef1 * ef)) . a1 is Element of the carrier of f
b1 is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len b1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
Sum b1 is Element of the carrier of f
dom b1 is Element of K19(NAT)
(rho *' ef) . a1 is Element of the carrier of f
a19 is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len a19 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
Sum a19 is Element of the carrier of f
dom a19 is Element of K19(NAT)
ef1 * a19 is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len (ef1 * a19) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
Seg (len (ef1 * a19)) is V40() V47( len (ef1 * a19)) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len (ef1 * a19) ) } is set
dom (ef1 * a19) is Element of K19(NAT)
Seg (len a19) is V40() V47( len a19) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len a19 ) } is set
Seg (len b1) is V40() V47( len b1) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len b1 ) } is set
b19 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
a19 /. b19 is Element of the carrier of f
a19 . b19 is set
(ef1 * a19) . b19 is set
(ef1 * a19) /. b19 is Element of the carrier of f
ef1 * (a19 /. b19) is Element of the carrier of f
b19 -' 1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
rho . (b19 -' 1) is Element of the carrier of f
(a1 + 1) -' b19 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef . ((a1 + 1) -' b19) is Element of the carrier of f
(rho . (b19 -' 1)) * (ef . ((a1 + 1) -' b19)) is Element of the carrier of f
ef1 * ((rho . (b19 -' 1)) * (ef . ((a1 + 1) -' b19))) is Element of the carrier of f
ef1 * (ef . ((a1 + 1) -' b19)) is Element of the carrier of f
(rho . (b19 -' 1)) * (ef1 * (ef . ((a1 + 1) -' b19))) is Element of the carrier of f
(ef1 * ef) . ((a1 + 1) -' b19) is Element of the carrier of f
(rho . (b19 -' 1)) * ((ef1 * ef) . ((a1 + 1) -' b19)) is Element of the carrier of f
b1 . b19 is set
(ef1 * (rho *' ef)) . a1 is Element of the carrier of f
ef1 * (Sum a19) is Element of the carrier of f
Sum (ef1 * a19) is Element of the carrier of f
(rho *' (ef1 * ef)) . zz is set
(ef1 * (rho *' ef)) . zz is set
dom (ef1 * (rho *' ef)) is Element of K19(NAT)
f is non empty ZeroStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
len rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len rho) - 1 is complex V32() ext-real integer set
f is non empty ZeroStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
f is non empty ZeroStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
0. f is zero Element of the carrier of f
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
len rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len rho) - 1 is complex V32() ext-real integer set
rho . ((len rho) - 1) is set
0 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
1 - 1 is complex V32() ext-real integer set
ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
rho . ef1 is Element of the carrier of f
ef + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
rho . ef1 is Element of the carrier of f
(len rho) + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
((len rho) + 1) - 1 is complex V32() ext-real integer set
- 1 is non empty complex V32() ext-real non positive negative integer set
f is non empty ZeroStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,rho) is complex V32() ext-real integer set
len rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len rho) - 1 is complex V32() ext-real integer set
f is non empty ZeroStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
0. f is zero Element of the carrier of f
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,rho) is complex V32() ext-real integer set
len rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len rho) - 1 is complex V32() ext-real integer set
rho . (f,rho) is set
f is non empty ZeroStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,rho) is complex V32() ext-real integer set
len rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len rho) - 1 is complex V32() ext-real integer set
(len rho) + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
0 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
1 - 1 is complex V32() ext-real integer set
f is non empty left_add-cancelable right_add-cancelable right_complementable add-associative right_zeroed V150() V151() V152() V153() addLoopStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,rho) is complex V32() ext-real integer set
len rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len rho) - 1 is complex V32() ext-real integer set
ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,ef) is complex V32() ext-real integer set
len ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len ef) - 1 is complex V32() ext-real integer set
rho + ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,(rho + ef)) is complex V32() ext-real integer set
len (rho + ef) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len (rho + ef)) - 1 is complex V32() ext-real integer set
max ((f,rho),(f,ef)) is complex V32() ext-real set
max ((len rho),(len ef)) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
(max ((len rho),(len ef))) - 1 is complex V32() ext-real integer set
f is non empty ZeroStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,rho) is complex V32() ext-real integer set
len rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len rho) - 1 is complex V32() ext-real integer set
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
f is non empty left_add-cancelable right_add-cancelable right_complementable Abelian add-associative right_zeroed V150() V151() V152() V153() addLoopStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho + ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,(rho + ef)) is complex V32() ext-real integer set
len (rho + ef) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len (rho + ef)) - 1 is complex V32() ext-real integer set
(f,rho) is complex V32() ext-real integer set
len rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len rho) - 1 is complex V32() ext-real integer set
(f,ef) is complex V32() ext-real integer set
len ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len ef) - 1 is complex V32() ext-real integer set
max ((f,rho),(f,ef)) is complex V32() ext-real set
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef1 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
(rho + ef) . t is Element of the carrier of f
(f,ef) + 1 is complex V32() ext-real integer set
ef . t is Element of the carrier of f
(f,rho) + 1 is complex V32() ext-real integer set
rho . t is Element of the carrier of f
(0. f) + (0. f) is Element of the carrier of f
(ef1 + 1) - 1 is complex V32() ext-real integer set
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
f is non empty left_add-cancelable right_add-cancelable right_complementable unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support with_roots Element of K19(K20(NAT, the carrier of f))
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho *' ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,(rho *' ef)) is complex V32() ext-real integer set
len (rho *' ef) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len (rho *' ef)) - 1 is complex V32() ext-real integer set
(f,rho) is complex V32() ext-real integer set
len rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len rho) - 1 is complex V32() ext-real integer set
(f,ef) is complex V32() ext-real integer set
len ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len ef) - 1 is complex V32() ext-real integer set
(f,rho) + (f,ef) is complex V32() ext-real integer set
dom ef is Element of K19(NAT)
ef /. (f,ef) is Element of the carrier of f
ef . (f,ef) is set
dom rho is Element of K19(NAT)
rho /. (f,rho) is Element of the carrier of f
rho . (f,rho) is set
(len ef) + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
0 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
1 - 1 is complex V32() ext-real integer set
(len ef) -' 1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef . ((len ef) -' 1) is Element of the carrier of f
(len rho) + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(len rho) -' 1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
rho . ((len rho) -' 1) is Element of the carrier of f
(rho . ((len rho) -' 1)) * (ef . ((len ef) -' 1)) is Element of the carrier of f
(len rho) + (len ef) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
((len rho) + (len ef)) - 1 is complex V32() ext-real integer set
(((len rho) + (len ef)) - 1) - 1 is complex V32() ext-real integer set
f is non empty left_add-cancelable right_add-cancelable right_complementable unital add-associative right_zeroed V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,rho) is complex V32() ext-real integer set
len rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len rho) - 1 is complex V32() ext-real integer set
rho . 0 is Element of the carrier of f
<%(rho . 0)%> is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef is Element of the carrier of f
0. f is zero Element of the carrier of f
eval (rho,ef) is Element of the carrier of f
f is non empty unital doubleLoopStr
the carrier of f is non empty set
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support with_roots Element of K19(K20(NAT, the carrier of f))
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
power f is Relation-like K20( the carrier of f,NAT) -defined the carrier of f -valued Function-like total V18(K20( the carrier of f,NAT), the carrier of f) Element of K19(K20(K20( the carrier of f,NAT), the carrier of f))
K20( the carrier of f,NAT) is V40() set
K20(K20( the carrier of f,NAT), the carrier of f) is V40() set
K19(K20(K20( the carrier of f,NAT), the carrier of f)) is V40() set
1_ f is Element of the carrier of f
rho is Element of the carrier of f
ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power f) . (rho,ef) is Element of the carrier of f
- ((power f) . (rho,ef)) is Element of the carrier of f
(0,ef) --> ((- ((power f) . (rho,ef))),(1_ f)) is Relation-like {0,ef} -defined the carrier of f -valued Function-like non empty total V18({0,ef}, the carrier of f) Element of K19(K20({0,ef}, the carrier of f))
{0,ef} is non empty set
K20({0,ef}, the carrier of f) is set
K19(K20({0,ef}, the carrier of f)) is set
(0_. f) +* ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f))) is Relation-like Function-like set
((0_. f) +* ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f)))) . 0 is set
((0_. f) +* ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f)))) . ef is set
dom ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f))) is Element of K19({0,ef})
K19({0,ef}) is set
zz is set
dom (0_. f) is Element of K19(NAT)
(dom (0_. f)) \/ (dom ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f)))) is set
((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f))) . 0 is set
((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f))) . ef is set
f is non empty unital doubleLoopStr
the carrier of f is non empty set
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support with_roots Element of K19(K20(NAT, the carrier of f))
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
power f is Relation-like K20( the carrier of f,NAT) -defined the carrier of f -valued Function-like total V18(K20( the carrier of f,NAT), the carrier of f) Element of K19(K20(K20( the carrier of f,NAT), the carrier of f))
K20( the carrier of f,NAT) is V40() set
K20(K20( the carrier of f,NAT), the carrier of f) is V40() set
K19(K20(K20( the carrier of f,NAT), the carrier of f)) is V40() set
1_ f is Element of the carrier of f
rho is Element of the carrier of f
ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power f) . (rho,ef) is Element of the carrier of f
- ((power f) . (rho,ef)) is Element of the carrier of f
(0,ef) --> ((- ((power f) . (rho,ef))),(1_ f)) is Relation-like {0,ef} -defined the carrier of f -valued Function-like non empty total V18({0,ef}, the carrier of f) Element of K19(K20({0,ef}, the carrier of f))
{0,ef} is non empty set
K20({0,ef}, the carrier of f) is set
K19(K20({0,ef}, the carrier of f)) is set
(0_. f) +* ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f))) is Relation-like Function-like set
ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
((0_. f) +* ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f)))) . ef1 is set
dom (0_. f) is Element of K19(NAT)
zz is set
dom ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f))) is Element of K19({0,ef})
K19({0,ef}) is set
(dom (0_. f)) \/ (dom ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f)))) is set
(0_. f) . ef1 is Element of the carrier of f
f is non empty unital doubleLoopStr
the carrier of f is non empty set
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support with_roots Element of K19(K20(NAT, the carrier of f))
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
power f is Relation-like K20( the carrier of f,NAT) -defined the carrier of f -valued Function-like total V18(K20( the carrier of f,NAT), the carrier of f) Element of K19(K20(K20( the carrier of f,NAT), the carrier of f))
K20( the carrier of f,NAT) is V40() set
K20(K20( the carrier of f,NAT), the carrier of f) is V40() set
K19(K20(K20( the carrier of f,NAT), the carrier of f)) is V40() set
rho is Element of the carrier of f
(power f) . (rho,ef) is Element of the carrier of f
- ((power f) . (rho,ef)) is Element of the carrier of f
1_ f is Element of the carrier of f
(0,ef) --> ((- ((power f) . (rho,ef))),(1_ f)) is Relation-like {0,ef} -defined the carrier of f -valued Function-like non empty total V18({0,ef}, the carrier of f) Element of K19(K20({0,ef}, the carrier of f))
{0,ef} is non empty set
K20({0,ef}, the carrier of f) is set
K19(K20({0,ef}, the carrier of f)) is set
(0_. f) +* ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f))) is Relation-like Function-like set
ef1 is set
dom ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f))) is Element of K19({0,ef})
K19({0,ef}) is set
{ef} is non empty V12() V47(1) set
{ef} --> (1_ f) is Relation-like {ef} -defined the carrier of f -valued Function-like constant non empty total V18({ef}, the carrier of f) Element of K19(K20({ef}, the carrier of f))
K20({ef}, the carrier of f) is set
K19(K20({ef}, the carrier of f)) is set
{(1_ f)} is non empty V12() V47(1) set
K20({ef},{(1_ f)}) is set
dom ({ef} --> (1_ f)) is Element of K19({ef})
K19({ef}) is set
zz is set
a1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
((0_. f) +* ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f)))) . a1 is set
((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f))) . a1 is set
0 .--> (- ((power f) . (rho,ef))) is Relation-like NAT -defined {0} -defined the carrier of f -valued Function-like one-to-one set
{0} is non empty V12() V47(1) set
{0} --> (- ((power f) . (rho,ef))) is Relation-like {0} -defined the carrier of f -valued {(- ((power f) . (rho,ef)))} -valued Function-like constant non empty total V18({0},{(- ((power f) . (rho,ef)))}) Element of K19(K20({0},{(- ((power f) . (rho,ef)))}))
{(- ((power f) . (rho,ef)))} is non empty V12() V47(1) set
K20({0},{(- ((power f) . (rho,ef)))}) is set
K19(K20({0},{(- ((power f) . (rho,ef)))})) is set
ef .--> (1_ f) is Relation-like NAT -defined {ef} -defined the carrier of f -valued Function-like one-to-one set
{ef} --> (1_ f) is Relation-like {ef} -defined the carrier of f -valued {(1_ f)} -valued Function-like constant non empty total V18({ef},{(1_ f)}) Element of K19(K20({ef},{(1_ f)}))
K19(K20({ef},{(1_ f)})) is set
(0 .--> (- ((power f) . (rho,ef)))) +* (ef .--> (1_ f)) is Relation-like Function-like set
((0 .--> (- ((power f) . (rho,ef)))) +* (ef .--> (1_ f))) . a1 is set
(ef .--> (1_ f)) . a1 is set
((0_. f) +* ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f)))) . zz is set
a1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
((0_. f) +* ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f)))) . a1 is set
((0_. f) +* ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f)))) . zz is set
a1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
((0_. f) +* ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f)))) . a1 is set
((0_. f) +* ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f)))) . zz is set
a1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
((0_. f) +* ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f)))) . a1 is set
((0_. f) +* ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f)))) . zz is set
a1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
dom (0_. f) is Element of K19(NAT)
(dom (0_. f)) \/ (dom ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f)))) is set
dom ((0_. f) +* ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f)))) is set
zz is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) Element of K19(K20(NAT, the carrier of f))
ef + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
b1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
a1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) Element of K19(K20(NAT, the carrier of f))
a1 . b1 is Element of the carrier of f
b1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
f is non empty unital doubleLoopStr
the carrier of f is non empty set
ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
rho is Element of the carrier of f
(f,rho,ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support with_roots Element of K19(K20(NAT, the carrier of f))
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
power f is Relation-like K20( the carrier of f,NAT) -defined the carrier of f -valued Function-like total V18(K20( the carrier of f,NAT), the carrier of f) Element of K19(K20(K20( the carrier of f,NAT), the carrier of f))
K20( the carrier of f,NAT) is V40() set
K20(K20( the carrier of f,NAT), the carrier of f) is V40() set
K19(K20(K20( the carrier of f,NAT), the carrier of f)) is V40() set
(power f) . (rho,ef) is Element of the carrier of f
- ((power f) . (rho,ef)) is Element of the carrier of f
1_ f is Element of the carrier of f
(0,ef) --> ((- ((power f) . (rho,ef))),(1_ f)) is Relation-like {0,ef} -defined the carrier of f -valued Function-like non empty total V18({0,ef}, the carrier of f) Element of K19(K20({0,ef}, the carrier of f))
{0,ef} is non empty set
K20({0,ef}, the carrier of f) is set
K19(K20({0,ef}, the carrier of f)) is set
(0_. f) +* ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f))) is Relation-like Function-like set
(f,rho,ef) . 0 is Element of the carrier of f
(f,rho,ef) . ef is Element of the carrier of f
f is non empty unital doubleLoopStr
the carrier of f is non empty set
ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
rho is Element of the carrier of f
(f,rho,ef1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support with_roots Element of K19(K20(NAT, the carrier of f))
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
power f is Relation-like K20( the carrier of f,NAT) -defined the carrier of f -valued Function-like total V18(K20( the carrier of f,NAT), the carrier of f) Element of K19(K20(K20( the carrier of f,NAT), the carrier of f))
K20( the carrier of f,NAT) is V40() set
K20(K20( the carrier of f,NAT), the carrier of f) is V40() set
K19(K20(K20( the carrier of f,NAT), the carrier of f)) is V40() set
(power f) . (rho,ef1) is Element of the carrier of f
- ((power f) . (rho,ef1)) is Element of the carrier of f
1_ f is Element of the carrier of f
(0,ef1) --> ((- ((power f) . (rho,ef1))),(1_ f)) is Relation-like {0,ef1} -defined the carrier of f -valued Function-like non empty total V18({0,ef1}, the carrier of f) Element of K19(K20({0,ef1}, the carrier of f))
{0,ef1} is non empty set
K20({0,ef1}, the carrier of f) is set
K19(K20({0,ef1}, the carrier of f)) is set
(0_. f) +* ((0,ef1) --> ((- ((power f) . (rho,ef1))),(1_ f))) is Relation-like Function-like set
(f,rho,ef1) . ef is Element of the carrier of f
f is non empty non degenerated V72() unital right_unital well-unital left_unital doubleLoopStr
the carrier of f is non empty V12() set
rho is Element of the carrier of f
ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(f,rho,ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support with_roots Element of K19(K20(NAT, the carrier of f))
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
power f is Relation-like K20( the carrier of f,NAT) -defined the carrier of f -valued Function-like total V18(K20( the carrier of f,NAT), the carrier of f) Element of K19(K20(K20( the carrier of f,NAT), the carrier of f))
K20( the carrier of f,NAT) is V40() set
K20(K20( the carrier of f,NAT), the carrier of f) is V40() set
K19(K20(K20( the carrier of f,NAT), the carrier of f)) is V40() set
(power f) . (rho,ef) is Element of the carrier of f
- ((power f) . (rho,ef)) is Element of the carrier of f
1_ f is Element of the carrier of f
1. f is non zero Element of the carrier of f
(0,ef) --> ((- ((power f) . (rho,ef))),(1_ f)) is Relation-like {0,ef} -defined the carrier of f -valued Function-like non empty total V18({0,ef}, the carrier of f) Element of K19(K20({0,ef}, the carrier of f))
{0,ef} is non empty set
K20({0,ef}, the carrier of f) is set
K19(K20({0,ef}, the carrier of f)) is set
(0_. f) +* ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f))) is Relation-like Function-like set
(f,(f,rho,ef)) is complex V32() ext-real integer set
len (f,rho,ef) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len (f,rho,ef)) - 1 is complex V32() ext-real integer set
zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
{ef} is non empty V12() V47(1) set
{ef} --> (1_ f) is Relation-like {ef} -defined the carrier of f -valued Function-like constant non empty total V18({ef}, the carrier of f) Element of K19(K20({ef}, the carrier of f))
K20({ef}, the carrier of f) is set
K19(K20({ef}, the carrier of f)) is set
{(1_ f)} is non empty V12() V47(1) set
K20({ef},{(1_ f)}) is set
dom ({ef} --> (1_ f)) is Element of K19({ef})
K19({ef}) is set
dom ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f))) is Element of K19({0,ef})
K19({0,ef}) is set
(f,rho,ef) . 0 is Element of the carrier of f
((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f))) . 0 is set
0 .--> (- ((power f) . (rho,ef))) is Relation-like NAT -defined {0} -defined the carrier of f -valued Function-like one-to-one set
{0} is non empty V12() V47(1) set
{0} --> (- ((power f) . (rho,ef))) is Relation-like {0} -defined the carrier of f -valued {(- ((power f) . (rho,ef)))} -valued Function-like constant non empty total V18({0},{(- ((power f) . (rho,ef)))}) Element of K19(K20({0},{(- ((power f) . (rho,ef)))}))
{(- ((power f) . (rho,ef)))} is non empty V12() V47(1) set
K20({0},{(- ((power f) . (rho,ef)))}) is set
K19(K20({0},{(- ((power f) . (rho,ef)))})) is set
ef .--> (1_ f) is Relation-like NAT -defined {ef} -defined the carrier of f -valued Function-like one-to-one set
{ef} --> (1_ f) is Relation-like {ef} -defined the carrier of f -valued {(1_ f)} -valued Function-like constant non empty total V18({ef},{(1_ f)}) Element of K19(K20({ef},{(1_ f)}))
K19(K20({ef},{(1_ f)})) is set
(0 .--> (- ((power f) . (rho,ef)))) +* (ef .--> (1_ f)) is Relation-like Function-like set
((0 .--> (- ((power f) . (rho,ef)))) +* (ef .--> (1_ f))) . 0 is set
0 .--> (1_ f) is Relation-like NAT -defined {0} -defined the carrier of f -valued Function-like one-to-one set
{0} --> (1_ f) is Relation-like {0} -defined the carrier of f -valued {(1_ f)} -valued Function-like constant non empty total V18({0},{(1_ f)}) Element of K19(K20({0},{(1_ f)}))
K20({0},{(1_ f)}) is set
K19(K20({0},{(1_ f)})) is set
(0 .--> (1_ f)) . 0 is set
zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
(f,rho,ef) . zz is Element of the carrier of f
(0_. f) . zz is Element of the carrier of f
zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
ef + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(f,rho,ef) . ef is Element of the carrier of f
zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
(f,rho,ef) . zz is Element of the carrier of f
f is non empty non degenerated V72() left_add-cancelable right_add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed domRing-like V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty V12() set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
0. f is zero Element of the carrier of f
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,rho) is complex V32() ext-real integer set
len rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len rho) - 1 is complex V32() ext-real integer set
rho . 1 is Element of the carrier of f
rho . 0 is Element of the carrier of f
- (rho . 0) is Element of the carrier of f
(rho . 1) " is Element of the carrier of f
(- (rho . 0)) * ((rho . 1) ") is Element of the carrier of f
(f,((- (rho . 0)) * ((rho . 1) ")),1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support with_roots Element of K19(K20(NAT, the carrier of f))
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
power f is Relation-like K20( the carrier of f,NAT) -defined the carrier of f -valued Function-like total V18(K20( the carrier of f,NAT), the carrier of f) Element of K19(K20(K20( the carrier of f,NAT), the carrier of f))
K20( the carrier of f,NAT) is V40() set
K20(K20( the carrier of f,NAT), the carrier of f) is V40() set
K19(K20(K20( the carrier of f,NAT), the carrier of f)) is V40() set
(power f) . (((- (rho . 0)) * ((rho . 1) ")),1) is Element of the carrier of f
- ((power f) . (((- (rho . 0)) * ((rho . 1) ")),1)) is Element of the carrier of f
1_ f is Element of the carrier of f
1. f is non zero Element of the carrier of f
(0,1) --> ((- ((power f) . (((- (rho . 0)) * ((rho . 1) ")),1))),(1_ f)) is Relation-like {0,1} -defined the carrier of f -valued Function-like non empty total V18({0,1}, the carrier of f) Element of K19(K20({0,1}, the carrier of f))
{0,1} is non empty set
K20({0,1}, the carrier of f) is set
K19(K20({0,1}, the carrier of f)) is set
(0_. f) +* ((0,1) --> ((- ((power f) . (((- (rho . 0)) * ((rho . 1) ")),1))),(1_ f))) is Relation-like Function-like set
(rho . 1) * (f,((- (rho . 0)) * ((rho . 1) ")),1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
1 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
((rho . 1) * (f,((- (rho . 0)) * ((rho . 1) ")),1)) . b9 is Element of the carrier of f
(f,((- (rho . 0)) * ((rho . 1) ")),1) . 1 is Element of the carrier of f
(rho . 1) * ((f,((- (rho . 0)) * ((rho . 1) ")),1) . 1) is Element of the carrier of f
(rho . 1) * (1_ f) is Element of the carrier of f
rho . b9 is Element of the carrier of f
((rho . 1) * (f,((- (rho . 0)) * ((rho . 1) ")),1)) . b9 is Element of the carrier of f
(f,((- (rho . 0)) * ((rho . 1) ")),1) . 0 is Element of the carrier of f
(rho . 1) * ((f,((- (rho . 0)) * ((rho . 1) ")),1) . 0) is Element of the carrier of f
1 + 0 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(power f) . (((- (rho . 0)) * ((rho . 1) ")),(1 + 0)) is Element of the carrier of f
- ((power f) . (((- (rho . 0)) * ((rho . 1) ")),(1 + 0))) is Element of the carrier of f
(rho . 1) * (- ((power f) . (((- (rho . 0)) * ((rho . 1) ")),(1 + 0)))) is Element of the carrier of f
(power f) . (((- (rho . 0)) * ((rho . 1) ")),0) is Element of the carrier of f
((power f) . (((- (rho . 0)) * ((rho . 1) ")),0)) * ((- (rho . 0)) * ((rho . 1) ")) is Element of the carrier of f
- (((power f) . (((- (rho . 0)) * ((rho . 1) ")),0)) * ((- (rho . 0)) * ((rho . 1) "))) is Element of the carrier of f
(rho . 1) * (- (((power f) . (((- (rho . 0)) * ((rho . 1) ")),0)) * ((- (rho . 0)) * ((rho . 1) ")))) is Element of the carrier of f
(1_ f) * ((- (rho . 0)) * ((rho . 1) ")) is Element of the carrier of f
- ((1_ f) * ((- (rho . 0)) * ((rho . 1) "))) is Element of the carrier of f
(rho . 1) * (- ((1_ f) * ((- (rho . 0)) * ((rho . 1) ")))) is Element of the carrier of f
- ((- (rho . 0)) * ((rho . 1) ")) is Element of the carrier of f
(rho . 1) * (- ((- (rho . 0)) * ((rho . 1) "))) is Element of the carrier of f
(rho . 0) * ((rho . 1) ") is Element of the carrier of f
- ((rho . 0) * ((rho . 1) ")) is Element of the carrier of f
- (- ((rho . 0) * ((rho . 1) "))) is Element of the carrier of f
(rho . 1) * (- (- ((rho . 0) * ((rho . 1) ")))) is Element of the carrier of f
(rho . 1) * ((rho . 0) * ((rho . 1) ")) is Element of the carrier of f
(rho . 1) * ((rho . 1) ") is Element of the carrier of f
((rho . 1) * ((rho . 1) ")) * (rho . 0) is Element of the carrier of f
(1_ f) * (rho . 0) is Element of the carrier of f
rho . b9 is Element of the carrier of f
len ((rho . 1) * (f,((- (rho . 0)) * ((rho . 1) ")),1)) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(f,(f,((- (rho . 0)) * ((rho . 1) ")),1)) is complex V32() ext-real integer set
len (f,((- (rho . 0)) * ((rho . 1) ")),1) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len (f,((- (rho . 0)) * ((rho . 1) ")),1)) - 1 is complex V32() ext-real integer set
(f,(f,((- (rho . 0)) * ((rho . 1) ")),1)) + 1 is complex V32() ext-real integer set
ef is Element of the carrier of f
ef1 is Element of the carrier of f
(f,ef1,1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(power f) . (ef1,1) is Element of the carrier of f
- ((power f) . (ef1,1)) is Element of the carrier of f
(0,1) --> ((- ((power f) . (ef1,1))),(1_ f)) is Relation-like {0,1} -defined the carrier of f -valued Function-like non empty total V18({0,1}, the carrier of f) Element of K19(K20({0,1}, the carrier of f))
(0_. f) +* ((0,1) --> ((- ((power f) . (ef1,1))),(1_ f))) is Relation-like Function-like set
ef * (f,ef1,1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,(f,ef1,1)) is complex V32() ext-real integer set
len (f,ef1,1) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len (f,ef1,1)) - 1 is complex V32() ext-real integer set
ef is Element of the carrier of f
ef1 is Element of the carrier of f
(f,ef1,1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(power f) . (ef1,1) is Element of the carrier of f
- ((power f) . (ef1,1)) is Element of the carrier of f
(0,1) --> ((- ((power f) . (ef1,1))),(1_ f)) is Relation-like {0,1} -defined the carrier of f -valued Function-like non empty total V18({0,1}, the carrier of f) Element of K19(K20({0,1}, the carrier of f))
(0_. f) +* ((0,1) --> ((- ((power f) . (ef1,1))),(1_ f))) is Relation-like Function-like set
ef * (f,ef1,1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
t is Element of the carrier of f
b9 is Element of the carrier of f
(f,b9,1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(power f) . (b9,1) is Element of the carrier of f
- ((power f) . (b9,1)) is Element of the carrier of f
(0,1) --> ((- ((power f) . (b9,1))),(1_ f)) is Relation-like {0,1} -defined the carrier of f -valued Function-like non empty total V18({0,1}, the carrier of f) Element of K19(K20({0,1}, the carrier of f))
(0_. f) +* ((0,1) --> ((- ((power f) . (b9,1))),(1_ f))) is Relation-like Function-like set
t * (f,b9,1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
2 -' 1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
2 - 1 is complex V32() ext-real integer set
1 -' 1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
1 - 1 is complex V32() ext-real integer set
f is non empty non degenerated V72() left_add-cancelable right_add-cancelable right_complementable unital right_unital well-unital left_unital Abelian add-associative right_zeroed V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty V12() set
ef is Element of the carrier of f
(f,ef,1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support with_roots Element of K19(K20(NAT, the carrier of f))
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
power f is Relation-like K20( the carrier of f,NAT) -defined the carrier of f -valued Function-like total V18(K20( the carrier of f,NAT), the carrier of f) Element of K19(K20(K20( the carrier of f,NAT), the carrier of f))
K20( the carrier of f,NAT) is V40() set
K20(K20( the carrier of f,NAT), the carrier of f) is V40() set
K19(K20(K20( the carrier of f,NAT), the carrier of f)) is V40() set
(power f) . (ef,1) is Element of the carrier of f
- ((power f) . (ef,1)) is Element of the carrier of f
1_ f is Element of the carrier of f
1. f is non zero Element of the carrier of f
(0,1) --> ((- ((power f) . (ef,1))),(1_ f)) is Relation-like {0,1} -defined the carrier of f -valued Function-like non empty total V18({0,1}, the carrier of f) Element of K19(K20({0,1}, the carrier of f))
{0,1} is non empty set
K20({0,1}, the carrier of f) is set
K19(K20({0,1}, the carrier of f)) is set
(0_. f) +* ((0,1) --> ((- ((power f) . (ef,1))),(1_ f))) is Relation-like Function-like set
rho is Element of the carrier of f
eval ((f,ef,1),rho) is Element of the carrier of f
rho - ef is Element of the carrier of f
len (f,ef,1) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
t is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
Sum t is Element of the carrier of f
len t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
dom t is Element of K19(NAT)
(f,(f,ef,1)) is complex V32() ext-real integer set
(len (f,ef,1)) - 1 is complex V32() ext-real integer set
t . 1 is set
t . 2 is set
<*(t . 1),(t . 2)*> is Relation-like NAT -defined Function-like non empty V40() V47(2) FinSequence-like FinSubsequence-like set
<*(t . 1)*> is Relation-like NAT -defined Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like set
[1,(t . 1)] is set
{[1,(t . 1)]} is non empty V12() V47(1) set
<*(t . 2)*> is Relation-like NAT -defined Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like set
[1,(t . 2)] is set
{[1,(t . 2)]} is non empty V12() V47(1) set
<*(t . 1)*> ^ <*(t . 2)*> is Relation-like NAT -defined Function-like non empty V40() V47(1 + 1) FinSequence-like FinSubsequence-like set
1 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
Seg (len t) is V40() V47( len t) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len t ) } is set
(f,ef,1) . 1 is Element of the carrier of f
1 + 0 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(power f) . (rho,(1 + 0)) is Element of the carrier of f
((f,ef,1) . 1) * ((power f) . (rho,(1 + 0))) is Element of the carrier of f
(power f) . (rho,0) is Element of the carrier of f
((power f) . (rho,0)) * rho is Element of the carrier of f
((f,ef,1) . 1) * (((power f) . (rho,0)) * rho) is Element of the carrier of f
(1_ f) * rho is Element of the carrier of f
((f,ef,1) . 1) * ((1_ f) * rho) is Element of the carrier of f
((f,ef,1) . 1) * rho is Element of the carrier of f
(f,ef,1) . 0 is Element of the carrier of f
(power f) . (rho,(1 -' 1)) is Element of the carrier of f
((f,ef,1) . 0) * ((power f) . (rho,(1 -' 1))) is Element of the carrier of f
((f,ef,1) . 0) * (1_ f) is Element of the carrier of f
(power f) . (ef,(1 + 0)) is Element of the carrier of f
- ((power f) . (ef,(1 + 0))) is Element of the carrier of f
(power f) . (ef,0) is Element of the carrier of f
((power f) . (ef,0)) * ef is Element of the carrier of f
- (((power f) . (ef,0)) * ef) is Element of the carrier of f
(1_ f) * ef is Element of the carrier of f
- ((1_ f) * ef) is Element of the carrier of f
- ef is Element of the carrier of f
<*(- ef)*> is Relation-like NAT -defined the carrier of f -valued Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of f
[1,(- ef)] is set
{[1,(- ef)]} is non empty V12() V47(1) set
Sum <*(- ef)*> is Element of the carrier of f
<*rho*> is Relation-like NAT -defined the carrier of f -valued Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of f
[1,rho] is set
{[1,rho]} is non empty V12() V47(1) set
Sum <*rho*> is Element of the carrier of f
(Sum <*(- ef)*>) + (Sum <*rho*>) is Element of the carrier of f
(Sum <*(- ef)*>) + rho is Element of the carrier of f
(- ef) + rho is Element of the carrier of f
f is non empty non degenerated V72() left_add-cancelable right_add-cancelable right_complementable unital right_unital well-unital left_unital Abelian add-associative right_zeroed V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty V12() set
rho is Element of the carrier of f
(f,rho,1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support with_roots Element of K19(K20(NAT, the carrier of f))
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
power f is Relation-like K20( the carrier of f,NAT) -defined the carrier of f -valued Function-like total V18(K20( the carrier of f,NAT), the carrier of f) Element of K19(K20(K20( the carrier of f,NAT), the carrier of f))
K20( the carrier of f,NAT) is V40() set
K20(K20( the carrier of f,NAT), the carrier of f) is V40() set
K19(K20(K20( the carrier of f,NAT), the carrier of f)) is V40() set
(power f) . (rho,1) is Element of the carrier of f
- ((power f) . (rho,1)) is Element of the carrier of f
1_ f is Element of the carrier of f
1. f is non zero Element of the carrier of f
(0,1) --> ((- ((power f) . (rho,1))),(1_ f)) is Relation-like {0,1} -defined the carrier of f -valued Function-like non empty total V18({0,1}, the carrier of f) Element of K19(K20({0,1}, the carrier of f))
{0,1} is non empty set
K20({0,1}, the carrier of f) is set
K19(K20({0,1}, the carrier of f)) is set
(0_. f) +* ((0,1) --> ((- ((power f) . (rho,1))),(1_ f))) is Relation-like Function-like set
eval ((f,rho,1),rho) is Element of the carrier of f
rho - rho is Element of the carrier of f
f is non empty unital right_unital well-unital left_unital doubleLoopStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
power f is Relation-like K20( the carrier of f,NAT) -defined the carrier of f -valued Function-like total V18(K20( the carrier of f,NAT), the carrier of f) Element of K19(K20(K20( the carrier of f,NAT), the carrier of f))
K20( the carrier of f,NAT) is V40() set
K20(K20( the carrier of f,NAT), the carrier of f) is V40() set
K19(K20(K20( the carrier of f,NAT), the carrier of f)) is V40() set
rho is Element of the carrier of f
0. f is zero Element of the carrier of f
ef1 is set
t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef - t is complex V32() ext-real integer set
b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef - ef is complex V32() ext-real integer set
b9 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
0 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(ef - t) - 1 is complex V32() ext-real integer set
(power f) . (rho,((ef - t) - 1)) is set
zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power f) . (rho,zz) is Element of the carrier of f
t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) Element of K19(K20(NAT, the carrier of f))
t is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) Element of K19(K20(NAT, the carrier of f))
b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
t . b9 is Element of the carrier of f
zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef - zz is complex V32() ext-real integer set
(ef - zz) - 1 is complex V32() ext-real integer set
(power f) . (rho,((ef - zz) - 1)) is set
b9 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
t . zz is Element of the carrier of f
b9 . zz is Element of the carrier of f
ef - zz is complex V32() ext-real integer set
(ef - zz) - 1 is complex V32() ext-real integer set
(power f) . (rho,((ef - zz) - 1)) is set
a1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef - a1 is complex V32() ext-real integer set
(ef - a1) - 1 is complex V32() ext-real integer set
(power f) . (rho,((ef - a1) - 1)) is set
zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
b9 . zz is Element of the carrier of f
ef - zz is complex V32() ext-real integer set
(ef - zz) - 1 is complex V32() ext-real integer set
(power f) . (rho,((ef - zz) - 1)) is set
a1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
b9 . a1 is Element of the carrier of f
ef1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
t is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
b9 is set
dom ef1 is Element of K19(NAT)
zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef1 . b9 is set
ef - zz is complex V32() ext-real integer set
(ef - zz) - 1 is complex V32() ext-real integer set
(power f) . (rho,((ef - zz) - 1)) is set
t . b9 is set
zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef1 . b9 is set
t . b9 is set
zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
dom t is Element of K19(NAT)
f is non empty non degenerated V72() unital right_unital well-unital left_unital doubleLoopStr
the carrier of f is non empty V12() set
rho is Element of the carrier of f
ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(f,rho,ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
(f,(f,rho,ef)) is complex V32() ext-real integer set
len (f,rho,ef) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len (f,rho,ef)) - 1 is complex V32() ext-real integer set
ef - 1 is complex V32() ext-real integer set
ef - 0 is complex V32() ext-real non negative integer set
1 - 1 is complex V32() ext-real integer set
t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef - t is complex V32() ext-real integer set
(ef - t) - 1 is complex V32() ext-real integer set
(f,rho,ef) . (ef - 1) is set
power f is Relation-like K20( the carrier of f,NAT) -defined the carrier of f -valued Function-like total V18(K20( the carrier of f,NAT), the carrier of f) Element of K19(K20(K20( the carrier of f,NAT), the carrier of f))
K20( the carrier of f,NAT) is V40() set
K20(K20( the carrier of f,NAT), the carrier of f) is V40() set
K19(K20(K20( the carrier of f,NAT), the carrier of f)) is V40() set
(power f) . (rho,0) is Element of the carrier of f
1_ f is Element of the carrier of f
1. f is non zero Element of the carrier of f
0. f is zero Element of the carrier of f
b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
t + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
(f,rho,ef) . b9 is Element of the carrier of f
f is non empty left_add-cancelable right_add-cancelable right_complementable unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital add-associative right_zeroed V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty set
rho is Element of the carrier of f
(f,rho,1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support with_roots Element of K19(K20(NAT, the carrier of f))
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
power f is Relation-like K20( the carrier of f,NAT) -defined the carrier of f -valued Function-like total V18(K20( the carrier of f,NAT), the carrier of f) Element of K19(K20(K20( the carrier of f,NAT), the carrier of f))
K20( the carrier of f,NAT) is V40() set
K20(K20( the carrier of f,NAT), the carrier of f) is V40() set
K19(K20(K20( the carrier of f,NAT), the carrier of f)) is V40() set
(power f) . (rho,1) is Element of the carrier of f
- ((power f) . (rho,1)) is Element of the carrier of f
1_ f is Element of the carrier of f
1. f is Element of the carrier of f
(0,1) --> ((- ((power f) . (rho,1))),(1_ f)) is Relation-like {0,1} -defined the carrier of f -valued Function-like non empty total V18({0,1}, the carrier of f) Element of K19(K20({0,1}, the carrier of f))
{0,1} is non empty set
K20({0,1}, the carrier of f) is set
K19(K20({0,1}, the carrier of f)) is set
(0_. f) +* ((0,1) --> ((- ((power f) . (rho,1))),(1_ f))) is Relation-like Function-like set
ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(f,rho,ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,rho,1) *' (f,rho,ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,rho,ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(power f) . (rho,ef) is Element of the carrier of f
- ((power f) . (rho,ef)) is Element of the carrier of f
(0,ef) --> ((- ((power f) . (rho,ef))),(1_ f)) is Relation-like {0,ef} -defined the carrier of f -valued Function-like non empty total V18({0,ef}, the carrier of f) Element of K19(K20({0,ef}, the carrier of f))
{0,ef} is non empty set
K20({0,ef}, the carrier of f) is set
K19(K20({0,ef}, the carrier of f)) is set
(0_. f) +* ((0,ef) --> ((- ((power f) . (rho,ef))),(1_ f))) is Relation-like Function-like set
ef - 1 is complex V32() ext-real integer set
b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
b9 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
1 - 1 is complex V32() ext-real integer set
0 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
zz is set
dom ((f,rho,1) *' (f,rho,ef)) is Element of K19(NAT)
a1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
a1 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
((f,rho,1) *' (f,rho,ef)) . a1 is Element of the carrier of f
b1 is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len b1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
Sum b1 is Element of the carrier of f
dom b1 is Element of K19(NAT)
(a1 + 1) - 2 is complex V32() ext-real integer set
a1 - 1 is complex V32() ext-real integer set
Seg (len b1) is V40() V47( len b1) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len b1 ) } is set
b1 /. 1 is Element of the carrier of f
b1 . 1 is set
1 -' 1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(f,rho,1) . (1 -' 1) is Element of the carrier of f
(a1 + 1) -' 1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(f,rho,ef) . ((a1 + 1) -' 1) is Element of the carrier of f
((f,rho,1) . (1 -' 1)) * ((f,rho,ef) . ((a1 + 1) -' 1)) is Element of the carrier of f
(f,rho,1) . 0 is Element of the carrier of f
((f,rho,1) . 0) * ((f,rho,ef) . ((a1 + 1) -' 1)) is Element of the carrier of f
(- ((power f) . (rho,1))) * ((f,rho,ef) . ((a1 + 1) -' 1)) is Element of the carrier of f
(power f) . (rho,0) is Element of the carrier of f
((power f) . (rho,0)) * rho is Element of the carrier of f
- (((power f) . (rho,0)) * rho) is Element of the carrier of f
(- (((power f) . (rho,0)) * rho)) * ((f,rho,ef) . ((a1 + 1) -' 1)) is Element of the carrier of f
(1_ f) * rho is Element of the carrier of f
- ((1_ f) * rho) is Element of the carrier of f
(- ((1_ f) * rho)) * ((f,rho,ef) . ((a1 + 1) -' 1)) is Element of the carrier of f
- rho is Element of the carrier of f
(- rho) * ((f,rho,ef) . ((a1 + 1) -' 1)) is Element of the carrier of f
(f,rho,ef) . a1 is Element of the carrier of f
(- rho) * ((f,rho,ef) . a1) is Element of the carrier of f
a19 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
a19 -' 1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
a19 - 1 is complex V32() ext-real integer set
a19 - 1 is complex V32() ext-real integer set
(a19 - 1) + 1 is complex V32() ext-real integer set
a19 - 1 is complex V32() ext-real integer set
(f,rho,1) . (a19 -' 1) is Element of the carrier of f
b1 . a19 is set
(a1 + 1) -' a19 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(f,rho,ef) . ((a1 + 1) -' a19) is Element of the carrier of f
((f,rho,1) . (a19 -' 1)) * ((f,rho,ef) . ((a1 + 1) -' a19)) is Element of the carrier of f
1 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
a19 is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len a19 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
b19 is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len b19 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
a19 ^ b19 is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
a19 . 1 is set
<*(a19 . 1)*> is Relation-like NAT -defined Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like set
[1,(a19 . 1)] is set
{[1,(a19 . 1)]} is non empty V12() V47(1) set
<*(b1 . 1)*> is Relation-like NAT -defined Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like set
[1,(b1 . 1)] is set
{[1,(b1 . 1)]} is non empty V12() V47(1) set
<*(b1 /. 1)*> is Relation-like NAT -defined the carrier of f -valued Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of f
[1,(b1 /. 1)] is set
{[1,(b1 /. 1)]} is non empty V12() V47(1) set
Seg (len b19) is V40() V47( len b19) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len b19 ) } is set
dom b19 is Element of K19(NAT)
z is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
z + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
1 + (len b19) is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
b1 . (z + 1) is set
b19 . z is set
b19 /. z is Element of the carrier of f
Sum b19 is Element of the carrier of f
b19 /. 1 is Element of the carrier of f
b19 . 1 is set
b1 . 2 is set
b1 /. 2 is Element of the carrier of f
Sum a19 is Element of the carrier of f
(Sum a19) + (b1 /. 2) is Element of the carrier of f
(b1 /. 1) + (b1 /. 2) is Element of the carrier of f
2 - 1 is complex V32() ext-real integer set
2 -' 1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(f,rho,1) . (2 -' 1) is Element of the carrier of f
(a1 + 1) -' 2 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(f,rho,ef) . ((a1 + 1) -' 2) is Element of the carrier of f
((f,rho,1) . (2 -' 1)) * ((f,rho,ef) . ((a1 + 1) -' 2)) is Element of the carrier of f
(f,rho,1) . 1 is Element of the carrier of f
((f,rho,1) . 1) * ((f,rho,ef) . ((a1 + 1) -' 2)) is Element of the carrier of f
(1_ f) * ((f,rho,ef) . ((a1 + 1) -' 2)) is Element of the carrier of f
a19 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(f,rho,ef) . a19 is Element of the carrier of f
a1 -' 1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(f,rho,ef) . (a1 -' 1) is Element of the carrier of f
ef - 0 is complex V32() ext-real non negative integer set
(ef - 0) - 1 is complex V32() ext-real integer set
((f,rho,1) *' (f,rho,ef)) . zz is set
(f,rho,ef) . 0 is Element of the carrier of f
(- rho) * ((f,rho,ef) . 0) is Element of the carrier of f
(power f) . (rho,b9) is Element of the carrier of f
(- rho) * ((power f) . (rho,b9)) is Element of the carrier of f
rho * ((power f) . (rho,b9)) is Element of the carrier of f
- (rho * ((power f) . (rho,b9))) is Element of the carrier of f
(f,rho,ef) . zz is set
ef - (a1 -' 1) is complex V32() ext-real integer set
(ef - (a1 -' 1)) - 1 is complex V32() ext-real integer set
ef - a1 is complex V32() ext-real integer set
a1 - a1 is complex V32() ext-real integer set
a19 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
a19 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(ef - a1) - 1 is complex V32() ext-real integer set
ef - 0 is complex V32() ext-real non negative integer set
b19 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
b19 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
((f,rho,1) *' (f,rho,ef)) . zz is set
(power f) . (rho,b19) is Element of the carrier of f
(- rho) * ((power f) . (rho,b19)) is Element of the carrier of f
((- rho) * ((power f) . (rho,b19))) + ((f,rho,ef) . (a1 -' 1)) is Element of the carrier of f
(power f) . (rho,a19) is Element of the carrier of f
((- rho) * ((power f) . (rho,b19))) + ((power f) . (rho,a19)) is Element of the carrier of f
rho * ((power f) . (rho,b19)) is Element of the carrier of f
- (rho * ((power f) . (rho,b19))) is Element of the carrier of f
(- (rho * ((power f) . (rho,b19)))) + ((power f) . (rho,a19)) is Element of the carrier of f
- ((power f) . (rho,a19)) is Element of the carrier of f
(- ((power f) . (rho,a19))) + ((power f) . (rho,a19)) is Element of the carrier of f
(f,rho,ef) . zz is set
ef - b9 is complex V32() ext-real integer set
(ef - b9) - 1 is complex V32() ext-real integer set
(- rho) * (0. f) is Element of the carrier of f
((f,rho,1) *' (f,rho,ef)) . zz is set
(f,rho,ef) . b9 is Element of the carrier of f
(f,rho,ef) . zz is set
ef + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(ef + 1) - 1 is complex V32() ext-real integer set
(- rho) * (0. f) is Element of the carrier of f
((f,rho,1) *' (f,rho,ef)) . zz is set
(f,rho,ef) . zz is set
dom (f,rho,ef) is Element of K19(NAT)
f is non empty left_add-cancelable right_add-cancelable right_complementable unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef is Element of the carrier of f
(f,ef,1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support with_roots Element of K19(K20(NAT, the carrier of f))
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
power f is Relation-like K20( the carrier of f,NAT) -defined the carrier of f -valued Function-like total V18(K20( the carrier of f,NAT), the carrier of f) Element of K19(K20(K20( the carrier of f,NAT), the carrier of f))
K20( the carrier of f,NAT) is V40() set
K20(K20( the carrier of f,NAT), the carrier of f) is V40() set
K19(K20(K20( the carrier of f,NAT), the carrier of f)) is V40() set
(power f) . (ef,1) is Element of the carrier of f
- ((power f) . (ef,1)) is Element of the carrier of f
1_ f is Element of the carrier of f
1. f is Element of the carrier of f
(0,1) --> ((- ((power f) . (ef,1))),(1_ f)) is Relation-like {0,1} -defined the carrier of f -valued Function-like non empty total V18({0,1}, the carrier of f) Element of K19(K20({0,1}, the carrier of f))
{0,1} is non empty set
K20({0,1}, the carrier of f) is set
K19(K20({0,1}, the carrier of f)) is set
(0_. f) +* ((0,1) --> ((- ((power f) . (ef,1))),(1_ f))) is Relation-like Function-like set
len rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(f,ef,1) *' (0_. f) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
0 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(len rho) - 1 is complex V32() ext-real integer set
1_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho . 1 is Element of the carrier of f
(rho . 1) * (1_. f) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
Seg t is V40() V47(t) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= t ) } is set
Polynom-Ring f is non empty left_add-cancelable right_add-cancelable right_complementable strict unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed V150() V151() V152() V153() doubleLoopStr
the carrier of (Polynom-Ring f) is non empty set
b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
rho . b9 is set
dom rho is Element of K19(NAT)
zz is Element of the carrier of (Polynom-Ring f)
(f,ef,b9) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho /. b9 is Element of the carrier of f
(rho /. b9) * (f,ef,b9) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
zz is Element of the carrier of (Polynom-Ring f)
rho . b9 is Element of the carrier of f
a1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(f,ef,a1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(rho /. b9) * (f,ef,a1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
a1 is Element of the carrier of f
b1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(f,ef,b1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
a1 * (f,ef,b1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
b9 is Relation-like NAT -defined the carrier of (Polynom-Ring f) -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring f)
dom b9 is Element of K19(NAT)
zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
rho . zz is Element of the carrier of f
b9 . zz is set
(f,ef,zz) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(rho . zz) * (f,ef,zz) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
a1 is Element of the carrier of f
b1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(f,ef,b1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
a1 * (f,ef,b1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
rho . zz is set
a1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(f,ef,a1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(power f) . (ef,a1) is Element of the carrier of f
- ((power f) . (ef,a1)) is Element of the carrier of f
(0,a1) --> ((- ((power f) . (ef,a1))),(1_ f)) is Relation-like {0,a1} -defined the carrier of f -valued Function-like non empty total V18({0,a1}, the carrier of f) Element of K19(K20({0,a1}, the carrier of f))
{0,a1} is non empty set
K20({0,a1}, the carrier of f) is set
K19(K20({0,a1}, the carrier of f)) is set
(0_. f) +* ((0,a1) --> ((- ((power f) . (ef,a1))),(1_ f))) is Relation-like Function-like set
rho /. zz is Element of the carrier of f
(rho /. zz) * (f,ef,a1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
b1 is Element of the carrier of (Polynom-Ring f)
dom rho is Element of K19(NAT)
zz is Relation-like NAT -defined the carrier of (Polynom-Ring f) -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring f)
dom zz is Element of K19(NAT)
Sum b9 is Element of the carrier of (Polynom-Ring f)
Sum zz is Element of the carrier of (Polynom-Ring f)
z is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
rho . z is Element of the carrier of f
zz . z is set
(f,ef,z) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(power f) . (ef,z) is Element of the carrier of f
- ((power f) . (ef,z)) is Element of the carrier of f
(0,z) --> ((- ((power f) . (ef,z))),(1_ f)) is Relation-like {0,z} -defined the carrier of f -valued Function-like non empty total V18({0,z}, the carrier of f) Element of K19(K20({0,z}, the carrier of f))
{0,z} is non empty set
K20({0,z}, the carrier of f) is set
K19(K20({0,z}, the carrier of f)) is set
(0_. f) +* ((0,z) --> ((- ((power f) . (ef,z))),(1_ f))) is Relation-like Function-like set
(rho . z) * (f,ef,z) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
g1 is Element of the carrier of f
s1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(f,ef,s1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(power f) . (ef,s1) is Element of the carrier of f
- ((power f) . (ef,s1)) is Element of the carrier of f
(0,s1) --> ((- ((power f) . (ef,s1))),(1_ f)) is Relation-like {0,s1} -defined the carrier of f -valued Function-like non empty total V18({0,s1}, the carrier of f) Element of K19(K20({0,s1}, the carrier of f))
{0,s1} is non empty set
K20({0,s1}, the carrier of f) is set
K19(K20({0,s1}, the carrier of f)) is set
(0_. f) +* ((0,s1) --> ((- ((power f) . (ef,s1))),(1_ f))) is Relation-like Function-like set
g1 * (f,ef,s1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
t + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
z is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(f,zz,z) is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
Seg (len zz) is V40() V47( len zz) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len zz ) } is set
len (f,zz,z) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
Seg (len (f,zz,z)) is V40() V47( len (f,zz,z)) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len (f,zz,z) ) } is set
dom (f,zz,z) is Element of K19(NAT)
s1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
zz . s1 is set
(f,zz,z) . s1 is set
(f,ef,s1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(power f) . (ef,s1) is Element of the carrier of f
- ((power f) . (ef,s1)) is Element of the carrier of f
(0,s1) --> ((- ((power f) . (ef,s1))),(1_ f)) is Relation-like {0,s1} -defined the carrier of f -valued Function-like non empty total V18({0,s1}, the carrier of f) Element of K19(K20({0,s1}, the carrier of f))
{0,s1} is non empty set
K20({0,s1}, the carrier of f) is set
K19(K20({0,s1}, the carrier of f)) is set
(0_. f) +* ((0,s1) --> ((- ((power f) . (ef,s1))),(1_ f))) is Relation-like Function-like set
rho . s1 is Element of the carrier of f
(rho . s1) * (f,ef,s1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
((rho . s1) * (f,ef,s1)) . z is Element of the carrier of f
(f,ef,s1) . z is Element of the carrier of f
(rho . s1) * ((f,ef,s1) . z) is Element of the carrier of f
(rho . s1) * (0. f) is Element of the carrier of f
i is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
i . z is Element of the carrier of f
Sum (f,zz,z) is Element of the carrier of f
b19 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
b19 . z is Element of the carrier of f
z is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
z + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
zz . z is set
(f,ef,z) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(power f) . (ef,z) is Element of the carrier of f
- ((power f) . (ef,z)) is Element of the carrier of f
(0,z) --> ((- ((power f) . (ef,z))),(1_ f)) is Relation-like {0,z} -defined the carrier of f -valued Function-like non empty total V18({0,z}, the carrier of f) Element of K19(K20({0,z}, the carrier of f))
{0,z} is non empty set
K20({0,z}, the carrier of f) is set
K19(K20({0,z}, the carrier of f)) is set
(0_. f) +* ((0,z) --> ((- ((power f) . (ef,z))),(1_ f))) is Relation-like Function-like set
rho . z is Element of the carrier of f
(rho . z) * (f,ef,z) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,zz,z) is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len (f,zz,z) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
Seg (len (f,zz,z)) is V40() V47( len (f,zz,z)) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len (f,zz,z) ) } is set
dom (f,zz,z) is Element of K19(NAT)
(f,zz,z) . z is set
s1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
zz . s1 is set
(f,zz,z) . s1 is set
(f,ef,s1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(power f) . (ef,s1) is Element of the carrier of f
- ((power f) . (ef,s1)) is Element of the carrier of f
(0,s1) --> ((- ((power f) . (ef,s1))),(1_ f)) is Relation-like {0,s1} -defined the carrier of f -valued Function-like non empty total V18({0,s1}, the carrier of f) Element of K19(K20({0,s1}, the carrier of f))
{0,s1} is non empty set
K20({0,s1}, the carrier of f) is set
K19(K20({0,s1}, the carrier of f)) is set
(0_. f) +* ((0,s1) --> ((- ((power f) . (ef,s1))),(1_ f))) is Relation-like Function-like set
rho . s1 is Element of the carrier of f
(rho . s1) * (f,ef,s1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
((rho . s1) * (f,ef,s1)) . z is Element of the carrier of f
(f,ef,s1) . z is Element of the carrier of f
(rho . s1) * ((f,ef,s1) . z) is Element of the carrier of f
(rho . s1) * (0. f) is Element of the carrier of f
i is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
i . z is Element of the carrier of f
(f,zz,z) /. s1 is Element of the carrier of f
Sum (f,zz,z) is Element of the carrier of f
(f,zz,z) /. z is Element of the carrier of f
b19 . z is Element of the carrier of f
((rho . z) * (f,ef,z)) . z is Element of the carrier of f
s1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
s1 . z is Element of the carrier of f
z is set
dom rho is Element of K19(NAT)
g1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(f,zz,0) is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
eval (rho,ef) is Element of the carrier of f
i is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
Sum i is Element of the carrier of f
len i is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
dom i is Element of K19(NAT)
rho . 0 is Element of the carrier of f
- (rho . 0) is Element of the carrier of f
<*(- (rho . 0))*> is Relation-like NAT -defined the carrier of f -valued Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of f
[1,(- (rho . 0))] is set
{[1,(- (rho . 0))]} is non empty V12() V47(1) set
<*(- (rho . 0))*> ^ (f,zz,0) is Relation-like NAT -defined the carrier of f -valued Function-like non empty V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len (<*(- (rho . 0))*> ^ (f,zz,0)) is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
len <*(- (rho . 0))*> is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
len (f,zz,0) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len <*(- (rho . 0))*>) + (len (f,zz,0)) is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
1 + (len (f,zz,0)) is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
1 + (len zz) is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
dom (<*(- (rho . 0))*> ^ (f,zz,0)) is Element of K19(NAT)
Seg (len i) is V40() V47( len i) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len i ) } is set
Seg (len (f,zz,0)) is V40() V47( len (f,zz,0)) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len (f,zz,0) ) } is set
dom (f,zz,0) is Element of K19(NAT)
e is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power f) . (ef,e) is Element of the carrier of f
- ((power f) . (ef,e)) is Element of the carrier of f
zz . e is set
(f,zz,0) . e is set
(f,ef,e) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(0,e) --> ((- ((power f) . (ef,e))),(1_ f)) is Relation-like {0,e} -defined the carrier of f -valued Function-like non empty total V18({0,e}, the carrier of f) Element of K19(K20({0,e}, the carrier of f))
{0,e} is non empty set
K20({0,e}, the carrier of f) is set
K19(K20({0,e}, the carrier of f)) is set
(0_. f) +* ((0,e) --> ((- ((power f) . (ef,e))),(1_ f))) is Relation-like Function-like set
rho . e is Element of the carrier of f
(rho . e) * (f,ef,e) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
((rho . e) * (f,ef,e)) . g1 is Element of the carrier of f
(f,ef,e) . g1 is Element of the carrier of f
(rho . e) * ((f,ef,e) . g1) is Element of the carrier of f
j1 is Element of the carrier of f
(rho . e) * j1 is Element of the carrier of f
(rho . e) * ((power f) . (ef,e)) is Element of the carrier of f
- ((rho . e) * ((power f) . (ef,e))) is Element of the carrier of f
c₁₉ is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
c₁₉ . g1 is Element of the carrier of f
dom <*(- (rho . 0))*> is non empty V12() V47(1) Element of K19(NAT)
e is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
i /. e is Element of the carrier of f
i . e is set
e -' 1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
rho . (e -' 1) is Element of the carrier of f
(power f) . (ef,(e -' 1)) is Element of the carrier of f
(rho . (e -' 1)) * ((power f) . (ef,(e -' 1))) is Element of the carrier of f
Seg (len (<*(- (rho . 0))*> ^ (f,zz,0))) is non empty V40() V47( len (<*(- (rho . 0))*> ^ (f,zz,0))) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len (<*(- (rho . 0))*> ^ (f,zz,0)) ) } is set
1 - 1 is complex V32() ext-real integer set
(rho . 0) * (1_ f) is Element of the carrier of f
(<*(- (rho . 0))*> ^ (f,zz,0)) . e is set
<*(- (rho . 0))*> . e is set
(<*(- (rho . 0))*> ^ (f,zz,0)) /. e is Element of the carrier of f
- (i /. e) is Element of the carrier of f
e - 1 is complex V32() ext-real integer set
j1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
j1 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(len (<*(- (rho . 0))*> ^ (f,zz,0))) - 1 is complex V32() ext-real integer set
1 - 1 is complex V32() ext-real integer set
(<*(- (rho . 0))*> ^ (f,zz,0)) . e is set
e - (len <*(- (rho . 0))*>) is complex V32() ext-real integer set
(f,zz,0) . (e - (len <*(- (rho . 0))*>)) is set
(f,zz,0) . (e - 1) is set
rho . j1 is Element of the carrier of f
(power f) . (ef,j1) is Element of the carrier of f
(rho . j1) * ((power f) . (ef,j1)) is Element of the carrier of f
- ((rho . j1) * ((power f) . (ef,j1))) is Element of the carrier of f
(<*(- (rho . 0))*> ^ (f,zz,0)) /. e is Element of the carrier of f
- (i /. e) is Element of the carrier of f
- (Sum i) is Element of the carrier of f
Sum (<*(- (rho . 0))*> ^ (f,zz,0)) is Element of the carrier of f
Sum <*(- (rho . 0))*> is Element of the carrier of f
Sum (f,zz,0) is Element of the carrier of f
(Sum <*(- (rho . 0))*>) + (Sum (f,zz,0)) is Element of the carrier of f
(- (rho . 0)) + (Sum (f,zz,0)) is Element of the carrier of f
(rho . 0) + ((- (rho . 0)) + (Sum (f,zz,0))) is Element of the carrier of f
(rho . 0) + (- (rho . 0)) is Element of the carrier of f
((rho . 0) + (- (rho . 0))) + (Sum (f,zz,0)) is Element of the carrier of f
(0. f) + (Sum (f,zz,0)) is Element of the carrier of f
rho . z is set
b19 . z is set
g1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
b19 . z is set
rho . z is set
b19 . z is set
(f,ef,g1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(power f) . (ef,g1) is Element of the carrier of f
- ((power f) . (ef,g1)) is Element of the carrier of f
(0,g1) --> ((- ((power f) . (ef,g1))),(1_ f)) is Relation-like {0,g1} -defined the carrier of f -valued Function-like non empty total V18({0,g1}, the carrier of f) Element of K19(K20({0,g1}, the carrier of f))
{0,g1} is non empty set
K20({0,g1}, the carrier of f) is set
K19(K20({0,g1}, the carrier of f)) is set
(0_. f) +* ((0,g1) --> ((- ((power f) . (ef,g1))),(1_ f))) is Relation-like Function-like set
rho . g1 is Element of the carrier of f
(rho . g1) * (f,ef,g1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
((rho . g1) * (f,ef,g1)) . g1 is Element of the carrier of f
(f,ef,g1) . g1 is Element of the carrier of f
(rho . g1) * ((f,ef,g1) . g1) is Element of the carrier of f
(rho . g1) * (1_ f) is Element of the carrier of f
rho . z is set
g1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(f,rho) is complex V32() ext-real integer set
b9 . 1 is set
g1 is set
dom b19 is Element of K19(NAT)
z is Element of the carrier of (Polynom-Ring f)
z * b9 is Relation-like NAT -defined the carrier of (Polynom-Ring f) -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring f)
dom (z * b9) is Element of K19(NAT)
s1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
b9 /. s1 is Element of the carrier of (Polynom-Ring f)
(z * b9) . s1 is set
(z * b9) /. s1 is Element of the carrier of (Polynom-Ring f)
z * (b9 /. s1) is Element of the carrier of (Polynom-Ring f)
(f,ef,1) *' ((rho . 1) * (1_. f)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,ef,1) *' (1_. f) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(rho . 1) * ((f,ef,1) *' (1_. f)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(rho . 1) * (f,ef,1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
zz . s1 is set
b9 /. s1 is Element of the carrier of (Polynom-Ring f)
b9 . s1 is set
i is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(f,ef,i) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho . i is Element of the carrier of f
(rho . i) * (f,ef,i) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(z * b9) . s1 is set
(z * b9) /. s1 is Element of the carrier of (Polynom-Ring f)
z * (b9 /. s1) is Element of the carrier of (Polynom-Ring f)
(f,ef,1) *' ((rho . i) * (f,ef,i)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,ef,1) *' (f,ef,i) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(rho . i) * ((f,ef,1) *' (f,ef,i)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,ef,i) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(power f) . (ef,i) is Element of the carrier of f
- ((power f) . (ef,i)) is Element of the carrier of f
(0,i) --> ((- ((power f) . (ef,i))),(1_ f)) is Relation-like {0,i} -defined the carrier of f -valued Function-like non empty total V18({0,i}, the carrier of f) Element of K19(K20({0,i}, the carrier of f))
{0,i} is non empty set
K20({0,i}, the carrier of f) is set
K19(K20({0,i}, the carrier of f)) is set
(0_. f) +* ((0,i) --> ((- ((power f) . (ef,i))),(1_ f))) is Relation-like Function-like set
(rho . i) * (f,ef,i) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
zz . s1 is set
b19 . g1 is set
a19 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,ef,1) *' a19 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
((f,ef,1) *' a19) . g1 is set
dom ((f,ef,1) *' a19) is Element of K19(NAT)
f is non empty left_add-cancelable right_add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support with_roots Element of K19(K20(NAT, the carrier of f))
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,ef) is complex V32() ext-real integer set
len ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len ef) - 1 is complex V32() ext-real integer set
{ (rho - (b₁ *' ef)) where b₁ is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f)) : 1 = 1 } is set
(len ef) + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
0 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
1 - 1 is complex V32() ext-real integer set
ef . ((len ef) - 1) is set
(len ef) -' 1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef . ((len ef) -' 1) is Element of the carrier of f
rho + (0_. f) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- (0_. f) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho + (- (0_. f)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(0_. f) *' ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho - ((0_. f) *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- ((0_. f) *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho + (- ((0_. f) *' ef)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
len rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
t is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
len t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
b9 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
len b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
b9 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
len b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
zz is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
zz *' ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho - (zz *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- (zz *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho + (- (zz *' ef)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(zz *' ef) + (rho - (zz *' ef)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(zz *' ef) + (- (zz *' ef)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
((zz *' ef) + (- (zz *' ef))) + rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(zz *' ef) - (zz *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(zz *' ef) + (- (zz *' ef)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
((zz *' ef) - (zz *' ef)) + rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(0_. f) + rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
a1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
(f,b9) is complex V32() ext-real integer set
(len b9) - 1 is complex V32() ext-real integer set
(len b9) + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(len b9) - 1 is complex V32() ext-real integer set
a1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
a1 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
dom b9 is Element of K19(NAT)
(f,b9) is complex V32() ext-real integer set
(f,b9) - (f,ef) is complex V32() ext-real integer set
(len b9) -' 1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
b9 . ((len b9) -' 1) is Element of the carrier of f
(ef . ((len ef) -' 1)) " is Element of the carrier of f
(b9 . ((len b9) -' 1)) * ((ef . ((len ef) -' 1)) ") is Element of the carrier of f
b1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
{b1} is non empty V12() V47(1) set
{b1} --> ((b9 . ((len b9) -' 1)) * ((ef . ((len ef) -' 1)) ")) is Relation-like {b1} -defined the carrier of f -valued Function-like constant non empty total V18({b1}, the carrier of f) Element of K19(K20({b1}, the carrier of f))
K20({b1}, the carrier of f) is set
K19(K20({b1}, the carrier of f)) is set
{((b9 . ((len b9) -' 1)) * ((ef . ((len ef) -' 1)) "))} is non empty V12() V47(1) set
K20({b1},{((b9 . ((len b9) -' 1)) * ((ef . ((len ef) -' 1)) "))}) is set
(0_. f) +* ({b1} --> ((b9 . ((len b9) -' 1)) * ((ef . ((len ef) -' 1)) "))) is Relation-like Function-like set
dom (0_. f) is Element of K19(NAT)
z is set
z is set
g1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
dom ({b1} --> ((b9 . ((len b9) -' 1)) * ((ef . ((len ef) -' 1)) "))) is Element of K19({b1})
K19({b1}) is set
((0_. f) +* ({b1} --> ((b9 . ((len b9) -' 1)) * ((ef . ((len ef) -' 1)) ")))) . g1 is set
({b1} --> ((b9 . ((len b9) -' 1)) * ((ef . ((len ef) -' 1)) "))) . b1 is set
((0_. f) +* ({b1} --> ((b9 . ((len b9) -' 1)) * ((ef . ((len ef) -' 1)) ")))) . z is set
g1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
dom ({b1} --> ((b9 . ((len b9) -' 1)) * ((ef . ((len ef) -' 1)) "))) is Element of K19({b1})
K19({b1}) is set
((0_. f) +* ({b1} --> ((b9 . ((len b9) -' 1)) * ((ef . ((len ef) -' 1)) ")))) . g1 is set
(0_. f) . g1 is Element of the carrier of f
((0_. f) +* ({b1} --> ((b9 . ((len b9) -' 1)) * ((ef . ((len ef) -' 1)) ")))) . z is set
g1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
dom ({b1} --> ((b9 . ((len b9) -' 1)) * ((ef . ((len ef) -' 1)) "))) is Element of K19({b1})
K19({b1}) is set
dom ({b1} --> ((b9 . ((len b9) -' 1)) * ((ef . ((len ef) -' 1)) "))) is Element of K19({b1})
K19({b1}) is set
(dom (0_. f)) \/ (dom ({b1} --> ((b9 . ((len b9) -' 1)) * ((ef . ((len ef) -' 1)) ")))) is set
dom ((0_. f) +* ({b1} --> ((b9 . ((len b9) -' 1)) * ((ef . ((len ef) -' 1)) ")))) is set
z is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) Element of K19(K20(NAT, the carrier of f))
g1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
z . g1 is Element of the carrier of f
(0_. f) . g1 is Element of the carrier of f
b1 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
g1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
s1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
z . s1 is Element of the carrier of f
s1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
z . s1 is Element of the carrier of f
z . b1 is Element of the carrier of f
({b1} --> ((b9 . ((len b9) -' 1)) * ((ef . ((len ef) -' 1)) "))) . b1 is set
s1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
g1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
zz + g1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(zz + g1) *' ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho - ((zz + g1) *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- ((zz + g1) *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho + (- ((zz + g1) *' ef)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
b1 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
i is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
i + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
t - (f,ef) is complex V32() ext-real integer set
(i + 1) - (b1 + 1) is complex V32() ext-real integer set
g1 *' ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(g1 *' ef) . i is Element of the carrier of f
sf is Relation-like NAT -defined the carrier of f -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len sf is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
Sum sf is Element of the carrier of f
dom sf is Element of K19(NAT)
Seg (len sf) is V40() V47( len sf) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len sf ) } is set
e is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
e - 1 is complex V32() ext-real integer set
e -' 1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
g1 . (e -' 1) is Element of the carrier of f
e is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
sf . e is set
e -' 1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
g1 . (e -' 1) is Element of the carrier of f
(i + 1) -' e is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef . ((i + 1) -' e) is Element of the carrier of f
(g1 . (e -' 1)) * (ef . ((i + 1) -' e)) is Element of the carrier of f
(0. f) * (ef . ((i + 1) -' e)) is Element of the carrier of f
sf /. e is Element of the carrier of f
sf /. (b1 + 1) is Element of the carrier of f
sf . (b1 + 1) is set
(b1 + 1) -' 1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
g1 . ((b1 + 1) -' 1) is Element of the carrier of f
(i + 1) -' (b1 + 1) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef . ((i + 1) -' (b1 + 1)) is Element of the carrier of f
(g1 . ((b1 + 1) -' 1)) * (ef . ((i + 1) -' (b1 + 1))) is Element of the carrier of f
((b9 . ((len b9) -' 1)) * ((ef . ((len ef) -' 1)) ")) * (ef . ((i + 1) -' (b1 + 1))) is Element of the carrier of f
(rho - ((zz + g1) *' ef)) - b9 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- b9 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(rho - ((zz + g1) *' ef)) + (- b9) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho + (- ((zz + g1) *' ef)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- (- (zz *' ef)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(- rho) + (- (- (zz *' ef))) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(rho + (- ((zz + g1) *' ef))) + ((- rho) + (- (- (zz *' ef)))) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(rho + (- ((zz + g1) *' ef))) + (- rho) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
((rho + (- ((zz + g1) *' ef))) + (- rho)) + (- (- (zz *' ef))) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho - rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho + (- rho) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(rho - rho) + (- ((zz + g1) *' ef)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
((rho - rho) + (- ((zz + g1) *' ef))) + (- (- (zz *' ef))) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(0_. f) + (- ((zz + g1) *' ef)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
((0_. f) + (- ((zz + g1) *' ef))) + (- (- (zz *' ef))) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(- ((zz + g1) *' ef)) + (- (- (zz *' ef))) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- (zz + g1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(- (zz + g1)) *' ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
((- (zz + g1)) *' ef) + (- (- (zz *' ef))) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- zz is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- g1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(- zz) + (- g1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
((- zz) + (- g1)) *' ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(((- zz) + (- g1)) *' ef) + (- (- (zz *' ef))) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(((- zz) + (- g1)) *' ef) + (zz *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(- zz) *' ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(- g1) *' ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
((- zz) *' ef) + ((- g1) *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(((- zz) *' ef) + ((- g1) *' ef)) + (zz *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
((- zz) *' ef) + (zz *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
((- g1) *' ef) + (((- zz) *' ef) + (zz *' ef)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
((- g1) *' ef) + ((zz *' ef) - (zz *' ef)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
((- g1) *' ef) + (0_. f) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- (g1 *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
dom (g1 *' ef) is Element of K19(NAT)
(rho - ((zz + g1) *' ef)) + (0_. f) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
b9 - b9 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
b9 + (- b9) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(rho - ((zz + g1) *' ef)) + (b9 - b9) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(rho - ((zz + g1) *' ef)) + (- b9) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
((rho - ((zz + g1) *' ef)) + (- b9)) + b9 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
b9 - (g1 *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
b9 + (- (g1 *' ef)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(rho - ((zz + g1) *' ef)) . i is Element of the carrier of f
b9 . i is Element of the carrier of f
(- (g1 *' ef)) . i is Element of the carrier of f
(b9 . i) + ((- (g1 *' ef)) . i) is Element of the carrier of f
- ((g1 *' ef) . i) is Element of the carrier of f
(b9 . i) + (- ((g1 *' ef) . i)) is Element of the carrier of f
b9 /. i is Element of the carrier of f
(b9 /. i) + (- ((g1 *' ef) . i)) is Element of the carrier of f
(g1 *' ef) /. i is Element of the carrier of f
- ((g1 *' ef) /. i) is Element of the carrier of f
(b9 /. i) + (- ((g1 *' ef) /. i)) is Element of the carrier of f
i - a1 is complex V32() ext-real integer set
a1 - a1 is complex V32() ext-real integer set
e is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
e + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(i - a1) - 1 is complex V32() ext-real integer set
0 + (len ef) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
((i - a1) - 1) + (len ef) is complex V32() ext-real integer set
(i - a1) + ((len ef) - 1) is complex V32() ext-real integer set
- (0. f) is Element of the carrier of f
(0. f) + (- (0. f)) is Element of the carrier of f
(0. f) + (0. f) is Element of the carrier of f
((ef . ((len ef) -' 1)) ") * (ef . ((len ef) -' 1)) is Element of the carrier of f
(b9 . ((len b9) -' 1)) * (((ef . ((len ef) -' 1)) ") * (ef . ((len ef) -' 1))) is Element of the carrier of f
1_ f is Element of the carrier of f
1. f is Element of the carrier of f
(b9 . ((len b9) -' 1)) * (1_ f) is Element of the carrier of f
b9 . ((len b9) - 1) is set
b9 /. ((len b9) - 1) is Element of the carrier of f
- (b9 /. ((len b9) - 1)) is Element of the carrier of f
(b9 /. ((len b9) - 1)) + (- (b9 /. ((len b9) - 1))) is Element of the carrier of f
len (rho - ((zz + g1) *' ef)) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
i is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
len i is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef1 *' ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
t is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
t *' ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
b9 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(ef1 *' ef) + b9 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,b9) is complex V32() ext-real integer set
len b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len b9) - 1 is complex V32() ext-real integer set
zz is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(t *' ef) + zz is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,zz) is complex V32() ext-real integer set
len zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len zz) - 1 is complex V32() ext-real integer set
t - ef1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- ef1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
t + (- ef1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(t - ef1) *' ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(- ef1) *' ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(t *' ef) + ((- ef1) *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(t *' ef) - (ef1 *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- (ef1 *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(t *' ef) + (- (ef1 *' ef)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(t *' ef) + (0_. f) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
zz - zz is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- zz is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
zz + (- zz) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(t *' ef) + (zz - zz) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
((ef1 *' ef) + b9) + (- zz) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
b9 + (- zz) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(ef1 *' ef) + (b9 + (- zz)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
((ef1 *' ef) + (b9 + (- zz))) + (- (ef1 *' ef)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(ef1 *' ef) - (ef1 *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(ef1 *' ef) + (- (ef1 *' ef)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(b9 + (- zz)) + ((ef1 *' ef) - (ef1 *' ef)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(b9 + (- zz)) + (0_. f) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
b9 - zz is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
b9 + (- zz) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
t + (- ef1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(t + (- ef1)) + ef1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef1 - ef1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef1 + (- ef1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
t + (ef1 - ef1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
t + (0_. f) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,(t - ef1)) is complex V32() ext-real integer set
len (t - ef1) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len (t - ef1)) - 1 is complex V32() ext-real integer set
(f,(b9 - zz)) is complex V32() ext-real integer set
len (b9 - zz) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len (b9 - zz)) - 1 is complex V32() ext-real integer set
(f,(- zz)) is complex V32() ext-real integer set
len (- zz) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len (- zz)) - 1 is complex V32() ext-real integer set
max ((f,b9),(f,(- zz))) is complex V32() ext-real set
max ((f,b9),(f,zz)) is complex V32() ext-real set
b1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
a1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
a1 + b1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
f is non empty left_add-cancelable right_add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,rho,ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,rho,ef) *' ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho - ((f,rho,ef) *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- ((f,rho,ef) *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho + (- ((f,rho,ef) *' ef)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
f is non empty left_add-cancelable right_add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
f is non empty left_add-cancelable right_add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support with_roots Element of K19(K20(NAT, the carrier of f))
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,ef) is complex V32() ext-real integer set
len ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len ef) - 1 is complex V32() ext-real integer set
(f,ef) - 0 is complex V32() ext-real integer set
0 - 1 is non empty complex V32() ext-real non positive negative integer set
(f,(0_. f)) is complex V32() ext-real integer set
len (0_. f) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len (0_. f)) - 1 is complex V32() ext-real integer set
ef1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef1 *' ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(ef1 *' ef) + (0_. f) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,rho,ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,rho,ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,rho,ef) *' ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho - ((f,rho,ef) *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
- ((f,rho,ef) *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
rho + (- ((f,rho,ef) *' ef)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
((f,rho,ef) *' ef) + ef1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,ef1) is complex V32() ext-real integer set
len ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len ef1) - 1 is complex V32() ext-real integer set
((f,rho,ef) *' ef) - ((f,rho,ef) *' ef) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
((f,rho,ef) *' ef) + (- ((f,rho,ef) *' ef)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef1 + (((f,rho,ef) *' ef) - ((f,rho,ef) *' ef)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef1 + (0_. f) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef1 *' ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
t is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
t *' ef is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
f is non empty non degenerated V72() left_add-cancelable right_add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty V12() set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef is Element of the carrier of f
(f,ef,1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support with_roots Element of K19(K20(NAT, the carrier of f))
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
power f is Relation-like K20( the carrier of f,NAT) -defined the carrier of f -valued Function-like total V18(K20( the carrier of f,NAT), the carrier of f) Element of K19(K20(K20( the carrier of f,NAT), the carrier of f))
K20( the carrier of f,NAT) is V40() set
K20(K20( the carrier of f,NAT), the carrier of f) is V40() set
K19(K20(K20( the carrier of f,NAT), the carrier of f)) is V40() set
(power f) . (ef,1) is Element of the carrier of f
- ((power f) . (ef,1)) is Element of the carrier of f
1_ f is Element of the carrier of f
1. f is non zero Element of the carrier of f
(0,1) --> ((- ((power f) . (ef,1))),(1_ f)) is Relation-like {0,1} -defined the carrier of f -valued Function-like non empty total V18({0,1}, the carrier of f) Element of K19(K20({0,1}, the carrier of f))
{0,1} is non empty set
K20({0,1}, the carrier of f) is set
K19(K20({0,1}, the carrier of f)) is set
(0_. f) +* ((0,1) --> ((- ((power f) . (ef,1))),(1_ f))) is Relation-like Function-like set
(f,ef,1) . 1 is Element of the carrier of f
ef1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,ef,1) *' ef1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
f is non empty non degenerated V72() left_add-cancelable right_add-cancelable right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed domRing-like V150() V151() V152() V153() doubleLoopStr
the carrier of f is non empty V12() set
K20(NAT, the carrier of f) is V40() set
K19(K20(NAT, the carrier of f)) is V40() set
0_. f is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support with_roots Element of K19(K20(NAT, the carrier of f))
0. f is zero Element of the carrier of f
NAT --> (0. f) is Relation-like NAT -defined the carrier of f -valued Function-like constant non empty total V18( NAT , the carrier of f) V28() Element of K19(K20(NAT, the carrier of f))
{(0. f)} is non empty V12() V47(1) set
K20(NAT,{(0. f)}) is V40() set
rho is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,rho) is complex V32() ext-real integer set
len rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len rho) - 1 is complex V32() ext-real integer set
(f,rho) - 1 is complex V32() ext-real integer set
ef is Element of the carrier of f
(f,ef,1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
power f is Relation-like K20( the carrier of f,NAT) -defined the carrier of f -valued Function-like total V18(K20( the carrier of f,NAT), the carrier of f) Element of K19(K20(K20( the carrier of f,NAT), the carrier of f))
K20( the carrier of f,NAT) is V40() set
K20(K20( the carrier of f,NAT), the carrier of f) is V40() set
K19(K20(K20( the carrier of f,NAT), the carrier of f)) is V40() set
(power f) . (ef,1) is Element of the carrier of f
- ((power f) . (ef,1)) is Element of the carrier of f
1_ f is Element of the carrier of f
1. f is non zero Element of the carrier of f
(0,1) --> ((- ((power f) . (ef,1))),(1_ f)) is Relation-like {0,1} -defined the carrier of f -valued Function-like non empty total V18({0,1}, the carrier of f) Element of K19(K20({0,1}, the carrier of f))
{0,1} is non empty set
K20({0,1}, the carrier of f) is set
K19(K20({0,1}, the carrier of f)) is set
(0_. f) +* ((0,1) --> ((- ((power f) . (ef,1))),(1_ f))) is Relation-like Function-like set
(f,rho,(f,ef,1)) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,(f,rho,(f,ef,1))) is complex V32() ext-real integer set
len (f,rho,(f,ef,1)) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len (f,rho,(f,ef,1))) - 1 is complex V32() ext-real integer set
ef1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,ef,1) *' ef1 is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
ef1 *' (f,ef,1) is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,(f,ef,1)) is complex V32() ext-real integer set
len (f,ef,1) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len (f,ef,1)) - 1 is complex V32() ext-real integer set
t is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support with_roots Element of K19(K20(NAT, the carrier of f))
(ef1 *' (f,ef,1)) + t is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,t) is complex V32() ext-real integer set
len t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len t) - 1 is complex V32() ext-real integer set
(f,ef1) is complex V32() ext-real integer set
len ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len ef1) - 1 is complex V32() ext-real integer set
(f,(f,ef,1)) + (f,ef1) is complex V32() ext-real integer set
1 + (f,ef1) is complex V32() ext-real integer set
t is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(ef1 *' (f,ef,1)) + t is Relation-like NAT -defined the carrier of f -valued Function-like non empty total V18( NAT , the carrier of f) finite-Support Element of K19(K20(NAT, the carrier of f))
(f,t) is complex V32() ext-real integer set
len t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len t) - 1 is complex V32() ext-real integer set
0_. F_Complex is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support with_roots Element of K19(K20(NAT, the carrier of F_Complex))
NAT --> (0. F_Complex) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like constant non empty total V18( NAT , the carrier of F_Complex) V28() Element of K19(K20(NAT, the carrier of F_Complex))
{(0. F_Complex)} is non empty V12() V47(1) set
K20(NAT,{(0. F_Complex)}) is V40() set
eval ((0_. F_Complex),(1_ F_Complex)) is complex Element of the carrier of F_Complex
1_. F_Complex is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
f is complex Element of the carrier of F_Complex
f * (1_. F_Complex) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
ef is complex Element of the carrier of F_Complex
eval ((f * (1_. F_Complex)),ef) is complex Element of the carrier of F_Complex
eval ((1_. F_Complex),ef) is complex Element of the carrier of F_Complex
f * (eval ((1_. F_Complex),ef)) is complex Element of the carrier of F_Complex
K182(f,(eval ((1_. F_Complex),ef))) is complex Element of COMPLEX
f * (1_ F_Complex) is complex Element of the carrier of F_Complex
K182(f,(1_ F_Complex)) is complex Element of COMPLEX
Re ef is complex V32() ext-real Element of REAL
f is complex Element of the carrier of F_Complex
rho is complex Element of the carrier of F_Complex
(F_Complex,rho,1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(power F_Complex) . (rho,1) is complex Element of the carrier of F_Complex
- ((power F_Complex) . (rho,1)) is complex Element of the carrier of F_Complex
(0,1) --> ((- ((power F_Complex) . (rho,1))),(1_ F_Complex)) is Relation-like {0,1} -defined the carrier of F_Complex -valued Function-like non empty total V18({0,1}, the carrier of F_Complex) Element of K19(K20({0,1}, the carrier of F_Complex))
{0,1} is non empty set
K20({0,1}, the carrier of F_Complex) is set
K19(K20({0,1}, the carrier of F_Complex)) is set
(0_. F_Complex) +* ((0,1) --> ((- ((power F_Complex) . (rho,1))),(1_ F_Complex))) is Relation-like Function-like set
f * (F_Complex,rho,1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
Re rho is complex V32() ext-real Element of REAL
ef1 is complex Element of the carrier of F_Complex
eval ((f * (F_Complex,rho,1)),ef1) is complex Element of the carrier of F_Complex
eval ((F_Complex,rho,1),ef1) is complex Element of the carrier of F_Complex
f * (eval ((F_Complex,rho,1),ef1)) is complex Element of the carrier of F_Complex
K182(f,(eval ((F_Complex,rho,1),ef1))) is complex Element of COMPLEX
ef1 - rho is complex Element of the carrier of F_Complex
f * (ef1 - rho) is complex Element of the carrier of F_Complex
K182(f,(ef1 - rho)) is complex Element of COMPLEX
Re ef1 is complex V32() ext-real Element of REAL
eval ((f * (F_Complex,rho,1)),rho) is complex Element of the carrier of F_Complex
eval ((F_Complex,rho,1),rho) is complex Element of the carrier of F_Complex
f * (eval ((F_Complex,rho,1),rho)) is complex Element of the carrier of F_Complex
K182(f,(eval ((F_Complex,rho,1),rho))) is complex Element of COMPLEX
rho - rho is complex Element of the carrier of F_Complex
f * (rho - rho) is complex Element of the carrier of F_Complex
K182(f,(rho - rho)) is complex Element of COMPLEX
f * (0. F_Complex) is complex Element of the carrier of F_Complex
K182(f,(0. F_Complex)) is complex Element of COMPLEX
f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
rho is complex Element of the carrier of F_Complex
rho * f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
ef is complex Element of the carrier of F_Complex
eval ((rho * f),ef) is complex Element of the carrier of F_Complex
eval (f,ef) is complex Element of the carrier of F_Complex
rho * (eval (f,ef)) is complex Element of the carrier of F_Complex
K182(rho,(eval (f,ef))) is complex Element of COMPLEX
Re ef is complex V32() ext-real Element of REAL
ef is complex Element of the carrier of F_Complex
eval ((rho * f),ef) is complex Element of the carrier of F_Complex
eval (f,ef) is complex Element of the carrier of F_Complex
rho * (eval (f,ef)) is complex Element of the carrier of F_Complex
K182(rho,(eval (f,ef))) is complex Element of COMPLEX
rho * (0. F_Complex) is complex Element of the carrier of F_Complex
K182(rho,(0. F_Complex)) is complex Element of COMPLEX
Re ef is complex V32() ext-real Element of REAL
f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
rho is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
ef is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
rho *' ef is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
ef1 is complex Element of the carrier of F_Complex
eval (f,ef1) is complex Element of the carrier of F_Complex
eval (rho,ef1) is complex Element of the carrier of F_Complex
eval (ef,ef1) is complex Element of the carrier of F_Complex
(eval (rho,ef1)) * (eval (ef,ef1)) is complex Element of the carrier of F_Complex
K182((eval (rho,ef1)),(eval (ef,ef1))) is complex Element of COMPLEX
f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
rho is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
f *' rho is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
ef is complex Element of the carrier of F_Complex
eval ((f *' rho),ef) is complex Element of the carrier of F_Complex
eval (f,ef) is complex Element of the carrier of F_Complex
eval (rho,ef) is complex Element of the carrier of F_Complex
(eval (f,ef)) * (eval (rho,ef)) is complex Element of the carrier of F_Complex
K182((eval (f,ef)),(eval (rho,ef))) is complex Element of COMPLEX
Re ef is complex V32() ext-real Element of REAL
Re ef is complex V32() ext-real Element of REAL
ef is complex Element of the carrier of F_Complex
Re ef is complex V32() ext-real Element of REAL
ef is complex Element of the carrier of F_Complex
Re ef is complex V32() ext-real Element of REAL
f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
rho is set
ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power F_Complex) . ((- (1_ F_Complex)),ef) is complex Element of the carrier of F_Complex
f . ef is complex Element of the carrier of F_Complex
(f . ef) *' is complex Element of the carrier of F_Complex
Re (f . ef) is complex V32() ext-real Element of REAL
Im (f . ef) is complex V32() ext-real Element of REAL
(Im (f . ef)) * <i> is complex set
(Re (f . ef)) - ((Im (f . ef)) * <i>) is complex set
((power F_Complex) . ((- (1_ F_Complex)),ef)) * ((f . ef) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),ef)),((f . ef) *')) is complex Element of COMPLEX
rho is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) Element of K19(K20(NAT, the carrier of F_Complex))
ef is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) Element of K19(K20(NAT, the carrier of F_Complex))
len f is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef . b9 is complex Element of the carrier of F_Complex
ef . t is complex Element of the carrier of F_Complex
(power F_Complex) . ((- (1_ F_Complex)),b9) is complex Element of the carrier of F_Complex
((power F_Complex) . ((- (1_ F_Complex)),b9)) * ((0. F_Complex) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),b9)),((0. F_Complex) *')) is complex Element of COMPLEX
zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power F_Complex) . ((- (1_ F_Complex)),zz) is complex Element of the carrier of F_Complex
f . zz is complex Element of the carrier of F_Complex
(f . zz) *' is complex Element of the carrier of F_Complex
Re (f . zz) is complex V32() ext-real Element of REAL
Im (f . zz) is complex V32() ext-real Element of REAL
(Im (f . zz)) * <i> is complex set
(Re (f . zz)) - ((Im (f . zz)) * <i>) is complex set
((power F_Complex) . ((- (1_ F_Complex)),zz)) * ((f . zz) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),zz)),((f . zz) *')) is complex Element of COMPLEX
t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
ef . t is complex Element of the carrier of F_Complex
t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
ef1 is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef1 . t is complex Element of the carrier of F_Complex
(power F_Complex) . ((- (1_ F_Complex)),t) is complex Element of the carrier of F_Complex
f . t is complex Element of the carrier of F_Complex
(f . t) *' is complex Element of the carrier of F_Complex
Re (f . t) is complex V32() ext-real Element of REAL
Im (f . t) is complex V32() ext-real Element of REAL
(Im (f . t)) * <i> is complex set
(Re (f . t)) - ((Im (f . t)) * <i>) is complex set
((power F_Complex) . ((- (1_ F_Complex)),t)) * ((f . t) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),t)),((f . t) *')) is complex Element of COMPLEX
b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power F_Complex) . ((- (1_ F_Complex)),b9) is complex Element of the carrier of F_Complex
f . b9 is complex Element of the carrier of F_Complex
(f . b9) *' is complex Element of the carrier of F_Complex
Re (f . b9) is complex V32() ext-real Element of REAL
Im (f . b9) is complex V32() ext-real Element of REAL
(Im (f . b9)) * <i> is complex set
(Re (f . b9)) - ((Im (f . b9)) * <i>) is complex set
((power F_Complex) . ((- (1_ F_Complex)),b9)) * ((f . b9) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),b9)),((f . b9) *')) is complex Element of COMPLEX
t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef1 . t is complex Element of the carrier of F_Complex
(power F_Complex) . ((- (1_ F_Complex)),t) is complex Element of the carrier of F_Complex
f . t is complex Element of the carrier of F_Complex
(f . t) *' is complex Element of the carrier of F_Complex
Re (f . t) is complex V32() ext-real Element of REAL
Im (f . t) is complex V32() ext-real Element of REAL
(Im (f . t)) * <i> is complex set
(Re (f . t)) - ((Im (f . t)) * <i>) is complex set
((power F_Complex) . ((- (1_ F_Complex)),t)) * ((f . t) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),t)),((f . t) *')) is complex Element of COMPLEX
rho is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
ef is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
ef1 is set
dom rho is Element of K19(NAT)
rho . ef1 is set
t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power F_Complex) . ((- (1_ F_Complex)),t) is complex Element of the carrier of F_Complex
f . t is complex Element of the carrier of F_Complex
(f . t) *' is complex Element of the carrier of F_Complex
Re (f . t) is complex V32() ext-real Element of REAL
Im (f . t) is complex V32() ext-real Element of REAL
(Im (f . t)) * <i> is complex set
(Re (f . t)) - ((Im (f . t)) * <i>) is complex set
((power F_Complex) . ((- (1_ F_Complex)),t)) * ((f . t) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),t)),((f . t) *')) is complex Element of COMPLEX
ef . ef1 is set
dom ef is Element of K19(NAT)
rho is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
ef is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef . ef1 is complex Element of the carrier of F_Complex
(power F_Complex) . ((- (1_ F_Complex)),ef1) is complex Element of the carrier of F_Complex
rho . ef1 is complex Element of the carrier of F_Complex
(rho . ef1) *' is complex Element of the carrier of F_Complex
Re (rho . ef1) is complex V32() ext-real Element of REAL
Im (rho . ef1) is complex V32() ext-real Element of REAL
(Im (rho . ef1)) * <i> is complex set
(Re (rho . ef1)) - ((Im (rho . ef1)) * <i>) is complex set
((power F_Complex) . ((- (1_ F_Complex)),ef1)) * ((rho . ef1) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),ef1)),((rho . ef1) *')) is complex Element of COMPLEX
(1_ F_Complex) * (ef . ef1) is complex Element of the carrier of F_Complex
K182((1_ F_Complex),(ef . ef1)) is complex Element of COMPLEX
2 * ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power F_Complex) . ((- (1_ F_Complex)),(2 * ef1)) is complex Element of the carrier of F_Complex
((power F_Complex) . ((- (1_ F_Complex)),(2 * ef1))) * (ef . ef1) is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),(2 * ef1))),(ef . ef1)) is complex Element of COMPLEX
ef1 + ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power F_Complex) . ((- (1_ F_Complex)),(ef1 + ef1)) is complex Element of the carrier of F_Complex
((power F_Complex) . ((- (1_ F_Complex)),(ef1 + ef1))) * (ef . ef1) is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),(ef1 + ef1))),(ef . ef1)) is complex Element of COMPLEX
((power F_Complex) . ((- (1_ F_Complex)),ef1)) * ((power F_Complex) . ((- (1_ F_Complex)),ef1)) is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),ef1)),((power F_Complex) . ((- (1_ F_Complex)),ef1))) is complex Element of COMPLEX
(((power F_Complex) . ((- (1_ F_Complex)),ef1)) * ((power F_Complex) . ((- (1_ F_Complex)),ef1))) * (ef . ef1) is complex Element of the carrier of F_Complex
K182((((power F_Complex) . ((- (1_ F_Complex)),ef1)) * ((power F_Complex) . ((- (1_ F_Complex)),ef1))),(ef . ef1)) is complex Element of COMPLEX
(- (1_ F_Complex)) *' is complex Element of the carrier of F_Complex
Re (- (1_ F_Complex)) is complex V32() 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
(power F_Complex) . (((- (1_ F_Complex)) *'),ef1) is complex Element of the carrier of F_Complex
((power F_Complex) . ((- (1_ F_Complex)),ef1)) * ((power F_Complex) . (((- (1_ F_Complex)) *'),ef1)) is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),ef1)),((power F_Complex) . (((- (1_ F_Complex)) *'),ef1))) is complex Element of COMPLEX
(((power F_Complex) . ((- (1_ F_Complex)),ef1)) * ((power F_Complex) . (((- (1_ F_Complex)) *'),ef1))) * (ef . ef1) is complex Element of the carrier of F_Complex
K182((((power F_Complex) . ((- (1_ F_Complex)),ef1)) * ((power F_Complex) . (((- (1_ F_Complex)) *'),ef1))),(ef . ef1)) is complex Element of COMPLEX
((power F_Complex) . ((- (1_ F_Complex)),ef1)) *' is complex Element of the carrier of F_Complex
Re ((power F_Complex) . ((- (1_ F_Complex)),ef1)) is complex V32() ext-real Element of REAL
Im ((power F_Complex) . ((- (1_ F_Complex)),ef1)) is complex V32() ext-real Element of REAL
(Im ((power F_Complex) . ((- (1_ F_Complex)),ef1))) * <i> is complex set
(Re ((power F_Complex) . ((- (1_ F_Complex)),ef1))) - ((Im ((power F_Complex) . ((- (1_ F_Complex)),ef1))) * <i>) is complex set
((power F_Complex) . ((- (1_ F_Complex)),ef1)) * (((power F_Complex) . ((- (1_ F_Complex)),ef1)) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),ef1)),(((power F_Complex) . ((- (1_ F_Complex)),ef1)) *')) is complex Element of COMPLEX
(((power F_Complex) . ((- (1_ F_Complex)),ef1)) * (((power F_Complex) . ((- (1_ F_Complex)),ef1)) *')) * (ef . ef1) is complex Element of the carrier of F_Complex
K182((((power F_Complex) . ((- (1_ F_Complex)),ef1)) * (((power F_Complex) . ((- (1_ F_Complex)),ef1)) *')),(ef . ef1)) is complex Element of COMPLEX
(ef . ef1) *' is complex Element of the carrier of F_Complex
Re (ef . ef1) is complex V32() ext-real Element of REAL
Im (ef . ef1) is complex V32() ext-real Element of REAL
(Im (ef . ef1)) * <i> is complex set
(Re (ef . ef1)) - ((Im (ef . ef1)) * <i>) is complex set
((ef . ef1) *') *' is complex Element of the carrier of F_Complex
Re ((ef . ef1) *') is complex V32() ext-real Element of REAL
Im ((ef . ef1) *') is complex V32() ext-real Element of REAL
(Im ((ef . ef1) *')) * <i> is complex set
(Re ((ef . ef1) *')) - ((Im ((ef . ef1) *')) * <i>) is complex set
(((power F_Complex) . ((- (1_ F_Complex)),ef1)) *') * (((ef . ef1) *') *') is complex Element of the carrier of F_Complex
K182((((power F_Complex) . ((- (1_ F_Complex)),ef1)) *'),(((ef . ef1) *') *')) is complex Element of COMPLEX
((power F_Complex) . ((- (1_ F_Complex)),ef1)) * ((((power F_Complex) . ((- (1_ F_Complex)),ef1)) *') * (((ef . ef1) *') *')) is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),ef1)),((((power F_Complex) . ((- (1_ F_Complex)),ef1)) *') * (((ef . ef1) *') *'))) is complex Element of COMPLEX
((power F_Complex) . ((- (1_ F_Complex)),ef1)) * ((ef . ef1) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),ef1)),((ef . ef1) *')) is complex Element of COMPLEX
(((power F_Complex) . ((- (1_ F_Complex)),ef1)) * ((ef . ef1) *')) *' is complex Element of the carrier of F_Complex
Re (((power F_Complex) . ((- (1_ F_Complex)),ef1)) * ((ef . ef1) *')) is complex V32() ext-real Element of REAL
Im (((power F_Complex) . ((- (1_ F_Complex)),ef1)) * ((ef . ef1) *')) is complex V32() ext-real Element of REAL
(Im (((power F_Complex) . ((- (1_ F_Complex)),ef1)) * ((ef . ef1) *'))) * <i> is complex set
(Re (((power F_Complex) . ((- (1_ F_Complex)),ef1)) * ((ef . ef1) *'))) - ((Im (((power F_Complex) . ((- (1_ F_Complex)),ef1)) * ((ef . ef1) *'))) * <i>) is complex set
((power F_Complex) . ((- (1_ F_Complex)),ef1)) * ((((power F_Complex) . ((- (1_ F_Complex)),ef1)) * ((ef . ef1) *')) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),ef1)),((((power F_Complex) . ((- (1_ F_Complex)),ef1)) * ((ef . ef1) *')) *')) is complex Element of COMPLEX
f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(F_Complex,(f)) is complex V32() ext-real integer set
len (f) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len (f)) - 1 is complex V32() ext-real integer set
(F_Complex,f) is complex V32() ext-real integer set
len f is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len f) - 1 is complex V32() ext-real integer set
rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
f . rho is complex Element of the carrier of F_Complex
(f) . rho is complex Element of the carrier of F_Complex
ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(power F_Complex) . ((- (1_ F_Complex)),ef) is complex Element of the carrier of F_Complex
((power F_Complex) . ((- (1_ F_Complex)),ef)) * (0. F_Complex) is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),ef)),(0. F_Complex)) is complex Element of COMPLEX
(f . rho) *' is complex Element of the carrier of F_Complex
Re (f . rho) is complex V32() ext-real Element of REAL
Im (f . rho) is complex V32() ext-real Element of REAL
(Im (f . rho)) * <i> is complex set
(Re (f . rho)) - ((Im (f . rho)) * <i>) is complex set
((power F_Complex) . ((- (1_ F_Complex)),ef)) * ((f . rho) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),ef)),((f . rho) *')) is complex Element of COMPLEX
(len f) + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
0 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
rho + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(f) . rho is complex Element of the carrier of F_Complex
f . rho is complex Element of the carrier of F_Complex
rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
f . rho is complex Element of the carrier of F_Complex
(f) . rho is complex Element of the carrier of F_Complex
f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
rho is complex Element of the carrier of F_Complex
rho * f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((rho * f)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
rho *' is complex Element of the carrier of F_Complex
Re rho is complex V32() ext-real Element of REAL
Im rho is complex V32() ext-real Element of REAL
(Im rho) * <i> is complex set
(Re rho) - ((Im rho) * <i>) is complex set
(rho *') * (f) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
t is set
dom ((rho * f)) is Element of K19(NAT)
b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(rho * f) . b9 is complex Element of the carrier of F_Complex
f . b9 is complex Element of the carrier of F_Complex
rho * (f . b9) is complex Element of the carrier of F_Complex
K182(rho,(f . b9)) is complex Element of COMPLEX
((rho * f)) . b9 is complex Element of the carrier of F_Complex
(power F_Complex) . ((- (1_ F_Complex)),b9) is complex Element of the carrier of F_Complex
(rho * (f . b9)) *' is complex Element of the carrier of F_Complex
Re (rho * (f . b9)) is complex V32() ext-real Element of REAL
Im (rho * (f . b9)) is complex V32() ext-real Element of REAL
(Im (rho * (f . b9))) * <i> is complex set
(Re (rho * (f . b9))) - ((Im (rho * (f . b9))) * <i>) is complex set
((power F_Complex) . ((- (1_ F_Complex)),b9)) * ((rho * (f . b9)) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),b9)),((rho * (f . b9)) *')) is complex Element of COMPLEX
(f . b9) *' is complex Element of the carrier of F_Complex
Re (f . b9) is complex V32() ext-real Element of REAL
Im (f . b9) is complex V32() ext-real Element of REAL
(Im (f . b9)) * <i> is complex set
(Re (f . b9)) - ((Im (f . b9)) * <i>) is complex set
(rho *') * ((f . b9) *') is complex Element of the carrier of F_Complex
K182((rho *'),((f . b9) *')) is complex Element of COMPLEX
((power F_Complex) . ((- (1_ F_Complex)),b9)) * ((rho *') * ((f . b9) *')) is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),b9)),((rho *') * ((f . b9) *'))) is complex Element of COMPLEX
((power F_Complex) . ((- (1_ F_Complex)),b9)) * ((f . b9) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),b9)),((f . b9) *')) is complex Element of COMPLEX
(rho *') * (((power F_Complex) . ((- (1_ F_Complex)),b9)) * ((f . b9) *')) is complex Element of the carrier of F_Complex
K182((rho *'),(((power F_Complex) . ((- (1_ F_Complex)),b9)) * ((f . b9) *'))) is complex Element of COMPLEX
(f) . b9 is complex Element of the carrier of F_Complex
(rho *') * ((f) . b9) is complex Element of the carrier of F_Complex
K182((rho *'),((f) . b9)) is complex Element of COMPLEX
((rho * f)) . t is set
((rho *') * (f)) . t is set
dom ((rho *') * (f)) is Element of K19(NAT)
f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
- f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((- f)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
- (f) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
ef is set
dom ((- f)) is Element of K19(NAT)
ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(- f) . ef1 is complex Element of the carrier of F_Complex
f . ef1 is complex Element of the carrier of F_Complex
- (f . ef1) is complex Element of the carrier of F_Complex
((- f)) . ef1 is complex Element of the carrier of F_Complex
(power F_Complex) . ((- (1_ F_Complex)),ef1) is complex Element of the carrier of F_Complex
(- (f . ef1)) *' is complex Element of the carrier of F_Complex
Re (- (f . ef1)) is complex V32() ext-real Element of REAL
Im (- (f . ef1)) is complex V32() ext-real Element of REAL
(Im (- (f . ef1))) * <i> is complex set
(Re (- (f . ef1))) - ((Im (- (f . ef1))) * <i>) is complex set
((power F_Complex) . ((- (1_ F_Complex)),ef1)) * ((- (f . ef1)) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),ef1)),((- (f . ef1)) *')) is complex Element of COMPLEX
(f . ef1) *' is complex Element of the carrier of F_Complex
Re (f . ef1) is complex V32() ext-real Element of REAL
Im (f . ef1) is complex V32() ext-real Element of REAL
(Im (f . ef1)) * <i> is complex set
(Re (f . ef1)) - ((Im (f . ef1)) * <i>) is complex set
- ((f . ef1) *') is complex Element of the carrier of F_Complex
((power F_Complex) . ((- (1_ F_Complex)),ef1)) * (- ((f . ef1) *')) is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),ef1)),(- ((f . ef1) *'))) is complex Element of COMPLEX
((power F_Complex) . ((- (1_ F_Complex)),ef1)) * ((f . ef1) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),ef1)),((f . ef1) *')) is complex Element of COMPLEX
- (((power F_Complex) . ((- (1_ F_Complex)),ef1)) * ((f . ef1) *')) is complex Element of the carrier of F_Complex
(f) . ef1 is complex Element of the carrier of F_Complex
- ((f) . ef1) is complex Element of the carrier of F_Complex
((- f)) . ef is set
(- (f)) . ef is set
dom (- (f)) is Element of K19(NAT)
f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
rho is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
f + rho is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f + rho)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(rho) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f) + (rho) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
ef1 is set
dom ((f + rho)) is Element of K19(NAT)
t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(f + rho) . t is complex Element of the carrier of F_Complex
f . t is complex Element of the carrier of F_Complex
rho . t is complex Element of the carrier of F_Complex
(f . t) + (rho . t) is complex Element of the carrier of F_Complex
K180((f . t),(rho . t)) is complex Element of COMPLEX
((f + rho)) . t is complex Element of the carrier of F_Complex
(power F_Complex) . ((- (1_ F_Complex)),t) is complex Element of the carrier of F_Complex
((f . t) + (rho . t)) *' is complex Element of the carrier of F_Complex
Re ((f . t) + (rho . t)) is complex V32() ext-real Element of REAL
Im ((f . t) + (rho . t)) is complex V32() ext-real Element of REAL
(Im ((f . t) + (rho . t))) * <i> is complex set
(Re ((f . t) + (rho . t))) - ((Im ((f . t) + (rho . t))) * <i>) is complex set
((power F_Complex) . ((- (1_ F_Complex)),t)) * (((f . t) + (rho . t)) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),t)),(((f . t) + (rho . t)) *')) is complex Element of COMPLEX
(f . t) *' is complex Element of the carrier of F_Complex
Re (f . t) is complex V32() ext-real Element of REAL
Im (f . t) is complex V32() ext-real Element of REAL
(Im (f . t)) * <i> is complex set
(Re (f . t)) - ((Im (f . t)) * <i>) is complex set
(rho . t) *' is complex Element of the carrier of F_Complex
Re (rho . t) is complex V32() ext-real Element of REAL
Im (rho . t) is complex V32() ext-real Element of REAL
(Im (rho . t)) * <i> is complex set
(Re (rho . t)) - ((Im (rho . t)) * <i>) is complex set
((f . t) *') + ((rho . t) *') is complex Element of the carrier of F_Complex
K180(((f . t) *'),((rho . t) *')) is complex Element of COMPLEX
((power F_Complex) . ((- (1_ F_Complex)),t)) * (((f . t) *') + ((rho . t) *')) is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),t)),(((f . t) *') + ((rho . t) *'))) is complex Element of COMPLEX
((power F_Complex) . ((- (1_ F_Complex)),t)) * ((f . t) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),t)),((f . t) *')) is complex Element of COMPLEX
((power F_Complex) . ((- (1_ F_Complex)),t)) * ((rho . t) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),t)),((rho . t) *')) is complex Element of COMPLEX
(((power F_Complex) . ((- (1_ F_Complex)),t)) * ((f . t) *')) + (((power F_Complex) . ((- (1_ F_Complex)),t)) * ((rho . t) *')) is complex Element of the carrier of F_Complex
K180((((power F_Complex) . ((- (1_ F_Complex)),t)) * ((f . t) *')),(((power F_Complex) . ((- (1_ F_Complex)),t)) * ((rho . t) *'))) is complex Element of COMPLEX
(f) . t is complex Element of the carrier of F_Complex
((f) . t) + (((power F_Complex) . ((- (1_ F_Complex)),t)) * ((rho . t) *')) is complex Element of the carrier of F_Complex
K180(((f) . t),(((power F_Complex) . ((- (1_ F_Complex)),t)) * ((rho . t) *'))) is complex Element of COMPLEX
(rho) . t is complex Element of the carrier of F_Complex
((f) . t) + ((rho) . t) is complex Element of the carrier of F_Complex
K180(((f) . t),((rho) . t)) is complex Element of COMPLEX
((f + rho)) . ef1 is set
((f) + (rho)) . ef1 is set
dom ((f) + (rho)) is Element of K19(NAT)
f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
rho is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
f *' rho is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f *' rho)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(rho) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f) *' (rho) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
ef1 is set
dom ((f *' rho)) is Element of K19(NAT)
t is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
t + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(f *' rho) . t is complex Element of the carrier of F_Complex
b9 is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
len b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
Sum b9 is complex Element of the carrier of F_Complex
dom b9 is Element of K19(NAT)
((f) *' (rho)) . t is complex Element of the carrier of F_Complex
zz is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
len zz is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
Sum zz is complex Element of the carrier of F_Complex
dom zz is Element of K19(NAT)
Seg (len b9) is V40() V47( len b9) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len b9 ) } is set
a1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
b9 /. a1 is complex Element of the carrier of F_Complex
(b9 /. a1) *' is complex Element of the carrier of F_Complex
Re (b9 /. a1) is complex V32() ext-real Element of REAL
Im (b9 /. a1) is complex V32() ext-real Element of REAL
(Im (b9 /. a1)) * <i> is complex set
(Re (b9 /. a1)) - ((Im (b9 /. a1)) * <i>) is complex set
a1 is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
dom a1 is Element of K19(NAT)
b1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
a1 /. b1 is complex Element of the carrier of F_Complex
a1 . b1 is set
b9 /. b1 is complex Element of the carrier of F_Complex
(b9 /. b1) *' is complex Element of the carrier of F_Complex
Re (b9 /. b1) is complex V32() ext-real Element of REAL
Im (b9 /. b1) is complex V32() ext-real Element of REAL
(Im (b9 /. b1)) * <i> is complex set
(Re (b9 /. b1)) - ((Im (b9 /. b1)) * <i>) is complex set
Seg (len zz) is V40() V47( len zz) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len zz ) } is set
b1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
b9 . b1 is set
b9 /. b1 is complex Element of the carrier of F_Complex
(b9 /. b1) *' is complex Element of the carrier of F_Complex
Re (b9 /. b1) is complex V32() ext-real Element of REAL
Im (b9 /. b1) is complex V32() ext-real Element of REAL
(Im (b9 /. b1)) * <i> is complex set
(Re (b9 /. b1)) - ((Im (b9 /. b1)) * <i>) is complex set
b1 -' 1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
f . (b1 -' 1) is complex Element of the carrier of F_Complex
(t + 1) -' b1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
rho . ((t + 1) -' b1) is complex Element of the carrier of F_Complex
(f . (b1 -' 1)) * (rho . ((t + 1) -' b1)) is complex Element of the carrier of F_Complex
K182((f . (b1 -' 1)),(rho . ((t + 1) -' b1))) is complex Element of COMPLEX
((f . (b1 -' 1)) * (rho . ((t + 1) -' b1))) *' is complex Element of the carrier of F_Complex
Re ((f . (b1 -' 1)) * (rho . ((t + 1) -' b1))) is complex V32() ext-real Element of REAL
Im ((f . (b1 -' 1)) * (rho . ((t + 1) -' b1))) is complex V32() ext-real Element of REAL
(Im ((f . (b1 -' 1)) * (rho . ((t + 1) -' b1)))) * <i> is complex set
(Re ((f . (b1 -' 1)) * (rho . ((t + 1) -' b1)))) - ((Im ((f . (b1 -' 1)) * (rho . ((t + 1) -' b1)))) * <i>) is complex set
b1 - b1 is complex V32() ext-real integer set
(t + 1) - b1 is complex V32() ext-real integer set
1 - 1 is complex V32() ext-real integer set
b1 - 1 is complex V32() ext-real integer set
(b1 -' 1) + ((t + 1) -' b1) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(b1 - 1) + ((t + 1) -' b1) is complex V32() ext-real integer set
(b1 - 1) + ((t + 1) - b1) is complex V32() ext-real integer set
zz . b1 is set
(f) . (b1 -' 1) is complex Element of the carrier of F_Complex
(rho) . ((t + 1) -' b1) is complex Element of the carrier of F_Complex
((f) . (b1 -' 1)) * ((rho) . ((t + 1) -' b1)) is complex Element of the carrier of F_Complex
K182(((f) . (b1 -' 1)),((rho) . ((t + 1) -' b1))) is complex Element of COMPLEX
(power F_Complex) . ((- (1_ F_Complex)),(b1 -' 1)) is complex Element of the carrier of F_Complex
(f . (b1 -' 1)) *' is complex Element of the carrier of F_Complex
Re (f . (b1 -' 1)) is complex V32() ext-real Element of REAL
Im (f . (b1 -' 1)) is complex V32() ext-real Element of REAL
(Im (f . (b1 -' 1))) * <i> is complex set
(Re (f . (b1 -' 1))) - ((Im (f . (b1 -' 1))) * <i>) is complex set
((power F_Complex) . ((- (1_ F_Complex)),(b1 -' 1))) * ((f . (b1 -' 1)) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),(b1 -' 1))),((f . (b1 -' 1)) *')) is complex Element of COMPLEX
(((power F_Complex) . ((- (1_ F_Complex)),(b1 -' 1))) * ((f . (b1 -' 1)) *')) * ((rho) . ((t + 1) -' b1)) is complex Element of the carrier of F_Complex
K182((((power F_Complex) . ((- (1_ F_Complex)),(b1 -' 1))) * ((f . (b1 -' 1)) *')),((rho) . ((t + 1) -' b1))) is complex Element of COMPLEX
(power F_Complex) . ((- (1_ F_Complex)),((t + 1) -' b1)) is complex Element of the carrier of F_Complex
(rho . ((t + 1) -' b1)) *' is complex Element of the carrier of F_Complex
Re (rho . ((t + 1) -' b1)) is complex V32() ext-real Element of REAL
Im (rho . ((t + 1) -' b1)) is complex V32() ext-real Element of REAL
(Im (rho . ((t + 1) -' b1))) * <i> is complex set
(Re (rho . ((t + 1) -' b1))) - ((Im (rho . ((t + 1) -' b1))) * <i>) is complex set
((power F_Complex) . ((- (1_ F_Complex)),((t + 1) -' b1))) * ((rho . ((t + 1) -' b1)) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),((t + 1) -' b1))),((rho . ((t + 1) -' b1)) *')) is complex Element of COMPLEX
(((power F_Complex) . ((- (1_ F_Complex)),(b1 -' 1))) * ((f . (b1 -' 1)) *')) * (((power F_Complex) . ((- (1_ F_Complex)),((t + 1) -' b1))) * ((rho . ((t + 1) -' b1)) *')) is complex Element of the carrier of F_Complex
K182((((power F_Complex) . ((- (1_ F_Complex)),(b1 -' 1))) * ((f . (b1 -' 1)) *')),(((power F_Complex) . ((- (1_ F_Complex)),((t + 1) -' b1))) * ((rho . ((t + 1) -' b1)) *'))) is complex Element of COMPLEX
((power F_Complex) . ((- (1_ F_Complex)),(b1 -' 1))) * ((power F_Complex) . ((- (1_ F_Complex)),((t + 1) -' b1))) is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),(b1 -' 1))),((power F_Complex) . ((- (1_ F_Complex)),((t + 1) -' b1)))) is complex Element of COMPLEX
((f . (b1 -' 1)) *') * ((rho . ((t + 1) -' b1)) *') is complex Element of the carrier of F_Complex
K182(((f . (b1 -' 1)) *'),((rho . ((t + 1) -' b1)) *')) is complex Element of COMPLEX
(((power F_Complex) . ((- (1_ F_Complex)),(b1 -' 1))) * ((power F_Complex) . ((- (1_ F_Complex)),((t + 1) -' b1)))) * (((f . (b1 -' 1)) *') * ((rho . ((t + 1) -' b1)) *')) is complex Element of the carrier of F_Complex
K182((((power F_Complex) . ((- (1_ F_Complex)),(b1 -' 1))) * ((power F_Complex) . ((- (1_ F_Complex)),((t + 1) -' b1)))),(((f . (b1 -' 1)) *') * ((rho . ((t + 1) -' b1)) *'))) is complex Element of COMPLEX
(power F_Complex) . ((- (1_ F_Complex)),t) is complex Element of the carrier of F_Complex
((power F_Complex) . ((- (1_ F_Complex)),t)) * (((f . (b1 -' 1)) *') * ((rho . ((t + 1) -' b1)) *')) is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),t)),(((f . (b1 -' 1)) *') * ((rho . ((t + 1) -' b1)) *'))) is complex Element of COMPLEX
((power F_Complex) . ((- (1_ F_Complex)),t)) * ((b9 /. b1) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),t)),((b9 /. b1) *')) is complex Element of COMPLEX
((power F_Complex) . ((- (1_ F_Complex)),t)) * a1 is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
dom (((power F_Complex) . ((- (1_ F_Complex)),t)) * a1) is Element of K19(NAT)
b19 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer set
(((power F_Complex) . ((- (1_ F_Complex)),t)) * a1) . b19 is set
(((power F_Complex) . ((- (1_ F_Complex)),t)) * a1) /. b19 is complex Element of the carrier of F_Complex
a1 /. b19 is complex Element of the carrier of F_Complex
((power F_Complex) . ((- (1_ F_Complex)),t)) * (a1 /. b19) is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),t)),(a1 /. b19)) is complex Element of COMPLEX
b9 /. b19 is complex Element of the carrier of F_Complex
(b9 /. b19) *' is complex Element of the carrier of F_Complex
Re (b9 /. b19) is complex V32() ext-real Element of REAL
Im (b9 /. b19) is complex V32() ext-real Element of REAL
(Im (b9 /. b19)) * <i> is complex set
(Re (b9 /. b19)) - ((Im (b9 /. b19)) * <i>) is complex set
((power F_Complex) . ((- (1_ F_Complex)),t)) * ((b9 /. b19) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),t)),((b9 /. b19) *')) is complex Element of COMPLEX
zz . b19 is set
len a1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
Sum a1 is complex Element of the carrier of F_Complex
(Sum b9) *' is complex Element of the carrier of F_Complex
Re (Sum b9) is complex V32() ext-real Element of REAL
Im (Sum b9) is complex V32() ext-real Element of REAL
(Im (Sum b9)) * <i> is complex set
(Re (Sum b9)) - ((Im (Sum b9)) * <i>) is complex set
((f *' rho)) . t is complex Element of the carrier of F_Complex
((power F_Complex) . ((- (1_ F_Complex)),t)) * (Sum a1) is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),t)),(Sum a1)) is complex Element of COMPLEX
((f *' rho)) . ef1 is set
((f) *' (rho)) . ef1 is set
dom ((f) *' (rho)) is Element of K19(NAT)
4 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
f is complex Element of COMPLEX
rho is complex Element of COMPLEX
rho *' is complex Element of COMPLEX
Re rho is complex V32() ext-real Element of REAL
Im rho is complex V32() ext-real Element of REAL
(Im rho) * <i> is complex set
(Re rho) - ((Im rho) * <i>) is complex set
f + (rho *') is complex Element of COMPLEX
|.(f + (rho *')).| is complex V32() ext-real Element of REAL
Re (f + (rho *')) is complex V32() ext-real Element of REAL
(Re (f + (rho *'))) ^2 is complex V32() ext-real Element of REAL
(Re (f + (rho *'))) * (Re (f + (rho *'))) is complex V32() ext-real set
Im (f + (rho *')) is complex V32() ext-real Element of REAL
(Im (f + (rho *'))) ^2 is complex V32() ext-real Element of REAL
(Im (f + (rho *'))) * (Im (f + (rho *'))) is complex V32() ext-real set
K114(((Re (f + (rho *'))) ^2),((Im (f + (rho *'))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (f + (rho *'))) ^2),((Im (f + (rho *'))) ^2)) is complex V32() ext-real Element of REAL
|.(f + (rho *')).| ^2 is complex V32() ext-real Element of REAL
|.(f + (rho *')).| * |.(f + (rho *')).| is complex V32() ext-real set
f - rho is complex Element of COMPLEX
|.(f - rho).| is complex V32() ext-real Element of REAL
Re (f - rho) is complex V32() ext-real Element of REAL
(Re (f - rho)) ^2 is complex V32() ext-real Element of REAL
(Re (f - rho)) * (Re (f - rho)) is complex V32() ext-real set
Im (f - rho) is complex V32() ext-real Element of REAL
(Im (f - rho)) ^2 is complex V32() ext-real Element of REAL
(Im (f - rho)) * (Im (f - rho)) is complex V32() ext-real set
K114(((Re (f - rho)) ^2),((Im (f - rho)) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (f - rho)) ^2),((Im (f - rho)) ^2)) is complex V32() ext-real Element of REAL
|.(f - rho).| ^2 is complex V32() ext-real Element of REAL
|.(f - rho).| * |.(f - rho).| is complex V32() ext-real set
(|.(f + (rho *')).| ^2) - (|.(f - rho).| ^2) is complex V32() ext-real set
ef is complex V32() ext-real Element of REAL
ef1 is complex V32() ext-real Element of REAL
ef1 * <i> is complex set
ef + (ef1 * <i>) is complex set
t is complex V32() ext-real Element of REAL
b9 is complex V32() ext-real Element of REAL
b9 * <i> is complex set
t + (b9 * <i>) is complex set
4 * ef is complex V32() ext-real set
(4 * ef) * t is complex V32() ext-real set
ef + t is complex V32() ext-real set
(ef + t) ^2 is complex V32() ext-real set
(ef + t) * (ef + t) is complex V32() ext-real set
- b9 is complex V32() ext-real set
ef1 + (- b9) is complex V32() ext-real set
(ef1 + (- b9)) ^2 is complex V32() ext-real set
(ef1 + (- b9)) * (ef1 + (- b9)) is complex V32() ext-real set
Re f is complex V32() ext-real Element of REAL
Re (rho *') is complex V32() ext-real Element of REAL
(Re f) + (Re (rho *')) is complex V32() ext-real set
((Re f) + (Re (rho *'))) ^2 is complex V32() ext-real set
((Re f) + (Re (rho *'))) * ((Re f) + (Re (rho *'))) is complex V32() ext-real set
(((Re f) + (Re (rho *'))) ^2) + ((Im (f + (rho *'))) ^2) is complex V32() ext-real set
sqrt ((((Re f) + (Re (rho *'))) ^2) + ((Im (f + (rho *'))) ^2)) is complex V32() ext-real set
ef + (Re (rho *')) is complex V32() ext-real set
(ef + (Re (rho *'))) ^2 is complex V32() ext-real set
(ef + (Re (rho *'))) * (ef + (Re (rho *'))) is complex V32() ext-real set
((ef + (Re (rho *'))) ^2) + ((Im (f + (rho *'))) ^2) is complex V32() ext-real set
sqrt (((ef + (Re (rho *'))) ^2) + ((Im (f + (rho *'))) ^2)) is complex V32() ext-real set
ef + (Re rho) is complex V32() ext-real set
(ef + (Re rho)) ^2 is complex V32() ext-real set
(ef + (Re rho)) * (ef + (Re rho)) is complex V32() ext-real set
((ef + (Re rho)) ^2) + ((Im (f + (rho *'))) ^2) is complex V32() ext-real set
sqrt (((ef + (Re rho)) ^2) + ((Im (f + (rho *'))) ^2)) is complex V32() ext-real set
((ef + t) ^2) + ((Im (f + (rho *'))) ^2) is complex V32() ext-real set
sqrt (((ef + t) ^2) + ((Im (f + (rho *'))) ^2)) is complex V32() ext-real set
Im f is complex V32() ext-real Element of REAL
Im (rho *') is complex V32() ext-real Element of REAL
(Im f) + (Im (rho *')) is complex V32() ext-real set
((Im f) + (Im (rho *'))) ^2 is complex V32() ext-real set
((Im f) + (Im (rho *'))) * ((Im f) + (Im (rho *'))) is complex V32() ext-real set
((ef + t) ^2) + (((Im f) + (Im (rho *'))) ^2) is complex V32() ext-real set
sqrt (((ef + t) ^2) + (((Im f) + (Im (rho *'))) ^2)) is complex V32() ext-real set
ef1 + (Im (rho *')) is complex V32() ext-real set
(ef1 + (Im (rho *'))) ^2 is complex V32() ext-real set
(ef1 + (Im (rho *'))) * (ef1 + (Im (rho *'))) is complex V32() ext-real set
((ef + t) ^2) + ((ef1 + (Im (rho *'))) ^2) is complex V32() ext-real set
sqrt (((ef + t) ^2) + ((ef1 + (Im (rho *'))) ^2)) is complex V32() ext-real set
- (Im rho) is complex V32() ext-real set
ef1 + (- (Im rho)) is complex V32() ext-real set
(ef1 + (- (Im rho))) ^2 is complex V32() ext-real set
(ef1 + (- (Im rho))) * (ef1 + (- (Im rho))) is complex V32() ext-real set
((ef + t) ^2) + ((ef1 + (- (Im rho))) ^2) is complex V32() ext-real set
sqrt (((ef + t) ^2) + ((ef1 + (- (Im rho))) ^2)) is complex V32() ext-real set
((ef + t) ^2) + ((ef1 + (- b9)) ^2) is complex V32() ext-real set
sqrt (((ef + t) ^2) + ((ef1 + (- b9)) ^2)) is complex V32() ext-real set
ef - t is complex V32() ext-real set
(ef - t) ^2 is complex V32() ext-real set
(ef - t) * (ef - t) is complex V32() ext-real set
ef1 - b9 is complex V32() ext-real set
(ef1 - b9) ^2 is complex V32() ext-real set
(ef1 - b9) * (ef1 - b9) is complex V32() ext-real set
((ef - t) ^2) + ((ef1 - b9) ^2) is complex V32() ext-real set
(((ef + t) ^2) + ((ef1 + (- b9)) ^2)) - (((ef - t) ^2) + ((ef1 - b9) ^2)) is complex V32() ext-real set
(Re f) - (Re rho) is complex V32() ext-real set
((Re f) - (Re rho)) ^2 is complex V32() ext-real set
((Re f) - (Re rho)) * ((Re f) - (Re rho)) is complex V32() ext-real set
(((Re f) - (Re rho)) ^2) + ((Im (f - rho)) ^2) is complex V32() ext-real set
sqrt ((((Re f) - (Re rho)) ^2) + ((Im (f - rho)) ^2)) is complex V32() ext-real set
ef - (Re rho) is complex V32() ext-real set
(ef - (Re rho)) ^2 is complex V32() ext-real set
(ef - (Re rho)) * (ef - (Re rho)) is complex V32() ext-real set
((ef - (Re rho)) ^2) + ((Im (f - rho)) ^2) is complex V32() ext-real set
sqrt (((ef - (Re rho)) ^2) + ((Im (f - rho)) ^2)) is complex V32() ext-real set
((ef - t) ^2) + ((Im (f - rho)) ^2) is complex V32() ext-real set
sqrt (((ef - t) ^2) + ((Im (f - rho)) ^2)) is complex V32() ext-real set
(Im f) - (Im rho) is complex V32() ext-real set
((Im f) - (Im rho)) ^2 is complex V32() ext-real set
((Im f) - (Im rho)) * ((Im f) - (Im rho)) is complex V32() ext-real set
((ef - t) ^2) + (((Im f) - (Im rho)) ^2) is complex V32() ext-real set
sqrt (((ef - t) ^2) + (((Im f) - (Im rho)) ^2)) is complex V32() ext-real set
ef1 - (Im rho) is complex V32() ext-real set
(ef1 - (Im rho)) ^2 is complex V32() ext-real set
(ef1 - (Im rho)) * (ef1 - (Im rho)) is complex V32() ext-real set
((ef - t) ^2) + ((ef1 - (Im rho)) ^2) is complex V32() ext-real set
sqrt (((ef - t) ^2) + ((ef1 - (Im rho)) ^2)) is complex V32() ext-real set
sqrt (((ef - t) ^2) + ((ef1 - b9) ^2)) is complex V32() ext-real set
f is complex Element of COMPLEX
rho is complex Element of COMPLEX
rho *' is complex Element of COMPLEX
Re rho is complex V32() ext-real Element of REAL
Im rho is complex V32() ext-real Element of REAL
(Im rho) * <i> is complex set
(Re rho) - ((Im rho) * <i>) is complex set
f + (rho *') is complex Element of COMPLEX
|.(f + (rho *')).| is complex V32() ext-real Element of REAL
Re (f + (rho *')) is complex V32() ext-real Element of REAL
(Re (f + (rho *'))) ^2 is complex V32() ext-real Element of REAL
(Re (f + (rho *'))) * (Re (f + (rho *'))) is complex V32() ext-real set
Im (f + (rho *')) is complex V32() ext-real Element of REAL
(Im (f + (rho *'))) ^2 is complex V32() ext-real Element of REAL
(Im (f + (rho *'))) * (Im (f + (rho *'))) is complex V32() ext-real set
K114(((Re (f + (rho *'))) ^2),((Im (f + (rho *'))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (f + (rho *'))) ^2),((Im (f + (rho *'))) ^2)) is complex V32() ext-real Element of REAL
f - rho is complex Element of COMPLEX
|.(f - rho).| is complex V32() ext-real Element of REAL
Re (f - rho) is complex V32() ext-real Element of REAL
(Re (f - rho)) ^2 is complex V32() ext-real Element of REAL
(Re (f - rho)) * (Re (f - rho)) is complex V32() ext-real set
Im (f - rho) is complex V32() ext-real Element of REAL
(Im (f - rho)) ^2 is complex V32() ext-real Element of REAL
(Im (f - rho)) * (Im (f - rho)) is complex V32() ext-real set
K114(((Re (f - rho)) ^2),((Im (f - rho)) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (f - rho)) ^2),((Im (f - rho)) ^2)) is complex V32() ext-real Element of REAL
ef is complex V32() ext-real Element of REAL
ef1 is complex V32() ext-real Element of REAL
ef1 * <i> is complex set
ef + (ef1 * <i>) is complex set
t is complex V32() ext-real Element of REAL
b9 is complex V32() ext-real Element of REAL
b9 * <i> is complex set
t + (b9 * <i>) is complex set
4 * ef is complex V32() ext-real set
(4 * ef) * t is complex V32() ext-real set
|.(f + (rho *')).| ^2 is complex V32() ext-real Element of REAL
|.(f + (rho *')).| * |.(f + (rho *')).| is complex V32() ext-real set
|.(f - rho).| ^2 is complex V32() ext-real Element of REAL
|.(f - rho).| * |.(f - rho).| is complex V32() ext-real set
(|.(f + (rho *')).| ^2) - (|.(f - rho).| ^2) is complex V32() ext-real set
((|.(f + (rho *')).| ^2) - (|.(f - rho).| ^2)) + (|.(f - rho).| ^2) is complex V32() ext-real set
0 + (|.(f - rho).| ^2) is complex V32() ext-real set
rho is complex Element of the carrier of F_Complex
(F_Complex,rho,1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(power F_Complex) . (rho,1) is complex Element of the carrier of F_Complex
- ((power F_Complex) . (rho,1)) is complex Element of the carrier of F_Complex
(0,1) --> ((- ((power F_Complex) . (rho,1))),(1_ F_Complex)) is Relation-like {0,1} -defined the carrier of F_Complex -valued Function-like non empty total V18({0,1}, the carrier of F_Complex) Element of K19(K20({0,1}, the carrier of F_Complex))
{0,1} is non empty set
K20({0,1}, the carrier of F_Complex) is set
K19(K20({0,1}, the carrier of F_Complex)) is set
(0_. F_Complex) +* ((0,1) --> ((- ((power F_Complex) . (rho,1))),(1_ F_Complex))) is Relation-like Function-like set
((F_Complex,rho,1)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
f is complex Element of the carrier of F_Complex
eval (((F_Complex,rho,1)),f) is complex Element of the carrier of F_Complex
- f is complex Element of the carrier of F_Complex
rho *' is complex Element of the carrier of F_Complex
Re rho is complex V32() ext-real Element of REAL
Im rho is complex V32() ext-real Element of REAL
(Im rho) * <i> is complex set
(Re rho) - ((Im rho) * <i>) is complex set
(- f) - (rho *') is complex Element of the carrier of F_Complex
len ((F_Complex,rho,1)) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef1 is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
Sum ef1 is complex Element of the carrier of F_Complex
len ef1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
dom ef1 is Element of K19(NAT)
(F_Complex,((F_Complex,rho,1))) is complex V32() ext-real integer set
(len ((F_Complex,rho,1))) - 1 is complex V32() ext-real integer set
(F_Complex,(F_Complex,rho,1)) is complex V32() ext-real integer set
len (F_Complex,rho,1) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len (F_Complex,rho,1)) - 1 is complex V32() ext-real integer set
ef1 . 1 is set
ef1 . 2 is set
<*(ef1 . 1),(ef1 . 2)*> is Relation-like NAT -defined Function-like non empty V40() V47(2) FinSequence-like FinSubsequence-like set
<*(ef1 . 1)*> is Relation-like NAT -defined Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like set
[1,(ef1 . 1)] is set
{[1,(ef1 . 1)]} is non empty V12() V47(1) set
<*(ef1 . 2)*> is Relation-like NAT -defined Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like set
[1,(ef1 . 2)] is set
{[1,(ef1 . 2)]} is non empty V12() V47(1) set
<*(ef1 . 1)*> ^ <*(ef1 . 2)*> is Relation-like NAT -defined Function-like non empty V40() V47(1 + 1) FinSequence-like FinSubsequence-like set
1 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
1 + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
Seg (len ef1) is V40() V47( len ef1) Element of K19(NAT)
{ b₁ where b₁ is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT : ( 1 <= b₁ & b₁ <= len ef1 ) } is set
2 -' 1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
2 - 1 is complex V32() ext-real integer set
((F_Complex,rho,1)) . 1 is complex Element of the carrier of F_Complex
1 + 0 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(power F_Complex) . (f,(1 + 0)) is complex Element of the carrier of F_Complex
(((F_Complex,rho,1)) . 1) * ((power F_Complex) . (f,(1 + 0))) is complex Element of the carrier of F_Complex
K182((((F_Complex,rho,1)) . 1),((power F_Complex) . (f,(1 + 0)))) is complex Element of COMPLEX
(power F_Complex) . (f,0) is complex Element of the carrier of F_Complex
((power F_Complex) . (f,0)) * f is complex Element of the carrier of F_Complex
K182(((power F_Complex) . (f,0)),f) is complex Element of COMPLEX
(((F_Complex,rho,1)) . 1) * (((power F_Complex) . (f,0)) * f) is complex Element of the carrier of F_Complex
K182((((F_Complex,rho,1)) . 1),(((power F_Complex) . (f,0)) * f)) is complex Element of COMPLEX
(1_ F_Complex) * f is complex Element of the carrier of F_Complex
K182((1_ F_Complex),f) is complex Element of COMPLEX
(((F_Complex,rho,1)) . 1) * ((1_ F_Complex) * f) is complex Element of the carrier of F_Complex
K182((((F_Complex,rho,1)) . 1),((1_ F_Complex) * f)) is complex Element of COMPLEX
(((F_Complex,rho,1)) . 1) * f is complex Element of the carrier of F_Complex
K182((((F_Complex,rho,1)) . 1),f) is complex Element of COMPLEX
(power F_Complex) . ((- (1_ F_Complex)),1) is complex Element of the carrier of F_Complex
(F_Complex,rho,1) . 1 is complex Element of the carrier of F_Complex
((F_Complex,rho,1) . 1) *' is complex Element of the carrier of F_Complex
Re ((F_Complex,rho,1) . 1) is complex V32() ext-real Element of REAL
Im ((F_Complex,rho,1) . 1) is complex V32() ext-real Element of REAL
(Im ((F_Complex,rho,1) . 1)) * <i> is complex set
(Re ((F_Complex,rho,1) . 1)) - ((Im ((F_Complex,rho,1) . 1)) * <i>) is complex set
((power F_Complex) . ((- (1_ F_Complex)),1)) * (((F_Complex,rho,1) . 1) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),1)),(((F_Complex,rho,1) . 1) *')) is complex Element of COMPLEX
(((power F_Complex) . ((- (1_ F_Complex)),1)) * (((F_Complex,rho,1) . 1) *')) * f is complex Element of the carrier of F_Complex
K182((((power F_Complex) . ((- (1_ F_Complex)),1)) * (((F_Complex,rho,1) . 1) *')),f) is complex Element of COMPLEX
((power F_Complex) . ((- (1_ F_Complex)),1)) * (1_ F_Complex) is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),1)),(1_ F_Complex)) is complex Element of COMPLEX
(((power F_Complex) . ((- (1_ F_Complex)),1)) * (1_ F_Complex)) * f is complex Element of the carrier of F_Complex
K182((((power F_Complex) . ((- (1_ F_Complex)),1)) * (1_ F_Complex)),f) is complex Element of COMPLEX
(power F_Complex) . ((- (1_ F_Complex)),(1 + 0)) is complex Element of the carrier of F_Complex
((power F_Complex) . ((- (1_ F_Complex)),(1 + 0))) * f is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),(1 + 0))),f) is complex Element of COMPLEX
(power F_Complex) . ((- (1_ F_Complex)),0) is complex Element of the carrier of F_Complex
((power F_Complex) . ((- (1_ F_Complex)),0)) * (- (1_ F_Complex)) is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),0)),(- (1_ F_Complex))) is complex Element of COMPLEX
(((power F_Complex) . ((- (1_ F_Complex)),0)) * (- (1_ F_Complex))) * f is complex Element of the carrier of F_Complex
K182((((power F_Complex) . ((- (1_ F_Complex)),0)) * (- (1_ F_Complex))),f) is complex Element of COMPLEX
(1_ F_Complex) * (- (1_ F_Complex)) is complex Element of the carrier of F_Complex
K182((1_ F_Complex),(- (1_ F_Complex))) is complex Element of COMPLEX
((1_ F_Complex) * (- (1_ F_Complex))) * f is complex Element of the carrier of F_Complex
K182(((1_ F_Complex) * (- (1_ F_Complex))),f) is complex Element of COMPLEX
(- (1_ F_Complex)) * f is complex Element of the carrier of F_Complex
K182((- (1_ F_Complex)),f) is complex Element of COMPLEX
- ((1_ F_Complex) * f) is complex Element of the carrier of F_Complex
(F_Complex,rho,1) . 0 is complex Element of the carrier of F_Complex
(power F_Complex) . (rho,(1 + 0)) is complex Element of the carrier of F_Complex
- ((power F_Complex) . (rho,(1 + 0))) is complex Element of the carrier of F_Complex
(power F_Complex) . (rho,0) is complex Element of the carrier of F_Complex
((power F_Complex) . (rho,0)) * rho is complex Element of the carrier of F_Complex
K182(((power F_Complex) . (rho,0)),rho) is complex Element of COMPLEX
- (((power F_Complex) . (rho,0)) * rho) is complex Element of the carrier of F_Complex
(1_ F_Complex) * rho is complex Element of the carrier of F_Complex
K182((1_ F_Complex),rho) is complex Element of COMPLEX
- ((1_ F_Complex) * rho) is complex Element of the carrier of F_Complex
- rho is complex Element of the carrier of F_Complex
1 -' 1 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
1 - 1 is complex V32() ext-real integer set
((F_Complex,rho,1)) . 0 is complex Element of the carrier of F_Complex
(((F_Complex,rho,1)) . 0) * ((power F_Complex) . (f,0)) is complex Element of the carrier of F_Complex
K182((((F_Complex,rho,1)) . 0),((power F_Complex) . (f,0))) is complex Element of COMPLEX
(((F_Complex,rho,1)) . 0) * (1_ F_Complex) is complex Element of the carrier of F_Complex
K182((((F_Complex,rho,1)) . 0),(1_ F_Complex)) is complex Element of COMPLEX
(- rho) *' is complex Element of the carrier of F_Complex
Re (- rho) is complex V32() ext-real Element of REAL
Im (- rho) is complex V32() ext-real Element of REAL
(Im (- rho)) * <i> is complex set
(Re (- rho)) - ((Im (- rho)) * <i>) is complex set
((power F_Complex) . ((- (1_ F_Complex)),0)) * ((- rho) *') is complex Element of the carrier of F_Complex
K182(((power F_Complex) . ((- (1_ F_Complex)),0)),((- rho) *')) is complex Element of COMPLEX
(1_ F_Complex) * ((- rho) *') is complex Element of the carrier of F_Complex
K182((1_ F_Complex),((- rho) *')) is complex Element of COMPLEX
- (rho *') is complex Element of the carrier of F_Complex
<*(- (rho *'))*> is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
[1,(- (rho *'))] is set
{[1,(- (rho *'))]} is non empty V12() V47(1) set
Sum <*(- (rho *'))*> is complex Element of the carrier of F_Complex
<*(- f)*> is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty V12() V40() V47(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
[1,(- f)] is set
{[1,(- f)]} is non empty V12() V47(1) set
Sum <*(- f)*> is complex Element of the carrier of F_Complex
(Sum <*(- (rho *'))*>) + (Sum <*(- f)*>) is complex Element of the carrier of F_Complex
K180((Sum <*(- (rho *'))*>),(Sum <*(- f)*>)) is complex Element of COMPLEX
(Sum <*(- (rho *'))*>) + (- f) is complex Element of the carrier of F_Complex
K180((Sum <*(- (rho *'))*>),(- f)) is complex Element of COMPLEX
(- (rho *')) + (- f) is complex Element of the carrier of F_Complex
K180((- (rho *')),(- f)) is complex Element of COMPLEX
f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
rho is complex Element of the carrier of F_Complex
Re rho is complex V32() ext-real Element of REAL
eval (f,rho) is complex Element of the carrier of F_Complex
|.(eval (f,rho)).| is complex V32() ext-real Element of REAL
Re (eval (f,rho)) is complex V32() ext-real Element of REAL
(Re (eval (f,rho))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (f,rho))) * (Re (eval (f,rho))) is complex V32() ext-real set
Im (eval (f,rho)) is complex V32() ext-real Element of REAL
(Im (eval (f,rho))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (f,rho))) * (Im (eval (f,rho))) is complex V32() ext-real set
K114(((Re (eval (f,rho))) ^2),((Im (eval (f,rho))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (f,rho))) ^2),((Im (eval (f,rho))) ^2)) is complex V32() ext-real Element of REAL
rho is complex Element of the carrier of F_Complex
(F_Complex,rho,1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(power F_Complex) . (rho,1) is complex Element of the carrier of F_Complex
- ((power F_Complex) . (rho,1)) is complex Element of the carrier of F_Complex
(0,1) --> ((- ((power F_Complex) . (rho,1))),(1_ F_Complex)) is Relation-like {0,1} -defined the carrier of F_Complex -valued Function-like non empty total V18({0,1}, the carrier of F_Complex) Element of K19(K20({0,1}, the carrier of F_Complex))
{0,1} is non empty set
K20({0,1}, the carrier of F_Complex) is set
K19(K20({0,1}, the carrier of F_Complex)) is set
(0_. F_Complex) +* ((0,1) --> ((- ((power F_Complex) . (rho,1))),(1_ F_Complex))) is Relation-like Function-like set
Re rho is complex V32() ext-real Element of REAL
f is complex Element of the carrier of F_Complex
Re f is complex V32() ext-real Element of REAL
Im f is complex V32() ext-real Element of REAL
(Im f) * <i> is complex set
(Re f) + ((Im f) * <i>) is complex set
f - rho is complex Element of the carrier of F_Complex
eval ((F_Complex,rho,1),f) is complex Element of the carrier of F_Complex
Im rho is complex V32() ext-real Element of REAL
(Im rho) * <i> is complex set
(Re rho) + ((Im rho) * <i>) is complex set
- f is complex Element of the carrier of F_Complex
ef is complex Element of COMPLEX
- ef is complex Element of COMPLEX
((F_Complex,rho,1)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval (((F_Complex,rho,1)),f) is complex Element of the carrier of F_Complex
rho *' is complex Element of the carrier of F_Complex
(Re rho) - ((Im rho) * <i>) is complex set
(- f) - (rho *') is complex Element of the carrier of F_Complex
ef1 is complex Element of COMPLEX
ef1 *' is complex Element of COMPLEX
Re ef1 is complex V32() ext-real Element of REAL
Im ef1 is complex V32() ext-real Element of REAL
(Im ef1) * <i> is complex set
(Re ef1) - ((Im ef1) * <i>) is complex set
(- ef) - (ef1 *') is complex Element of COMPLEX
ef + (ef1 *') is complex Element of COMPLEX
|.(ef + (ef1 *')).| is complex V32() ext-real Element of REAL
Re (ef + (ef1 *')) is complex V32() ext-real Element of REAL
(Re (ef + (ef1 *'))) ^2 is complex V32() ext-real Element of REAL
(Re (ef + (ef1 *'))) * (Re (ef + (ef1 *'))) is complex V32() ext-real set
Im (ef + (ef1 *')) is complex V32() ext-real Element of REAL
(Im (ef + (ef1 *'))) ^2 is complex V32() ext-real Element of REAL
(Im (ef + (ef1 *'))) * (Im (ef + (ef1 *'))) is complex V32() ext-real set
K114(((Re (ef + (ef1 *'))) ^2),((Im (ef + (ef1 *'))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (ef + (ef1 *'))) ^2),((Im (ef + (ef1 *'))) ^2)) is complex V32() ext-real Element of REAL
- (ef + (ef1 *')) is complex Element of COMPLEX
|.(- (ef + (ef1 *'))).| is complex V32() ext-real Element of REAL
Re (- (ef + (ef1 *'))) is complex V32() ext-real Element of REAL
(Re (- (ef + (ef1 *')))) ^2 is complex V32() ext-real Element of REAL
(Re (- (ef + (ef1 *')))) * (Re (- (ef + (ef1 *')))) is complex V32() ext-real set
Im (- (ef + (ef1 *'))) is complex V32() ext-real Element of REAL
(Im (- (ef + (ef1 *')))) ^2 is complex V32() ext-real Element of REAL
(Im (- (ef + (ef1 *')))) * (Im (- (ef + (ef1 *')))) is complex V32() ext-real set
K114(((Re (- (ef + (ef1 *')))) ^2),((Im (- (ef + (ef1 *')))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (- (ef + (ef1 *')))) ^2),((Im (- (ef + (ef1 *')))) ^2)) is complex V32() ext-real Element of REAL
ef - ef1 is complex Element of COMPLEX
|.(ef - ef1).| is complex V32() ext-real Element of REAL
Re (ef - ef1) is complex V32() ext-real Element of REAL
(Re (ef - ef1)) ^2 is complex V32() ext-real Element of REAL
(Re (ef - ef1)) * (Re (ef - ef1)) is complex V32() ext-real set
Im (ef - ef1) is complex V32() ext-real Element of REAL
(Im (ef - ef1)) ^2 is complex V32() ext-real Element of REAL
(Im (ef - ef1)) * (Im (ef - ef1)) is complex V32() ext-real set
K114(((Re (ef - ef1)) ^2),((Im (ef - ef1)) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (ef - ef1)) ^2),((Im (ef - ef1)) ^2)) is complex V32() ext-real Element of REAL
|.(eval ((F_Complex,rho,1),f)).| is complex V32() ext-real Element of REAL
Re (eval ((F_Complex,rho,1),f)) is complex V32() ext-real Element of REAL
(Re (eval ((F_Complex,rho,1),f))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((F_Complex,rho,1),f))) * (Re (eval ((F_Complex,rho,1),f))) is complex V32() ext-real set
Im (eval ((F_Complex,rho,1),f)) is complex V32() ext-real Element of REAL
(Im (eval ((F_Complex,rho,1),f))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((F_Complex,rho,1),f))) * (Im (eval ((F_Complex,rho,1),f))) is complex V32() ext-real set
K114(((Re (eval ((F_Complex,rho,1),f))) ^2),((Im (eval ((F_Complex,rho,1),f))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((F_Complex,rho,1),f))) ^2),((Im (eval ((F_Complex,rho,1),f))) ^2)) is complex V32() ext-real Element of REAL
|.(eval (((F_Complex,rho,1)),f)).| is complex V32() ext-real Element of REAL
Re (eval (((F_Complex,rho,1)),f)) is complex V32() ext-real Element of REAL
(Re (eval (((F_Complex,rho,1)),f))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (((F_Complex,rho,1)),f))) * (Re (eval (((F_Complex,rho,1)),f))) is complex V32() ext-real set
Im (eval (((F_Complex,rho,1)),f)) is complex V32() ext-real Element of REAL
(Im (eval (((F_Complex,rho,1)),f))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (((F_Complex,rho,1)),f))) * (Im (eval (((F_Complex,rho,1)),f))) is complex V32() ext-real set
K114(((Re (eval (((F_Complex,rho,1)),f))) ^2),((Im (eval (((F_Complex,rho,1)),f))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (((F_Complex,rho,1)),f))) ^2),((Im (eval (((F_Complex,rho,1)),f))) ^2)) is complex V32() ext-real Element of REAL
ef is complex Element of the carrier of F_Complex
(F_Complex,ef,1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(power F_Complex) . (ef,1) is complex Element of the carrier of F_Complex
- ((power F_Complex) . (ef,1)) is complex Element of the carrier of F_Complex
(0,1) --> ((- ((power F_Complex) . (ef,1))),(1_ F_Complex)) is Relation-like {0,1} -defined the carrier of F_Complex -valued Function-like non empty total V18({0,1}, the carrier of F_Complex) Element of K19(K20({0,1}, the carrier of F_Complex))
(0_. F_Complex) +* ((0,1) --> ((- ((power F_Complex) . (ef,1))),(1_ F_Complex))) is Relation-like Function-like set
f is complex Element of the carrier of F_Complex
rho is complex Element of the carrier of F_Complex
Re rho is complex V32() ext-real Element of REAL
|.f.| is complex V32() ext-real Element of REAL
Re f is complex V32() ext-real Element of REAL
(Re f) ^2 is complex V32() ext-real Element of REAL
(Re f) * (Re f) is complex V32() ext-real set
Im f is complex V32() ext-real Element of REAL
(Im f) ^2 is complex V32() ext-real Element of REAL
(Im f) * (Im f) is complex V32() ext-real set
K114(((Re f) ^2),((Im f) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re f) ^2),((Im f) ^2)) is complex V32() ext-real Element of REAL
((F_Complex,ef,1)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval (((F_Complex,ef,1)),rho) is complex Element of the carrier of F_Complex
|.(eval (((F_Complex,ef,1)),rho)).| is complex V32() ext-real Element of REAL
Re (eval (((F_Complex,ef,1)),rho)) is complex V32() ext-real Element of REAL
(Re (eval (((F_Complex,ef,1)),rho))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (((F_Complex,ef,1)),rho))) * (Re (eval (((F_Complex,ef,1)),rho))) is complex V32() ext-real set
Im (eval (((F_Complex,ef,1)),rho)) is complex V32() ext-real Element of REAL
(Im (eval (((F_Complex,ef,1)),rho))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (((F_Complex,ef,1)),rho))) * (Im (eval (((F_Complex,ef,1)),rho))) is complex V32() ext-real set
K114(((Re (eval (((F_Complex,ef,1)),rho))) ^2),((Im (eval (((F_Complex,ef,1)),rho))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (((F_Complex,ef,1)),rho))) ^2),((Im (eval (((F_Complex,ef,1)),rho))) ^2)) is complex V32() ext-real Element of REAL
|.f.| * |.(eval (((F_Complex,ef,1)),rho)).| is complex V32() ext-real set
f *' is complex Element of the carrier of F_Complex
(Im f) * <i> is complex set
(Re f) - ((Im f) * <i>) is complex set
|.(f *').| is complex V32() ext-real Element of REAL
Re (f *') is complex V32() ext-real Element of REAL
(Re (f *')) ^2 is complex V32() ext-real Element of REAL
(Re (f *')) * (Re (f *')) is complex V32() ext-real set
Im (f *') is complex V32() ext-real Element of REAL
(Im (f *')) ^2 is complex V32() ext-real Element of REAL
(Im (f *')) * (Im (f *')) is complex V32() ext-real set
K114(((Re (f *')) ^2),((Im (f *')) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (f *')) ^2),((Im (f *')) ^2)) is complex V32() ext-real Element of REAL
|.(f *').| * |.(eval (((F_Complex,ef,1)),rho)).| is complex V32() ext-real set
(f *') * (eval (((F_Complex,ef,1)),rho)) is complex Element of the carrier of F_Complex
K182((f *'),(eval (((F_Complex,ef,1)),rho))) is complex Element of COMPLEX
|.((f *') * (eval (((F_Complex,ef,1)),rho))).| is complex V32() ext-real Element of REAL
Re ((f *') * (eval (((F_Complex,ef,1)),rho))) is complex V32() ext-real Element of REAL
(Re ((f *') * (eval (((F_Complex,ef,1)),rho)))) ^2 is complex V32() ext-real Element of REAL
(Re ((f *') * (eval (((F_Complex,ef,1)),rho)))) * (Re ((f *') * (eval (((F_Complex,ef,1)),rho)))) is complex V32() ext-real set
Im ((f *') * (eval (((F_Complex,ef,1)),rho))) is complex V32() ext-real Element of REAL
(Im ((f *') * (eval (((F_Complex,ef,1)),rho)))) ^2 is complex V32() ext-real Element of REAL
(Im ((f *') * (eval (((F_Complex,ef,1)),rho)))) * (Im ((f *') * (eval (((F_Complex,ef,1)),rho)))) is complex V32() ext-real set
K114(((Re ((f *') * (eval (((F_Complex,ef,1)),rho)))) ^2),((Im ((f *') * (eval (((F_Complex,ef,1)),rho)))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re ((f *') * (eval (((F_Complex,ef,1)),rho)))) ^2),((Im ((f *') * (eval (((F_Complex,ef,1)),rho)))) ^2)) is complex V32() ext-real Element of REAL
(f *') * ((F_Complex,ef,1)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval (((f *') * ((F_Complex,ef,1))),rho) is complex Element of the carrier of F_Complex
|.(eval (((f *') * ((F_Complex,ef,1))),rho)).| is complex V32() ext-real Element of REAL
Re (eval (((f *') * ((F_Complex,ef,1))),rho)) is complex V32() ext-real Element of REAL
(Re (eval (((f *') * ((F_Complex,ef,1))),rho))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (((f *') * ((F_Complex,ef,1))),rho))) * (Re (eval (((f *') * ((F_Complex,ef,1))),rho))) is complex V32() ext-real set
Im (eval (((f *') * ((F_Complex,ef,1))),rho)) is complex V32() ext-real Element of REAL
(Im (eval (((f *') * ((F_Complex,ef,1))),rho))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (((f *') * ((F_Complex,ef,1))),rho))) * (Im (eval (((f *') * ((F_Complex,ef,1))),rho))) is complex V32() ext-real set
K114(((Re (eval (((f *') * ((F_Complex,ef,1))),rho))) ^2),((Im (eval (((f *') * ((F_Complex,ef,1))),rho))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (((f *') * ((F_Complex,ef,1))),rho))) ^2),((Im (eval (((f *') * ((F_Complex,ef,1))),rho))) ^2)) is complex V32() ext-real Element of REAL
f * (F_Complex,ef,1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f * (F_Complex,ef,1))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval (((f * (F_Complex,ef,1))),rho) is complex Element of the carrier of F_Complex
|.(eval (((f * (F_Complex,ef,1))),rho)).| is complex V32() ext-real Element of REAL
Re (eval (((f * (F_Complex,ef,1))),rho)) is complex V32() ext-real Element of REAL
(Re (eval (((f * (F_Complex,ef,1))),rho))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (((f * (F_Complex,ef,1))),rho))) * (Re (eval (((f * (F_Complex,ef,1))),rho))) is complex V32() ext-real set
Im (eval (((f * (F_Complex,ef,1))),rho)) is complex V32() ext-real Element of REAL
(Im (eval (((f * (F_Complex,ef,1))),rho))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (((f * (F_Complex,ef,1))),rho))) * (Im (eval (((f * (F_Complex,ef,1))),rho))) is complex V32() ext-real set
K114(((Re (eval (((f * (F_Complex,ef,1))),rho))) ^2),((Im (eval (((f * (F_Complex,ef,1))),rho))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (((f * (F_Complex,ef,1))),rho))) ^2),((Im (eval (((f * (F_Complex,ef,1))),rho))) ^2)) is complex V32() ext-real Element of REAL
eval ((f * (F_Complex,ef,1)),rho) is complex Element of the carrier of F_Complex
|.(eval ((f * (F_Complex,ef,1)),rho)).| is complex V32() ext-real Element of REAL
Re (eval ((f * (F_Complex,ef,1)),rho)) is complex V32() ext-real Element of REAL
(Re (eval ((f * (F_Complex,ef,1)),rho))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((f * (F_Complex,ef,1)),rho))) * (Re (eval ((f * (F_Complex,ef,1)),rho))) is complex V32() ext-real set
Im (eval ((f * (F_Complex,ef,1)),rho)) is complex V32() ext-real Element of REAL
(Im (eval ((f * (F_Complex,ef,1)),rho))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((f * (F_Complex,ef,1)),rho))) * (Im (eval ((f * (F_Complex,ef,1)),rho))) is complex V32() ext-real set
K114(((Re (eval ((f * (F_Complex,ef,1)),rho))) ^2),((Im (eval ((f * (F_Complex,ef,1)),rho))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((f * (F_Complex,ef,1)),rho))) ^2),((Im (eval ((f * (F_Complex,ef,1)),rho))) ^2)) is complex V32() ext-real Element of REAL
eval ((F_Complex,ef,1),rho) is complex Element of the carrier of F_Complex
f * (eval ((F_Complex,ef,1),rho)) is complex Element of the carrier of F_Complex
K182(f,(eval ((F_Complex,ef,1),rho))) is complex Element of COMPLEX
|.(f * (eval ((F_Complex,ef,1),rho))).| is complex V32() ext-real Element of REAL
Re (f * (eval ((F_Complex,ef,1),rho))) is complex V32() ext-real Element of REAL
(Re (f * (eval ((F_Complex,ef,1),rho)))) ^2 is complex V32() ext-real Element of REAL
(Re (f * (eval ((F_Complex,ef,1),rho)))) * (Re (f * (eval ((F_Complex,ef,1),rho)))) is complex V32() ext-real set
Im (f * (eval ((F_Complex,ef,1),rho))) is complex V32() ext-real Element of REAL
(Im (f * (eval ((F_Complex,ef,1),rho)))) ^2 is complex V32() ext-real Element of REAL
(Im (f * (eval ((F_Complex,ef,1),rho)))) * (Im (f * (eval ((F_Complex,ef,1),rho)))) is complex V32() ext-real set
K114(((Re (f * (eval ((F_Complex,ef,1),rho)))) ^2),((Im (f * (eval ((F_Complex,ef,1),rho)))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (f * (eval ((F_Complex,ef,1),rho)))) ^2),((Im (f * (eval ((F_Complex,ef,1),rho)))) ^2)) is complex V32() ext-real Element of REAL
|.(eval ((F_Complex,ef,1),rho)).| is complex V32() ext-real Element of REAL
Re (eval ((F_Complex,ef,1),rho)) is complex V32() ext-real Element of REAL
(Re (eval ((F_Complex,ef,1),rho))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((F_Complex,ef,1),rho))) * (Re (eval ((F_Complex,ef,1),rho))) is complex V32() ext-real set
Im (eval ((F_Complex,ef,1),rho)) is complex V32() ext-real Element of REAL
(Im (eval ((F_Complex,ef,1),rho))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((F_Complex,ef,1),rho))) * (Im (eval ((F_Complex,ef,1),rho))) is complex V32() ext-real set
K114(((Re (eval ((F_Complex,ef,1),rho))) ^2),((Im (eval ((F_Complex,ef,1),rho))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((F_Complex,ef,1),rho))) ^2),((Im (eval ((F_Complex,ef,1),rho))) ^2)) is complex V32() ext-real Element of REAL
|.f.| * |.(eval ((F_Complex,ef,1),rho)).| is complex V32() ext-real set
rho is complex Element of the carrier of F_Complex
(F_Complex,rho,1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(power F_Complex) . (rho,1) is complex Element of the carrier of F_Complex
- ((power F_Complex) . (rho,1)) is complex Element of the carrier of F_Complex
(0,1) --> ((- ((power F_Complex) . (rho,1))),(1_ F_Complex)) is Relation-like {0,1} -defined the carrier of F_Complex -valued Function-like non empty total V18({0,1}, the carrier of F_Complex) Element of K19(K20({0,1}, the carrier of F_Complex))
(0_. F_Complex) +* ((0,1) --> ((- ((power F_Complex) . (rho,1))),(1_ F_Complex))) is Relation-like Function-like set
Re rho is complex V32() ext-real Element of REAL
f is complex Element of the carrier of F_Complex
Re f is complex V32() ext-real Element of REAL
Im f is complex V32() ext-real Element of REAL
(Im f) * <i> is complex set
(Re f) + ((Im f) * <i>) is complex set
f - rho is complex Element of the carrier of F_Complex
eval ((F_Complex,rho,1),f) is complex Element of the carrier of F_Complex
Im rho is complex V32() ext-real Element of REAL
(Im rho) * <i> is complex set
(Re rho) + ((Im rho) * <i>) is complex set
- f is complex Element of the carrier of F_Complex
ef is complex Element of COMPLEX
- ef is complex Element of COMPLEX
((F_Complex,rho,1)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval (((F_Complex,rho,1)),f) is complex Element of the carrier of F_Complex
rho *' is complex Element of the carrier of F_Complex
(Re rho) - ((Im rho) * <i>) is complex set
(- f) - (rho *') is complex Element of the carrier of F_Complex
ef1 is complex Element of COMPLEX
ef1 *' is complex Element of COMPLEX
Re ef1 is complex V32() ext-real Element of REAL
Im ef1 is complex V32() ext-real Element of REAL
(Im ef1) * <i> is complex set
(Re ef1) - ((Im ef1) * <i>) is complex set
(- ef) - (ef1 *') is complex Element of COMPLEX
ef + (ef1 *') is complex Element of COMPLEX
|.(ef + (ef1 *')).| is complex V32() ext-real Element of REAL
Re (ef + (ef1 *')) is complex V32() ext-real Element of REAL
(Re (ef + (ef1 *'))) ^2 is complex V32() ext-real Element of REAL
(Re (ef + (ef1 *'))) * (Re (ef + (ef1 *'))) is complex V32() ext-real set
Im (ef + (ef1 *')) is complex V32() ext-real Element of REAL
(Im (ef + (ef1 *'))) ^2 is complex V32() ext-real Element of REAL
(Im (ef + (ef1 *'))) * (Im (ef + (ef1 *'))) is complex V32() ext-real set
K114(((Re (ef + (ef1 *'))) ^2),((Im (ef + (ef1 *'))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (ef + (ef1 *'))) ^2),((Im (ef + (ef1 *'))) ^2)) is complex V32() ext-real Element of REAL
- (ef + (ef1 *')) is complex Element of COMPLEX
|.(- (ef + (ef1 *'))).| is complex V32() ext-real Element of REAL
Re (- (ef + (ef1 *'))) is complex V32() ext-real Element of REAL
(Re (- (ef + (ef1 *')))) ^2 is complex V32() ext-real Element of REAL
(Re (- (ef + (ef1 *')))) * (Re (- (ef + (ef1 *')))) is complex V32() ext-real set
Im (- (ef + (ef1 *'))) is complex V32() ext-real Element of REAL
(Im (- (ef + (ef1 *')))) ^2 is complex V32() ext-real Element of REAL
(Im (- (ef + (ef1 *')))) * (Im (- (ef + (ef1 *')))) is complex V32() ext-real set
K114(((Re (- (ef + (ef1 *')))) ^2),((Im (- (ef + (ef1 *')))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (- (ef + (ef1 *')))) ^2),((Im (- (ef + (ef1 *')))) ^2)) is complex V32() ext-real Element of REAL
ef - ef1 is complex Element of COMPLEX
|.(ef - ef1).| is complex V32() ext-real Element of REAL
Re (ef - ef1) is complex V32() ext-real Element of REAL
(Re (ef - ef1)) ^2 is complex V32() ext-real Element of REAL
(Re (ef - ef1)) * (Re (ef - ef1)) is complex V32() ext-real set
Im (ef - ef1) is complex V32() ext-real Element of REAL
(Im (ef - ef1)) ^2 is complex V32() ext-real Element of REAL
(Im (ef - ef1)) * (Im (ef - ef1)) is complex V32() ext-real set
K114(((Re (ef - ef1)) ^2),((Im (ef - ef1)) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (ef - ef1)) ^2),((Im (ef - ef1)) ^2)) is complex V32() ext-real Element of REAL
|.(eval (((F_Complex,rho,1)),f)).| is complex V32() ext-real Element of REAL
Re (eval (((F_Complex,rho,1)),f)) is complex V32() ext-real Element of REAL
(Re (eval (((F_Complex,rho,1)),f))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (((F_Complex,rho,1)),f))) * (Re (eval (((F_Complex,rho,1)),f))) is complex V32() ext-real set
Im (eval (((F_Complex,rho,1)),f)) is complex V32() ext-real Element of REAL
(Im (eval (((F_Complex,rho,1)),f))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (((F_Complex,rho,1)),f))) * (Im (eval (((F_Complex,rho,1)),f))) is complex V32() ext-real set
K114(((Re (eval (((F_Complex,rho,1)),f))) ^2),((Im (eval (((F_Complex,rho,1)),f))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (((F_Complex,rho,1)),f))) ^2),((Im (eval (((F_Complex,rho,1)),f))) ^2)) is complex V32() ext-real Element of REAL
|.(eval ((F_Complex,rho,1),f)).| is complex V32() ext-real Element of REAL
Re (eval ((F_Complex,rho,1),f)) is complex V32() ext-real Element of REAL
(Re (eval ((F_Complex,rho,1),f))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((F_Complex,rho,1),f))) * (Re (eval ((F_Complex,rho,1),f))) is complex V32() ext-real set
Im (eval ((F_Complex,rho,1),f)) is complex V32() ext-real Element of REAL
(Im (eval ((F_Complex,rho,1),f))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((F_Complex,rho,1),f))) * (Im (eval ((F_Complex,rho,1),f))) is complex V32() ext-real set
K114(((Re (eval ((F_Complex,rho,1),f))) ^2),((Im (eval ((F_Complex,rho,1),f))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((F_Complex,rho,1),f))) ^2),((Im (eval ((F_Complex,rho,1),f))) ^2)) is complex V32() ext-real Element of REAL
ef is complex Element of the carrier of F_Complex
(F_Complex,ef,1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(power F_Complex) . (ef,1) is complex Element of the carrier of F_Complex
- ((power F_Complex) . (ef,1)) is complex Element of the carrier of F_Complex
(0,1) --> ((- ((power F_Complex) . (ef,1))),(1_ F_Complex)) is Relation-like {0,1} -defined the carrier of F_Complex -valued Function-like non empty total V18({0,1}, the carrier of F_Complex) Element of K19(K20({0,1}, the carrier of F_Complex))
(0_. F_Complex) +* ((0,1) --> ((- ((power F_Complex) . (ef,1))),(1_ F_Complex))) is Relation-like Function-like set
f is complex Element of the carrier of F_Complex
rho is complex Element of the carrier of F_Complex
Re rho is complex V32() ext-real Element of REAL
|.f.| is complex V32() ext-real Element of REAL
Re f is complex V32() ext-real Element of REAL
(Re f) ^2 is complex V32() ext-real Element of REAL
(Re f) * (Re f) is complex V32() ext-real set
Im f is complex V32() ext-real Element of REAL
(Im f) ^2 is complex V32() ext-real Element of REAL
(Im f) * (Im f) is complex V32() ext-real set
K114(((Re f) ^2),((Im f) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re f) ^2),((Im f) ^2)) is complex V32() ext-real Element of REAL
((F_Complex,ef,1)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval (((F_Complex,ef,1)),rho) is complex Element of the carrier of F_Complex
|.(eval (((F_Complex,ef,1)),rho)).| is complex V32() ext-real Element of REAL
Re (eval (((F_Complex,ef,1)),rho)) is complex V32() ext-real Element of REAL
(Re (eval (((F_Complex,ef,1)),rho))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (((F_Complex,ef,1)),rho))) * (Re (eval (((F_Complex,ef,1)),rho))) is complex V32() ext-real set
Im (eval (((F_Complex,ef,1)),rho)) is complex V32() ext-real Element of REAL
(Im (eval (((F_Complex,ef,1)),rho))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (((F_Complex,ef,1)),rho))) * (Im (eval (((F_Complex,ef,1)),rho))) is complex V32() ext-real set
K114(((Re (eval (((F_Complex,ef,1)),rho))) ^2),((Im (eval (((F_Complex,ef,1)),rho))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (((F_Complex,ef,1)),rho))) ^2),((Im (eval (((F_Complex,ef,1)),rho))) ^2)) is complex V32() ext-real Element of REAL
|.f.| * |.(eval (((F_Complex,ef,1)),rho)).| is complex V32() ext-real set
f *' is complex Element of the carrier of F_Complex
(Im f) * <i> is complex set
(Re f) - ((Im f) * <i>) is complex set
|.(f *').| is complex V32() ext-real Element of REAL
Re (f *') is complex V32() ext-real Element of REAL
(Re (f *')) ^2 is complex V32() ext-real Element of REAL
(Re (f *')) * (Re (f *')) is complex V32() ext-real set
Im (f *') is complex V32() ext-real Element of REAL
(Im (f *')) ^2 is complex V32() ext-real Element of REAL
(Im (f *')) * (Im (f *')) is complex V32() ext-real set
K114(((Re (f *')) ^2),((Im (f *')) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (f *')) ^2),((Im (f *')) ^2)) is complex V32() ext-real Element of REAL
|.(f *').| * |.(eval (((F_Complex,ef,1)),rho)).| is complex V32() ext-real set
(f *') * (eval (((F_Complex,ef,1)),rho)) is complex Element of the carrier of F_Complex
K182((f *'),(eval (((F_Complex,ef,1)),rho))) is complex Element of COMPLEX
|.((f *') * (eval (((F_Complex,ef,1)),rho))).| is complex V32() ext-real Element of REAL
Re ((f *') * (eval (((F_Complex,ef,1)),rho))) is complex V32() ext-real Element of REAL
(Re ((f *') * (eval (((F_Complex,ef,1)),rho)))) ^2 is complex V32() ext-real Element of REAL
(Re ((f *') * (eval (((F_Complex,ef,1)),rho)))) * (Re ((f *') * (eval (((F_Complex,ef,1)),rho)))) is complex V32() ext-real set
Im ((f *') * (eval (((F_Complex,ef,1)),rho))) is complex V32() ext-real Element of REAL
(Im ((f *') * (eval (((F_Complex,ef,1)),rho)))) ^2 is complex V32() ext-real Element of REAL
(Im ((f *') * (eval (((F_Complex,ef,1)),rho)))) * (Im ((f *') * (eval (((F_Complex,ef,1)),rho)))) is complex V32() ext-real set
K114(((Re ((f *') * (eval (((F_Complex,ef,1)),rho)))) ^2),((Im ((f *') * (eval (((F_Complex,ef,1)),rho)))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re ((f *') * (eval (((F_Complex,ef,1)),rho)))) ^2),((Im ((f *') * (eval (((F_Complex,ef,1)),rho)))) ^2)) is complex V32() ext-real Element of REAL
(f *') * ((F_Complex,ef,1)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval (((f *') * ((F_Complex,ef,1))),rho) is complex Element of the carrier of F_Complex
|.(eval (((f *') * ((F_Complex,ef,1))),rho)).| is complex V32() ext-real Element of REAL
Re (eval (((f *') * ((F_Complex,ef,1))),rho)) is complex V32() ext-real Element of REAL
(Re (eval (((f *') * ((F_Complex,ef,1))),rho))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (((f *') * ((F_Complex,ef,1))),rho))) * (Re (eval (((f *') * ((F_Complex,ef,1))),rho))) is complex V32() ext-real set
Im (eval (((f *') * ((F_Complex,ef,1))),rho)) is complex V32() ext-real Element of REAL
(Im (eval (((f *') * ((F_Complex,ef,1))),rho))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (((f *') * ((F_Complex,ef,1))),rho))) * (Im (eval (((f *') * ((F_Complex,ef,1))),rho))) is complex V32() ext-real set
K114(((Re (eval (((f *') * ((F_Complex,ef,1))),rho))) ^2),((Im (eval (((f *') * ((F_Complex,ef,1))),rho))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (((f *') * ((F_Complex,ef,1))),rho))) ^2),((Im (eval (((f *') * ((F_Complex,ef,1))),rho))) ^2)) is complex V32() ext-real Element of REAL
f * (F_Complex,ef,1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f * (F_Complex,ef,1))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval (((f * (F_Complex,ef,1))),rho) is complex Element of the carrier of F_Complex
|.(eval (((f * (F_Complex,ef,1))),rho)).| is complex V32() ext-real Element of REAL
Re (eval (((f * (F_Complex,ef,1))),rho)) is complex V32() ext-real Element of REAL
(Re (eval (((f * (F_Complex,ef,1))),rho))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (((f * (F_Complex,ef,1))),rho))) * (Re (eval (((f * (F_Complex,ef,1))),rho))) is complex V32() ext-real set
Im (eval (((f * (F_Complex,ef,1))),rho)) is complex V32() ext-real Element of REAL
(Im (eval (((f * (F_Complex,ef,1))),rho))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (((f * (F_Complex,ef,1))),rho))) * (Im (eval (((f * (F_Complex,ef,1))),rho))) is complex V32() ext-real set
K114(((Re (eval (((f * (F_Complex,ef,1))),rho))) ^2),((Im (eval (((f * (F_Complex,ef,1))),rho))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (((f * (F_Complex,ef,1))),rho))) ^2),((Im (eval (((f * (F_Complex,ef,1))),rho))) ^2)) is complex V32() ext-real Element of REAL
eval ((f * (F_Complex,ef,1)),rho) is complex Element of the carrier of F_Complex
|.(eval ((f * (F_Complex,ef,1)),rho)).| is complex V32() ext-real Element of REAL
Re (eval ((f * (F_Complex,ef,1)),rho)) is complex V32() ext-real Element of REAL
(Re (eval ((f * (F_Complex,ef,1)),rho))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((f * (F_Complex,ef,1)),rho))) * (Re (eval ((f * (F_Complex,ef,1)),rho))) is complex V32() ext-real set
Im (eval ((f * (F_Complex,ef,1)),rho)) is complex V32() ext-real Element of REAL
(Im (eval ((f * (F_Complex,ef,1)),rho))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((f * (F_Complex,ef,1)),rho))) * (Im (eval ((f * (F_Complex,ef,1)),rho))) is complex V32() ext-real set
K114(((Re (eval ((f * (F_Complex,ef,1)),rho))) ^2),((Im (eval ((f * (F_Complex,ef,1)),rho))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((f * (F_Complex,ef,1)),rho))) ^2),((Im (eval ((f * (F_Complex,ef,1)),rho))) ^2)) is complex V32() ext-real Element of REAL
eval ((F_Complex,ef,1),rho) is complex Element of the carrier of F_Complex
f * (eval ((F_Complex,ef,1),rho)) is complex Element of the carrier of F_Complex
K182(f,(eval ((F_Complex,ef,1),rho))) is complex Element of COMPLEX
|.(f * (eval ((F_Complex,ef,1),rho))).| is complex V32() ext-real Element of REAL
Re (f * (eval ((F_Complex,ef,1),rho))) is complex V32() ext-real Element of REAL
(Re (f * (eval ((F_Complex,ef,1),rho)))) ^2 is complex V32() ext-real Element of REAL
(Re (f * (eval ((F_Complex,ef,1),rho)))) * (Re (f * (eval ((F_Complex,ef,1),rho)))) is complex V32() ext-real set
Im (f * (eval ((F_Complex,ef,1),rho))) is complex V32() ext-real Element of REAL
(Im (f * (eval ((F_Complex,ef,1),rho)))) ^2 is complex V32() ext-real Element of REAL
(Im (f * (eval ((F_Complex,ef,1),rho)))) * (Im (f * (eval ((F_Complex,ef,1),rho)))) is complex V32() ext-real set
K114(((Re (f * (eval ((F_Complex,ef,1),rho)))) ^2),((Im (f * (eval ((F_Complex,ef,1),rho)))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (f * (eval ((F_Complex,ef,1),rho)))) ^2),((Im (f * (eval ((F_Complex,ef,1),rho)))) ^2)) is complex V32() ext-real Element of REAL
|.(eval ((F_Complex,ef,1),rho)).| is complex V32() ext-real Element of REAL
Re (eval ((F_Complex,ef,1),rho)) is complex V32() ext-real Element of REAL
(Re (eval ((F_Complex,ef,1),rho))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((F_Complex,ef,1),rho))) * (Re (eval ((F_Complex,ef,1),rho))) is complex V32() ext-real set
Im (eval ((F_Complex,ef,1),rho)) is complex V32() ext-real Element of REAL
(Im (eval ((F_Complex,ef,1),rho))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((F_Complex,ef,1),rho))) * (Im (eval ((F_Complex,ef,1),rho))) is complex V32() ext-real set
K114(((Re (eval ((F_Complex,ef,1),rho))) ^2),((Im (eval ((F_Complex,ef,1),rho))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((F_Complex,ef,1),rho))) ^2),((Im (eval ((F_Complex,ef,1),rho))) ^2)) is complex V32() ext-real Element of REAL
|.f.| * |.(eval ((F_Complex,ef,1),rho)).| is complex V32() ext-real set
f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(F_Complex,f) is complex V32() ext-real integer set
len f is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len f) - 1 is complex V32() ext-real integer set
(f) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
ef is complex Element of the carrier of F_Complex
(F_Complex,ef,1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(power F_Complex) . (ef,1) is complex Element of the carrier of F_Complex
- ((power F_Complex) . (ef,1)) is complex Element of the carrier of F_Complex
(0,1) --> ((- ((power F_Complex) . (ef,1))),(1_ F_Complex)) is Relation-like {0,1} -defined the carrier of F_Complex -valued Function-like non empty total V18({0,1}, the carrier of F_Complex) Element of K19(K20({0,1}, the carrier of F_Complex))
(0_. F_Complex) +* ((0,1) --> ((- ((power F_Complex) . (ef,1))),(1_ F_Complex))) is Relation-like Function-like set
Re ef is complex V32() ext-real Element of REAL
rho is complex Element of the carrier of F_Complex
Re rho is complex V32() ext-real Element of REAL
Im rho is complex V32() ext-real Element of REAL
(Im rho) * <i> is complex set
(Re rho) + ((Im rho) * <i>) is complex set
rho - ef is complex Element of the carrier of F_Complex
eval ((F_Complex,ef,1),rho) is complex Element of the carrier of F_Complex
Im ef is complex V32() ext-real Element of REAL
(Im ef) * <i> is complex set
(Re ef) + ((Im ef) * <i>) is complex set
- rho is complex Element of the carrier of F_Complex
ef1 is complex Element of COMPLEX
- ef1 is complex Element of COMPLEX
((F_Complex,ef,1)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval (((F_Complex,ef,1)),rho) is complex Element of the carrier of F_Complex
ef *' is complex Element of the carrier of F_Complex
(Re ef) - ((Im ef) * <i>) is complex set
(- rho) - (ef *') is complex Element of the carrier of F_Complex
t is complex Element of COMPLEX
t *' is complex Element of COMPLEX
Re t is complex V32() ext-real Element of REAL
Im t is complex V32() ext-real Element of REAL
(Im t) * <i> is complex set
(Re t) - ((Im t) * <i>) is complex set
(- ef1) - (t *') is complex Element of COMPLEX
ef1 + (t *') is complex Element of COMPLEX
|.(ef1 + (t *')).| is complex V32() ext-real Element of REAL
Re (ef1 + (t *')) is complex V32() ext-real Element of REAL
(Re (ef1 + (t *'))) ^2 is complex V32() ext-real Element of REAL
(Re (ef1 + (t *'))) * (Re (ef1 + (t *'))) is complex V32() ext-real set
Im (ef1 + (t *')) is complex V32() ext-real Element of REAL
(Im (ef1 + (t *'))) ^2 is complex V32() ext-real Element of REAL
(Im (ef1 + (t *'))) * (Im (ef1 + (t *'))) is complex V32() ext-real set
K114(((Re (ef1 + (t *'))) ^2),((Im (ef1 + (t *'))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (ef1 + (t *'))) ^2),((Im (ef1 + (t *'))) ^2)) is complex V32() ext-real Element of REAL
- (ef1 + (t *')) is complex Element of COMPLEX
|.(- (ef1 + (t *'))).| is complex V32() ext-real Element of REAL
Re (- (ef1 + (t *'))) is complex V32() ext-real Element of REAL
(Re (- (ef1 + (t *')))) ^2 is complex V32() ext-real Element of REAL
(Re (- (ef1 + (t *')))) * (Re (- (ef1 + (t *')))) is complex V32() ext-real set
Im (- (ef1 + (t *'))) is complex V32() ext-real Element of REAL
(Im (- (ef1 + (t *')))) ^2 is complex V32() ext-real Element of REAL
(Im (- (ef1 + (t *')))) * (Im (- (ef1 + (t *')))) is complex V32() ext-real set
K114(((Re (- (ef1 + (t *')))) ^2),((Im (- (ef1 + (t *')))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (- (ef1 + (t *')))) ^2),((Im (- (ef1 + (t *')))) ^2)) is complex V32() ext-real Element of REAL
ef1 - t is complex Element of COMPLEX
|.(ef1 - t).| is complex V32() ext-real Element of REAL
Re (ef1 - t) is complex V32() ext-real Element of REAL
(Re (ef1 - t)) ^2 is complex V32() ext-real Element of REAL
(Re (ef1 - t)) * (Re (ef1 - t)) is complex V32() ext-real set
Im (ef1 - t) is complex V32() ext-real Element of REAL
(Im (ef1 - t)) ^2 is complex V32() ext-real Element of REAL
(Im (ef1 - t)) * (Im (ef1 - t)) is complex V32() ext-real set
K114(((Re (ef1 - t)) ^2),((Im (ef1 - t)) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (ef1 - t)) ^2),((Im (ef1 - t)) ^2)) is complex V32() ext-real Element of REAL
|.(eval ((F_Complex,ef,1),rho)).| is complex V32() ext-real Element of REAL
Re (eval ((F_Complex,ef,1),rho)) is complex V32() ext-real Element of REAL
(Re (eval ((F_Complex,ef,1),rho))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((F_Complex,ef,1),rho))) * (Re (eval ((F_Complex,ef,1),rho))) is complex V32() ext-real set
Im (eval ((F_Complex,ef,1),rho)) is complex V32() ext-real Element of REAL
(Im (eval ((F_Complex,ef,1),rho))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((F_Complex,ef,1),rho))) * (Im (eval ((F_Complex,ef,1),rho))) is complex V32() ext-real set
K114(((Re (eval ((F_Complex,ef,1),rho))) ^2),((Im (eval ((F_Complex,ef,1),rho))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((F_Complex,ef,1),rho))) ^2),((Im (eval ((F_Complex,ef,1),rho))) ^2)) is complex V32() ext-real Element of REAL
|.(eval (((F_Complex,ef,1)),rho)).| is complex V32() ext-real Element of REAL
Re (eval (((F_Complex,ef,1)),rho)) is complex V32() ext-real Element of REAL
(Re (eval (((F_Complex,ef,1)),rho))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (((F_Complex,ef,1)),rho))) * (Re (eval (((F_Complex,ef,1)),rho))) is complex V32() ext-real set
Im (eval (((F_Complex,ef,1)),rho)) is complex V32() ext-real Element of REAL
(Im (eval (((F_Complex,ef,1)),rho))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (((F_Complex,ef,1)),rho))) * (Im (eval (((F_Complex,ef,1)),rho))) is complex V32() ext-real set
K114(((Re (eval (((F_Complex,ef,1)),rho))) ^2),((Im (eval (((F_Complex,ef,1)),rho))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (((F_Complex,ef,1)),rho))) ^2),((Im (eval (((F_Complex,ef,1)),rho))) ^2)) is complex V32() ext-real Element of REAL
ef1 is complex Element of the carrier of F_Complex
(F_Complex,ef1,1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(power F_Complex) . (ef1,1) is complex Element of the carrier of F_Complex
- ((power F_Complex) . (ef1,1)) is complex Element of the carrier of F_Complex
(0,1) --> ((- ((power F_Complex) . (ef1,1))),(1_ F_Complex)) is Relation-like {0,1} -defined the carrier of F_Complex -valued Function-like non empty total V18({0,1}, the carrier of F_Complex) Element of K19(K20({0,1}, the carrier of F_Complex))
(0_. F_Complex) +* ((0,1) --> ((- ((power F_Complex) . (ef1,1))),(1_ F_Complex))) is Relation-like Function-like set
rho is complex Element of the carrier of F_Complex
rho * (F_Complex,ef1,1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
ef is complex Element of the carrier of F_Complex
eval ((rho * (F_Complex,ef1,1)),ef) is complex Element of the carrier of F_Complex
|.(eval ((rho * (F_Complex,ef1,1)),ef)).| is complex V32() ext-real Element of REAL
Re (eval ((rho * (F_Complex,ef1,1)),ef)) is complex V32() ext-real Element of REAL
(Re (eval ((rho * (F_Complex,ef1,1)),ef))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((rho * (F_Complex,ef1,1)),ef))) * (Re (eval ((rho * (F_Complex,ef1,1)),ef))) is complex V32() ext-real set
Im (eval ((rho * (F_Complex,ef1,1)),ef)) is complex V32() ext-real Element of REAL
(Im (eval ((rho * (F_Complex,ef1,1)),ef))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((rho * (F_Complex,ef1,1)),ef))) * (Im (eval ((rho * (F_Complex,ef1,1)),ef))) is complex V32() ext-real set
K114(((Re (eval ((rho * (F_Complex,ef1,1)),ef))) ^2),((Im (eval ((rho * (F_Complex,ef1,1)),ef))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((rho * (F_Complex,ef1,1)),ef))) ^2),((Im (eval ((rho * (F_Complex,ef1,1)),ef))) ^2)) is complex V32() ext-real Element of REAL
eval ((F_Complex,ef1,1),ef) is complex Element of the carrier of F_Complex
rho * (eval ((F_Complex,ef1,1),ef)) is complex Element of the carrier of F_Complex
K182(rho,(eval ((F_Complex,ef1,1),ef))) is complex Element of COMPLEX
|.(rho * (eval ((F_Complex,ef1,1),ef))).| is complex V32() ext-real Element of REAL
Re (rho * (eval ((F_Complex,ef1,1),ef))) is complex V32() ext-real Element of REAL
(Re (rho * (eval ((F_Complex,ef1,1),ef)))) ^2 is complex V32() ext-real Element of REAL
(Re (rho * (eval ((F_Complex,ef1,1),ef)))) * (Re (rho * (eval ((F_Complex,ef1,1),ef)))) is complex V32() ext-real set
Im (rho * (eval ((F_Complex,ef1,1),ef))) is complex V32() ext-real Element of REAL
(Im (rho * (eval ((F_Complex,ef1,1),ef)))) ^2 is complex V32() ext-real Element of REAL
(Im (rho * (eval ((F_Complex,ef1,1),ef)))) * (Im (rho * (eval ((F_Complex,ef1,1),ef)))) is complex V32() ext-real set
K114(((Re (rho * (eval ((F_Complex,ef1,1),ef)))) ^2),((Im (rho * (eval ((F_Complex,ef1,1),ef)))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (rho * (eval ((F_Complex,ef1,1),ef)))) ^2),((Im (rho * (eval ((F_Complex,ef1,1),ef)))) ^2)) is complex V32() ext-real Element of REAL
|.rho.| is complex V32() ext-real Element of REAL
Re rho is complex V32() ext-real Element of REAL
(Re rho) ^2 is complex V32() ext-real Element of REAL
(Re rho) * (Re rho) is complex V32() ext-real set
Im rho is complex V32() ext-real Element of REAL
(Im rho) ^2 is complex V32() ext-real Element of REAL
(Im rho) * (Im rho) is complex V32() ext-real set
K114(((Re rho) ^2),((Im rho) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re rho) ^2),((Im rho) ^2)) is complex V32() ext-real Element of REAL
|.(eval ((F_Complex,ef1,1),ef)).| is complex V32() ext-real Element of REAL
Re (eval ((F_Complex,ef1,1),ef)) is complex V32() ext-real Element of REAL
(Re (eval ((F_Complex,ef1,1),ef))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((F_Complex,ef1,1),ef))) * (Re (eval ((F_Complex,ef1,1),ef))) is complex V32() ext-real set
Im (eval ((F_Complex,ef1,1),ef)) is complex V32() ext-real Element of REAL
(Im (eval ((F_Complex,ef1,1),ef))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((F_Complex,ef1,1),ef))) * (Im (eval ((F_Complex,ef1,1),ef))) is complex V32() ext-real set
K114(((Re (eval ((F_Complex,ef1,1),ef))) ^2),((Im (eval ((F_Complex,ef1,1),ef))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((F_Complex,ef1,1),ef))) ^2),((Im (eval ((F_Complex,ef1,1),ef))) ^2)) is complex V32() ext-real Element of REAL
|.rho.| * |.(eval ((F_Complex,ef1,1),ef)).| is complex V32() ext-real set
((F_Complex,ef1,1)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval (((F_Complex,ef1,1)),ef) is complex Element of the carrier of F_Complex
|.(eval (((F_Complex,ef1,1)),ef)).| is complex V32() ext-real Element of REAL
Re (eval (((F_Complex,ef1,1)),ef)) is complex V32() ext-real Element of REAL
(Re (eval (((F_Complex,ef1,1)),ef))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (((F_Complex,ef1,1)),ef))) * (Re (eval (((F_Complex,ef1,1)),ef))) is complex V32() ext-real set
Im (eval (((F_Complex,ef1,1)),ef)) is complex V32() ext-real Element of REAL
(Im (eval (((F_Complex,ef1,1)),ef))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (((F_Complex,ef1,1)),ef))) * (Im (eval (((F_Complex,ef1,1)),ef))) is complex V32() ext-real set
K114(((Re (eval (((F_Complex,ef1,1)),ef))) ^2),((Im (eval (((F_Complex,ef1,1)),ef))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (((F_Complex,ef1,1)),ef))) ^2),((Im (eval (((F_Complex,ef1,1)),ef))) ^2)) is complex V32() ext-real Element of REAL
|.rho.| * |.(eval (((F_Complex,ef1,1)),ef)).| is complex V32() ext-real set
rho *' is complex Element of the carrier of F_Complex
(Im rho) * <i> is complex set
(Re rho) - ((Im rho) * <i>) is complex set
|.(rho *').| is complex V32() ext-real Element of REAL
Re (rho *') is complex V32() ext-real Element of REAL
(Re (rho *')) ^2 is complex V32() ext-real Element of REAL
(Re (rho *')) * (Re (rho *')) is complex V32() ext-real set
Im (rho *') is complex V32() ext-real Element of REAL
(Im (rho *')) ^2 is complex V32() ext-real Element of REAL
(Im (rho *')) * (Im (rho *')) is complex V32() ext-real set
K114(((Re (rho *')) ^2),((Im (rho *')) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (rho *')) ^2),((Im (rho *')) ^2)) is complex V32() ext-real Element of REAL
|.(rho *').| * |.(eval (((F_Complex,ef1,1)),ef)).| is complex V32() ext-real set
(rho *') * (eval (((F_Complex,ef1,1)),ef)) is complex Element of the carrier of F_Complex
K182((rho *'),(eval (((F_Complex,ef1,1)),ef))) is complex Element of COMPLEX
|.((rho *') * (eval (((F_Complex,ef1,1)),ef))).| is complex V32() ext-real Element of REAL
Re ((rho *') * (eval (((F_Complex,ef1,1)),ef))) is complex V32() ext-real Element of REAL
(Re ((rho *') * (eval (((F_Complex,ef1,1)),ef)))) ^2 is complex V32() ext-real Element of REAL
(Re ((rho *') * (eval (((F_Complex,ef1,1)),ef)))) * (Re ((rho *') * (eval (((F_Complex,ef1,1)),ef)))) is complex V32() ext-real set
Im ((rho *') * (eval (((F_Complex,ef1,1)),ef))) is complex V32() ext-real Element of REAL
(Im ((rho *') * (eval (((F_Complex,ef1,1)),ef)))) ^2 is complex V32() ext-real Element of REAL
(Im ((rho *') * (eval (((F_Complex,ef1,1)),ef)))) * (Im ((rho *') * (eval (((F_Complex,ef1,1)),ef)))) is complex V32() ext-real set
K114(((Re ((rho *') * (eval (((F_Complex,ef1,1)),ef)))) ^2),((Im ((rho *') * (eval (((F_Complex,ef1,1)),ef)))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re ((rho *') * (eval (((F_Complex,ef1,1)),ef)))) ^2),((Im ((rho *') * (eval (((F_Complex,ef1,1)),ef)))) ^2)) is complex V32() ext-real Element of REAL
(rho *') * ((F_Complex,ef1,1)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval (((rho *') * ((F_Complex,ef1,1))),ef) is complex Element of the carrier of F_Complex
|.(eval (((rho *') * ((F_Complex,ef1,1))),ef)).| is complex V32() ext-real Element of REAL
Re (eval (((rho *') * ((F_Complex,ef1,1))),ef)) is complex V32() ext-real Element of REAL
(Re (eval (((rho *') * ((F_Complex,ef1,1))),ef))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (((rho *') * ((F_Complex,ef1,1))),ef))) * (Re (eval (((rho *') * ((F_Complex,ef1,1))),ef))) is complex V32() ext-real set
Im (eval (((rho *') * ((F_Complex,ef1,1))),ef)) is complex V32() ext-real Element of REAL
(Im (eval (((rho *') * ((F_Complex,ef1,1))),ef))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (((rho *') * ((F_Complex,ef1,1))),ef))) * (Im (eval (((rho *') * ((F_Complex,ef1,1))),ef))) is complex V32() ext-real set
K114(((Re (eval (((rho *') * ((F_Complex,ef1,1))),ef))) ^2),((Im (eval (((rho *') * ((F_Complex,ef1,1))),ef))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (((rho *') * ((F_Complex,ef1,1))),ef))) ^2),((Im (eval (((rho *') * ((F_Complex,ef1,1))),ef))) ^2)) is complex V32() ext-real Element of REAL
((rho * (F_Complex,ef1,1))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval (((rho * (F_Complex,ef1,1))),ef) is complex Element of the carrier of F_Complex
|.(eval (((rho * (F_Complex,ef1,1))),ef)).| is complex V32() ext-real Element of REAL
Re (eval (((rho * (F_Complex,ef1,1))),ef)) is complex V32() ext-real Element of REAL
(Re (eval (((rho * (F_Complex,ef1,1))),ef))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (((rho * (F_Complex,ef1,1))),ef))) * (Re (eval (((rho * (F_Complex,ef1,1))),ef))) is complex V32() ext-real set
Im (eval (((rho * (F_Complex,ef1,1))),ef)) is complex V32() ext-real Element of REAL
(Im (eval (((rho * (F_Complex,ef1,1))),ef))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (((rho * (F_Complex,ef1,1))),ef))) * (Im (eval (((rho * (F_Complex,ef1,1))),ef))) is complex V32() ext-real set
K114(((Re (eval (((rho * (F_Complex,ef1,1))),ef))) ^2),((Im (eval (((rho * (F_Complex,ef1,1))),ef))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (((rho * (F_Complex,ef1,1))),ef))) ^2),((Im (eval (((rho * (F_Complex,ef1,1))),ef))) ^2)) is complex V32() ext-real Element of REAL
Re ef is complex V32() ext-real Element of REAL
rho is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
ef is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(F_Complex,ef) is complex V32() ext-real integer set
len ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len ef) - 1 is complex V32() ext-real integer set
rho + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
t is complex Element of the carrier of F_Complex
b9 is complex Element of the carrier of F_Complex
(F_Complex,b9,1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(power F_Complex) . (b9,1) is complex Element of the carrier of F_Complex
- ((power F_Complex) . (b9,1)) is complex Element of the carrier of F_Complex
(0,1) --> ((- ((power F_Complex) . (b9,1))),(1_ F_Complex)) is Relation-like {0,1} -defined the carrier of F_Complex -valued Function-like non empty total V18({0,1}, the carrier of F_Complex) Element of K19(K20({0,1}, the carrier of F_Complex))
(0_. F_Complex) +* ((0,1) --> ((- ((power F_Complex) . (b9,1))),(1_ F_Complex))) is Relation-like Function-like set
t * (F_Complex,b9,1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
ef1 is complex Element of the carrier of F_Complex
Re ef1 is complex V32() ext-real Element of REAL
(ef) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval ((ef),ef1) is complex Element of the carrier of F_Complex
|.(eval ((ef),ef1)).| is complex V32() ext-real Element of REAL
Re (eval ((ef),ef1)) is complex V32() ext-real Element of REAL
(Re (eval ((ef),ef1))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((ef),ef1))) * (Re (eval ((ef),ef1))) is complex V32() ext-real set
Im (eval ((ef),ef1)) is complex V32() ext-real Element of REAL
(Im (eval ((ef),ef1))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((ef),ef1))) * (Im (eval ((ef),ef1))) is complex V32() ext-real set
K114(((Re (eval ((ef),ef1))) ^2),((Im (eval ((ef),ef1))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((ef),ef1))) ^2),((Im (eval ((ef),ef1))) ^2)) is complex V32() ext-real Element of REAL
eval (ef,ef1) is complex Element of the carrier of F_Complex
|.(eval (ef,ef1)).| is complex V32() ext-real Element of REAL
Re (eval (ef,ef1)) is complex V32() ext-real Element of REAL
(Re (eval (ef,ef1))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (ef,ef1))) * (Re (eval (ef,ef1))) is complex V32() ext-real set
Im (eval (ef,ef1)) is complex V32() ext-real Element of REAL
(Im (eval (ef,ef1))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (ef,ef1))) * (Im (eval (ef,ef1))) is complex V32() ext-real set
K114(((Re (eval (ef,ef1))) ^2),((Im (eval (ef,ef1))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (ef,ef1))) ^2),((Im (eval (ef,ef1))) ^2)) is complex V32() ext-real Element of REAL
(rho + 1) + 1 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
(rho + 1) + 0 is non empty V24() V25() V26() V30() complex V32() ext-real positive non negative V40() V45() integer Element of NAT
t is complex Element of the carrier of F_Complex
(F_Complex,t,1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(power F_Complex) . (t,1) is complex Element of the carrier of F_Complex
- ((power F_Complex) . (t,1)) is complex Element of the carrier of F_Complex
(0,1) --> ((- ((power F_Complex) . (t,1))),(1_ F_Complex)) is Relation-like {0,1} -defined the carrier of F_Complex -valued Function-like non empty total V18({0,1}, the carrier of F_Complex) Element of K19(K20({0,1}, the carrier of F_Complex))
(0_. F_Complex) +* ((0,1) --> ((- ((power F_Complex) . (t,1))),(1_ F_Complex))) is Relation-like Function-like set
b9 is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(F_Complex,t,1) *' b9 is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(F_Complex,(F_Complex,t,1)) is complex V32() ext-real integer set
len (F_Complex,t,1) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len (F_Complex,t,1)) - 1 is complex V32() ext-real integer set
(F_Complex,b9) is complex V32() ext-real integer set
len b9 is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len b9) - 1 is complex V32() ext-real integer set
(F_Complex,(F_Complex,t,1)) + (F_Complex,b9) is complex V32() ext-real integer set
1 + (F_Complex,b9) is complex V32() ext-real integer set
((F_Complex,t,1)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
ef1 is complex Element of the carrier of F_Complex
eval (((F_Complex,t,1)),ef1) is complex Element of the carrier of F_Complex
(b9) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval ((b9),ef1) is complex Element of the carrier of F_Complex
eval ((F_Complex,t,1),ef1) is complex Element of the carrier of F_Complex
eval (b9,ef1) is complex Element of the carrier of F_Complex
(eval (((F_Complex,t,1)),ef1)) * (eval ((b9),ef1)) is complex Element of the carrier of F_Complex
K182((eval (((F_Complex,t,1)),ef1)),(eval ((b9),ef1))) is complex Element of COMPLEX
((F_Complex,t,1)) *' (b9) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval ((((F_Complex,t,1)) *' (b9)),ef1) is complex Element of the carrier of F_Complex
Re ef1 is complex V32() ext-real Element of REAL
a19 is complex Element of COMPLEX
|.a19.| is complex V32() ext-real Element of REAL
Re a19 is complex V32() ext-real Element of REAL
(Re a19) ^2 is complex V32() ext-real Element of REAL
(Re a19) * (Re a19) is complex V32() ext-real set
Im a19 is complex V32() ext-real Element of REAL
(Im a19) ^2 is complex V32() ext-real Element of REAL
(Im a19) * (Im a19) is complex V32() ext-real set
K114(((Re a19) ^2),((Im a19) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re a19) ^2),((Im a19) ^2)) is complex V32() ext-real Element of REAL
a1 is complex Element of COMPLEX
|.a1.| is complex V32() ext-real Element of REAL
Re a1 is complex V32() ext-real Element of REAL
(Re a1) ^2 is complex V32() ext-real Element of REAL
(Re a1) * (Re a1) is complex V32() ext-real set
Im a1 is complex V32() ext-real Element of REAL
(Im a1) ^2 is complex V32() ext-real Element of REAL
(Im a1) * (Im a1) is complex V32() ext-real set
K114(((Re a1) ^2),((Im a1) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re a1) ^2),((Im a1) ^2)) is complex V32() ext-real Element of REAL
zz is complex Element of COMPLEX
|.zz.| is complex V32() ext-real Element of REAL
Re zz is complex V32() ext-real Element of REAL
(Re zz) ^2 is complex V32() ext-real Element of REAL
(Re zz) * (Re zz) is complex V32() ext-real set
Im zz is complex V32() ext-real Element of REAL
(Im zz) ^2 is complex V32() ext-real Element of REAL
(Im zz) * (Im zz) is complex V32() ext-real set
K114(((Re zz) ^2),((Im zz) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re zz) ^2),((Im zz) ^2)) is complex V32() ext-real Element of REAL
|.zz.| * |.a1.| is complex V32() ext-real set
|.zz.| * |.a19.| is complex V32() ext-real set
b1 is complex Element of COMPLEX
|.b1.| is complex V32() ext-real Element of REAL
Re b1 is complex V32() ext-real Element of REAL
(Re b1) ^2 is complex V32() ext-real Element of REAL
(Re b1) * (Re b1) is complex V32() ext-real set
Im b1 is complex V32() ext-real Element of REAL
(Im b1) ^2 is complex V32() ext-real Element of REAL
(Im b1) * (Im b1) is complex V32() ext-real set
K114(((Re b1) ^2),((Im b1) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re b1) ^2),((Im b1) ^2)) is complex V32() ext-real Element of REAL
|.b1.| * |.a19.| is complex V32() ext-real set
b1 * a19 is complex Element of COMPLEX
|.(b1 * a19).| is complex V32() ext-real Element of REAL
Re (b1 * a19) is complex V32() ext-real Element of REAL
(Re (b1 * a19)) ^2 is complex V32() ext-real Element of REAL
(Re (b1 * a19)) * (Re (b1 * a19)) is complex V32() ext-real set
Im (b1 * a19) is complex V32() ext-real Element of REAL
(Im (b1 * a19)) ^2 is complex V32() ext-real Element of REAL
(Im (b1 * a19)) * (Im (b1 * a19)) is complex V32() ext-real set
K114(((Re (b1 * a19)) ^2),((Im (b1 * a19)) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (b1 * a19)) ^2),((Im (b1 * a19)) ^2)) is complex V32() ext-real Element of REAL
(eval ((F_Complex,t,1),ef1)) * (eval (b9,ef1)) is complex Element of the carrier of F_Complex
K182((eval ((F_Complex,t,1),ef1)),(eval (b9,ef1))) is complex Element of COMPLEX
|.((eval ((F_Complex,t,1),ef1)) * (eval (b9,ef1))).| is complex V32() ext-real Element of REAL
Re ((eval ((F_Complex,t,1),ef1)) * (eval (b9,ef1))) is complex V32() ext-real Element of REAL
(Re ((eval ((F_Complex,t,1),ef1)) * (eval (b9,ef1)))) ^2 is complex V32() ext-real Element of REAL
(Re ((eval ((F_Complex,t,1),ef1)) * (eval (b9,ef1)))) * (Re ((eval ((F_Complex,t,1),ef1)) * (eval (b9,ef1)))) is complex V32() ext-real set
Im ((eval ((F_Complex,t,1),ef1)) * (eval (b9,ef1))) is complex V32() ext-real Element of REAL
(Im ((eval ((F_Complex,t,1),ef1)) * (eval (b9,ef1)))) ^2 is complex V32() ext-real Element of REAL
(Im ((eval ((F_Complex,t,1),ef1)) * (eval (b9,ef1)))) * (Im ((eval ((F_Complex,t,1),ef1)) * (eval (b9,ef1)))) is complex V32() ext-real set
K114(((Re ((eval ((F_Complex,t,1),ef1)) * (eval (b9,ef1)))) ^2),((Im ((eval ((F_Complex,t,1),ef1)) * (eval (b9,ef1)))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re ((eval ((F_Complex,t,1),ef1)) * (eval (b9,ef1)))) ^2),((Im ((eval ((F_Complex,t,1),ef1)) * (eval (b9,ef1)))) ^2)) is complex V32() ext-real Element of REAL
|.((eval (((F_Complex,t,1)),ef1)) * (eval ((b9),ef1))).| is complex V32() ext-real Element of REAL
Re ((eval (((F_Complex,t,1)),ef1)) * (eval ((b9),ef1))) is complex V32() ext-real Element of REAL
(Re ((eval (((F_Complex,t,1)),ef1)) * (eval ((b9),ef1)))) ^2 is complex V32() ext-real Element of REAL
(Re ((eval (((F_Complex,t,1)),ef1)) * (eval ((b9),ef1)))) * (Re ((eval (((F_Complex,t,1)),ef1)) * (eval ((b9),ef1)))) is complex V32() ext-real set
Im ((eval (((F_Complex,t,1)),ef1)) * (eval ((b9),ef1))) is complex V32() ext-real Element of REAL
(Im ((eval (((F_Complex,t,1)),ef1)) * (eval ((b9),ef1)))) ^2 is complex V32() ext-real Element of REAL
(Im ((eval (((F_Complex,t,1)),ef1)) * (eval ((b9),ef1)))) * (Im ((eval (((F_Complex,t,1)),ef1)) * (eval ((b9),ef1)))) is complex V32() ext-real set
K114(((Re ((eval (((F_Complex,t,1)),ef1)) * (eval ((b9),ef1)))) ^2),((Im ((eval (((F_Complex,t,1)),ef1)) * (eval ((b9),ef1)))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re ((eval (((F_Complex,t,1)),ef1)) * (eval ((b9),ef1)))) ^2),((Im ((eval (((F_Complex,t,1)),ef1)) * (eval ((b9),ef1)))) ^2)) is complex V32() ext-real Element of REAL
eval (((F_Complex,t,1) *' b9),ef1) is complex Element of the carrier of F_Complex
eval (ef,ef1) is complex Element of the carrier of F_Complex
|.(eval (ef,ef1)).| is complex V32() ext-real Element of REAL
Re (eval (ef,ef1)) is complex V32() ext-real Element of REAL
(Re (eval (ef,ef1))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (ef,ef1))) * (Re (eval (ef,ef1))) is complex V32() ext-real set
Im (eval (ef,ef1)) is complex V32() ext-real Element of REAL
(Im (eval (ef,ef1))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (ef,ef1))) * (Im (eval (ef,ef1))) is complex V32() ext-real set
K114(((Re (eval (ef,ef1))) ^2),((Im (eval (ef,ef1))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (ef,ef1))) ^2),((Im (eval (ef,ef1))) ^2)) is complex V32() ext-real Element of REAL
(ef) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval ((ef),ef1) is complex Element of the carrier of F_Complex
|.(eval ((ef),ef1)).| is complex V32() ext-real Element of REAL
Re (eval ((ef),ef1)) is complex V32() ext-real Element of REAL
(Re (eval ((ef),ef1))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((ef),ef1))) * (Re (eval ((ef),ef1))) is complex V32() ext-real set
Im (eval ((ef),ef1)) is complex V32() ext-real Element of REAL
(Im (eval ((ef),ef1))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((ef),ef1))) * (Im (eval ((ef),ef1))) is complex V32() ext-real set
K114(((Re (eval ((ef),ef1))) ^2),((Im (eval ((ef),ef1))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((ef),ef1))) ^2),((Im (eval ((ef),ef1))) ^2)) is complex V32() ext-real Element of REAL
b1 is complex Element of COMPLEX
|.b1.| is complex V32() ext-real Element of REAL
Re b1 is complex V32() ext-real Element of REAL
(Re b1) ^2 is complex V32() ext-real Element of REAL
(Re b1) * (Re b1) is complex V32() ext-real set
Im b1 is complex V32() ext-real Element of REAL
(Im b1) ^2 is complex V32() ext-real Element of REAL
(Im b1) * (Im b1) is complex V32() ext-real set
K114(((Re b1) ^2),((Im b1) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re b1) ^2),((Im b1) ^2)) is complex V32() ext-real Element of REAL
zz is complex Element of COMPLEX
|.zz.| is complex V32() ext-real Element of REAL
Re zz is complex V32() ext-real Element of REAL
(Re zz) ^2 is complex V32() ext-real Element of REAL
(Re zz) * (Re zz) is complex V32() ext-real set
Im zz is complex V32() ext-real Element of REAL
(Im zz) ^2 is complex V32() ext-real Element of REAL
(Im zz) * (Im zz) is complex V32() ext-real set
K114(((Re zz) ^2),((Im zz) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re zz) ^2),((Im zz) ^2)) is complex V32() ext-real Element of REAL
a19 is complex Element of COMPLEX
|.a19.| is complex V32() ext-real Element of REAL
Re a19 is complex V32() ext-real Element of REAL
(Re a19) ^2 is complex V32() ext-real Element of REAL
(Re a19) * (Re a19) is complex V32() ext-real set
Im a19 is complex V32() ext-real Element of REAL
(Im a19) ^2 is complex V32() ext-real Element of REAL
(Im a19) * (Im a19) is complex V32() ext-real set
K114(((Re a19) ^2),((Im a19) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re a19) ^2),((Im a19) ^2)) is complex V32() ext-real Element of REAL
|.b1.| * |.a19.| is complex V32() ext-real set
|.zz.| * |.a19.| is complex V32() ext-real set
a1 is complex Element of COMPLEX
|.a1.| is complex V32() ext-real Element of REAL
Re a1 is complex V32() ext-real Element of REAL
(Re a1) ^2 is complex V32() ext-real Element of REAL
(Re a1) * (Re a1) is complex V32() ext-real set
Im a1 is complex V32() ext-real Element of REAL
(Im a1) ^2 is complex V32() ext-real Element of REAL
(Im a1) * (Im a1) is complex V32() ext-real set
K114(((Re a1) ^2),((Im a1) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re a1) ^2),((Im a1) ^2)) is complex V32() ext-real Element of REAL
|.zz.| * |.a1.| is complex V32() ext-real set
b1 * a19 is complex Element of COMPLEX
|.(b1 * a19).| is complex V32() ext-real Element of REAL
Re (b1 * a19) is complex V32() ext-real Element of REAL
(Re (b1 * a19)) ^2 is complex V32() ext-real Element of REAL
(Re (b1 * a19)) * (Re (b1 * a19)) is complex V32() ext-real set
Im (b1 * a19) is complex V32() ext-real Element of REAL
(Im (b1 * a19)) ^2 is complex V32() ext-real Element of REAL
(Im (b1 * a19)) * (Im (b1 * a19)) is complex V32() ext-real set
K114(((Re (b1 * a19)) ^2),((Im (b1 * a19)) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (b1 * a19)) ^2),((Im (b1 * a19)) ^2)) is complex V32() ext-real Element of REAL
|.(eval (b9,ef1)).| is complex V32() ext-real Element of REAL
Re (eval (b9,ef1)) is complex V32() ext-real Element of REAL
(Re (eval (b9,ef1))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (b9,ef1))) * (Re (eval (b9,ef1))) is complex V32() ext-real set
Im (eval (b9,ef1)) is complex V32() ext-real Element of REAL
(Im (eval (b9,ef1))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (b9,ef1))) * (Im (eval (b9,ef1))) is complex V32() ext-real set
K114(((Re (eval (b9,ef1))) ^2),((Im (eval (b9,ef1))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (b9,ef1))) ^2),((Im (eval (b9,ef1))) ^2)) is complex V32() ext-real Element of REAL
|.(eval ((b9),ef1)).| is complex V32() ext-real Element of REAL
Re (eval ((b9),ef1)) is complex V32() ext-real Element of REAL
(Re (eval ((b9),ef1))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((b9),ef1))) * (Re (eval ((b9),ef1))) is complex V32() ext-real set
Im (eval ((b9),ef1)) is complex V32() ext-real Element of REAL
(Im (eval ((b9),ef1))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((b9),ef1))) * (Im (eval ((b9),ef1))) is complex V32() ext-real set
K114(((Re (eval ((b9),ef1))) ^2),((Im (eval ((b9),ef1))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((b9),ef1))) ^2),((Im (eval ((b9),ef1))) ^2)) is complex V32() ext-real Element of REAL
b1 is complex Element of COMPLEX
|.b1.| is complex V32() ext-real Element of REAL
Re b1 is complex V32() ext-real Element of REAL
(Re b1) ^2 is complex V32() ext-real Element of REAL
(Re b1) * (Re b1) is complex V32() ext-real set
Im b1 is complex V32() ext-real Element of REAL
(Im b1) ^2 is complex V32() ext-real Element of REAL
(Im b1) * (Im b1) is complex V32() ext-real set
K114(((Re b1) ^2),((Im b1) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re b1) ^2),((Im b1) ^2)) is complex V32() ext-real Element of REAL
a19 is complex Element of COMPLEX
|.a19.| is complex V32() ext-real Element of REAL
Re a19 is complex V32() ext-real Element of REAL
(Re a19) ^2 is complex V32() ext-real Element of REAL
(Re a19) * (Re a19) is complex V32() ext-real set
Im a19 is complex V32() ext-real Element of REAL
(Im a19) ^2 is complex V32() ext-real Element of REAL
(Im a19) * (Im a19) is complex V32() ext-real set
K114(((Re a19) ^2),((Im a19) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re a19) ^2),((Im a19) ^2)) is complex V32() ext-real Element of REAL
|.b1.| * |.a19.| is complex V32() ext-real set
zz is complex Element of COMPLEX
|.zz.| is complex V32() ext-real Element of REAL
Re zz is complex V32() ext-real Element of REAL
(Re zz) ^2 is complex V32() ext-real Element of REAL
(Re zz) * (Re zz) is complex V32() ext-real set
Im zz is complex V32() ext-real Element of REAL
(Im zz) ^2 is complex V32() ext-real Element of REAL
(Im zz) * (Im zz) is complex V32() ext-real set
K114(((Re zz) ^2),((Im zz) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re zz) ^2),((Im zz) ^2)) is complex V32() ext-real Element of REAL
a1 is complex Element of COMPLEX
|.a1.| is complex V32() ext-real Element of REAL
Re a1 is complex V32() ext-real Element of REAL
(Re a1) ^2 is complex V32() ext-real Element of REAL
(Re a1) * (Re a1) is complex V32() ext-real set
Im a1 is complex V32() ext-real Element of REAL
(Im a1) ^2 is complex V32() ext-real Element of REAL
(Im a1) * (Im a1) is complex V32() ext-real set
K114(((Re a1) ^2),((Im a1) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re a1) ^2),((Im a1) ^2)) is complex V32() ext-real Element of REAL
|.zz.| * |.a1.| is complex V32() ext-real set
b1 * a19 is complex Element of COMPLEX
|.(b1 * a19).| is complex V32() ext-real Element of REAL
Re (b1 * a19) is complex V32() ext-real Element of REAL
(Re (b1 * a19)) ^2 is complex V32() ext-real Element of REAL
(Re (b1 * a19)) * (Re (b1 * a19)) is complex V32() ext-real set
Im (b1 * a19) is complex V32() ext-real Element of REAL
(Im (b1 * a19)) ^2 is complex V32() ext-real Element of REAL
(Im (b1 * a19)) * (Im (b1 * a19)) is complex V32() ext-real set
K114(((Re (b1 * a19)) ^2),((Im (b1 * a19)) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (b1 * a19)) ^2),((Im (b1 * a19)) ^2)) is complex V32() ext-real Element of REAL
ef is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(F_Complex,ef) is complex V32() ext-real integer set
len ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len ef) - 1 is complex V32() ext-real integer set
ef1 is complex Element of the carrier of F_Complex
Re ef1 is complex V32() ext-real Element of REAL
(ef) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval ((ef),ef1) is complex Element of the carrier of F_Complex
|.(eval ((ef),ef1)).| is complex V32() ext-real Element of REAL
Re (eval ((ef),ef1)) is complex V32() ext-real Element of REAL
(Re (eval ((ef),ef1))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((ef),ef1))) * (Re (eval ((ef),ef1))) is complex V32() ext-real set
Im (eval ((ef),ef1)) is complex V32() ext-real Element of REAL
(Im (eval ((ef),ef1))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((ef),ef1))) * (Im (eval ((ef),ef1))) is complex V32() ext-real set
K114(((Re (eval ((ef),ef1))) ^2),((Im (eval ((ef),ef1))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((ef),ef1))) ^2),((Im (eval ((ef),ef1))) ^2)) is complex V32() ext-real Element of REAL
eval (ef,ef1) is complex Element of the carrier of F_Complex
|.(eval (ef,ef1)).| is complex V32() ext-real Element of REAL
Re (eval (ef,ef1)) is complex V32() ext-real Element of REAL
(Re (eval (ef,ef1))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (ef,ef1))) * (Re (eval (ef,ef1))) is complex V32() ext-real set
Im (eval (ef,ef1)) is complex V32() ext-real Element of REAL
(Im (eval (ef,ef1))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (ef,ef1))) * (Im (eval (ef,ef1))) is complex V32() ext-real set
K114(((Re (eval (ef,ef1))) ^2),((Im (eval (ef,ef1))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (ef,ef1))) ^2),((Im (eval (ef,ef1))) ^2)) is complex V32() ext-real Element of REAL
t is complex Element of the carrier of F_Complex
Re t is complex V32() ext-real Element of REAL
eval (ef,t) is complex Element of the carrier of F_Complex
|.(eval (ef,t)).| is complex V32() ext-real Element of REAL
Re (eval (ef,t)) is complex V32() ext-real Element of REAL
(Re (eval (ef,t))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (ef,t))) * (Re (eval (ef,t))) is complex V32() ext-real set
Im (eval (ef,t)) is complex V32() ext-real Element of REAL
(Im (eval (ef,t))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (ef,t))) * (Im (eval (ef,t))) is complex V32() ext-real set
K114(((Re (eval (ef,t))) ^2),((Im (eval (ef,t))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (ef,t))) ^2),((Im (eval (ef,t))) ^2)) is complex V32() ext-real Element of REAL
eval ((ef),t) is complex Element of the carrier of F_Complex
|.(eval ((ef),t)).| is complex V32() ext-real Element of REAL
Re (eval ((ef),t)) is complex V32() ext-real Element of REAL
(Re (eval ((ef),t))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((ef),t))) * (Re (eval ((ef),t))) is complex V32() ext-real set
Im (eval ((ef),t)) is complex V32() ext-real Element of REAL
(Im (eval ((ef),t))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((ef),t))) * (Im (eval ((ef),t))) is complex V32() ext-real set
K114(((Re (eval ((ef),t))) ^2),((Im (eval ((ef),t))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((ef),t))) ^2),((Im (eval ((ef),t))) ^2)) is complex V32() ext-real Element of REAL
b9 is complex Element of the carrier of F_Complex
Re b9 is complex V32() ext-real Element of REAL
eval (ef,b9) is complex Element of the carrier of F_Complex
|.(eval (ef,b9)).| is complex V32() ext-real Element of REAL
Re (eval (ef,b9)) is complex V32() ext-real Element of REAL
(Re (eval (ef,b9))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (ef,b9))) * (Re (eval (ef,b9))) is complex V32() ext-real set
Im (eval (ef,b9)) is complex V32() ext-real Element of REAL
(Im (eval (ef,b9))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (ef,b9))) * (Im (eval (ef,b9))) is complex V32() ext-real set
K114(((Re (eval (ef,b9))) ^2),((Im (eval (ef,b9))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (ef,b9))) ^2),((Im (eval (ef,b9))) ^2)) is complex V32() ext-real Element of REAL
eval ((ef),b9) is complex Element of the carrier of F_Complex
|.(eval ((ef),b9)).| is complex V32() ext-real Element of REAL
Re (eval ((ef),b9)) is complex V32() ext-real Element of REAL
(Re (eval ((ef),b9))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((ef),b9))) * (Re (eval ((ef),b9))) is complex V32() ext-real set
Im (eval ((ef),b9)) is complex V32() ext-real Element of REAL
(Im (eval ((ef),b9))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((ef),b9))) * (Im (eval ((ef),b9))) is complex V32() ext-real set
K114(((Re (eval ((ef),b9))) ^2),((Im (eval ((ef),b9))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((ef),b9))) ^2),((Im (eval ((ef),b9))) ^2)) is complex V32() ext-real Element of REAL
rho is complex Element of the carrier of F_Complex
Re rho is complex V32() ext-real Element of REAL
eval ((f),rho) is complex Element of the carrier of F_Complex
|.(eval ((f),rho)).| is complex V32() ext-real Element of REAL
Re (eval ((f),rho)) is complex V32() ext-real Element of REAL
(Re (eval ((f),rho))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((f),rho))) * (Re (eval ((f),rho))) is complex V32() ext-real set
Im (eval ((f),rho)) is complex V32() ext-real Element of REAL
(Im (eval ((f),rho))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((f),rho))) * (Im (eval ((f),rho))) is complex V32() ext-real set
K114(((Re (eval ((f),rho))) ^2),((Im (eval ((f),rho))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((f),rho))) ^2),((Im (eval ((f),rho))) ^2)) is complex V32() ext-real Element of REAL
eval (f,rho) is complex Element of the carrier of F_Complex
|.(eval (f,rho)).| is complex V32() ext-real Element of REAL
Re (eval (f,rho)) is complex V32() ext-real Element of REAL
(Re (eval (f,rho))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (f,rho))) * (Re (eval (f,rho))) is complex V32() ext-real set
Im (eval (f,rho)) is complex V32() ext-real Element of REAL
(Im (eval (f,rho))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (f,rho))) * (Im (eval (f,rho))) is complex V32() ext-real set
K114(((Re (eval (f,rho))) ^2),((Im (eval (f,rho))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (f,rho))) ^2),((Im (eval (f,rho))) ^2)) is complex V32() ext-real Element of REAL
ef is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(F_Complex,ef) is complex V32() ext-real integer set
len ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len ef) - 1 is complex V32() ext-real integer set
ef1 is complex Element of the carrier of F_Complex
Re ef1 is complex V32() ext-real Element of REAL
(ef) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval ((ef),ef1) is complex Element of the carrier of F_Complex
|.(eval ((ef),ef1)).| is complex V32() ext-real Element of REAL
Re (eval ((ef),ef1)) is complex V32() ext-real Element of REAL
(Re (eval ((ef),ef1))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((ef),ef1))) * (Re (eval ((ef),ef1))) is complex V32() ext-real set
Im (eval ((ef),ef1)) is complex V32() ext-real Element of REAL
(Im (eval ((ef),ef1))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((ef),ef1))) * (Im (eval ((ef),ef1))) is complex V32() ext-real set
K114(((Re (eval ((ef),ef1))) ^2),((Im (eval ((ef),ef1))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((ef),ef1))) ^2),((Im (eval ((ef),ef1))) ^2)) is complex V32() ext-real Element of REAL
eval (ef,ef1) is complex Element of the carrier of F_Complex
|.(eval (ef,ef1)).| is complex V32() ext-real Element of REAL
Re (eval (ef,ef1)) is complex V32() ext-real Element of REAL
(Re (eval (ef,ef1))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (ef,ef1))) * (Re (eval (ef,ef1))) is complex V32() ext-real set
Im (eval (ef,ef1)) is complex V32() ext-real Element of REAL
(Im (eval (ef,ef1))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (ef,ef1))) * (Im (eval (ef,ef1))) is complex V32() ext-real set
K114(((Re (eval (ef,ef1))) ^2),((Im (eval (ef,ef1))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (ef,ef1))) ^2),((Im (eval (ef,ef1))) ^2)) is complex V32() ext-real Element of REAL
t is complex Element of the carrier of F_Complex
Re t is complex V32() ext-real Element of REAL
eval (ef,t) is complex Element of the carrier of F_Complex
|.(eval (ef,t)).| is complex V32() ext-real Element of REAL
Re (eval (ef,t)) is complex V32() ext-real Element of REAL
(Re (eval (ef,t))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (ef,t))) * (Re (eval (ef,t))) is complex V32() ext-real set
Im (eval (ef,t)) is complex V32() ext-real Element of REAL
(Im (eval (ef,t))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (ef,t))) * (Im (eval (ef,t))) is complex V32() ext-real set
K114(((Re (eval (ef,t))) ^2),((Im (eval (ef,t))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (ef,t))) ^2),((Im (eval (ef,t))) ^2)) is complex V32() ext-real Element of REAL
eval ((ef),t) is complex Element of the carrier of F_Complex
|.(eval ((ef),t)).| is complex V32() ext-real Element of REAL
Re (eval ((ef),t)) is complex V32() ext-real Element of REAL
(Re (eval ((ef),t))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((ef),t))) * (Re (eval ((ef),t))) is complex V32() ext-real set
Im (eval ((ef),t)) is complex V32() ext-real Element of REAL
(Im (eval ((ef),t))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((ef),t))) * (Im (eval ((ef),t))) is complex V32() ext-real set
K114(((Re (eval ((ef),t))) ^2),((Im (eval ((ef),t))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((ef),t))) ^2),((Im (eval ((ef),t))) ^2)) is complex V32() ext-real Element of REAL
b9 is complex Element of the carrier of F_Complex
Re b9 is complex V32() ext-real Element of REAL
eval (ef,b9) is complex Element of the carrier of F_Complex
|.(eval (ef,b9)).| is complex V32() ext-real Element of REAL
Re (eval (ef,b9)) is complex V32() ext-real Element of REAL
(Re (eval (ef,b9))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (ef,b9))) * (Re (eval (ef,b9))) is complex V32() ext-real set
Im (eval (ef,b9)) is complex V32() ext-real Element of REAL
(Im (eval (ef,b9))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (ef,b9))) * (Im (eval (ef,b9))) is complex V32() ext-real set
K114(((Re (eval (ef,b9))) ^2),((Im (eval (ef,b9))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (ef,b9))) ^2),((Im (eval (ef,b9))) ^2)) is complex V32() ext-real Element of REAL
eval ((ef),b9) is complex Element of the carrier of F_Complex
|.(eval ((ef),b9)).| is complex V32() ext-real Element of REAL
Re (eval ((ef),b9)) is complex V32() ext-real Element of REAL
(Re (eval ((ef),b9))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((ef),b9))) * (Re (eval ((ef),b9))) is complex V32() ext-real set
Im (eval ((ef),b9)) is complex V32() ext-real Element of REAL
(Im (eval ((ef),b9))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((ef),b9))) * (Im (eval ((ef),b9))) is complex V32() ext-real set
K114(((Re (eval ((ef),b9))) ^2),((Im (eval ((ef),b9))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((ef),b9))) ^2),((Im (eval ((ef),b9))) ^2)) is complex V32() ext-real Element of REAL
f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
rho is complex Element of the carrier of F_Complex
eval ((f),rho) is complex Element of the carrier of F_Complex
(eval ((f),rho)) * f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval (f,rho) is complex Element of the carrier of F_Complex
(eval (f,rho)) * (f) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((eval ((f),rho)) * f) - ((eval (f,rho)) * (f)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
- ((eval (f,rho)) * (f)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((eval ((f),rho)) * f) + (- ((eval (f,rho)) * (f))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
f is complex Element of the carrier of F_Complex
|.f.| is complex V32() ext-real Element of REAL
Re f is complex V32() ext-real Element of REAL
(Re f) ^2 is complex V32() ext-real Element of REAL
(Re f) * (Re f) is complex V32() ext-real set
Im f is complex V32() ext-real Element of REAL
(Im f) ^2 is complex V32() ext-real Element of REAL
(Im f) * (Im f) is complex V32() ext-real set
K114(((Re f) ^2),((Im f) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re f) ^2),((Im f) ^2)) is complex V32() ext-real Element of REAL
rho is complex Element of the carrier of F_Complex
|.rho.| is complex V32() ext-real Element of REAL
Re rho is complex V32() ext-real Element of REAL
(Re rho) ^2 is complex V32() ext-real Element of REAL
(Re rho) * (Re rho) is complex V32() ext-real set
Im rho is complex V32() ext-real Element of REAL
(Im rho) ^2 is complex V32() ext-real Element of REAL
(Im rho) * (Im rho) is complex V32() ext-real set
K114(((Re rho) ^2),((Im rho) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re rho) ^2),((Im rho) ^2)) is complex V32() ext-real Element of REAL
ef is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(F_Complex,ef) is complex V32() ext-real integer set
len ef is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len ef) - 1 is complex V32() ext-real integer set
f * ef is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(ef) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
rho * (ef) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f * ef) - (rho * (ef)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
- (rho * (ef)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f * ef) + (- (rho * (ef))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f * ef) - (0_. F_Complex) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
- (0_. F_Complex) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f * ef) + (- (0_. F_Complex)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f * ef) + (0_. F_Complex) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
|.f.| ^2 is complex V32() ext-real Element of REAL
|.f.| * |.f.| is complex V32() ext-real set
|.rho.| ^2 is complex V32() ext-real Element of REAL
|.rho.| * |.rho.| is complex V32() ext-real set
(|.f.| ^2) - (|.rho.| ^2) is complex V32() ext-real set
((|.f.| ^2) - (|.rho.| ^2)) " is complex V32() ext-real set
f *' is complex Element of the carrier of F_Complex
(Im f) * <i> is complex set
(Re f) - ((Im f) * <i>) is complex set
zz is complex Element of the carrier of F_Complex
(f *') * zz is complex Element of the carrier of F_Complex
K182((f *'),zz) is complex Element of COMPLEX
rho * zz is complex Element of the carrier of F_Complex
K182(rho,zz) is complex Element of COMPLEX
- (rho * zz) is complex Element of the carrier of F_Complex
rho " is complex Element of the carrier of F_Complex
(f *') * (rho ") is complex Element of the carrier of F_Complex
K182((f *'),(rho ")) is complex Element of COMPLEX
t is complex Element of COMPLEX
t *' is complex Element of COMPLEX
Re t is complex V32() ext-real Element of REAL
Im t is complex V32() ext-real Element of REAL
(Im t) * <i> is complex set
(Re t) - ((Im t) * <i>) is complex set
b9 is complex Element of COMPLEX
b9 " is complex Element of COMPLEX
Re b9 is complex V32() ext-real Element of REAL
(Re b9) ^2 is complex V32() ext-real Element of REAL
(Re b9) * (Re b9) is complex V32() ext-real set
Im b9 is complex V32() ext-real Element of REAL
(Im b9) ^2 is complex V32() ext-real Element of REAL
(Im b9) * (Im b9) is complex V32() ext-real set
K114(((Re b9) ^2),((Im b9) ^2)) is complex V32() ext-real Element of REAL
K117((Re b9),K114(((Re b9) ^2),((Im b9) ^2))) is complex V32() ext-real Element of REAL
K108((Im b9)) is complex V32() ext-real Element of REAL
K117(K108((Im b9)),K114(((Re b9) ^2),((Im b9) ^2))) is complex V32() ext-real Element of REAL
K117(K108((Im b9)),K114(((Re b9) ^2),((Im b9) ^2))) * <i> is complex set
K117((Re b9),K114(((Re b9) ^2),((Im b9) ^2))) + (K117(K108((Im b9)),K114(((Re b9) ^2),((Im b9) ^2))) * <i>) is complex set
(t *') * (b9 ") is complex Element of COMPLEX
b19 is complex Element of COMPLEX
b9 * (((|.f.| ^2) - (|.rho.| ^2)) ") is complex set
- (b9 * (((|.f.| ^2) - (|.rho.| ^2)) ")) is complex set
|.t.| is complex V32() ext-real Element of REAL
(Re t) ^2 is complex V32() ext-real Element of REAL
(Re t) * (Re t) is complex V32() ext-real set
(Im t) ^2 is complex V32() ext-real Element of REAL
(Im t) * (Im t) is complex V32() ext-real set
K114(((Re t) ^2),((Im t) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re t) ^2),((Im t) ^2)) is complex V32() ext-real Element of REAL
|.b9.| is complex V32() ext-real Element of REAL
sqrt K114(((Re b9) ^2),((Im b9) ^2)) is complex V32() ext-real Element of REAL
|.t.| * |.b9.| is complex V32() ext-real set
|.b9.| * |.b9.| is complex V32() ext-real set
|.t.| ^2 is complex V32() ext-real Element of REAL
|.t.| * |.t.| is complex V32() ext-real set
|.b9.| ^2 is complex V32() ext-real Element of REAL
(|.t.| ^2) - (|.b9.| ^2) is complex V32() ext-real set
- (- (rho * zz)) is complex Element of the carrier of F_Complex
z is complex Element of the carrier of F_Complex
eval (((f * ef) - (rho * (ef))),z) is complex Element of the carrier of F_Complex
eval ((f * ef),z) is complex Element of the carrier of F_Complex
eval ((rho * (ef)),z) is complex Element of the carrier of F_Complex
(eval ((f * ef),z)) - (eval ((rho * (ef)),z)) is complex Element of the carrier of F_Complex
eval (ef,z) is complex Element of the carrier of F_Complex
f * (eval (ef,z)) is complex Element of the carrier of F_Complex
K182(f,(eval (ef,z))) is complex Element of COMPLEX
(f * (eval (ef,z))) - (eval ((rho * (ef)),z)) is complex Element of the carrier of F_Complex
eval ((ef),z) is complex Element of the carrier of F_Complex
rho * (eval ((ef),z)) is complex Element of the carrier of F_Complex
K182(rho,(eval ((ef),z))) is complex Element of COMPLEX
(f * (eval (ef,z))) - (rho * (eval ((ef),z))) is complex Element of the carrier of F_Complex
|.(eval (ef,z)).| is complex V32() ext-real Element of REAL
Re (eval (ef,z)) is complex V32() ext-real Element of REAL
(Re (eval (ef,z))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (ef,z))) * (Re (eval (ef,z))) is complex V32() ext-real set
Im (eval (ef,z)) is complex V32() ext-real Element of REAL
(Im (eval (ef,z))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (ef,z))) * (Im (eval (ef,z))) is complex V32() ext-real set
K114(((Re (eval (ef,z))) ^2),((Im (eval (ef,z))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (ef,z))) ^2),((Im (eval (ef,z))) ^2)) is complex V32() ext-real Element of REAL
|.f.| * |.(eval (ef,z)).| is complex V32() ext-real set
|.(f * (eval (ef,z))).| is complex V32() ext-real Element of REAL
Re (f * (eval (ef,z))) is complex V32() ext-real Element of REAL
(Re (f * (eval (ef,z)))) ^2 is complex V32() ext-real Element of REAL
(Re (f * (eval (ef,z)))) * (Re (f * (eval (ef,z)))) is complex V32() ext-real set
Im (f * (eval (ef,z))) is complex V32() ext-real Element of REAL
(Im (f * (eval (ef,z)))) ^2 is complex V32() ext-real Element of REAL
(Im (f * (eval (ef,z)))) * (Im (f * (eval (ef,z)))) is complex V32() ext-real set
K114(((Re (f * (eval (ef,z)))) ^2),((Im (f * (eval (ef,z)))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (f * (eval (ef,z)))) ^2),((Im (f * (eval (ef,z)))) ^2)) is complex V32() ext-real Element of REAL
|.(eval ((ef),z)).| is complex V32() ext-real Element of REAL
Re (eval ((ef),z)) is complex V32() ext-real Element of REAL
(Re (eval ((ef),z))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((ef),z))) * (Re (eval ((ef),z))) is complex V32() ext-real set
Im (eval ((ef),z)) is complex V32() ext-real Element of REAL
(Im (eval ((ef),z))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((ef),z))) * (Im (eval ((ef),z))) is complex V32() ext-real set
K114(((Re (eval ((ef),z))) ^2),((Im (eval ((ef),z))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((ef),z))) ^2),((Im (eval ((ef),z))) ^2)) is complex V32() ext-real Element of REAL
|.rho.| * |.(eval ((ef),z)).| is complex V32() ext-real set
|.(rho * (eval ((ef),z))).| is complex V32() ext-real Element of REAL
Re (rho * (eval ((ef),z))) is complex V32() ext-real Element of REAL
(Re (rho * (eval ((ef),z)))) ^2 is complex V32() ext-real Element of REAL
(Re (rho * (eval ((ef),z)))) * (Re (rho * (eval ((ef),z)))) is complex V32() ext-real set
Im (rho * (eval ((ef),z))) is complex V32() ext-real Element of REAL
(Im (rho * (eval ((ef),z)))) ^2 is complex V32() ext-real Element of REAL
(Im (rho * (eval ((ef),z)))) * (Im (rho * (eval ((ef),z)))) is complex V32() ext-real set
K114(((Re (rho * (eval ((ef),z)))) ^2),((Im (rho * (eval ((ef),z)))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (rho * (eval ((ef),z)))) ^2),((Im (rho * (eval ((ef),z)))) ^2)) is complex V32() ext-real Element of REAL
Re z is complex V32() ext-real Element of REAL
|.rho.| * |.(eval (ef,z)).| is complex V32() ext-real set
|.((f *') * zz).| is complex V32() ext-real Element of REAL
Re ((f *') * zz) is complex V32() ext-real Element of REAL
(Re ((f *') * zz)) ^2 is complex V32() ext-real Element of REAL
(Re ((f *') * zz)) * (Re ((f *') * zz)) is complex V32() ext-real set
Im ((f *') * zz) is complex V32() ext-real Element of REAL
(Im ((f *') * zz)) ^2 is complex V32() ext-real Element of REAL
(Im ((f *') * zz)) * (Im ((f *') * zz)) is complex V32() ext-real set
K114(((Re ((f *') * zz)) ^2),((Im ((f *') * zz)) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re ((f *') * zz)) ^2),((Im ((f *') * zz)) ^2)) is complex V32() ext-real Element of REAL
|.(f *').| is complex V32() ext-real Element of REAL
Re (f *') is complex V32() ext-real Element of REAL
(Re (f *')) ^2 is complex V32() ext-real Element of REAL
(Re (f *')) * (Re (f *')) is complex V32() ext-real set
Im (f *') is complex V32() ext-real Element of REAL
(Im (f *')) ^2 is complex V32() ext-real Element of REAL
(Im (f *')) * (Im (f *')) is complex V32() ext-real set
K114(((Re (f *')) ^2),((Im (f *')) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (f *')) ^2),((Im (f *')) ^2)) is complex V32() ext-real Element of REAL
|.(((|.f.| ^2) - (|.rho.| ^2)) ").| is complex V32() ext-real Element of REAL
Re (((|.f.| ^2) - (|.rho.| ^2)) ") is complex V32() ext-real Element of REAL
(Re (((|.f.| ^2) - (|.rho.| ^2)) ")) ^2 is complex V32() ext-real Element of REAL
(Re (((|.f.| ^2) - (|.rho.| ^2)) ")) * (Re (((|.f.| ^2) - (|.rho.| ^2)) ")) is complex V32() ext-real set
Im (((|.f.| ^2) - (|.rho.| ^2)) ") is complex V32() ext-real Element of REAL
(Im (((|.f.| ^2) - (|.rho.| ^2)) ")) ^2 is complex V32() ext-real Element of REAL
(Im (((|.f.| ^2) - (|.rho.| ^2)) ")) * (Im (((|.f.| ^2) - (|.rho.| ^2)) ")) is complex V32() ext-real set
K114(((Re (((|.f.| ^2) - (|.rho.| ^2)) ")) ^2),((Im (((|.f.| ^2) - (|.rho.| ^2)) ")) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (((|.f.| ^2) - (|.rho.| ^2)) ")) ^2),((Im (((|.f.| ^2) - (|.rho.| ^2)) ")) ^2)) is complex V32() ext-real Element of REAL
|.(f *').| * |.(((|.f.| ^2) - (|.rho.| ^2)) ").| is complex V32() ext-real set
|.f.| * |.(((|.f.| ^2) - (|.rho.| ^2)) ").| is complex V32() ext-real set
z is complex Element of COMPLEX
z *' is complex Element of COMPLEX
Re z is complex V32() ext-real Element of REAL
Im z is complex V32() ext-real Element of REAL
(Im z) * <i> is complex set
(Re z) - ((Im z) * <i>) is complex set
z * (z *') is complex Element of COMPLEX
Im (z * (z *')) is complex V32() ext-real Element of REAL
Re (z * (z *')) is complex V32() ext-real Element of REAL
(Im (z * (z *'))) * <i> is complex set
(Re (z * (z *'))) + ((Im (z * (z *'))) * <i>) is complex set
(Im z) ^2 is complex V32() ext-real Element of REAL
(Im z) * (Im z) is complex V32() ext-real set
(Re z) ^2 is complex V32() ext-real Element of REAL
(Re z) * (Re z) is complex V32() ext-real set
((Re z) ^2) + ((Im z) ^2) is complex V32() ext-real set
(z *') * z is complex Element of COMPLEX
|.z.| is complex V32() ext-real Element of REAL
K114(((Re z) ^2),((Im z) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re z) ^2),((Im z) ^2)) is complex V32() ext-real Element of REAL
|.z.| ^2 is complex V32() ext-real Element of REAL
|.z.| * |.z.| is complex V32() ext-real set
b9 *' is complex Element of COMPLEX
(Im b9) * <i> is complex set
(Re b9) - ((Im b9) * <i>) is complex set
(b9 *') * b9 is complex Element of COMPLEX
(t *') * t is complex Element of COMPLEX
((t *') * t) * (b9 ") is complex Element of COMPLEX
(((t *') * t) * (b9 ")) - (b9 *') is complex Element of COMPLEX
(|.t.| ^2) * (b9 ") is complex set
((|.t.| ^2) * (b9 ")) - (b9 *') is complex set
(((|.t.| ^2) * (b9 ")) - (b9 *')) * 1 is complex set
b9 * (b9 ") is complex Element of COMPLEX
(((|.t.| ^2) * (b9 ")) - (b9 *')) * (b9 * (b9 ")) is complex set
(b9 ") * b9 is complex Element of COMPLEX
(|.t.| ^2) * ((b9 ") * b9) is complex set
((|.t.| ^2) * ((b9 ") * b9)) - (|.b9.| ^2) is complex set
(((|.t.| ^2) * ((b9 ") * b9)) - (|.b9.| ^2)) * (b9 ") is complex set
(|.t.| ^2) * 1 is complex V32() ext-real set
((|.t.| ^2) * 1) - (|.b9.| ^2) is complex V32() ext-real set
(((|.t.| ^2) * 1) - (|.b9.| ^2)) * (b9 ") is complex set
((((t *') * t) * (b9 ")) - (b9 *')) " is complex Element of COMPLEX
Re ((((t *') * t) * (b9 ")) - (b9 *')) is complex V32() ext-real Element of REAL
(Re ((((t *') * t) * (b9 ")) - (b9 *'))) ^2 is complex V32() ext-real Element of REAL
(Re ((((t *') * t) * (b9 ")) - (b9 *'))) * (Re ((((t *') * t) * (b9 ")) - (b9 *'))) is complex V32() ext-real set
Im ((((t *') * t) * (b9 ")) - (b9 *')) is complex V32() ext-real Element of REAL
(Im ((((t *') * t) * (b9 ")) - (b9 *'))) ^2 is complex V32() ext-real Element of REAL
(Im ((((t *') * t) * (b9 ")) - (b9 *'))) * (Im ((((t *') * t) * (b9 ")) - (b9 *'))) is complex V32() ext-real set
K114(((Re ((((t *') * t) * (b9 ")) - (b9 *'))) ^2),((Im ((((t *') * t) * (b9 ")) - (b9 *'))) ^2)) is complex V32() ext-real Element of REAL
K117((Re ((((t *') * t) * (b9 ")) - (b9 *'))),K114(((Re ((((t *') * t) * (b9 ")) - (b9 *'))) ^2),((Im ((((t *') * t) * (b9 ")) - (b9 *'))) ^2))) is complex V32() ext-real Element of REAL
K108((Im ((((t *') * t) * (b9 ")) - (b9 *')))) is complex V32() ext-real Element of REAL
K117(K108((Im ((((t *') * t) * (b9 ")) - (b9 *')))),K114(((Re ((((t *') * t) * (b9 ")) - (b9 *'))) ^2),((Im ((((t *') * t) * (b9 ")) - (b9 *'))) ^2))) is complex V32() ext-real Element of REAL
K117(K108((Im ((((t *') * t) * (b9 ")) - (b9 *')))),K114(((Re ((((t *') * t) * (b9 ")) - (b9 *'))) ^2),((Im ((((t *') * t) * (b9 ")) - (b9 *'))) ^2))) * <i> is complex set
K117((Re ((((t *') * t) * (b9 ")) - (b9 *'))),K114(((Re ((((t *') * t) * (b9 ")) - (b9 *'))) ^2),((Im ((((t *') * t) * (b9 ")) - (b9 *'))) ^2))) + (K117(K108((Im ((((t *') * t) * (b9 ")) - (b9 *')))),K114(((Re ((((t *') * t) * (b9 ")) - (b9 *'))) ^2),((Im ((((t *') * t) * (b9 ")) - (b9 *'))) ^2))) * <i>) is complex set
- (((((t *') * t) * (b9 ")) - (b9 *')) ") is complex Element of COMPLEX
((|.t.| ^2) - (|.b9.| ^2)) " is complex V32() ext-real set
(b9 ") " is complex Element of COMPLEX
Re (b9 ") is complex V32() ext-real Element of REAL
(Re (b9 ")) ^2 is complex V32() ext-real Element of REAL
(Re (b9 ")) * (Re (b9 ")) is complex V32() ext-real set
Im (b9 ") is complex V32() ext-real Element of REAL
(Im (b9 ")) ^2 is complex V32() ext-real Element of REAL
(Im (b9 ")) * (Im (b9 ")) is complex V32() ext-real set
K114(((Re (b9 ")) ^2),((Im (b9 ")) ^2)) is complex V32() ext-real Element of REAL
K117((Re (b9 ")),K114(((Re (b9 ")) ^2),((Im (b9 ")) ^2))) is complex V32() ext-real Element of REAL
K108((Im (b9 "))) is complex V32() ext-real Element of REAL
K117(K108((Im (b9 "))),K114(((Re (b9 ")) ^2),((Im (b9 ")) ^2))) is complex V32() ext-real Element of REAL
K117(K108((Im (b9 "))),K114(((Re (b9 ")) ^2),((Im (b9 ")) ^2))) * <i> is complex set
K117((Re (b9 ")),K114(((Re (b9 ")) ^2),((Im (b9 ")) ^2))) + (K117(K108((Im (b9 "))),K114(((Re (b9 ")) ^2),((Im (b9 ")) ^2))) * <i>) is complex set
(((|.t.| ^2) - (|.b9.| ^2)) ") * ((b9 ") ") is complex set
- ((((|.t.| ^2) - (|.b9.| ^2)) ") * ((b9 ") ")) is complex set
- b9 is complex Element of COMPLEX
(- b9) * (((|.f.| ^2) - (|.rho.| ^2)) ") is complex set
(- (rho * zz)) " is complex Element of the carrier of F_Complex
b19 " is complex Element of COMPLEX
Re b19 is complex V32() ext-real Element of REAL
(Re b19) ^2 is complex V32() ext-real Element of REAL
(Re b19) * (Re b19) is complex V32() ext-real set
Im b19 is complex V32() ext-real Element of REAL
(Im b19) ^2 is complex V32() ext-real Element of REAL
(Im b19) * (Im b19) is complex V32() ext-real set
K114(((Re b19) ^2),((Im b19) ^2)) is complex V32() ext-real Element of REAL
K117((Re b19),K114(((Re b19) ^2),((Im b19) ^2))) is complex V32() ext-real Element of REAL
K108((Im b19)) is complex V32() ext-real Element of REAL
K117(K108((Im b19)),K114(((Re b19) ^2),((Im b19) ^2))) is complex V32() ext-real Element of REAL
K117(K108((Im b19)),K114(((Re b19) ^2),((Im b19) ^2))) * <i> is complex set
K117((Re b19),K114(((Re b19) ^2),((Im b19) ^2))) + (K117(K108((Im b19)),K114(((Re b19) ^2),((Im b19) ^2))) * <i>) is complex set
- ((- (rho * zz)) ") is complex Element of the carrier of F_Complex
- (b19 ") is complex Element of COMPLEX
((- (rho * zz)) ") * (- (rho * zz)) is complex Element of the carrier of F_Complex
K182(((- (rho * zz)) "),(- (rho * zz))) is complex Element of COMPLEX
- (- ((- (rho * zz)) ")) is complex Element of the carrier of F_Complex
(- ((- (rho * zz)) ")) " is complex Element of the carrier of F_Complex
(- (b19 ")) " is complex Element of COMPLEX
Re (- (b19 ")) is complex V32() ext-real Element of REAL
(Re (- (b19 "))) ^2 is complex V32() ext-real Element of REAL
(Re (- (b19 "))) * (Re (- (b19 "))) is complex V32() ext-real set
Im (- (b19 ")) is complex V32() ext-real Element of REAL
(Im (- (b19 "))) ^2 is complex V32() ext-real Element of REAL
(Im (- (b19 "))) * (Im (- (b19 "))) is complex V32() ext-real set
K114(((Re (- (b19 "))) ^2),((Im (- (b19 "))) ^2)) is complex V32() ext-real Element of REAL
K117((Re (- (b19 "))),K114(((Re (- (b19 "))) ^2),((Im (- (b19 "))) ^2))) is complex V32() ext-real Element of REAL
K108((Im (- (b19 ")))) is complex V32() ext-real Element of REAL
K117(K108((Im (- (b19 ")))),K114(((Re (- (b19 "))) ^2),((Im (- (b19 "))) ^2))) is complex V32() ext-real Element of REAL
K117(K108((Im (- (b19 ")))),K114(((Re (- (b19 "))) ^2),((Im (- (b19 "))) ^2))) * <i> is complex set
K117((Re (- (b19 "))),K114(((Re (- (b19 "))) ^2),((Im (- (b19 "))) ^2))) + (K117(K108((Im (- (b19 ")))),K114(((Re (- (b19 "))) ^2),((Im (- (b19 "))) ^2))) * <i>) is complex set
((- (rho * zz)) ") " is complex Element of the carrier of F_Complex
- (((- (rho * zz)) ") ") is complex Element of the carrier of F_Complex
((- (b19 ")) ") * ((t *') * (b9 ")) is complex Element of COMPLEX
- (- (b9 * (((|.f.| ^2) - (|.rho.| ^2)) "))) is complex set
(- (- (b9 * (((|.f.| ^2) - (|.rho.| ^2)) ")))) * ((t *') * (b9 ")) is complex set
(b9 * (b9 ")) * (((|.f.| ^2) - (|.rho.| ^2)) ") is complex set
((b9 * (b9 ")) * (((|.f.| ^2) - (|.rho.| ^2)) ")) * (t *') is complex set
1 * (((|.f.| ^2) - (|.rho.| ^2)) ") is complex V32() ext-real set
(1 * (((|.f.| ^2) - (|.rho.| ^2)) ")) * (t *') is complex set
a19 is complex Element of COMPLEX
((- ((- (rho * zz)) ")) ") * ((f *') * (rho ")) is complex Element of the carrier of F_Complex
K182(((- ((- (rho * zz)) ")) "),((f *') * (rho "))) is complex Element of COMPLEX
(b9 ") * t is complex Element of COMPLEX
(t *') * ((b9 ") * t) is complex Element of COMPLEX
(rho ") * f is complex Element of the carrier of F_Complex
K182((rho "),f) is complex Element of COMPLEX
(f *') * ((rho ") * f) is complex Element of the carrier of F_Complex
K182((f *'),((rho ") * f)) is complex Element of COMPLEX
|.(- (rho * zz)).| is complex V32() ext-real Element of REAL
Re (- (rho * zz)) is complex V32() ext-real Element of REAL
(Re (- (rho * zz))) ^2 is complex V32() ext-real Element of REAL
(Re (- (rho * zz))) * (Re (- (rho * zz))) is complex V32() ext-real set
Im (- (rho * zz)) is complex V32() ext-real Element of REAL
(Im (- (rho * zz))) ^2 is complex V32() ext-real Element of REAL
(Im (- (rho * zz))) * (Im (- (rho * zz))) is complex V32() ext-real set
K114(((Re (- (rho * zz))) ^2),((Im (- (rho * zz))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (- (rho * zz))) ^2),((Im (- (rho * zz))) ^2)) is complex V32() ext-real Element of REAL
rho * (((|.f.| ^2) - (|.rho.| ^2)) ") is complex set
- (rho * (((|.f.| ^2) - (|.rho.| ^2)) ")) is complex set
|.(- (rho * (((|.f.| ^2) - (|.rho.| ^2)) "))).| is complex V32() ext-real Element of REAL
Re (- (rho * (((|.f.| ^2) - (|.rho.| ^2)) "))) is complex V32() ext-real Element of REAL
(Re (- (rho * (((|.f.| ^2) - (|.rho.| ^2)) ")))) ^2 is complex V32() ext-real Element of REAL
(Re (- (rho * (((|.f.| ^2) - (|.rho.| ^2)) ")))) * (Re (- (rho * (((|.f.| ^2) - (|.rho.| ^2)) ")))) is complex V32() ext-real set
Im (- (rho * (((|.f.| ^2) - (|.rho.| ^2)) "))) is complex V32() ext-real Element of REAL
(Im (- (rho * (((|.f.| ^2) - (|.rho.| ^2)) ")))) ^2 is complex V32() ext-real Element of REAL
(Im (- (rho * (((|.f.| ^2) - (|.rho.| ^2)) ")))) * (Im (- (rho * (((|.f.| ^2) - (|.rho.| ^2)) ")))) is complex V32() ext-real set
K114(((Re (- (rho * (((|.f.| ^2) - (|.rho.| ^2)) ")))) ^2),((Im (- (rho * (((|.f.| ^2) - (|.rho.| ^2)) ")))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (- (rho * (((|.f.| ^2) - (|.rho.| ^2)) ")))) ^2),((Im (- (rho * (((|.f.| ^2) - (|.rho.| ^2)) ")))) ^2)) is complex V32() ext-real Element of REAL
|.(rho * (((|.f.| ^2) - (|.rho.| ^2)) ")).| is complex V32() ext-real Element of REAL
Re (rho * (((|.f.| ^2) - (|.rho.| ^2)) ")) is complex V32() ext-real Element of REAL
(Re (rho * (((|.f.| ^2) - (|.rho.| ^2)) "))) ^2 is complex V32() ext-real Element of REAL
(Re (rho * (((|.f.| ^2) - (|.rho.| ^2)) "))) * (Re (rho * (((|.f.| ^2) - (|.rho.| ^2)) "))) is complex V32() ext-real set
Im (rho * (((|.f.| ^2) - (|.rho.| ^2)) ")) is complex V32() ext-real Element of REAL
(Im (rho * (((|.f.| ^2) - (|.rho.| ^2)) "))) ^2 is complex V32() ext-real Element of REAL
(Im (rho * (((|.f.| ^2) - (|.rho.| ^2)) "))) * (Im (rho * (((|.f.| ^2) - (|.rho.| ^2)) "))) is complex V32() ext-real set
K114(((Re (rho * (((|.f.| ^2) - (|.rho.| ^2)) "))) ^2),((Im (rho * (((|.f.| ^2) - (|.rho.| ^2)) "))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (rho * (((|.f.| ^2) - (|.rho.| ^2)) "))) ^2),((Im (rho * (((|.f.| ^2) - (|.rho.| ^2)) "))) ^2)) is complex V32() ext-real Element of REAL
|.rho.| * |.(((|.f.| ^2) - (|.rho.| ^2)) ").| is complex V32() ext-real set
- b19 is complex Element of COMPLEX
(- b19) " is complex Element of COMPLEX
Re (- b19) is complex V32() ext-real Element of REAL
(Re (- b19)) ^2 is complex V32() ext-real Element of REAL
(Re (- b19)) * (Re (- b19)) is complex V32() ext-real set
Im (- b19) is complex V32() ext-real Element of REAL
(Im (- b19)) ^2 is complex V32() ext-real Element of REAL
(Im (- b19)) * (Im (- b19)) is complex V32() ext-real set
K114(((Re (- b19)) ^2),((Im (- b19)) ^2)) is complex V32() ext-real Element of REAL
K117((Re (- b19)),K114(((Re (- b19)) ^2),((Im (- b19)) ^2))) is complex V32() ext-real Element of REAL
K108((Im (- b19))) is complex V32() ext-real Element of REAL
K117(K108((Im (- b19))),K114(((Re (- b19)) ^2),((Im (- b19)) ^2))) is complex V32() ext-real Element of REAL
K117(K108((Im (- b19))),K114(((Re (- b19)) ^2),((Im (- b19)) ^2))) * <i> is complex set
K117((Re (- b19)),K114(((Re (- b19)) ^2),((Im (- b19)) ^2))) + (K117(K108((Im (- b19))),K114(((Re (- b19)) ^2),((Im (- b19)) ^2))) * <i>) is complex set
(- (- (rho * zz))) " is complex Element of the carrier of F_Complex
|.rho.| * |.f.| is complex V32() ext-real set
(|.rho.| ^2) - (|.rho.| ^2) is complex V32() ext-real set
- rho is complex Element of the carrier of F_Complex
(- rho) * zz is complex Element of the carrier of F_Complex
K182((- rho),zz) is complex Element of COMPLEX
- (0. F_Complex) is complex Element of the carrier of F_Complex
(rho * (ef)) + ((f * ef) - (rho * (ef))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(- (rho * (ef))) + (rho * (ef)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f * ef) + ((- (rho * (ef))) + (rho * (ef))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(rho * (ef)) - (rho * (ef)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(rho * (ef)) + (- (rho * (ef))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f * ef) + ((rho * (ef)) - (rho * (ef))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f * ef) + (0_. F_Complex) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f * ef) - ((f * ef) - (rho * (ef))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
- ((f * ef) - (rho * (ef))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f * ef) + (- ((f * ef) - (rho * (ef)))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((rho * (ef)) + ((f * ef) - (rho * (ef)))) - ((f * ef) - (rho * (ef))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((rho * (ef)) + ((f * ef) - (rho * (ef)))) + (- ((f * ef) - (rho * (ef)))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f * ef) - (rho * (ef))) - ((f * ef) - (rho * (ef))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f * ef) - (rho * (ef))) + (- ((f * ef) - (rho * (ef)))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(rho * (ef)) + (((f * ef) - (rho * (ef))) - ((f * ef) - (rho * (ef)))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(rho * (ef)) + (0_. F_Complex) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(1_ F_Complex) * (ef) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(rho ") * rho is complex Element of the carrier of F_Complex
K182((rho "),rho) is complex Element of COMPLEX
((rho ") * rho) * (ef) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(rho ") * (rho * (ef)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(rho ") * ((f * ef) - ((f * ef) - (rho * (ef)))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(((f * ef) - (rho * (ef)))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f * ef)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((- (rho * (ef)))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f * ef)) + ((- (rho * (ef)))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((rho * (ef))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
- ((rho * (ef))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f * ef)) + (- ((rho * (ef)))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f *') * (ef) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f *') * (ef)) + (- ((rho * (ef)))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((ef)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
rho *' is complex Element of the carrier of F_Complex
(Im rho) * <i> is complex set
(Re rho) - ((Im rho) * <i>) is complex set
(rho *') * ((ef)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
- ((rho *') * ((ef))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f *') * (ef)) + (- ((rho *') * ((ef)))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(rho *') * ef is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
- ((rho *') * ef) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f *') * (ef)) + (- ((rho *') * ef)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(rho ") * (f * ef) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(rho ") * (- ((f * ef) - (rho * (ef)))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((rho ") * (f * ef)) + ((rho ") * (- ((f * ef) - (rho * (ef))))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f *') * (((rho ") * (f * ef)) + ((rho ") * (- ((f * ef) - (rho * (ef)))))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f *') * (((rho ") * (f * ef)) + ((rho ") * (- ((f * ef) - (rho * (ef))))))) + (- ((rho *') * ef)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f *') * ((rho ") * (f * ef)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f *') * ((rho ") * (- ((f * ef) - (rho * (ef))))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f *') * ((rho ") * (f * ef))) + ((f *') * ((rho ") * (- ((f * ef) - (rho * (ef)))))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(((f *') * ((rho ") * (f * ef))) + ((f *') * ((rho ") * (- ((f * ef) - (rho * (ef))))))) + (- ((rho *') * ef)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f *') * ((rho ") * (f * ef))) + (- ((rho *') * ef)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f *') * ((rho ") * (- ((f * ef) - (rho * (ef)))))) + (((f *') * ((rho ") * (f * ef))) + (- ((rho *') * ef))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((rho ") * f) * ef is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f *') * (((rho ") * f) * ef) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f *') * (((rho ") * f) * ef)) + (- ((rho *') * ef)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f *') * ((rho ") * (- ((f * ef) - (rho * (ef)))))) + (((f *') * (((rho ") * f) * ef)) + (- ((rho *') * ef))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f *') * ((rho ") * f)) * ef is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(((f *') * ((rho ") * f)) * ef) + (- ((rho *') * ef)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f *') * ((rho ") * (- ((f * ef) - (rho * (ef)))))) + ((((f *') * ((rho ") * f)) * ef) + (- ((rho *') * ef))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
- (rho *') is complex Element of the carrier of F_Complex
(- (rho *')) * ef is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(((f *') * ((rho ") * f)) * ef) + ((- (rho *')) * ef) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f *') * ((rho ") * (- ((f * ef) - (rho * (ef)))))) + ((((f *') * ((rho ") * f)) * ef) + ((- (rho *')) * ef)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f *') * ((rho ") * f)) + (- (rho *')) is complex Element of the carrier of F_Complex
K180(((f *') * ((rho ") * f)),(- (rho *'))) is complex Element of COMPLEX
(((f *') * ((rho ") * f)) + (- (rho *'))) * ef is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f *') * ((rho ") * (- ((f * ef) - (rho * (ef)))))) + ((((f *') * ((rho ") * f)) + (- (rho *'))) * ef) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f *') * (rho ")) * (- ((f * ef) - (rho * (ef)))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(((f *') * (rho ")) * (- ((f * ef) - (rho * (ef))))) + ((((f *') * ((rho ") * f)) + (- (rho *'))) * ef) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
- (((f *') * (rho ")) * (- ((f * ef) - (rho * (ef))))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(((f * ef) - (rho * (ef)))) + (- (((f *') * (rho ")) * (- ((f * ef) - (rho * (ef)))))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(((f *') * (rho ")) * (- ((f * ef) - (rho * (ef))))) - (((f *') * (rho ")) * (- ((f * ef) - (rho * (ef))))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(((f *') * (rho ")) * (- ((f * ef) - (rho * (ef))))) + (- (((f *') * (rho ")) * (- ((f * ef) - (rho * (ef)))))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((((f *') * ((rho ") * f)) + (- (rho *'))) * ef) + ((((f *') * (rho ")) * (- ((f * ef) - (rho * (ef))))) - (((f *') * (rho ")) * (- ((f * ef) - (rho * (ef)))))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((((f *') * ((rho ") * f)) + (- (rho *'))) * ef) + (0_. F_Complex) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
- (b9 *') is complex Element of COMPLEX
(1_ F_Complex) * ef is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((- ((- (rho * zz)) ")) ") * (- ((- (rho * zz)) ")) is complex Element of the carrier of F_Complex
K182(((- ((- (rho * zz)) ")) "),(- ((- (rho * zz)) "))) is complex Element of COMPLEX
(((- ((- (rho * zz)) ")) ") * (- ((- (rho * zz)) "))) * ef is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(- ((- (rho * zz)) ")) * ef is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((- ((- (rho * zz)) ")) ") * ((- ((- (rho * zz)) ")) * ef) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((- ((- (rho * zz)) ")) ") * ((((f * ef) - (rho * (ef)))) + (- (((f *') * (rho ")) * (- ((f * ef) - (rho * (ef))))))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((- ((- (rho * zz)) ")) ") * (((f * ef) - (rho * (ef)))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((- ((- (rho * zz)) ")) ") * (- (((f *') * (rho ")) * (- ((f * ef) - (rho * (ef)))))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(((- ((- (rho * zz)) ")) ") * (((f * ef) - (rho * (ef))))) + (((- ((- (rho * zz)) ")) ") * (- (((f *') * (rho ")) * (- ((f * ef) - (rho * (ef))))))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
- (- ((f * ef) - (rho * (ef)))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f *') * (rho ")) * (- (- ((f * ef) - (rho * (ef))))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((- ((- (rho * zz)) ")) ") * (((f *') * (rho ")) * (- (- ((f * ef) - (rho * (ef)))))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(((- ((- (rho * zz)) ")) ") * (((f * ef) - (rho * (ef))))) + (((- ((- (rho * zz)) ")) ") * (((f *') * (rho ")) * (- (- ((f * ef) - (rho * (ef))))))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f *') * (rho ")) * ((f * ef) - (rho * (ef))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((- ((- (rho * zz)) ")) ") * (((f *') * (rho ")) * ((f * ef) - (rho * (ef)))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(((- ((- (rho * zz)) ")) ") * (((f * ef) - (rho * (ef))))) + (((- ((- (rho * zz)) ")) ") * (((f *') * (rho ")) * ((f * ef) - (rho * (ef))))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((f *') * zz) * ((f * ef) - (rho * (ef))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(((- ((- (rho * zz)) ")) ") * (((f * ef) - (rho * (ef))))) + (((f *') * zz) * ((f * ef) - (rho * (ef)))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((- (- (rho * zz))) ") " is complex Element of the carrier of F_Complex
(((- (- (rho * zz))) ") ") * (((f * ef) - (rho * (ef)))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((((- (- (rho * zz))) ") ") * (((f * ef) - (rho * (ef))))) + (((f *') * zz) * ((f * ef) - (rho * (ef)))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(- (- (rho * zz))) * (((f * ef) - (rho * (ef)))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((- (- (rho * zz))) * (((f * ef) - (rho * (ef))))) + (((f *') * zz) * ((f * ef) - (rho * (ef)))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(- (rho * zz)) * (((f * ef) - (rho * (ef)))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
- ((- (rho * zz)) * (((f * ef) - (rho * (ef))))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(- ((- (rho * zz)) * (((f * ef) - (rho * (ef)))))) + (((f *') * zz) * ((f * ef) - (rho * (ef)))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(F_Complex,(((f *') * zz) * ((f * ef) - (rho * (ef))))) is complex V32() ext-real integer set
len (((f *') * zz) * ((f * ef) - (rho * (ef)))) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len (((f *') * zz) * ((f * ef) - (rho * (ef))))) - 1 is complex V32() ext-real integer set
(F_Complex,(- ((- (rho * zz)) * (((f * ef) - (rho * (ef))))))) is complex V32() ext-real integer set
len (- ((- (rho * zz)) * (((f * ef) - (rho * (ef)))))) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len (- ((- (rho * zz)) * (((f * ef) - (rho * (ef))))))) - 1 is complex V32() ext-real integer set
max ((F_Complex,(((f *') * zz) * ((f * ef) - (rho * (ef))))),(F_Complex,(- ((- (rho * zz)) * (((f * ef) - (rho * (ef)))))))) is complex V32() ext-real set
(F_Complex,((- (rho * zz)) * (((f * ef) - (rho * (ef)))))) is complex V32() ext-real integer set
len ((- (rho * zz)) * (((f * ef) - (rho * (ef))))) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len ((- (rho * zz)) * (((f * ef) - (rho * (ef)))))) - 1 is complex V32() ext-real integer set
max ((F_Complex,(((f *') * zz) * ((f * ef) - (rho * (ef))))),(F_Complex,((- (rho * zz)) * (((f * ef) - (rho * (ef))))))) is complex V32() ext-real set
(F_Complex,((f * ef) - (rho * (ef)))) is complex V32() ext-real integer set
len ((f * ef) - (rho * (ef))) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len ((f * ef) - (rho * (ef)))) - 1 is complex V32() ext-real integer set
max ((F_Complex,((f * ef) - (rho * (ef)))),(F_Complex,((- (rho * zz)) * (((f * ef) - (rho * (ef))))))) is complex V32() ext-real set
(F_Complex,(((f * ef) - (rho * (ef))))) is complex V32() ext-real integer set
len (((f * ef) - (rho * (ef)))) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len (((f * ef) - (rho * (ef))))) - 1 is complex V32() ext-real integer set
max ((F_Complex,((f * ef) - (rho * (ef)))),(F_Complex,(((f * ef) - (rho * (ef)))))) is complex V32() ext-real set
max ((F_Complex,((f * ef) - (rho * (ef)))),(F_Complex,((f * ef) - (rho * (ef))))) is complex V32() ext-real set
z is complex Element of the carrier of F_Complex
(((f *') * zz) * ((f * ef) - (rho * (ef)))) - ((- (rho * zz)) * (((f * ef) - (rho * (ef))))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(((f *') * zz) * ((f * ef) - (rho * (ef)))) + (- ((- (rho * zz)) * (((f * ef) - (rho * (ef)))))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval (((((f *') * zz) * ((f * ef) - (rho * (ef)))) - ((- (rho * zz)) * (((f * ef) - (rho * (ef)))))),z) is complex Element of the carrier of F_Complex
eval ((((f *') * zz) * ((f * ef) - (rho * (ef)))),z) is complex Element of the carrier of F_Complex
eval (((- (rho * zz)) * (((f * ef) - (rho * (ef))))),z) is complex Element of the carrier of F_Complex
(eval ((((f *') * zz) * ((f * ef) - (rho * (ef)))),z)) - (eval (((- (rho * zz)) * (((f * ef) - (rho * (ef))))),z)) is complex Element of the carrier of F_Complex
eval (((f * ef) - (rho * (ef))),z) is complex Element of the carrier of F_Complex
((f *') * zz) * (eval (((f * ef) - (rho * (ef))),z)) is complex Element of the carrier of F_Complex
K182(((f *') * zz),(eval (((f * ef) - (rho * (ef))),z))) is complex Element of COMPLEX
(((f *') * zz) * (eval (((f * ef) - (rho * (ef))),z))) - (eval (((- (rho * zz)) * (((f * ef) - (rho * (ef))))),z)) is complex Element of the carrier of F_Complex
eval ((((f * ef) - (rho * (ef)))),z) is complex Element of the carrier of F_Complex
(- (rho * zz)) * (eval ((((f * ef) - (rho * (ef)))),z)) is complex Element of the carrier of F_Complex
K182((- (rho * zz)),(eval ((((f * ef) - (rho * (ef)))),z))) is complex Element of COMPLEX
(((f *') * zz) * (eval (((f * ef) - (rho * (ef))),z))) - ((- (rho * zz)) * (eval ((((f * ef) - (rho * (ef)))),z))) is complex Element of the carrier of F_Complex
|.(eval (((f * ef) - (rho * (ef))),z)).| is complex V32() ext-real Element of REAL
Re (eval (((f * ef) - (rho * (ef))),z)) is complex V32() ext-real Element of REAL
(Re (eval (((f * ef) - (rho * (ef))),z))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (((f * ef) - (rho * (ef))),z))) * (Re (eval (((f * ef) - (rho * (ef))),z))) is complex V32() ext-real set
Im (eval (((f * ef) - (rho * (ef))),z)) is complex V32() ext-real Element of REAL
(Im (eval (((f * ef) - (rho * (ef))),z))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (((f * ef) - (rho * (ef))),z))) * (Im (eval (((f * ef) - (rho * (ef))),z))) is complex V32() ext-real set
K114(((Re (eval (((f * ef) - (rho * (ef))),z))) ^2),((Im (eval (((f * ef) - (rho * (ef))),z))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (((f * ef) - (rho * (ef))),z))) ^2),((Im (eval (((f * ef) - (rho * (ef))),z))) ^2)) is complex V32() ext-real Element of REAL
|.((f *') * zz).| * |.(eval (((f * ef) - (rho * (ef))),z)).| is complex V32() ext-real set
|.(((f *') * zz) * (eval (((f * ef) - (rho * (ef))),z))).| is complex V32() ext-real Element of REAL
Re (((f *') * zz) * (eval (((f * ef) - (rho * (ef))),z))) is complex V32() ext-real Element of REAL
(Re (((f *') * zz) * (eval (((f * ef) - (rho * (ef))),z)))) ^2 is complex V32() ext-real Element of REAL
(Re (((f *') * zz) * (eval (((f * ef) - (rho * (ef))),z)))) * (Re (((f *') * zz) * (eval (((f * ef) - (rho * (ef))),z)))) is complex V32() ext-real set
Im (((f *') * zz) * (eval (((f * ef) - (rho * (ef))),z))) is complex V32() ext-real Element of REAL
(Im (((f *') * zz) * (eval (((f * ef) - (rho * (ef))),z)))) ^2 is complex V32() ext-real Element of REAL
(Im (((f *') * zz) * (eval (((f * ef) - (rho * (ef))),z)))) * (Im (((f *') * zz) * (eval (((f * ef) - (rho * (ef))),z)))) is complex V32() ext-real set
K114(((Re (((f *') * zz) * (eval (((f * ef) - (rho * (ef))),z)))) ^2),((Im (((f *') * zz) * (eval (((f * ef) - (rho * (ef))),z)))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (((f *') * zz) * (eval (((f * ef) - (rho * (ef))),z)))) ^2),((Im (((f *') * zz) * (eval (((f * ef) - (rho * (ef))),z)))) ^2)) is complex V32() ext-real Element of REAL
|.(eval ((((f * ef) - (rho * (ef)))),z)).| is complex V32() ext-real Element of REAL
Re (eval ((((f * ef) - (rho * (ef)))),z)) is complex V32() ext-real Element of REAL
(Re (eval ((((f * ef) - (rho * (ef)))),z))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((((f * ef) - (rho * (ef)))),z))) * (Re (eval ((((f * ef) - (rho * (ef)))),z))) is complex V32() ext-real set
Im (eval ((((f * ef) - (rho * (ef)))),z)) is complex V32() ext-real Element of REAL
(Im (eval ((((f * ef) - (rho * (ef)))),z))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((((f * ef) - (rho * (ef)))),z))) * (Im (eval ((((f * ef) - (rho * (ef)))),z))) is complex V32() ext-real set
K114(((Re (eval ((((f * ef) - (rho * (ef)))),z))) ^2),((Im (eval ((((f * ef) - (rho * (ef)))),z))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((((f * ef) - (rho * (ef)))),z))) ^2),((Im (eval ((((f * ef) - (rho * (ef)))),z))) ^2)) is complex V32() ext-real Element of REAL
|.(- (rho * zz)).| * |.(eval ((((f * ef) - (rho * (ef)))),z)).| is complex V32() ext-real set
|.((- (rho * zz)) * (eval ((((f * ef) - (rho * (ef)))),z))).| is complex V32() ext-real Element of REAL
Re ((- (rho * zz)) * (eval ((((f * ef) - (rho * (ef)))),z))) is complex V32() ext-real Element of REAL
(Re ((- (rho * zz)) * (eval ((((f * ef) - (rho * (ef)))),z)))) ^2 is complex V32() ext-real Element of REAL
(Re ((- (rho * zz)) * (eval ((((f * ef) - (rho * (ef)))),z)))) * (Re ((- (rho * zz)) * (eval ((((f * ef) - (rho * (ef)))),z)))) is complex V32() ext-real set
Im ((- (rho * zz)) * (eval ((((f * ef) - (rho * (ef)))),z))) is complex V32() ext-real Element of REAL
(Im ((- (rho * zz)) * (eval ((((f * ef) - (rho * (ef)))),z)))) ^2 is complex V32() ext-real Element of REAL
(Im ((- (rho * zz)) * (eval ((((f * ef) - (rho * (ef)))),z)))) * (Im ((- (rho * zz)) * (eval ((((f * ef) - (rho * (ef)))),z)))) is complex V32() ext-real set
K114(((Re ((- (rho * zz)) * (eval ((((f * ef) - (rho * (ef)))),z)))) ^2),((Im ((- (rho * zz)) * (eval ((((f * ef) - (rho * (ef)))),z)))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re ((- (rho * zz)) * (eval ((((f * ef) - (rho * (ef)))),z)))) ^2),((Im ((- (rho * zz)) * (eval ((((f * ef) - (rho * (ef)))),z)))) ^2)) is complex V32() ext-real Element of REAL
Re z is complex V32() ext-real Element of REAL
|.(- (rho * zz)).| * |.(eval (((f * ef) - (rho * (ef))),z)).| is complex V32() ext-real set
f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(F_Complex,f) is complex V32() ext-real integer set
len f is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len f) - 1 is complex V32() ext-real integer set
rho is complex Element of the carrier of F_Complex
Re rho is complex V32() ext-real Element of REAL
(f,rho) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(f) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval ((f),rho) is complex Element of the carrier of F_Complex
(eval ((f),rho)) * f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval (f,rho) is complex Element of the carrier of F_Complex
(eval (f,rho)) * (f) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((eval ((f),rho)) * f) - ((eval (f,rho)) * (f)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
- ((eval (f,rho)) * (f)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((eval ((f),rho)) * f) + (- ((eval (f,rho)) * (f))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(F_Complex,rho,1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(power F_Complex) . (rho,1) is complex Element of the carrier of F_Complex
- ((power F_Complex) . (rho,1)) is complex Element of the carrier of F_Complex
(0,1) --> ((- ((power F_Complex) . (rho,1))),(1_ F_Complex)) is Relation-like {0,1} -defined the carrier of F_Complex -valued Function-like non empty total V18({0,1}, the carrier of F_Complex) Element of K19(K20({0,1}, the carrier of F_Complex))
{0,1} is non empty set
K20({0,1}, the carrier of F_Complex) is set
K19(K20({0,1}, the carrier of F_Complex)) is set
(0_. F_Complex) +* ((0,1) --> ((- ((power F_Complex) . (rho,1))),(1_ F_Complex))) is Relation-like Function-like set
(F_Complex,(f,rho),(F_Complex,rho,1)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
ef1 is complex Element of the carrier of F_Complex
ef1 * f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
ef is complex Element of the carrier of F_Complex
ef * (f) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(ef1 * f) - (ef * (f)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
- (ef * (f)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(ef1 * f) + (- (ef * (f))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval (((ef1 * f) - (ef * (f))),rho) is complex Element of the carrier of F_Complex
eval ((ef1 * f),rho) is complex Element of the carrier of F_Complex
eval ((ef * (f)),rho) is complex Element of the carrier of F_Complex
(eval ((ef1 * f),rho)) - (eval ((ef * (f)),rho)) is complex Element of the carrier of F_Complex
ef1 * (eval (f,rho)) is complex Element of the carrier of F_Complex
K182(ef1,(eval (f,rho))) is complex Element of COMPLEX
(ef1 * (eval (f,rho))) - (eval ((ef * (f)),rho)) is complex Element of the carrier of F_Complex
ef * (eval ((f),rho)) is complex Element of the carrier of F_Complex
K182(ef,(eval ((f),rho))) is complex Element of COMPLEX
(ef1 * (eval (f,rho))) - (ef * (eval ((f),rho))) is complex Element of the carrier of F_Complex
t is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(F_Complex,rho,1) *' t is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
|.(eval ((f),rho)).| is complex V32() ext-real Element of REAL
Re (eval ((f),rho)) is complex V32() ext-real Element of REAL
(Re (eval ((f),rho))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((f),rho))) * (Re (eval ((f),rho))) is complex V32() ext-real set
Im (eval ((f),rho)) is complex V32() ext-real Element of REAL
(Im (eval ((f),rho))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((f),rho))) * (Im (eval ((f),rho))) is complex V32() ext-real set
K114(((Re (eval ((f),rho))) ^2),((Im (eval ((f),rho))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((f),rho))) ^2),((Im (eval ((f),rho))) ^2)) is complex V32() ext-real Element of REAL
|.(eval (f,rho)).| is complex V32() ext-real Element of REAL
Re (eval (f,rho)) is complex V32() ext-real Element of REAL
(Re (eval (f,rho))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (f,rho))) * (Re (eval (f,rho))) is complex V32() ext-real set
Im (eval (f,rho)) is complex V32() ext-real Element of REAL
(Im (eval (f,rho))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (f,rho))) * (Im (eval (f,rho))) is complex V32() ext-real set
K114(((Re (eval (f,rho))) ^2),((Im (eval (f,rho))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (f,rho))) ^2),((Im (eval (f,rho))) ^2)) is complex V32() ext-real Element of REAL
(F_Complex,(F_Complex,rho,1)) is complex V32() ext-real integer set
len (F_Complex,rho,1) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len (F_Complex,rho,1)) - 1 is complex V32() ext-real integer set
(F_Complex,(0_. F_Complex)) is complex V32() ext-real integer set
len (0_. F_Complex) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len (0_. F_Complex)) - 1 is complex V32() ext-real integer set
t *' (F_Complex,rho,1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(t *' (F_Complex,rho,1)) + (0_. F_Complex) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(F_Complex,f) is complex V32() ext-real integer set
len f is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len f) - 1 is complex V32() ext-real integer set
rho is complex Element of the carrier of F_Complex
Re rho is complex V32() ext-real Element of REAL
(f) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval ((f),rho) is complex Element of the carrier of F_Complex
|.(eval ((f),rho)).| is complex V32() ext-real Element of REAL
Re (eval ((f),rho)) is complex V32() ext-real Element of REAL
(Re (eval ((f),rho))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((f),rho))) * (Re (eval ((f),rho))) is complex V32() ext-real set
Im (eval ((f),rho)) is complex V32() ext-real Element of REAL
(Im (eval ((f),rho))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((f),rho))) * (Im (eval ((f),rho))) is complex V32() ext-real set
K114(((Re (eval ((f),rho))) ^2),((Im (eval ((f),rho))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((f),rho))) ^2),((Im (eval ((f),rho))) ^2)) is complex V32() ext-real Element of REAL
eval (f,rho) is complex Element of the carrier of F_Complex
|.(eval (f,rho)).| is complex V32() ext-real Element of REAL
Re (eval (f,rho)) is complex V32() ext-real Element of REAL
(Re (eval (f,rho))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (f,rho))) * (Re (eval (f,rho))) is complex V32() ext-real set
Im (eval (f,rho)) is complex V32() ext-real Element of REAL
(Im (eval (f,rho))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (f,rho))) * (Im (eval (f,rho))) is complex V32() ext-real set
K114(((Re (eval (f,rho))) ^2),((Im (eval (f,rho))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (f,rho))) ^2),((Im (eval (f,rho))) ^2)) is complex V32() ext-real Element of REAL
f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(F_Complex,f) is complex V32() ext-real integer set
len f is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len f) - 1 is complex V32() ext-real integer set
(f) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
rho is complex Element of the carrier of F_Complex
Re rho is complex V32() ext-real Element of REAL
eval ((f),rho) is complex Element of the carrier of F_Complex
|.(eval ((f),rho)).| is complex V32() ext-real Element of REAL
Re (eval ((f),rho)) is complex V32() ext-real Element of REAL
(Re (eval ((f),rho))) ^2 is complex V32() ext-real Element of REAL
(Re (eval ((f),rho))) * (Re (eval ((f),rho))) is complex V32() ext-real set
Im (eval ((f),rho)) is complex V32() ext-real Element of REAL
(Im (eval ((f),rho))) ^2 is complex V32() ext-real Element of REAL
(Im (eval ((f),rho))) * (Im (eval ((f),rho))) is complex V32() ext-real set
K114(((Re (eval ((f),rho))) ^2),((Im (eval ((f),rho))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval ((f),rho))) ^2),((Im (eval ((f),rho))) ^2)) is complex V32() ext-real Element of REAL
eval (f,rho) is complex Element of the carrier of F_Complex
|.(eval (f,rho)).| is complex V32() ext-real Element of REAL
Re (eval (f,rho)) is complex V32() ext-real Element of REAL
(Re (eval (f,rho))) ^2 is complex V32() ext-real Element of REAL
(Re (eval (f,rho))) * (Re (eval (f,rho))) is complex V32() ext-real set
Im (eval (f,rho)) is complex V32() ext-real Element of REAL
(Im (eval (f,rho))) ^2 is complex V32() ext-real Element of REAL
(Im (eval (f,rho))) * (Im (eval (f,rho))) is complex V32() ext-real set
K114(((Re (eval (f,rho))) ^2),((Im (eval (f,rho))) ^2)) is complex V32() ext-real Element of REAL
sqrt K114(((Re (eval (f,rho))) ^2),((Im (eval (f,rho))) ^2)) is complex V32() ext-real Element of REAL
(f,rho) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(eval ((f),rho)) * f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(eval (f,rho)) * (f) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((eval ((f),rho)) * f) - ((eval (f,rho)) * (f)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
- ((eval (f,rho)) * (f)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((eval ((f),rho)) * f) + (- ((eval (f,rho)) * (f))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(F_Complex,rho,1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(power F_Complex) . (rho,1) is complex Element of the carrier of F_Complex
- ((power F_Complex) . (rho,1)) is complex Element of the carrier of F_Complex
(0,1) --> ((- ((power F_Complex) . (rho,1))),(1_ F_Complex)) is Relation-like {0,1} -defined the carrier of F_Complex -valued Function-like non empty total V18({0,1}, the carrier of F_Complex) Element of K19(K20({0,1}, the carrier of F_Complex))
{0,1} is non empty set
K20({0,1}, the carrier of F_Complex) is set
K19(K20({0,1}, the carrier of F_Complex)) is set
(0_. F_Complex) +* ((0,1) --> ((- ((power F_Complex) . (rho,1))),(1_ F_Complex))) is Relation-like Function-like set
(F_Complex,(f,rho),(F_Complex,rho,1)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(F_Complex,(F_Complex,rho,1)) is complex V32() ext-real integer set
len (F_Complex,rho,1) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len (F_Complex,rho,1)) - 1 is complex V32() ext-real integer set
(F_Complex,(0_. F_Complex)) is complex V32() ext-real integer set
len (0_. F_Complex) is V24() V25() V26() V30() complex V32() ext-real non negative V40() V45() integer Element of NAT
(len (0_. F_Complex)) - 1 is complex V32() ext-real integer set
ef1 is complex Element of the carrier of F_Complex
ef1 * f is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
ef is complex Element of the carrier of F_Complex
ef * (f) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(ef1 * f) - (ef * (f)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
- (ef * (f)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(ef1 * f) + (- (ef * (f))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
eval (((ef1 * f) - (ef * (f))),rho) is complex Element of the carrier of F_Complex
eval ((ef1 * f),rho) is complex Element of the carrier of F_Complex
eval ((ef * (f)),rho) is complex Element of the carrier of F_Complex
(eval ((ef1 * f),rho)) - (eval ((ef * (f)),rho)) is complex Element of the carrier of F_Complex
ef1 * (eval (f,rho)) is complex Element of the carrier of F_Complex
K182(ef1,(eval (f,rho))) is complex Element of COMPLEX
(ef1 * (eval (f,rho))) - (eval ((ef * (f)),rho)) is complex Element of the carrier of F_Complex
ef * (eval ((f),rho)) is complex Element of the carrier of F_Complex
K182(ef,(eval ((f),rho))) is complex Element of COMPLEX
(ef1 * (eval (f,rho))) - (ef * (eval ((f),rho))) is complex Element of the carrier of F_Complex
t is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(F_Complex,rho,1) *' t is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
((F_Complex,rho,1) *' t) + (0_. F_Complex) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(F_Complex,(f,rho),(F_Complex,rho,1)) *' (F_Complex,rho,1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))
(1_ F_Complex) * (F_Complex,rho,1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total V18( NAT , the carrier of F_Complex) finite-Support Element of K19(K20(NAT, the carrier of F_Complex))