:: POLYNOM5 semantic presentation

REAL is non empty V24() V56() V57() V58() V62() set
NAT is epsilon-transitive epsilon-connected ordinal non empty V24() V29() V30() V56() V57() V58() V59() V60() V61() V62() Element of K27(REAL)
K27(REAL) is V24() set
INT is non empty V24() V56() V57() V58() V59() V60() V62() set
F_Complex is non empty non degenerated V94() left_add-cancelable right_add-cancelable right_complementable almost_left_invertible strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital domRing-like V174() V175() V176() V177() doubleLoopStr
the carrier of F_Complex is non empty V19() set
omega is epsilon-transitive epsilon-connected ordinal non empty V24() V29() V30() V56() V57() V58() V59() V60() V61() V62() set
K27(omega) is V24() set
K27(NAT) is V24() set
COMPLEX is non empty V24() V56() V62() set
RAT is non empty V24() V56() V57() V58() V59() V62() set
K28(COMPLEX,COMPLEX) is V24() complex-valued set
K27(K28(COMPLEX,COMPLEX)) is V24() set
K28(COMPLEX,REAL) is V24() complex-valued ext-real-valued real-valued set
K27(K28(COMPLEX,REAL)) is V24() set
K293(NAT) is V78() set
K28(REAL,REAL) is V24() complex-valued ext-real-valued real-valued set
K27(K28(REAL,REAL)) is V24() set
1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
2 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
{} is set
the epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Function-like functional empty V24() V29() V31( {} ) FinSequence-membered complex real ext-real non positive non negative V54() V56() V57() V58() V59() V60() V61() V62() set is epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Function-like functional empty V24() V29() V31( {} ) FinSequence-membered complex real ext-real non positive non negative V54() V56() V57() V58() V59() V60() V61() V62() set
K28(NAT,REAL) is V24() complex-valued ext-real-valued real-valued set
K27(K28(NAT,REAL)) is V24() set
K250(1,NAT) is M12( NAT )
K28(K28(COMPLEX,COMPLEX),COMPLEX) is V24() complex-valued set
K27(K28(K28(COMPLEX,COMPLEX),COMPLEX)) is V24() set
K28(K28(REAL,REAL),REAL) is V24() complex-valued ext-real-valued real-valued set
K27(K28(K28(REAL,REAL),REAL)) is V24() set
K28(RAT,RAT) is RAT -valued V24() complex-valued ext-real-valued real-valued set
K27(K28(RAT,RAT)) is V24() set
K28(K28(RAT,RAT),RAT) is RAT -valued V24() complex-valued ext-real-valued real-valued set
K27(K28(K28(RAT,RAT),RAT)) is V24() set
K28(INT,INT) is RAT -valued INT -valued V24() complex-valued ext-real-valued real-valued set
K27(K28(INT,INT)) is V24() set
K28(K28(INT,INT),INT) is RAT -valued INT -valued V24() complex-valued ext-real-valued real-valued set
K27(K28(K28(INT,INT),INT)) is V24() set
K28(NAT,NAT) is RAT -valued INT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28(NAT,NAT),NAT) is RAT -valued INT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K27(K28(K28(NAT,NAT),NAT)) is V24() set
3 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
Seg 1 is non empty V19() V24() V31(1) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
{1} is non empty V19() V31(1) V56() V57() V58() V59() V60() V61() set
Seg 2 is non empty V24() V31(2) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
{1,2} is V56() V57() V58() V59() V60() V61() set
Seg 3 is non empty V24() V31(3) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
K97(1,2,3) is V56() V57() V58() V59() V60() V61() set
<*> REAL is Relation-like NAT -defined REAL -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Function-like one-to-one constant functional empty V24() V29() V31( {} ) FinSequence-like FinSubsequence-like FinSequence-membered complex real ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V54() V56() V57() V58() V59() V60() V61() V62() Function-yielding V87() FinSequence of REAL
Sum (<*> REAL) is complex real ext-real Element of REAL
K623() is Relation-like K28(REAL,REAL) -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K27(K28(K28(REAL,REAL),REAL))
K294(REAL,(<*> REAL),K623()) is complex real ext-real Element of REAL
K28(NAT,COMPLEX) is V24() complex-valued set
K27(K28(NAT,COMPLEX)) is V24() set
K27(K28(NAT,NAT)) is V24() set
1r is complex Element of COMPLEX
|.0.| is complex real ext-real V55() Element of REAL
|.1r.| is complex real ext-real Element of REAL
K617() is Relation-like K28(COMPLEX,COMPLEX) -defined COMPLEX -valued Function-like total quasi_total complex-valued Element of K27(K28(K28(COMPLEX,COMPLEX),COMPLEX))
K619() is Relation-like K28(COMPLEX,COMPLEX) -defined COMPLEX -valued Function-like total quasi_total complex-valued Element of K27(K28(K28(COMPLEX,COMPLEX),COMPLEX))
0c is complex Element of COMPLEX
0. F_Complex is complex zero Element of the carrier of F_Complex
the ZeroF of F_Complex is complex 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
the OneF of F_Complex is complex Element of the carrier of F_Complex
|.(0. F_Complex).| is complex real ext-real Element of REAL
|.(1. F_Complex).| is complex real ext-real Element of REAL
power F_Complex is Relation-like K28( the carrier of F_Complex,NAT) -defined the carrier of F_Complex -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of F_Complex,NAT), the carrier of F_Complex))
K28( the carrier of F_Complex,NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of F_Complex,NAT), the carrier of F_Complex) is V24() set
K27(K28(K28( the carrier of F_Complex,NAT), the carrier of F_Complex)) is V24() set
len {} is epsilon-transitive epsilon-connected ordinal V29() set
c₁ is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₁ * np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁ * np) - c₁ is complex real ext-real V54() Element of REAL
- c₁ is complex real ext-real non positive V54() set
(c₁ * np) + (- c₁) is complex real ext-real V54() set
((c₁ * np) - c₁) - np is complex real ext-real V54() Element of REAL
- np is complex real ext-real non positive V54() set
((c₁ * np) - c₁) + (- np) is complex real ext-real V54() set
(((c₁ * np) - c₁) - np) + 1 is complex real ext-real V54() Element of REAL
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(0 + 1) - 1 is complex real ext-real V54() Element of REAL
- 1 is non empty complex real ext-real non positive negative V54() set
(0 + 1) + (- 1) is complex real ext-real V54() set
np - 1 is complex real ext-real V54() Element of REAL
np + (- 1) is complex real ext-real V54() set
c₁ - 1 is complex real ext-real V54() Element of REAL
c₁ + (- 1) is complex real ext-real V54() set
(c₁ - 1) * (np - 1) is complex real ext-real V54() Element of REAL
np is complex real ext-real set
c₁ is complex real ext-real set
min (c₁,np) is complex real ext-real set
max (c₁,np) is complex real ext-real set
(min (c₁,np)) / (max (c₁,np)) is complex real ext-real Element of COMPLEX
(max (c₁,np)) " is complex real ext-real set
(min (c₁,np)) * ((max (c₁,np)) ") is complex real ext-real set
np is complex real ext-real set
c₁ is complex real ext-real set
max (c₁,np) is complex real ext-real set
min (c₁,np) is complex real ext-real set
2 * (max (c₁,np)) is complex real ext-real Element of REAL
(min (c₁,np)) / (2 * (max (c₁,np))) is complex real ext-real Element of REAL
(2 * (max (c₁,np))) " is complex real ext-real set
(min (c₁,np)) * ((2 * (max (c₁,np))) ") is complex real ext-real set
np * 2 is complex real ext-real Element of REAL
(min (c₁,np)) / (max (c₁,np)) is complex real ext-real Element of COMPLEX
(max (c₁,np)) " is complex real ext-real set
(min (c₁,np)) * ((max (c₁,np)) ") is complex real ext-real set
((min (c₁,np)) / (max (c₁,np))) * 2 is complex real ext-real Element of REAL
((min (c₁,np)) / (max (c₁,np))) / 2 is complex real ext-real Element of REAL
2 " is non empty complex real ext-real positive non negative set
((min (c₁,np)) / (max (c₁,np))) * (2 ") is complex real ext-real set
(max (c₁,np)) * 2 is complex real ext-real Element of REAL
(min (c₁,np)) / ((max (c₁,np)) * 2) is complex real ext-real Element of REAL
((max (c₁,np)) * 2) " is complex real ext-real set
(min (c₁,np)) * (((max (c₁,np)) * 2) ") is complex real ext-real set
((min (c₁,np)) / (2 * (max (c₁,np)))) * c₁ is complex real ext-real Element of REAL
np / 2 is complex real ext-real Element of REAL
np * (2 ") is complex real ext-real set
2 * np is complex real ext-real Element of REAL
c₁ / (2 * np) is complex real ext-real Element of REAL
(2 * np) " is complex real ext-real set
c₁ * ((2 * np) ") is complex real ext-real set
(c₁ / (2 * np)) * np is complex real ext-real Element of REAL
c₁ / 2 is complex real ext-real Element of REAL
c₁ * (2 ") is complex real ext-real set
np / 2 is complex real ext-real Element of REAL
np * (2 ") is complex real ext-real set
1 / 2 is non empty complex real ext-real positive non negative Element of REAL
2 " is non empty complex real ext-real positive non negative set
1 * (2 ") is non empty complex real ext-real positive non negative set
(1 / 2) * c₁ is complex real ext-real Element of REAL
np is complex real ext-real Element of REAL
c₁ is complex real ext-real Element of REAL
z0 is complex real ext-real set
z0 * c₁ is complex real ext-real Element of REAL
c₁ is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
dom c₁ is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
Sum c₁ is complex real ext-real Element of REAL
K294(REAL,c₁,K623()) is complex real ext-real Element of REAL
np is complex real ext-real Element of REAL
<*np*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued increasing decreasing non-decreasing non-increasing FinSequence of REAL
c₁ ^ <*np*> is Relation-like NAT -defined REAL -valued Function-like non empty V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
dom (c₁ ^ <*np*>) is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
Sum (c₁ ^ <*np*>) is complex real ext-real Element of REAL
K294(REAL,(c₁ ^ <*np*>),K623()) is complex real ext-real Element of REAL
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁ ^ <*np*>) . z0 is complex real ext-real Element of REAL
c₁ . z0 is complex real ext-real Element of REAL
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₁ | z0 is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (c₁ | z0) is complex real ext-real Element of REAL
K294(REAL,(c₁ | z0),K623()) is complex real ext-real Element of REAL
z0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₁ | (z0 + 1) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (c₁ | (z0 + 1)) is complex real ext-real Element of REAL
K294(REAL,(c₁ | (z0 + 1)),K623()) is complex real ext-real Element of REAL
len c₁ is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₁ /. (z0 + 1) is complex real ext-real Element of REAL
<*(c₁ /. (z0 + 1))*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued increasing decreasing non-decreasing non-increasing FinSequence of REAL
(c₁ | z0) ^ <*(c₁ /. (z0 + 1))*> is Relation-like NAT -defined REAL -valued Function-like non empty V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(Sum (c₁ | z0)) + (c₁ /. (z0 + 1)) is complex real ext-real Element of REAL
c₁ . (z0 + 1) is complex real ext-real Element of REAL
len c₁ is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
len c₁ is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁ ^ <*np*>) . z0 is complex real ext-real Element of REAL
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
len c₁ is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(len c₁) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
len (c₁ ^ <*np*>) is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁ ^ <*np*>) . (len (c₁ ^ <*np*>)) is complex real ext-real Element of REAL
(c₁ ^ <*np*>) . ((len c₁) + 1) is complex real ext-real Element of REAL
c₁ . z0 is complex real ext-real Element of REAL
(c₁ . z0) + 0 is complex real ext-real Element of REAL
(c₁ . z0) + np is complex real ext-real Element of REAL
c₁ | (len c₁) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Seg ((len c₁) + 1) is non empty V24() V31((len c₁) + 1) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
Seg (len c₁) is V24() V31( len c₁) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
{((len c₁) + 1)} is non empty V19() V31(1) V56() V57() V58() V59() V60() V61() Element of K27(REAL)
(Seg (len c₁)) \/ {((len c₁) + 1)} is V56() V57() V58() V59() V60() V61() set
(dom c₁) \/ {((len c₁) + 1)} is V56() V57() V58() V59() V60() V61() set
c₁ | 0 is Relation-like NAT -defined REAL -valued RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Function-like one-to-one constant functional empty V24() V29() V31( {} ) FinSequence-like FinSubsequence-like FinSequence-membered complex real ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V54() V56() V57() V58() V59() V60() V61() V62() Function-yielding V87() FinSequence of REAL
Sum (c₁ | 0) is complex real ext-real Element of REAL
K294(REAL,(c₁ | 0),K623()) is complex real ext-real Element of REAL
(Sum c₁) + np is complex real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₁ . k is complex real ext-real Element of REAL
0 + ((c₁ ^ <*np*>) . z0) is complex real ext-real Element of REAL
(Sum c₁) + np is complex real ext-real Element of REAL
dom (<*> REAL) is epsilon-transitive epsilon-connected ordinal V56() V57() V58() V59() V60() V61() Element of K27(NAT)
c₁ is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(<*> REAL) . c₁ is Relation-like epsilon-transitive epsilon-connected ordinal natural Function-like V24() V29() complex real ext-real non negative V54() Element of REAL
c₁ is complex real ext-real Element of REAL
np is complex real ext-real Element of REAL
[**c₁,np**] is complex Element of the carrier of F_Complex
<i> is complex Element of COMPLEX
K286(REAL,0,1,0,1) is Relation-like {0,1} -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K27(K28({0,1},REAL))
{0,1} is V56() V57() V58() V59() V60() V61() set
K28({0,1},REAL) is complex-valued ext-real-valued real-valued set
K27(K28({0,1},REAL)) is set
np * <i> is complex set
c₁ + (np * <i>) is complex set
- [**c₁,np**] is complex Element of the carrier of F_Complex
- c₁ is complex real ext-real Element of REAL
- np is complex real ext-real Element of REAL
[**(- c₁),(- np)**] is complex Element of the carrier of F_Complex
(- np) * <i> is complex set
(- c₁) + ((- np) * <i>) is complex set
- (c₁ + (np * <i>)) is complex set
c₁ is complex real ext-real Element of REAL
np is complex real ext-real Element of REAL
[**c₁,np**] is complex Element of the carrier of F_Complex
<i> is complex Element of COMPLEX
K286(REAL,0,1,0,1) is Relation-like {0,1} -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K27(K28({0,1},REAL))
{0,1} is V56() V57() V58() V59() V60() V61() set
K28({0,1},REAL) is complex-valued ext-real-valued real-valued set
K27(K28({0,1},REAL)) is set
np * <i> is complex set
c₁ + (np * <i>) is complex set
z0 is complex real ext-real Element of REAL
k is complex real ext-real Element of REAL
[**z0,k**] is complex Element of the carrier of F_Complex
k * <i> is complex set
z0 + (k * <i>) is complex set
[**c₁,np**] - [**z0,k**] is complex Element of the carrier of F_Complex
- [**z0,k**] is complex Element of the carrier of F_Complex
[**c₁,np**] + (- [**z0,k**]) is complex Element of the carrier of F_Complex
the addF of F_Complex is Relation-like K28( the carrier of F_Complex, the carrier of F_Complex) -defined the carrier of F_Complex -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex))
K28( the carrier of F_Complex, the carrier of F_Complex) is set
K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex) is set
K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex)) is set
the addF of F_Complex . ([**c₁,np**],(- [**z0,k**])) is complex Element of the carrier of F_Complex
K593([**c₁,np**],(- [**z0,k**])) is complex Element of COMPLEX
c₁ - z0 is complex real ext-real Element of REAL
- z0 is complex real ext-real set
c₁ + (- z0) is complex real ext-real set
np - k is complex real ext-real Element of REAL
- k is complex real ext-real set
np + (- k) is complex real ext-real set
[**(c₁ - z0),(np - k)**] is complex Element of the carrier of F_Complex
(np - k) * <i> is complex set
(c₁ - z0) + ((np - k) * <i>) is complex set
- z0 is complex real ext-real Element of REAL
- k is complex real ext-real Element of REAL
[**(- z0),(- k)**] is complex Element of the carrier of F_Complex
(- k) * <i> is complex set
(- z0) + ((- k) * <i>) is complex set
[**c₁,np**] + [**(- z0),(- k)**] is complex Element of the carrier of F_Complex
the addF of F_Complex . ([**c₁,np**],[**(- z0),(- k)**]) is complex Element of the carrier of F_Complex
K593([**c₁,np**],[**(- z0),(- k)**]) is complex Element of COMPLEX
c₁ is complex Element of the carrier of F_Complex
|.c₁.| is complex real ext-real Element of REAL
np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(power F_Complex) . (c₁,np) is complex Element of the carrier of F_Complex
|.((power F_Complex) . (c₁,np)).| is complex real ext-real Element of REAL
|.c₁.| to_power np is complex real ext-real Element of REAL
np + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(power F_Complex) . (c₁,(np + 1)) is complex Element of the carrier of F_Complex
|.((power F_Complex) . (c₁,(np + 1))).| is complex real ext-real Element of REAL
|.c₁.| to_power (np + 1) is complex real ext-real Element of REAL
((power F_Complex) . (c₁,np)) * c₁ is complex Element of the carrier of F_Complex
the multF of F_Complex is Relation-like K28( the carrier of F_Complex, the carrier of F_Complex) -defined the carrier of F_Complex -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex))
K28( the carrier of F_Complex, the carrier of F_Complex) is set
K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex) is set
K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex)) is set
the multF of F_Complex . (((power F_Complex) . (c₁,np)),c₁) is complex Element of the carrier of F_Complex
K595(((power F_Complex) . (c₁,np)),c₁) is complex Element of COMPLEX
|.(((power F_Complex) . (c₁,np)) * c₁).| is complex real ext-real Element of REAL
(|.c₁.| to_power np) * |.c₁.| is complex real ext-real Element of REAL
|.c₁.| to_power 1 is complex real ext-real Element of REAL
(|.c₁.| to_power np) * (|.c₁.| to_power 1) is complex real ext-real Element of REAL
(power F_Complex) . (c₁,0) is complex Element of the carrier of F_Complex
|.((power F_Complex) . (c₁,0)).| is complex real ext-real Element of REAL
|.c₁.| to_power 0 is complex real ext-real Element of REAL
c₁ is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
len c₁ is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom c₁ is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
np is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom np is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np /. z0 is complex real ext-real Element of REAL
c₁ /. z0 is complex Element of the carrier of F_Complex
|.(c₁ /. z0).| is complex real ext-real Element of REAL
np is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
z0 is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
np /. k is complex real ext-real Element of REAL
c₁ /. k is complex Element of the carrier of F_Complex
|.(c₁ /. k).| is complex real ext-real Element of REAL
z0 /. k is complex real ext-real Element of REAL
dom np is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
dom z0 is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
<*> the carrier of F_Complex is Relation-like NAT -defined the carrier of F_Complex -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Function-like one-to-one constant functional empty V24() V29() V31( {} ) FinSequence-like FinSubsequence-like FinSequence-membered complex real ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V54() V56() V57() V58() V59() V60() V61() V62() Function-yielding V87() FinSequence of the carrier of F_Complex
((<*> the carrier of F_Complex)) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len ((<*> the carrier of F_Complex)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
len (<*> the carrier of F_Complex) is epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Function-like functional empty V24() V29() V31( {} ) FinSequence-membered complex real ext-real non positive non negative V54() V55() V56() V57() V58() V59() V60() V61() V62() Element of NAT
c₁ is complex Element of the carrier of F_Complex
<*c₁*> is Relation-like NAT -defined the carrier of F_Complex -valued Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
(<*c₁*>) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
|.c₁.| is complex real ext-real Element of REAL
<*|.c₁.|*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued increasing decreasing non-decreasing non-increasing FinSequence of REAL
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
Seg (0 + 1) is non empty V24() V31(0 + 1) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
dom <*c₁*> is non empty V19() V31(1) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
len (<*c₁*>) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
len <*c₁*> is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom (<*c₁*>) is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
(<*c₁*>) . np is complex real ext-real Element of REAL
(<*c₁*>) /. 1 is complex real ext-real Element of REAL
<*c₁*> /. 1 is complex Element of the carrier of F_Complex
|.(<*c₁*> /. 1).| is complex real ext-real Element of REAL
<*|.c₁.|*> . np is complex real ext-real Element of REAL
len <*|.c₁.|*> is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₁ is complex Element of the carrier of F_Complex
np is complex Element of the carrier of F_Complex
<*c₁,np*> is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like M13( the carrier of F_Complex,K250(2, the carrier of F_Complex))
K250(2, the carrier of F_Complex) is M12( the carrier of F_Complex)
(<*c₁,np*>) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
|.c₁.| is complex real ext-real Element of REAL
|.np.| is complex real ext-real Element of REAL
<*|.c₁.|,|.np.|*> is Relation-like NAT -defined REAL -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued M13( REAL ,K250(2,REAL))
K250(2,REAL) is M12( REAL )
len (<*c₁,np*>) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
len <*c₁,np*> is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom (<*c₁,np*>) is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
dom <*c₁,np*> is V31(2) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
(<*c₁,np*>) . 1 is complex real ext-real Element of REAL
(<*c₁,np*>) /. 1 is complex real ext-real Element of REAL
<*c₁,np*> /. 1 is complex Element of the carrier of F_Complex
|.(<*c₁,np*> /. 1).| is complex real ext-real Element of REAL
(<*c₁,np*>) . z0 is complex real ext-real Element of REAL
<*|.c₁.|,|.np.|*> . z0 is complex real ext-real Element of REAL
dom <*c₁,np*> is V31(2) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
(<*c₁,np*>) . 2 is complex real ext-real Element of REAL
(<*c₁,np*>) /. 2 is complex real ext-real Element of REAL
<*c₁,np*> /. 2 is complex Element of the carrier of F_Complex
|.(<*c₁,np*> /. 2).| is complex real ext-real Element of REAL
(<*c₁,np*>) . z0 is complex real ext-real Element of REAL
<*|.c₁.|,|.np.|*> . z0 is complex real ext-real Element of REAL
len <*|.c₁.|,|.np.|*> is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₁ is complex Element of the carrier of F_Complex
np is complex Element of the carrier of F_Complex
z0 is complex Element of the carrier of F_Complex
<*c₁,np,z0*> is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
(<*c₁,np,z0*>) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
|.c₁.| is complex real ext-real Element of REAL
|.np.| is complex real ext-real Element of REAL
|.z0.| is complex real ext-real Element of REAL
<*|.c₁.|,|.np.|,|.z0.|*> is Relation-like NAT -defined REAL -valued Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len (<*c₁,np,z0*>) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
len <*c₁,np,z0*> is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom (<*c₁,np,z0*>) is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
dom <*c₁,np,z0*> is V31(3) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
(<*c₁,np,z0*>) . 1 is complex real ext-real Element of REAL
(<*c₁,np,z0*>) /. 1 is complex real ext-real Element of REAL
<*c₁,np,z0*> /. 1 is complex Element of the carrier of F_Complex
|.(<*c₁,np,z0*> /. 1).| is complex real ext-real Element of REAL
(<*c₁,np,z0*>) . k is complex real ext-real Element of REAL
<*|.c₁.|,|.np.|,|.z0.|*> . k is complex real ext-real Element of REAL
dom <*c₁,np,z0*> is V31(3) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
(<*c₁,np,z0*>) . 2 is complex real ext-real Element of REAL
(<*c₁,np,z0*>) /. 2 is complex real ext-real Element of REAL
<*c₁,np,z0*> /. 2 is complex Element of the carrier of F_Complex
|.(<*c₁,np,z0*> /. 2).| is complex real ext-real Element of REAL
(<*c₁,np,z0*>) . k is complex real ext-real Element of REAL
<*|.c₁.|,|.np.|,|.z0.|*> . k is complex real ext-real Element of REAL
dom <*c₁,np,z0*> is V31(3) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
(<*c₁,np,z0*>) . 3 is complex real ext-real Element of REAL
(<*c₁,np,z0*>) /. 3 is complex real ext-real Element of REAL
<*c₁,np,z0*> /. 3 is complex Element of the carrier of F_Complex
|.(<*c₁,np,z0*> /. 3).| is complex real ext-real Element of REAL
(<*c₁,np,z0*>) . k is complex real ext-real Element of REAL
<*|.c₁.|,|.np.|,|.z0.|*> . k is complex real ext-real Element of REAL
len <*|.c₁.|,|.np.|,|.z0.|*> is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₁ is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
np is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
c₁ ^ np is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
((c₁ ^ np)) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(c₁) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(np) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(c₁) ^ (np) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
dom ((c₁ ^ np)) is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
len ((c₁ ^ np)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
Seg (len ((c₁ ^ np))) is V24() V31( len ((c₁ ^ np))) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
len (c₁) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
len c₁ is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
len (c₁ ^ np) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom (c₁ ^ np) is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
dom c₁ is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
(c₁ ^ np) /. z0 is complex Element of the carrier of F_Complex
(c₁ ^ np) . z0 is set
c₁ . z0 is set
c₁ /. z0 is complex Element of the carrier of F_Complex
dom (c₁) is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
((c₁ ^ np)) . z0 is complex real ext-real Element of REAL
((c₁ ^ np)) /. z0 is complex real ext-real Element of REAL
|.((c₁ ^ np) /. z0).| is complex real ext-real Element of REAL
(c₁) /. z0 is complex real ext-real Element of REAL
(c₁) . z0 is complex real ext-real Element of REAL
((c₁) ^ (np)) . z0 is complex real ext-real Element of REAL
dom c₁ is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
0 + (len c₁) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
z0 - (len c₁) is complex real ext-real V54() Element of REAL
- (len c₁) is complex real ext-real non positive V54() set
z0 + (- (len c₁)) is complex real ext-real V54() set
(len c₁) + (z0 - (len c₁)) is complex real ext-real V54() Element of REAL
z0 -' (len c₁) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(len c₁) + (z0 -' (len c₁)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(len np) + (len c₁) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
1 + (len c₁) is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
Seg (len np) is V24() V31( len np) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
dom np is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
len (np) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom (np) is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
(c₁ ^ np) /. z0 is complex Element of the carrier of F_Complex
(c₁ ^ np) . z0 is set
np . (z0 -' (len c₁)) is set
np /. (z0 -' (len c₁)) is complex Element of the carrier of F_Complex
((c₁ ^ np)) . z0 is complex real ext-real Element of REAL
((c₁ ^ np)) /. z0 is complex real ext-real Element of REAL
|.((c₁ ^ np) /. z0).| is complex real ext-real Element of REAL
(np) /. (z0 -' (len c₁)) is complex real ext-real Element of REAL
(np) . (z0 -' (len c₁)) is complex real ext-real Element of REAL
((c₁) ^ (np)) . z0 is complex real ext-real Element of REAL
dom c₁ is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(len c₁) + (len np) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
len (np) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(len c₁) + (len (np)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(len (c₁)) + (len (np)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
len ((c₁) ^ (np)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₁ is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
(c₁) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
np is complex Element of the carrier of F_Complex
<*np*> is Relation-like NAT -defined the carrier of F_Complex -valued Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
c₁ ^ <*np*> is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
((c₁ ^ <*np*>)) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
|.np.| is complex real ext-real Element of REAL
<*|.np.|*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued increasing decreasing non-decreasing non-increasing FinSequence of REAL
(c₁) ^ <*|.np.|*> is Relation-like NAT -defined REAL -valued Function-like non empty V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
<*np*> ^ c₁ is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
((<*np*> ^ c₁)) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
<*|.np.|*> ^ (c₁) is Relation-like NAT -defined REAL -valued Function-like non empty V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(<*np*>) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(c₁) ^ (<*np*>) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(<*np*>) ^ (c₁) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
np is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
Sum np is complex Element of the carrier of F_Complex
|.(Sum np).| is complex real ext-real Element of REAL
(np) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (np) is complex real ext-real Element of REAL
K294(REAL,(np),K623()) is complex real ext-real Element of REAL
z0 is complex Element of the carrier of F_Complex
|.z0.| is complex real ext-real Element of REAL
|.(Sum np).| + |.z0.| is complex real ext-real Element of REAL
(Sum (np)) + |.z0.| is complex real ext-real Element of REAL
<*z0*> is Relation-like NAT -defined the carrier of F_Complex -valued Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
np ^ <*z0*> is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
Sum (np ^ <*z0*>) is complex Element of the carrier of F_Complex
(Sum np) + z0 is complex Element of the carrier of F_Complex
the addF of F_Complex is Relation-like K28( the carrier of F_Complex, the carrier of F_Complex) -defined the carrier of F_Complex -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex))
K28( the carrier of F_Complex, the carrier of F_Complex) is set
K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex) is set
K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex)) is set
the addF of F_Complex . ((Sum np),z0) is complex Element of the carrier of F_Complex
K593((Sum np),z0) is complex Element of COMPLEX
|.(Sum (np ^ <*z0*>)).| is complex real ext-real Element of REAL
<*|.z0.|*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued increasing decreasing non-decreasing non-increasing FinSequence of REAL
Sum <*|.z0.|*> is complex real ext-real Element of REAL
K294(REAL,<*|.z0.|*>,K623()) is complex real ext-real Element of REAL
(Sum (np)) + (Sum <*|.z0.|*>) is complex real ext-real Element of REAL
(<*z0*>) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (<*z0*>) is complex real ext-real Element of REAL
K294(REAL,(<*z0*>),K623()) is complex real ext-real Element of REAL
(Sum (np)) + (Sum (<*z0*>)) is complex real ext-real Element of REAL
(np) ^ (<*z0*>) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum ((np) ^ (<*z0*>)) is complex real ext-real Element of REAL
K294(REAL,((np) ^ (<*z0*>)),K623()) is complex real ext-real Element of REAL
((np ^ <*z0*>)) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum ((np ^ <*z0*>)) is complex real ext-real Element of REAL
K294(REAL,((np ^ <*z0*>)),K623()) is complex real ext-real Element of REAL
Sum (<*> the carrier of F_Complex) is complex Element of the carrier of F_Complex
|.(Sum (<*> the carrier of F_Complex)).| is complex real ext-real Element of REAL
Sum ((<*> the carrier of F_Complex)) is complex real ext-real Element of REAL
K294(REAL,((<*> the carrier of F_Complex)),K623()) is complex real ext-real Element of REAL
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable Abelian add-associative right_zeroed commutative right-distributive left-distributive right_unital distributive V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
Polynom-Ring c₁ is non empty left_add-cancelable right_add-cancelable right_complementable strict Abelian add-associative right_zeroed commutative right-distributive left-distributive distributive V174() V175() V176() V177() doubleLoopStr
power (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁),NAT) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)))
the carrier of (Polynom-Ring c₁) is non empty set
K28( the carrier of (Polynom-Ring c₁),NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)) is V24() set
K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁))) is V24() set
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(power (Polynom-Ring c₁)) . (np,z0) is set
k is Element of the carrier of (Polynom-Ring c₁)
(power (Polynom-Ring c₁)) . (k,z0) is Element of the carrier of (Polynom-Ring c₁)
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable Abelian add-associative right_zeroed commutative right-distributive left-distributive right_unital distributive V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,np,z0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
Polynom-Ring c₁ is non empty left_add-cancelable right_add-cancelable right_complementable strict Abelian add-associative right_zeroed commutative right-distributive left-distributive distributive V174() V175() V176() V177() doubleLoopStr
power (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁),NAT) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)))
the carrier of (Polynom-Ring c₁) is non empty set
K28( the carrier of (Polynom-Ring c₁),NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)) is V24() set
K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁))) is V24() set
(power (Polynom-Ring c₁)) . (np,z0) is set
k is Element of the carrier of (Polynom-Ring c₁)
(power (Polynom-Ring c₁)) . (k,z0) is Element of the carrier of (Polynom-Ring c₁)
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable Abelian add-associative right_zeroed unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
1_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
1. c₁ is Element of the carrier of c₁
the OneF of c₁ is Element of the carrier of c₁
(0_. c₁) +* (0,(1. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,np,0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
Polynom-Ring c₁ is non empty left_add-cancelable right_add-cancelable right_complementable strict Abelian add-associative right_zeroed unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
power (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁),NAT) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)))
the carrier of (Polynom-Ring c₁) is non empty set
K28( the carrier of (Polynom-Ring c₁),NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)) is V24() set
K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁))) is V24() set
(power (Polynom-Ring c₁)) . (np,0) is set
z0 is Element of the carrier of (Polynom-Ring c₁)
(power (Polynom-Ring c₁)) . (z0,0) is Element of the carrier of (Polynom-Ring c₁)
1_ (Polynom-Ring c₁) is Element of the carrier of (Polynom-Ring c₁)
1. (Polynom-Ring c₁) is Element of the carrier of (Polynom-Ring c₁)
the OneF of (Polynom-Ring c₁) is Element of the carrier of (Polynom-Ring c₁)
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable Abelian add-associative right_zeroed unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,np,1) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
Polynom-Ring c₁ is non empty left_add-cancelable right_add-cancelable right_complementable strict Abelian add-associative right_zeroed unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
power (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁),NAT) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)))
the carrier of (Polynom-Ring c₁) is non empty set
K28( the carrier of (Polynom-Ring c₁),NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)) is V24() set
K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁))) is V24() set
(power (Polynom-Ring c₁)) . (np,1) is set
z0 is Element of the carrier of (Polynom-Ring c₁)
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(power (Polynom-Ring c₁)) . (z0,(0 + 1)) is Element of the carrier of (Polynom-Ring c₁)
(power (Polynom-Ring c₁)) . (z0,0) is Element of the carrier of (Polynom-Ring c₁)
((power (Polynom-Ring c₁)) . (z0,0)) * z0 is Element of the carrier of (Polynom-Ring c₁)
the multF of (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁)))
K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)) is set
K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁)) is set
K27(K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁))) is set
the multF of (Polynom-Ring c₁) . (((power (Polynom-Ring c₁)) . (z0,0)),z0) is Element of the carrier of (Polynom-Ring c₁)
1_ (Polynom-Ring c₁) is Element of the carrier of (Polynom-Ring c₁)
1. (Polynom-Ring c₁) is Element of the carrier of (Polynom-Ring c₁)
the OneF of (Polynom-Ring c₁) is Element of the carrier of (Polynom-Ring c₁)
(1_ (Polynom-Ring c₁)) * z0 is Element of the carrier of (Polynom-Ring c₁)
the multF of (Polynom-Ring c₁) . ((1_ (Polynom-Ring c₁)),z0) is Element of the carrier of (Polynom-Ring c₁)
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable Abelian add-associative right_zeroed unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,np,2) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
Polynom-Ring c₁ is non empty left_add-cancelable right_add-cancelable right_complementable strict Abelian add-associative right_zeroed unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
power (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁),NAT) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)))
the carrier of (Polynom-Ring c₁) is non empty set
K28( the carrier of (Polynom-Ring c₁),NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)) is V24() set
K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁))) is V24() set
(power (Polynom-Ring c₁)) . (np,2) is set
np *' np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
z0 is Element of the carrier of (Polynom-Ring c₁)
1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(power (Polynom-Ring c₁)) . (z0,(1 + 1)) is Element of the carrier of (Polynom-Ring c₁)
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(power (Polynom-Ring c₁)) . (z0,(0 + 1)) is Element of the carrier of (Polynom-Ring c₁)
((power (Polynom-Ring c₁)) . (z0,(0 + 1))) * z0 is Element of the carrier of (Polynom-Ring c₁)
the multF of (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁)))
K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)) is set
K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁)) is set
K27(K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁))) is set
the multF of (Polynom-Ring c₁) . (((power (Polynom-Ring c₁)) . (z0,(0 + 1))),z0) is Element of the carrier of (Polynom-Ring c₁)
(power (Polynom-Ring c₁)) . (z0,0) is Element of the carrier of (Polynom-Ring c₁)
((power (Polynom-Ring c₁)) . (z0,0)) * z0 is Element of the carrier of (Polynom-Ring c₁)
the multF of (Polynom-Ring c₁) . (((power (Polynom-Ring c₁)) . (z0,0)),z0) is Element of the carrier of (Polynom-Ring c₁)
(((power (Polynom-Ring c₁)) . (z0,0)) * z0) * z0 is Element of the carrier of (Polynom-Ring c₁)
the multF of (Polynom-Ring c₁) . ((((power (Polynom-Ring c₁)) . (z0,0)) * z0),z0) is Element of the carrier of (Polynom-Ring c₁)
1_ (Polynom-Ring c₁) is Element of the carrier of (Polynom-Ring c₁)
1. (Polynom-Ring c₁) is Element of the carrier of (Polynom-Ring c₁)
the OneF of (Polynom-Ring c₁) is Element of the carrier of (Polynom-Ring c₁)
(1_ (Polynom-Ring c₁)) * z0 is Element of the carrier of (Polynom-Ring c₁)
the multF of (Polynom-Ring c₁) . ((1_ (Polynom-Ring c₁)),z0) is Element of the carrier of (Polynom-Ring c₁)
((1_ (Polynom-Ring c₁)) * z0) * z0 is Element of the carrier of (Polynom-Ring c₁)
the multF of (Polynom-Ring c₁) . (((1_ (Polynom-Ring c₁)) * z0),z0) is Element of the carrier of (Polynom-Ring c₁)
z0 * z0 is Element of the carrier of (Polynom-Ring c₁)
the multF of (Polynom-Ring c₁) . (z0,z0) is Element of the carrier of (Polynom-Ring c₁)
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable Abelian add-associative right_zeroed unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,np,3) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
Polynom-Ring c₁ is non empty left_add-cancelable right_add-cancelable right_complementable strict Abelian add-associative right_zeroed unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
power (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁),NAT) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)))
the carrier of (Polynom-Ring c₁) is non empty set
K28( the carrier of (Polynom-Ring c₁),NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)) is V24() set
K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁))) is V24() set
(power (Polynom-Ring c₁)) . (np,3) is set
np *' np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(np *' np) *' np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
z0 is Element of the carrier of (Polynom-Ring c₁)
z0 * z0 is Element of the carrier of (Polynom-Ring c₁)
the multF of (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁)))
K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)) is set
K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁)) is set
K27(K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁))) is set
the multF of (Polynom-Ring c₁) . (z0,z0) is Element of the carrier of (Polynom-Ring c₁)
2 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(power (Polynom-Ring c₁)) . (z0,(2 + 1)) is Element of the carrier of (Polynom-Ring c₁)
1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(power (Polynom-Ring c₁)) . (z0,(1 + 1)) is Element of the carrier of (Polynom-Ring c₁)
((power (Polynom-Ring c₁)) . (z0,(1 + 1))) * z0 is Element of the carrier of (Polynom-Ring c₁)
the multF of (Polynom-Ring c₁) . (((power (Polynom-Ring c₁)) . (z0,(1 + 1))),z0) is Element of the carrier of (Polynom-Ring c₁)
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(power (Polynom-Ring c₁)) . (z0,(0 + 1)) is Element of the carrier of (Polynom-Ring c₁)
((power (Polynom-Ring c₁)) . (z0,(0 + 1))) * z0 is Element of the carrier of (Polynom-Ring c₁)
the multF of (Polynom-Ring c₁) . (((power (Polynom-Ring c₁)) . (z0,(0 + 1))),z0) is Element of the carrier of (Polynom-Ring c₁)
(((power (Polynom-Ring c₁)) . (z0,(0 + 1))) * z0) * z0 is Element of the carrier of (Polynom-Ring c₁)
the multF of (Polynom-Ring c₁) . ((((power (Polynom-Ring c₁)) . (z0,(0 + 1))) * z0),z0) is Element of the carrier of (Polynom-Ring c₁)
(power (Polynom-Ring c₁)) . (z0,0) is Element of the carrier of (Polynom-Ring c₁)
((power (Polynom-Ring c₁)) . (z0,0)) * z0 is Element of the carrier of (Polynom-Ring c₁)
the multF of (Polynom-Ring c₁) . (((power (Polynom-Ring c₁)) . (z0,0)),z0) is Element of the carrier of (Polynom-Ring c₁)
(((power (Polynom-Ring c₁)) . (z0,0)) * z0) * z0 is Element of the carrier of (Polynom-Ring c₁)
the multF of (Polynom-Ring c₁) . ((((power (Polynom-Ring c₁)) . (z0,0)) * z0),z0) is Element of the carrier of (Polynom-Ring c₁)
((((power (Polynom-Ring c₁)) . (z0,0)) * z0) * z0) * z0 is Element of the carrier of (Polynom-Ring c₁)
the multF of (Polynom-Ring c₁) . (((((power (Polynom-Ring c₁)) . (z0,0)) * z0) * z0),z0) is Element of the carrier of (Polynom-Ring c₁)
1_ (Polynom-Ring c₁) is Element of the carrier of (Polynom-Ring c₁)
1. (Polynom-Ring c₁) is Element of the carrier of (Polynom-Ring c₁)
the OneF of (Polynom-Ring c₁) is Element of the carrier of (Polynom-Ring c₁)
(1_ (Polynom-Ring c₁)) * z0 is Element of the carrier of (Polynom-Ring c₁)
the multF of (Polynom-Ring c₁) . ((1_ (Polynom-Ring c₁)),z0) is Element of the carrier of (Polynom-Ring c₁)
((1_ (Polynom-Ring c₁)) * z0) * z0 is Element of the carrier of (Polynom-Ring c₁)
the multF of (Polynom-Ring c₁) . (((1_ (Polynom-Ring c₁)) * z0),z0) is Element of the carrier of (Polynom-Ring c₁)
(((1_ (Polynom-Ring c₁)) * z0) * z0) * z0 is Element of the carrier of (Polynom-Ring c₁)
the multF of (Polynom-Ring c₁) . ((((1_ (Polynom-Ring c₁)) * z0) * z0),z0) is Element of the carrier of (Polynom-Ring c₁)
(z0 * z0) * z0 is Element of the carrier of (Polynom-Ring c₁)
the multF of (Polynom-Ring c₁) . ((z0 * z0),z0) is Element of the carrier of (Polynom-Ring c₁)
k is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
k *' np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable Abelian add-associative right_zeroed unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
z0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,np,(z0 + 1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
Polynom-Ring c₁ is non empty left_add-cancelable right_add-cancelable right_complementable strict Abelian add-associative right_zeroed unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
power (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁),NAT) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)))
the carrier of (Polynom-Ring c₁) is non empty set
K28( the carrier of (Polynom-Ring c₁),NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)) is V24() set
K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁))) is V24() set
(power (Polynom-Ring c₁)) . (np,(z0 + 1)) is set
(c₁,np,z0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . (np,z0) is set
(c₁,np,z0) *' np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
k is Element of the carrier of (Polynom-Ring c₁)
(power (Polynom-Ring c₁)) . (k,z0) is Element of the carrier of (Polynom-Ring c₁)
((power (Polynom-Ring c₁)) . (k,z0)) * k is Element of the carrier of (Polynom-Ring c₁)
the multF of (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁)))
K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)) is set
K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁)) is set
K27(K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁))) is set
the multF of (Polynom-Ring c₁) . (((power (Polynom-Ring c₁)) . (k,z0)),k) is Element of the carrier of (Polynom-Ring c₁)
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable Abelian add-associative right_zeroed unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,(0_. c₁),(np + 1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
Polynom-Ring c₁ is non empty left_add-cancelable right_add-cancelable right_complementable strict Abelian add-associative right_zeroed unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
power (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁),NAT) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)))
the carrier of (Polynom-Ring c₁) is non empty set
K28( the carrier of (Polynom-Ring c₁),NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)) is V24() set
K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁))) is V24() set
(power (Polynom-Ring c₁)) . ((0_. c₁),(np + 1)) is set
(c₁,(0_. c₁),np) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . ((0_. c₁),np) is set
(c₁,(0_. c₁),np) *' (0_. c₁) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable Abelian add-associative right_zeroed unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
1_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
1. c₁ is Element of the carrier of c₁
the OneF of c₁ is Element of the carrier of c₁
(0_. c₁) +* (0,(1. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,(1_. c₁),np) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
Polynom-Ring c₁ is non empty left_add-cancelable right_add-cancelable right_complementable strict Abelian add-associative right_zeroed unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
power (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁),NAT) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)))
the carrier of (Polynom-Ring c₁) is non empty set
K28( the carrier of (Polynom-Ring c₁),NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)) is V24() set
K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁))) is V24() set
(power (Polynom-Ring c₁)) . ((1_. c₁),np) is set
np + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,(1_. c₁),(np + 1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . ((1_. c₁),(np + 1)) is set
(1_. c₁) *' (1_. c₁) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,(1_. c₁),0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . ((1_. c₁),0) is set
c₁ is non empty non degenerated V94() left_add-cancelable right_add-cancelable right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital domRing-like V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty V19() set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
power c₁ is Relation-like K28( the carrier of c₁,NAT) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁))
K28( the carrier of c₁,NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of c₁,NAT), the carrier of c₁) is V24() set
K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁)) is V24() set
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
z0 is Element of the carrier of c₁
eval (np,z0) is Element of the carrier of c₁
k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,np,k) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
Polynom-Ring c₁ is non empty left_add-cancelable right_add-cancelable right_complementable strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
power (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁),NAT) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)))
the carrier of (Polynom-Ring c₁) is non empty set
K28( the carrier of (Polynom-Ring c₁),NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)) is V24() set
K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁))) is V24() set
(power (Polynom-Ring c₁)) . (np,k) is set
eval ((c₁,np,k),z0) is Element of the carrier of c₁
(power c₁) . ((eval (np,z0)),k) is Element of the carrier of c₁
k + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,np,(k + 1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . (np,(k + 1)) is set
eval ((c₁,np,(k + 1)),z0) is Element of the carrier of c₁
(c₁,np,k) *' np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
eval (((c₁,np,k) *' np),z0) is Element of the carrier of c₁
((power c₁) . ((eval (np,z0)),k)) * (eval (np,z0)) is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . (((power c₁) . ((eval (np,z0)),k)),(eval (np,z0))) is Element of the carrier of c₁
(power c₁) . ((eval (np,z0)),(k + 1)) is Element of the carrier of c₁
(c₁,np,0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . (np,0) is set
eval ((c₁,np,0),z0) is Element of the carrier of c₁
1_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
1. c₁ is non zero Element of the carrier of c₁
the OneF of c₁ is Element of the carrier of c₁
(0_. c₁) +* (0,(1. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
eval ((1_. c₁),z0) is Element of the carrier of c₁
1_ c₁ is Element of the carrier of c₁
(power c₁) . ((eval (np,z0)),0) is Element of the carrier of c₁
c₁ is non empty ZeroStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(len np) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . ((len np) -' 1) is Element of the carrier of c₁
((len np) -' 1) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
z0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₁ is non empty non degenerated V94() left_add-cancelable right_add-cancelable right_complementable Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital domRing-like V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty V19() set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(0 + 1) - 1 is complex real ext-real V54() Element of REAL
- 1 is non empty complex real ext-real non positive negative V54() set
(0 + 1) + (- 1) is complex real ext-real V54() set
(len np) - 1 is complex real ext-real V54() Element of REAL
(len np) + (- 1) is complex real ext-real V54() set
(len np) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . ((len np) -' 1) is Element of the carrier of c₁
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,np,z0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
Polynom-Ring c₁ is non empty left_add-cancelable right_add-cancelable right_complementable strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
power (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁),NAT) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)))
the carrier of (Polynom-Ring c₁) is non empty set
K28( the carrier of (Polynom-Ring c₁),NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)) is V24() set
K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁))) is V24() set
(power (Polynom-Ring c₁)) . (np,z0) is set
len (c₁,np,z0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
z0 * (len np) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(z0 * (len np)) - z0 is complex real ext-real V54() Element of REAL
- z0 is complex real ext-real non positive V54() set
(z0 * (len np)) + (- z0) is complex real ext-real V54() set
((z0 * (len np)) - z0) + 1 is complex real ext-real V54() Element of REAL
z0 * ((len np) -' 1) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(z0 * ((len np) -' 1)) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(len (c₁,np,z0)) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,np,z0) . ((len (c₁,np,z0)) -' 1) is Element of the carrier of c₁
((c₁,np,z0) . ((len (c₁,np,z0)) -' 1)) * (np . ((len np) -' 1)) is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . (((c₁,np,z0) . ((len (c₁,np,z0)) -' 1)),(np . ((len np) -' 1))) is Element of the carrier of c₁
z0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,np,(z0 + 1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . (np,(z0 + 1)) is set
len (c₁,np,(z0 + 1)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,np,z0) *' np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len ((c₁,np,z0) *' np) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(((z0 * (len np)) - z0) + 1) + (len np) is complex real ext-real V54() Element of REAL
((((z0 * (len np)) - z0) + 1) + (len np)) - 1 is complex real ext-real V54() Element of REAL
((((z0 * (len np)) - z0) + 1) + (len np)) + (- 1) is complex real ext-real V54() set
(z0 + 1) * (len np) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
((z0 + 1) * (len np)) - (z0 + 1) is complex real ext-real V54() Element of REAL
- (z0 + 1) is non empty complex real ext-real non positive negative V54() set
((z0 + 1) * (len np)) + (- (z0 + 1)) is complex real ext-real V54() set
(((z0 + 1) * (len np)) - (z0 + 1)) + 1 is complex real ext-real V54() Element of REAL
(c₁,np,0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . (np,0) is set
len (c₁,np,0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
1_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
1. c₁ is non zero Element of the carrier of c₁
the OneF of c₁ is Element of the carrier of c₁
(0_. c₁) +* (0,(1. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
len (1_. c₁) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
0 * (len np) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(0 * (len np)) - 0 is complex real ext-real V54() Element of REAL
- 0 is complex real ext-real non positive V54() set
(0 * (len np)) + (- 0) is complex real ext-real V54() set
((0 * (len np)) - 0) + 1 is complex real ext-real V54() Element of REAL
c₁ is non empty multMagma
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
z0 is Element of the carrier of c₁
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
k is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
k1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k . k1 is Element of the carrier of c₁
np . k1 is Element of the carrier of c₁
z0 * (np . k1) is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . (z0,(np . k1)) is Element of the carrier of c₁
k is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
k1 is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
sq is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k . sq is Element of the carrier of c₁
np . sq is Element of the carrier of c₁
z0 * (np . sq) is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . (z0,(np . sq)) is Element of the carrier of c₁
k1 . sq is Element of the carrier of c₁
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable add-associative right_zeroed right-distributive V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
z0 is Element of the carrier of c₁
(c₁,np,z0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
k1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
(c₁,np,z0) . k1 is set
sq is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . sq is Element of the carrier of c₁
z0 * (np . sq) is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . (z0,(np . sq)) is Element of the carrier of c₁
z0 * (0. c₁) is Element of the carrier of c₁
the multF of c₁ . (z0,(0. c₁)) is Element of the carrier of c₁
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable add-associative right_zeroed right-distributive left-distributive distributive V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,np,(0. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len (c₁,np,(0. c₁)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
(c₁,np,(0. c₁)) . z0 is set
k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . k is Element of the carrier of c₁
(0. c₁) * (np . k) is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . ((0. c₁),(np . k)) is Element of the carrier of c₁
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable almost_left_invertible add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital domRing-like V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
z0 is Element of the carrier of c₁
(c₁,np,z0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len (c₁,np,z0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
k1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
np . k1 is set
(c₁,np,z0) . k1 is set
sq is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . sq is Element of the carrier of c₁
z0 * (np . sq) is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . (z0,(np . sq)) is Element of the carrier of c₁
k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
(c₁,np,z0) . k is set
k1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . k1 is Element of the carrier of c₁
z0 * (np . k1) is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . (z0,(np . k1)) is Element of the carrier of c₁
z0 * (0. c₁) is Element of the carrier of c₁
the multF of c₁ . (z0,(0. c₁)) is Element of the carrier of c₁
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable add-associative right_zeroed left-distributive V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
(c₁,np,(0. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(0_. c₁) . z0 is Element of the carrier of c₁
np . z0 is Element of the carrier of c₁
(0. c₁) * (np . z0) is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . ((0. c₁),(np . z0)) is Element of the carrier of c₁
c₁ is non empty unital right_unital well-unital left_unital multLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
1. c₁ is Element of the carrier of c₁
the OneF of c₁ is Element of the carrier of c₁
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
(c₁,np,(1. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . z0 is Element of the carrier of c₁
(1. c₁) * (np . z0) is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . ((1. c₁),(np . z0)) is Element of the carrier of c₁
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable add-associative right_zeroed right-distributive V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
np is Element of the carrier of c₁
(c₁,(0_. c₁),np) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(0_. c₁) . z0 is Element of the carrier of c₁
np * (0. c₁) is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . (np,(0. c₁)) is Element of the carrier of c₁
np * ((0_. c₁) . z0) is Element of the carrier of c₁
the multF of c₁ . (np,((0_. c₁) . z0)) is Element of the carrier of c₁
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable add-associative right_zeroed unital right-distributive right_unital well-unital left_unital V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
1_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
1. c₁ is Element of the carrier of c₁
the OneF of c₁ is Element of the carrier of c₁
(0_. c₁) +* (0,(1. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
np is Element of the carrier of c₁
(c₁,(1_. c₁),np) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
<%np%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
<%np%> . z0 is Element of the carrier of c₁
np * (1. c₁) is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . (np,(1. c₁)) is Element of the carrier of c₁
(1_. c₁) . z0 is Element of the carrier of c₁
np * ((1_. c₁) . z0) is Element of the carrier of c₁
the multF of c₁ . (np,((1_. c₁) . z0)) is Element of the carrier of c₁
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
len <%np%> is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
<%np%> . z0 is Element of the carrier of c₁
np * (0. c₁) is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . (np,(0. c₁)) is Element of the carrier of c₁
(1_. c₁) . z0 is Element of the carrier of c₁
np * ((1_. c₁) . z0) is Element of the carrier of c₁
the multF of c₁ . (np,((1_. c₁) . z0)) is Element of the carrier of c₁
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable almost_left_invertible add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital domRing-like V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
z0 is Element of the carrier of c₁
(c₁,np,z0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
k is Element of the carrier of c₁
eval ((c₁,np,z0),k) is Element of the carrier of c₁
eval (np,k) is Element of the carrier of c₁
z0 * (eval (np,k)) is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . (z0,(eval (np,k))) is Element of the carrier of c₁
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
power c₁ is Relation-like K28( the carrier of c₁,NAT) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁))
K28( the carrier of c₁,NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of c₁,NAT), the carrier of c₁) is V24() set
K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁)) is V24() set
k1 is Relation-like NAT -defined the carrier of c₁ -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of c₁
Sum k1 is Element of the carrier of c₁
len k1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom k1 is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
len (c₁,np,z0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
sq is Relation-like NAT -defined the carrier of c₁ -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of c₁
Sum sq is Element of the carrier of c₁
len sq is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom sq is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
F2 is set
c₈ is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₈ -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . (c₈ -' 1) is Element of the carrier of c₁
(power c₁) . (k,(c₈ -' 1)) is Element of the carrier of c₁
(np . (c₈ -' 1)) * ((power c₁) . (k,(c₈ -' 1))) is Element of the carrier of c₁
the multF of c₁ . ((np . (c₈ -' 1)),((power c₁) . (k,(c₈ -' 1)))) is Element of the carrier of c₁
k1 . F2 is set
k1 /. F2 is Element of the carrier of c₁
sq /. F2 is Element of the carrier of c₁
sq . F2 is set
(c₁,np,z0) . (c₈ -' 1) is Element of the carrier of c₁
((c₁,np,z0) . (c₈ -' 1)) * ((power c₁) . (k,(c₈ -' 1))) is Element of the carrier of c₁
the multF of c₁ . (((c₁,np,z0) . (c₈ -' 1)),((power c₁) . (k,(c₈ -' 1)))) is Element of the carrier of c₁
z0 * (np . (c₈ -' 1)) is Element of the carrier of c₁
the multF of c₁ . (z0,(np . (c₈ -' 1))) is Element of the carrier of c₁
(z0 * (np . (c₈ -' 1))) * ((power c₁) . (k,(c₈ -' 1))) is Element of the carrier of c₁
the multF of c₁ . ((z0 * (np . (c₈ -' 1))),((power c₁) . (k,(c₈ -' 1)))) is Element of the carrier of c₁
z0 * (k1 /. F2) is Element of the carrier of c₁
the multF of c₁ . (z0,(k1 /. F2)) is Element of the carrier of c₁
z0 * k1 is Relation-like NAT -defined the carrier of c₁ -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of c₁
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
eval ((0_. c₁),k) is Element of the carrier of c₁
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable add-associative right_zeroed unital right-distributive V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
eval (np,(0. c₁)) is Element of the carrier of c₁
np . 0 is Element of the carrier of c₁
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
power c₁ is Relation-like K28( the carrier of c₁,NAT) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁))
K28( the carrier of c₁,NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of c₁,NAT), the carrier of c₁) is V24() set
K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁)) is V24() set
z0 is Relation-like NAT -defined the carrier of c₁ -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of c₁
Sum z0 is Element of the carrier of c₁
len z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom z0 is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k - 1 is complex real ext-real V54() Element of REAL
- 1 is non empty complex real ext-real non positive negative V54() set
k + (- 1) is complex real ext-real V54() set
k -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
z0 /. k is Element of the carrier of c₁
z0 . k is set
np . (k -' 1) is Element of the carrier of c₁
(power c₁) . ((0. c₁),(k -' 1)) is Element of the carrier of c₁
(np . (k -' 1)) * ((power c₁) . ((0. c₁),(k -' 1))) is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . ((np . (k -' 1)),((power c₁) . ((0. c₁),(k -' 1)))) is Element of the carrier of c₁
(np . (k -' 1)) * (0. c₁) is Element of the carrier of c₁
the multF of c₁ . ((np . (k -' 1)),(0. c₁)) is Element of the carrier of c₁
z0 /. 1 is Element of the carrier of c₁
z0 . 1 is set
1 -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . (1 -' 1) is Element of the carrier of c₁
(power c₁) . ((0. c₁),(1 -' 1)) is Element of the carrier of c₁
(np . (1 -' 1)) * ((power c₁) . ((0. c₁),(1 -' 1))) is Element of the carrier of c₁
the multF of c₁ . ((np . (1 -' 1)),((power c₁) . ((0. c₁),(1 -' 1)))) is Element of the carrier of c₁
(power c₁) . ((0. c₁),0) is Element of the carrier of c₁
(np . (1 -' 1)) * ((power c₁) . ((0. c₁),0)) is Element of the carrier of c₁
the multF of c₁ . ((np . (1 -' 1)),((power c₁) . ((0. c₁),0))) is Element of the carrier of c₁
1_ c₁ is Element of the carrier of c₁
(np . (1 -' 1)) * (1_ c₁) is Element of the carrier of c₁
the multF of c₁ . ((np . (1 -' 1)),(1_ c₁)) is Element of the carrier of c₁
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
c₁ is non empty ZeroStr
the carrier of c₁ is non empty set
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
np is Element of the carrier of c₁
(0_. c₁) +* (0,np) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
z0 is Element of the carrier of c₁
((0_. c₁) +* (0,np)) +* (1,z0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
c₁ is non empty ZeroStr
the carrier of c₁ is non empty set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
np is Element of the carrier of c₁
<%np%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
<%np%> . 0 is Element of the carrier of c₁
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
<%np%> . z0 is Element of the carrier of c₁
len <%np%> is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₁ is non empty ZeroStr
the carrier of c₁ is non empty set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
np is Element of the carrier of c₁
<%np%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
len <%np%> is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
<%np%> . 0 is Element of the carrier of c₁
<%(0. c₁)%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₁ is non empty ZeroStr
the carrier of c₁ is non empty set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
<%(0. c₁)%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
len <%(0. c₁)%> is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital domRing-like V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
np is Element of the carrier of c₁
<%np%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
z0 is Element of the carrier of c₁
<%z0%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
<%np%> *' <%z0%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
np * z0 is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . (np,z0) is Element of the carrier of c₁
<%(np * z0)%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len <%np%> is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
len <%z0%> is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
len <%(np * z0)%> is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(<%np%> *' <%z0%>) . 0 is Element of the carrier of c₁
k is Relation-like NAT -defined the carrier of c₁ -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of c₁
len k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
Sum k is Element of the carrier of c₁
dom k is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
k . 1 is set
1 -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
<%np%> . (1 -' 1) is Element of the carrier of c₁
(0 + 1) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
<%z0%> . ((0 + 1) -' 1) is Element of the carrier of c₁
(<%np%> . (1 -' 1)) * (<%z0%> . ((0 + 1) -' 1)) is Element of the carrier of c₁
the multF of c₁ . ((<%np%> . (1 -' 1)),(<%z0%> . ((0 + 1) -' 1))) is Element of the carrier of c₁
<%np%> . 0 is Element of the carrier of c₁
<%z0%> . (1 -' 1) is Element of the carrier of c₁
(<%np%> . 0) * (<%z0%> . (1 -' 1)) is Element of the carrier of c₁
the multF of c₁ . ((<%np%> . 0),(<%z0%> . (1 -' 1))) is Element of the carrier of c₁
<%z0%> . 0 is Element of the carrier of c₁
(<%np%> . 0) * (<%z0%> . 0) is Element of the carrier of c₁
the multF of c₁ . ((<%np%> . 0),(<%z0%> . 0)) is Element of the carrier of c₁
(<%np%> . 0) * z0 is Element of the carrier of c₁
the multF of c₁ . ((<%np%> . 0),z0) is Element of the carrier of c₁
<*(np * z0)*> is Relation-like NAT -defined the carrier of c₁ -valued Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of c₁
k1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
(<%np%> *' <%z0%>) . k1 is set
<%(np * z0)%> . k1 is set
(len <%np%>) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
<%np%> . ((len <%np%>) -' 1) is Element of the carrier of c₁
(len <%z0%>) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
<%z0%> . ((len <%z0%>) -' 1) is Element of the carrier of c₁
(<%np%> . ((len <%np%>) -' 1)) * (<%z0%> . ((len <%z0%>) -' 1)) is Element of the carrier of c₁
the multF of c₁ . ((<%np%> . ((len <%np%>) -' 1)),(<%z0%> . ((len <%z0%>) -' 1))) is Element of the carrier of c₁
len (<%np%> *' <%z0%>) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(1 + 1) - 1 is complex real ext-real V54() Element of REAL
- 1 is non empty complex real ext-real non positive negative V54() set
(1 + 1) + (- 1) is complex real ext-real V54() set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
<%(0. c₁)%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
<%(0. c₁)%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital domRing-like V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
power c₁ is Relation-like K28( the carrier of c₁,NAT) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁))
K28( the carrier of c₁,NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of c₁,NAT), the carrier of c₁) is V24() set
K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁)) is V24() set
np is Element of the carrier of c₁
<%np%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,<%np%>,z0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
Polynom-Ring c₁ is non empty left_add-cancelable right_add-cancelable right_complementable strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
power (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁),NAT) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)))
the carrier of (Polynom-Ring c₁) is non empty set
K28( the carrier of (Polynom-Ring c₁),NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)) is V24() set
K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁))) is V24() set
(power (Polynom-Ring c₁)) . (<%np%>,z0) is set
(power c₁) . (np,z0) is Element of the carrier of c₁
<%((power c₁) . (np,z0))%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
z0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,<%np%>,(z0 + 1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . (<%np%>,(z0 + 1)) is set
(power c₁) . (np,(z0 + 1)) is Element of the carrier of c₁
<%((power c₁) . (np,(z0 + 1)))%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
<%((power c₁) . (np,z0))%> *' <%np%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
((power c₁) . (np,z0)) * np is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . (((power c₁) . (np,z0)),np) is Element of the carrier of c₁
<%(((power c₁) . (np,z0)) * np)%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,<%np%>,0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
Polynom-Ring c₁ is non empty left_add-cancelable right_add-cancelable right_complementable strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
power (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁),NAT) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)))
the carrier of (Polynom-Ring c₁) is non empty set
K28( the carrier of (Polynom-Ring c₁),NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)) is V24() set
K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁))) is V24() set
(power (Polynom-Ring c₁)) . (<%np%>,0) is set
1_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
1. c₁ is Element of the carrier of c₁
the OneF of c₁ is Element of the carrier of c₁
(0_. c₁) +* (0,(1. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
(c₁,(1_. c₁),(1. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
1_ c₁ is Element of the carrier of c₁
<%(1_ c₁)%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power c₁) . (np,0) is Element of the carrier of c₁
<%((power c₁) . (np,0))%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable add-associative right_zeroed unital V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
np is Element of the carrier of c₁
<%np%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
z0 is Element of the carrier of c₁
eval (<%np%>,z0) is Element of the carrier of c₁
len <%np%> is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
power c₁ is Relation-like K28( the carrier of c₁,NAT) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁))
K28( the carrier of c₁,NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of c₁,NAT), the carrier of c₁) is V24() set
K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁)) is V24() set
k is Relation-like NAT -defined the carrier of c₁ -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of c₁
Sum k is Element of the carrier of c₁
len k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom k is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
(0_. c₁) . 0 is Element of the carrier of c₁
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
Seg (len k) is V24() V31( len k) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
k . 1 is set
1 -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
<%np%> . (1 -' 1) is Element of the carrier of c₁
(power c₁) . (z0,(1 -' 1)) is Element of the carrier of c₁
(<%np%> . (1 -' 1)) * ((power c₁) . (z0,(1 -' 1))) is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . ((<%np%> . (1 -' 1)),((power c₁) . (z0,(1 -' 1)))) is Element of the carrier of c₁
<%np%> . 0 is Element of the carrier of c₁
(<%np%> . 0) * ((power c₁) . (z0,(1 -' 1))) is Element of the carrier of c₁
the multF of c₁ . ((<%np%> . 0),((power c₁) . (z0,(1 -' 1)))) is Element of the carrier of c₁
(power c₁) . (z0,0) is Element of the carrier of c₁
(<%np%> . 0) * ((power c₁) . (z0,0)) is Element of the carrier of c₁
the multF of c₁ . ((<%np%> . 0),((power c₁) . (z0,0))) is Element of the carrier of c₁
np * ((power c₁) . (z0,0)) is Element of the carrier of c₁
the multF of c₁ . (np,((power c₁) . (z0,0))) is Element of the carrier of c₁
1_ c₁ is Element of the carrier of c₁
np * (1_ c₁) is Element of the carrier of c₁
the multF of c₁ . (np,(1_ c₁)) is Element of the carrier of c₁
<*np*> is Relation-like NAT -defined the carrier of c₁ -valued Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of c₁
c₁ is non empty ZeroStr
the carrier of c₁ is non empty set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
np is Element of the carrier of c₁
z0 is Element of the carrier of c₁
(c₁,np,z0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
(0_. c₁) +* (0,np) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
((0_. c₁) +* (0,np)) +* (1,z0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
(c₁,np,z0) . 0 is Element of the carrier of c₁
(c₁,np,z0) . 1 is Element of the carrier of c₁
dom (0_. c₁) is V56() V57() V58() V59() V60() V61() set
((0_. c₁) +* (0,np)) . 0 is Element of the carrier of c₁
dom ((0_. c₁) +* (0,np)) is V56() V57() V58() V59() V60() V61() set
k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
(c₁,np,z0) . k is set
1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
((0_. c₁) +* (0,np)) . k is set
(0_. c₁) . k is set
c₁ is non empty ZeroStr
the carrier of c₁ is non empty set
np is Element of the carrier of c₁
z0 is Element of the carrier of c₁
(c₁,np,z0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
(0_. c₁) +* (0,np) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
((0_. c₁) +* (0,np)) +* (1,z0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
(c₁,np,z0) . k is set
c₁ is non empty ZeroStr
the carrier of c₁ is non empty set
np is Element of the carrier of c₁
z0 is Element of the carrier of c₁
(c₁,np,z0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
(0_. c₁) +* (0,np) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
((0_. c₁) +* (0,np)) +* (1,z0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
len (c₁,np,z0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
(c₁,np,z0) . k is set
c₁ is non empty ZeroStr
the carrier of c₁ is non empty set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
z0 is Element of the carrier of c₁
np is Element of the carrier of c₁
(c₁,np,z0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
(0_. c₁) +* (0,np) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
((0_. c₁) +* (0,np)) +* (1,z0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
len (c₁,np,z0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,np,z0) . 1 is Element of the carrier of c₁
k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
(c₁,np,z0) . k is set
c₁ is non empty ZeroStr
the carrier of c₁ is non empty set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
np is Element of the carrier of c₁
(c₁,np,(0. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
(0_. c₁) +* (0,np) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
((0_. c₁) +* (0,np)) +* (1,(0. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
len (c₁,np,(0. c₁)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
(c₁,np,(0. c₁)) . z0 is set
1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,np,(0. c₁)) . 0 is Element of the carrier of c₁
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₁ is non empty ZeroStr
the carrier of c₁ is non empty set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
(c₁,(0. c₁),(0. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
(0_. c₁) +* (0,(0. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
((0_. c₁) +* (0,(0. c₁))) +* (1,(0. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
(c₁,(0. c₁),(0. c₁)) . np is set
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
len (c₁,(0. c₁),(0. c₁)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₁ is non empty ZeroStr
the carrier of c₁ is non empty set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
np is Element of the carrier of c₁
(c₁,np,(0. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
(0_. c₁) +* (0,np) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
((0_. c₁) +* (0,np)) +* (1,(0. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
<%np%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len <%np%> is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
(c₁,np,(0. c₁)) . z0 is set
<%np%> . z0 is set
len (c₁,np,(0. c₁)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable add-associative right_zeroed unital left-distributive V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
np is Element of the carrier of c₁
z0 is Element of the carrier of c₁
(c₁,np,z0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
(0_. c₁) +* (0,np) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
((0_. c₁) +* (0,np)) +* (1,z0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
k is Element of the carrier of c₁
eval ((c₁,np,z0),k) is Element of the carrier of c₁
z0 * k is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . (z0,k) is Element of the carrier of c₁
np + (z0 * k) is Element of the carrier of c₁
the addF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
the addF of c₁ . (np,(z0 * k)) is Element of the carrier of c₁
len (c₁,np,z0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
power c₁ is Relation-like K28( the carrier of c₁,NAT) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁))
K28( the carrier of c₁,NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of c₁,NAT), the carrier of c₁) is V24() set
K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁)) is V24() set
k1 is Relation-like NAT -defined the carrier of c₁ -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of c₁
Sum k1 is Element of the carrier of c₁
len k1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom k1 is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
(0_. c₁) . 0 is Element of the carrier of c₁
np + (0. c₁) is Element of the carrier of c₁
the addF of c₁ . (np,(0. c₁)) is Element of the carrier of c₁
(0. c₁) * k is Element of the carrier of c₁
the multF of c₁ . ((0. c₁),k) is Element of the carrier of c₁
np + ((0. c₁) * k) is Element of the carrier of c₁
the addF of c₁ . (np,((0. c₁) * k)) is Element of the carrier of c₁
(0_. c₁) . 1 is Element of the carrier of c₁
((0_. c₁) . 1) * k is Element of the carrier of c₁
the multF of c₁ . (((0_. c₁) . 1),k) is Element of the carrier of c₁
np + (((0_. c₁) . 1) * k) is Element of the carrier of c₁
the addF of c₁ . (np,(((0_. c₁) . 1) * k)) is Element of the carrier of c₁
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
Seg (len k1) is V24() V31( len k1) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
k1 . 1 is set
1 -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,np,z0) . (1 -' 1) is Element of the carrier of c₁
(power c₁) . (k,(1 -' 1)) is Element of the carrier of c₁
((c₁,np,z0) . (1 -' 1)) * ((power c₁) . (k,(1 -' 1))) is Element of the carrier of c₁
the multF of c₁ . (((c₁,np,z0) . (1 -' 1)),((power c₁) . (k,(1 -' 1)))) is Element of the carrier of c₁
(c₁,np,z0) . 0 is Element of the carrier of c₁
((c₁,np,z0) . 0) * ((power c₁) . (k,(1 -' 1))) is Element of the carrier of c₁
the multF of c₁ . (((c₁,np,z0) . 0),((power c₁) . (k,(1 -' 1)))) is Element of the carrier of c₁
(power c₁) . (k,0) is Element of the carrier of c₁
((c₁,np,z0) . 0) * ((power c₁) . (k,0)) is Element of the carrier of c₁
the multF of c₁ . (((c₁,np,z0) . 0),((power c₁) . (k,0))) is Element of the carrier of c₁
np * ((power c₁) . (k,0)) is Element of the carrier of c₁
the multF of c₁ . (np,((power c₁) . (k,0))) is Element of the carrier of c₁
1_ c₁ is Element of the carrier of c₁
np * (1_ c₁) is Element of the carrier of c₁
the multF of c₁ . (np,(1_ c₁)) is Element of the carrier of c₁
<*np*> is Relation-like NAT -defined the carrier of c₁ -valued Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of c₁
np + (0. c₁) is Element of the carrier of c₁
the addF of c₁ . (np,(0. c₁)) is Element of the carrier of c₁
(0. c₁) * k is Element of the carrier of c₁
the multF of c₁ . ((0. c₁),k) is Element of the carrier of c₁
np + ((0. c₁) * k) is Element of the carrier of c₁
the addF of c₁ . (np,((0. c₁) * k)) is Element of the carrier of c₁
(c₁,np,z0) . 1 is Element of the carrier of c₁
((c₁,np,z0) . 1) * k is Element of the carrier of c₁
the multF of c₁ . (((c₁,np,z0) . 1),k) is Element of the carrier of c₁
np + (((c₁,np,z0) . 1) * k) is Element of the carrier of c₁
the addF of c₁ . (np,(((c₁,np,z0) . 1) * k)) is Element of the carrier of c₁
k1 . 1 is set
1 -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,np,z0) . (1 -' 1) is Element of the carrier of c₁
(power c₁) . (k,(1 -' 1)) is Element of the carrier of c₁
((c₁,np,z0) . (1 -' 1)) * ((power c₁) . (k,(1 -' 1))) is Element of the carrier of c₁
the multF of c₁ . (((c₁,np,z0) . (1 -' 1)),((power c₁) . (k,(1 -' 1)))) is Element of the carrier of c₁
(c₁,np,z0) . 0 is Element of the carrier of c₁
((c₁,np,z0) . 0) * ((power c₁) . (k,(1 -' 1))) is Element of the carrier of c₁
the multF of c₁ . (((c₁,np,z0) . 0),((power c₁) . (k,(1 -' 1)))) is Element of the carrier of c₁
(power c₁) . (k,0) is Element of the carrier of c₁
((c₁,np,z0) . 0) * ((power c₁) . (k,0)) is Element of the carrier of c₁
the multF of c₁ . (((c₁,np,z0) . 0),((power c₁) . (k,0))) is Element of the carrier of c₁
np * ((power c₁) . (k,0)) is Element of the carrier of c₁
the multF of c₁ . (np,((power c₁) . (k,0))) is Element of the carrier of c₁
1_ c₁ is Element of the carrier of c₁
np * (1_ c₁) is Element of the carrier of c₁
the multF of c₁ . (np,(1_ c₁)) is Element of the carrier of c₁
2 -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
2 - 1 is complex real ext-real V54() Element of REAL
- 1 is non empty complex real ext-real non positive negative V54() set
2 + (- 1) is complex real ext-real V54() set
k1 . 2 is set
(c₁,np,z0) . (2 -' 1) is Element of the carrier of c₁
(power c₁) . (k,(2 -' 1)) is Element of the carrier of c₁
((c₁,np,z0) . (2 -' 1)) * ((power c₁) . (k,(2 -' 1))) is Element of the carrier of c₁
the multF of c₁ . (((c₁,np,z0) . (2 -' 1)),((power c₁) . (k,(2 -' 1)))) is Element of the carrier of c₁
(power c₁) . (k,1) is Element of the carrier of c₁
z0 * ((power c₁) . (k,1)) is Element of the carrier of c₁
the multF of c₁ . (z0,((power c₁) . (k,1))) is Element of the carrier of c₁
<*np,(z0 * k)*> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like M13( the carrier of c₁,K250(2, the carrier of c₁))
K250(2, the carrier of c₁) is M12( the carrier of c₁)
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable add-associative right_zeroed unital left-distributive right_unital well-unital left_unital V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
np is Element of the carrier of c₁
(c₁,np,(0. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
(0_. c₁) +* (0,np) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
((0_. c₁) +* (0,np)) +* (1,(0. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
k is Element of the carrier of c₁
eval ((c₁,np,(0. c₁)),k) is Element of the carrier of c₁
(0. c₁) * k is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . ((0. c₁),k) is Element of the carrier of c₁
np + ((0. c₁) * k) is Element of the carrier of c₁
the addF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
the addF of c₁ . (np,((0. c₁) * k)) is Element of the carrier of c₁
np + (0. c₁) is Element of the carrier of c₁
the addF of c₁ . (np,(0. c₁)) is Element of the carrier of c₁
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable add-associative right_zeroed unital left-distributive V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
z0 is Element of the carrier of c₁
(c₁,(0. c₁),z0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
(0_. c₁) +* (0,(0. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
((0_. c₁) +* (0,(0. c₁))) +* (1,z0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
k is Element of the carrier of c₁
eval ((c₁,(0. c₁),z0),k) is Element of the carrier of c₁
z0 * k is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . (z0,k) is Element of the carrier of c₁
(0. c₁) + (z0 * k) is Element of the carrier of c₁
the addF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
the addF of c₁ . ((0. c₁),(z0 * k)) is Element of the carrier of c₁
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable add-associative right_zeroed unital left-distributive right_unital well-unital left_unital V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
1. c₁ is Element of the carrier of c₁
the OneF of c₁ is Element of the carrier of c₁
np is Element of the carrier of c₁
(c₁,np,(1. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
(0_. c₁) +* (0,np) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
((0_. c₁) +* (0,np)) +* (1,(1. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
k is Element of the carrier of c₁
eval ((c₁,np,(1. c₁)),k) is Element of the carrier of c₁
np + k is Element of the carrier of c₁
the addF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the addF of c₁ . (np,k) is Element of the carrier of c₁
(1. c₁) * k is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
the multF of c₁ . ((1. c₁),k) is Element of the carrier of c₁
np + ((1. c₁) * k) is Element of the carrier of c₁
the addF of c₁ . (np,((1. c₁) * k)) is Element of the carrier of c₁
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable add-associative right_zeroed unital left-distributive right_unital well-unital left_unital V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
1. c₁ is Element of the carrier of c₁
the OneF of c₁ is Element of the carrier of c₁
(c₁,(0. c₁),(1. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
(0_. c₁) +* (0,(0. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
((0_. c₁) +* (0,(0. c₁))) +* (1,(1. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
k is Element of the carrier of c₁
eval ((c₁,(0. c₁),(1. c₁)),k) is Element of the carrier of c₁
(1. c₁) * k is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . ((1. c₁),k) is Element of the carrier of c₁
(0. c₁) + ((1. c₁) * k) is Element of the carrier of c₁
the addF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
the addF of c₁ . ((0. c₁),((1. c₁) * k)) is Element of the carrier of c₁
(0. c₁) + k is Element of the carrier of c₁
the addF of c₁ . ((0. c₁),k) is Element of the carrier of c₁
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable Abelian add-associative right_zeroed unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
Polynom-Ring c₁ is non empty left_add-cancelable right_add-cancelable right_complementable strict Abelian add-associative right_zeroed unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
the carrier of (Polynom-Ring c₁) is non empty set
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
z0 is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
k1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
Seg (len np) is V24() V31( len np) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
k1 -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,z0,(k1 -' 1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
power (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁),NAT) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)))
K28( the carrier of (Polynom-Ring c₁),NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)) is V24() set
K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁))) is V24() set
(power (Polynom-Ring c₁)) . (z0,(k1 -' 1)) is set
np . (k1 -' 1) is Element of the carrier of c₁
(c₁,(c₁,z0,(k1 -' 1)),(np . (k1 -' 1))) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
sq is Element of the carrier of (Polynom-Ring c₁)
F2 is Element of the carrier of (Polynom-Ring c₁)
k1 is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
dom k1 is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
Sum k1 is Element of the carrier of (Polynom-Ring c₁)
sq is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len k1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
F2 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k1 . F2 is set
F2 -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,z0,(F2 -' 1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . (z0,(F2 -' 1)) is set
np . (F2 -' 1) is Element of the carrier of c₁
(c₁,(c₁,z0,(F2 -' 1)),(np . (F2 -' 1))) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
k is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
k1 is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
sq is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
Sum sq is Element of the carrier of (Polynom-Ring c₁)
len sq is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom sq is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
F2 is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
Sum F2 is Element of the carrier of (Polynom-Ring c₁)
len F2 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom F2 is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
Seg (len sq) is V24() V31( len sq) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
c₈ is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
sq . c₈ is set
c₈ -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,z0,(c₈ -' 1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
power (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁),NAT) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)))
K28( the carrier of (Polynom-Ring c₁),NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)) is V24() set
K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁))) is V24() set
(power (Polynom-Ring c₁)) . (z0,(c₈ -' 1)) is set
np . (c₈ -' 1) is Element of the carrier of c₁
(c₁,(c₁,z0,(c₈ -' 1)),(np . (c₈ -' 1))) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
F2 . c₈ is set
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable Abelian add-associative right_zeroed unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,(0_. c₁),np) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
Polynom-Ring c₁ is non empty left_add-cancelable right_add-cancelable right_complementable strict Abelian add-associative right_zeroed unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
the carrier of (Polynom-Ring c₁) is non empty set
len (0_. c₁) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
z0 is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
Sum z0 is Element of the carrier of (Polynom-Ring c₁)
len z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom z0 is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
z0 . k is set
k -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,np,(k -' 1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
power (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁),NAT) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)))
K28( the carrier of (Polynom-Ring c₁),NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)) is V24() set
K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁))) is V24() set
(power (Polynom-Ring c₁)) . (np,(k -' 1)) is set
(0_. c₁) . (k -' 1) is Element of the carrier of c₁
(c₁,(c₁,np,(k -' 1)),((0_. c₁) . (k -' 1))) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,(c₁,np,(k -' 1)),(0. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0. (Polynom-Ring c₁) is zero Element of the carrier of (Polynom-Ring c₁)
the ZeroF of (Polynom-Ring c₁) is Element of the carrier of (Polynom-Ring c₁)
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable Abelian add-associative right_zeroed unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,np,(0_. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
np . 0 is Element of the carrier of c₁
<%(np . 0)%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
Polynom-Ring c₁ is non empty left_add-cancelable right_add-cancelable right_complementable strict Abelian add-associative right_zeroed unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
the carrier of (Polynom-Ring c₁) is non empty set
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
z0 is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
Sum z0 is Element of the carrier of (Polynom-Ring c₁)
len z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom z0 is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(1 + 1) - 2 is complex real ext-real V54() Element of REAL
- 2 is non empty complex real ext-real non positive negative V54() set
(1 + 1) + (- 2) is complex real ext-real V54() set
k - 2 is complex real ext-real V54() Element of REAL
k + (- 2) is complex real ext-real V54() set
k - 1 is complex real ext-real V54() Element of REAL
- 1 is non empty complex real ext-real non positive negative V54() set
k + (- 1) is complex real ext-real V54() set
k -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k - (1 + 1) is complex real ext-real V54() Element of REAL
- (1 + 1) is non empty complex real ext-real non positive negative V54() set
k + (- (1 + 1)) is complex real ext-real V54() set
(k - (1 + 1)) + 1 is complex real ext-real V54() Element of REAL
k -' 2 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(k -' 2) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
z0 /. k is Element of the carrier of (Polynom-Ring c₁)
z0 . k is set
(c₁,(0_. c₁),(k -' 1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
power (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁),NAT) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)))
K28( the carrier of (Polynom-Ring c₁),NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)) is V24() set
K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁))) is V24() set
(power (Polynom-Ring c₁)) . ((0_. c₁),(k -' 1)) is set
np . (k -' 1) is Element of the carrier of c₁
(c₁,(c₁,(0_. c₁),(k -' 1)),(np . (k -' 1))) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,(0_. c₁),(np . (k -' 1))) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0. (Polynom-Ring c₁) is zero Element of the carrier of (Polynom-Ring c₁)
the ZeroF of (Polynom-Ring c₁) is Element of the carrier of (Polynom-Ring c₁)
z0 /. 1 is Element of the carrier of (Polynom-Ring c₁)
z0 . 1 is set
1 -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,(0_. c₁),(1 -' 1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . ((0_. c₁),(1 -' 1)) is set
np . (1 -' 1) is Element of the carrier of c₁
(c₁,(c₁,(0_. c₁),(1 -' 1)),(np . (1 -' 1))) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,(0_. c₁),0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . ((0_. c₁),0) is set
(c₁,(c₁,(0_. c₁),0),(np . (1 -' 1))) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,(c₁,(0_. c₁),0),(np . 0)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
1_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
1. c₁ is Element of the carrier of c₁
the OneF of c₁ is Element of the carrier of c₁
(0_. c₁) +* (0,(1. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
(c₁,(1_. c₁),(np . 0)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
<%(0. c₁)%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital domRing-like V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
z0 is Element of the carrier of c₁
<%z0%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,np,<%z0%>) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len (c₁,np,<%z0%>) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
Polynom-Ring c₁ is non empty left_add-cancelable right_add-cancelable right_complementable strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
the carrier of (Polynom-Ring c₁) is non empty set
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
Sum k is Element of the carrier of (Polynom-Ring c₁)
len k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom k is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
k1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k | k1 is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
Sum (k | k1) is Element of the carrier of (Polynom-Ring c₁)
k1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k | (k1 + 1) is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
Sum (k | (k1 + 1)) is Element of the carrier of (Polynom-Ring c₁)
sq is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len sq is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,<%z0%>,k1) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
power (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁),NAT) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)))
K28( the carrier of (Polynom-Ring c₁),NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)) is V24() set
K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁))) is V24() set
(power (Polynom-Ring c₁)) . (<%z0%>,k1) is set
np . k1 is Element of the carrier of c₁
(c₁,(c₁,<%z0%>,k1),(np . k1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len (c₁,(c₁,<%z0%>,k1),(np . k1)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
max ((len sq),(len (c₁,(c₁,<%z0%>,k1),(np . k1)))) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
len (c₁,<%z0%>,k1) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
power c₁ is Relation-like K28( the carrier of c₁,NAT) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁))
K28( the carrier of c₁,NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of c₁,NAT), the carrier of c₁) is V24() set
K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁)) is V24() set
(power c₁) . (z0,k1) is Element of the carrier of c₁
<%((power c₁) . (z0,k1))%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len <%((power c₁) . (z0,k1))%> is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
F2 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₈ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len c₈ is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k /. (k1 + 1) is Element of the carrier of (Polynom-Ring c₁)
k . (k1 + 1) is set
(k1 + 1) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,<%z0%>,((k1 + 1) -' 1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . (<%z0%>,((k1 + 1) -' 1)) is set
np . ((k1 + 1) -' 1) is Element of the carrier of c₁
(c₁,(c₁,<%z0%>,((k1 + 1) -' 1)),(np . ((k1 + 1) -' 1))) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,(c₁,<%z0%>,((k1 + 1) -' 1)),(np . k1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
<*(k /. (k1 + 1))*> is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
(k | k1) ^ <*(k /. (k1 + 1))*> is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like non empty V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
(Sum (k | k1)) + (k /. (k1 + 1)) is Element of the carrier of (Polynom-Ring c₁)
the addF of (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁)))
K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)) is set
K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁)) is set
K27(K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁))) is set
the addF of (Polynom-Ring c₁) . ((Sum (k | k1)),(k /. (k1 + 1))) is Element of the carrier of (Polynom-Ring c₁)
sq + (c₁,(c₁,<%z0%>,k1),(np . k1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
k | (len k) is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
k | 0 is Relation-like NAT -defined RAT -valued the carrier of (Polynom-Ring c₁) -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Function-like one-to-one constant functional empty V24() V29() V31( {} ) FinSequence-like FinSubsequence-like FinSequence-membered complex real ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V54() V56() V57() V58() V59() V60() V61() V62() Function-yielding V87() FinSequence of the carrier of (Polynom-Ring c₁)
Sum (k | 0) is Element of the carrier of (Polynom-Ring c₁)
k1 is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len k1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
<*> the carrier of (Polynom-Ring c₁) is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Function-like one-to-one constant functional empty V24() V29() V31( {} ) FinSequence-like FinSubsequence-like FinSequence-membered complex real ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V54() V56() V57() V58() V59() V60() V61() V62() Function-yielding V87() FinSequence of the carrier of (Polynom-Ring c₁)
0. (Polynom-Ring c₁) is zero Element of the carrier of (Polynom-Ring c₁)
the ZeroF of (Polynom-Ring c₁) is Element of the carrier of (Polynom-Ring c₁)
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
c₁ is non empty non degenerated V94() left_add-cancelable right_add-cancelable right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital domRing-like V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty V19() set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
z0 is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,np,z0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len (c₁,np,z0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(len np) * (len z0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
((len np) * (len z0)) - (len np) is complex real ext-real V54() Element of REAL
- (len np) is complex real ext-real non positive V54() set
((len np) * (len z0)) + (- (len np)) is complex real ext-real V54() set
(((len np) * (len z0)) - (len np)) - (len z0) is complex real ext-real V54() Element of REAL
- (len z0) is complex real ext-real non positive V54() set
(((len np) * (len z0)) - (len np)) + (- (len z0)) is complex real ext-real V54() set
((((len np) * (len z0)) - (len np)) - (len z0)) + 2 is complex real ext-real V54() Element of REAL
Polynom-Ring c₁ is non empty left_add-cancelable right_add-cancelable right_complementable strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
the carrier of (Polynom-Ring c₁) is non empty set
k is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
Sum k is Element of the carrier of (Polynom-Ring c₁)
len k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom k is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
((((len np) * (len z0)) - (len np)) - (len z0)) + 1 is complex real ext-real V54() Element of REAL
(len np) - 1 is complex real ext-real V54() Element of REAL
- 1 is non empty complex real ext-real non positive negative V54() set
(len np) + (- 1) is complex real ext-real V54() set
(len k) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,z0,((len k) -' 1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
power (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁),NAT) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)))
K28( the carrier of (Polynom-Ring c₁),NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)) is V24() set
K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁))) is V24() set
(power (Polynom-Ring c₁)) . (z0,((len k) -' 1)) is set
len (c₁,z0,((len k) -' 1)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(len np) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
((len np) -' 1) * (len z0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(((len np) -' 1) * (len z0)) - ((len np) -' 1) is complex real ext-real V54() Element of REAL
- ((len np) -' 1) is complex real ext-real non positive V54() set
(((len np) -' 1) * (len z0)) + (- ((len np) -' 1)) is complex real ext-real V54() set
((((len np) -' 1) * (len z0)) - ((len np) -' 1)) + 1 is complex real ext-real V54() Element of REAL
(((len np) -' 1) * (len z0)) - ((len np) - 1) is complex real ext-real V54() Element of REAL
- ((len np) - 1) is complex real ext-real V54() set
(((len np) -' 1) * (len z0)) + (- ((len np) - 1)) is complex real ext-real V54() set
((((len np) -' 1) * (len z0)) - ((len np) - 1)) + 1 is complex real ext-real V54() Element of REAL
((len np) - 1) * (len z0) is complex real ext-real V54() Element of REAL
(((len np) - 1) * (len z0)) - ((len np) - 1) is complex real ext-real V54() Element of REAL
(((len np) - 1) * (len z0)) + (- ((len np) - 1)) is complex real ext-real V54() set
((((len np) - 1) * (len z0)) - ((len np) - 1)) + 1 is complex real ext-real V54() Element of REAL
1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
((((len np) * (len z0)) - (len np)) - (len z0)) + (1 + 1) is complex real ext-real V54() Element of REAL
k | ((len k) -' 1) is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
Sum (k | ((len k) -' 1)) is Element of the carrier of (Polynom-Ring c₁)
((len k) -' 1) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k /. (len k) is Element of the carrier of (Polynom-Ring c₁)
<*(k /. (len k))*> is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
(k | ((len k) -' 1)) ^ <*(k /. (len k))*> is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like non empty V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
(Sum (k | ((len k) -' 1))) + (k /. (len k)) is Element of the carrier of (Polynom-Ring c₁)
the addF of (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁)))
K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)) is set
K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁)) is set
K27(K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁))) is set
the addF of (Polynom-Ring c₁) . ((Sum (k | ((len k) -' 1))),(k /. (len k))) is Element of the carrier of (Polynom-Ring c₁)
len (k | ((len k) -' 1)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(len (k | ((len k) -' 1))) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,np,z0) . k1 is Element of the carrier of c₁
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
(k | ((len k) -' 1)) | (len (k | ((len k) -' 1))) is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
z1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() set
(k | ((len k) -' 1)) | z1 is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
Sum ((k | ((len k) -' 1)) | z1) is Element of the carrier of (Polynom-Ring c₁)
z1 * (len z0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(z1 * (len z0)) - (len z0) is complex real ext-real V54() Element of REAL
(z1 * (len z0)) + (- (len z0)) is complex real ext-real V54() set
((z1 * (len z0)) - (len z0)) - z1 is complex real ext-real V54() Element of REAL
- z1 is non empty complex real ext-real non positive negative V54() set
((z1 * (len z0)) - (len z0)) + (- z1) is complex real ext-real V54() set
(((z1 * (len z0)) - (len z0)) - z1) + 2 is complex real ext-real V54() Element of REAL
z1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(k | ((len k) -' 1)) | (z1 + 1) is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
Sum ((k | ((len k) -' 1)) | (z1 + 1)) is Element of the carrier of (Polynom-Ring c₁)
(z1 + 1) * (len z0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
((z1 + 1) * (len z0)) - (len z0) is complex real ext-real V54() Element of REAL
((z1 + 1) * (len z0)) + (- (len z0)) is complex real ext-real V54() set
(((z1 + 1) * (len z0)) - (len z0)) - (z1 + 1) is complex real ext-real V54() Element of REAL
- (z1 + 1) is non empty complex real ext-real non positive negative V54() set
(((z1 + 1) * (len z0)) - (len z0)) + (- (z1 + 1)) is complex real ext-real V54() set
((((z1 + 1) * (len z0)) - (len z0)) - (z1 + 1)) + 2 is complex real ext-real V54() Element of REAL
0 + (1 + 1) is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(len z0) - 2 is complex real ext-real V54() Element of REAL
- 2 is non empty complex real ext-real non positive negative V54() set
(len z0) + (- 2) is complex real ext-real V54() set
(z1 * (len z0)) - z1 is complex real ext-real V54() Element of REAL
(z1 * (len z0)) + (- z1) is complex real ext-real V54() set
((z1 * (len z0)) - z1) + 1 is complex real ext-real V54() Element of REAL
(((z1 * (len z0)) - z1) + 1) + 0 is complex real ext-real V54() Element of REAL
(((z1 * (len z0)) - z1) + 1) + ((len z0) - 2) is complex real ext-real V54() Element of REAL
((((z1 * (len z0)) - (len z0)) - z1) + 2) + 0 is complex real ext-real V54() Element of REAL
((((z1 * (len z0)) - (len z0)) - z1) + 2) + 1 is complex real ext-real V54() Element of REAL
(((z1 * (len z0)) - z1) + 1) - ((len z0) - 2) is complex real ext-real V54() Element of REAL
- ((len z0) - 2) is complex real ext-real V54() set
(((z1 * (len z0)) - z1) + 1) + (- ((len z0) - 2)) is complex real ext-real V54() set
gc is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len gc is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
F1 is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len F1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
i is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,z0,i) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . (z0,i) is set
np . i is Element of the carrier of c₁
(c₁,(c₁,z0,i),(np . i)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len (c₁,(c₁,z0,i),(np . i)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
max ((len F1),(len (c₁,(c₁,z0,i),(np . i)))) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
eg is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . z1 is set
len (c₁,z0,i) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . z1 is set
(len z0) - 1 is complex real ext-real V54() Element of REAL
(len z0) + (- 1) is complex real ext-real V54() set
z1 * ((len z0) - 1) is complex real ext-real V54() Element of REAL
(z1 * (len z0)) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
((z1 * (len z0)) + 1) - z1 is complex real ext-real V54() Element of REAL
((z1 * (len z0)) + 1) + (- z1) is complex real ext-real V54() set
np . z1 is set
dom (k | ((len k) -' 1)) is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
(k | ((len k) -' 1)) /. (z1 + 1) is Element of the carrier of (Polynom-Ring c₁)
(k | ((len k) -' 1)) . (z1 + 1) is set
k . (z1 + 1) is set
(z1 + 1) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,z0,((z1 + 1) -' 1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . (z0,((z1 + 1) -' 1)) is set
np . ((z1 + 1) -' 1) is Element of the carrier of c₁
(c₁,(c₁,z0,((z1 + 1) -' 1)),(np . ((z1 + 1) -' 1))) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,(c₁,z0,((z1 + 1) -' 1)),(np . i)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
i + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(k | ((len k) -' 1)) | (i + 1) is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
(k | ((len k) -' 1)) | i is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
(k | ((len k) -' 1)) /. (i + 1) is Element of the carrier of (Polynom-Ring c₁)
<*((k | ((len k) -' 1)) /. (i + 1))*> is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
((k | ((len k) -' 1)) | i) ^ <*((k | ((len k) -' 1)) /. (i + 1))*> is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like non empty V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
(Sum ((k | ((len k) -' 1)) | z1)) + ((k | ((len k) -' 1)) /. (z1 + 1)) is Element of the carrier of (Polynom-Ring c₁)
the addF of (Polynom-Ring c₁) . ((Sum ((k | ((len k) -' 1)) | z1)),((k | ((len k) -' 1)) /. (z1 + 1))) is Element of the carrier of (Polynom-Ring c₁)
F1 + (c₁,(c₁,z0,i),(np . i)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(z1 + 1) * (len z0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
((z1 + 1) * (len z0)) - (len z0) is complex real ext-real V54() Element of REAL
((z1 + 1) * (len z0)) + (- (len z0)) is complex real ext-real V54() set
(((z1 + 1) * (len z0)) - (len z0)) - (z1 + 1) is complex real ext-real V54() Element of REAL
(((z1 + 1) * (len z0)) - (len z0)) + (- (z1 + 1)) is complex real ext-real V54() set
((((z1 + 1) * (len z0)) - (len z0)) - (z1 + 1)) + 2 is complex real ext-real V54() Element of REAL
- 1 is non empty complex real ext-real non positive negative V54() Element of REAL
((z1 * (len z0)) - z1) + (- (len z0)) is complex real ext-real V54() Element of REAL
((z1 * (len z0)) - z1) + (- 1) is complex real ext-real V54() Element of REAL
(z1 + 1) * (len z0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
((z1 + 1) * (len z0)) - (len z0) is complex real ext-real V54() Element of REAL
((z1 + 1) * (len z0)) + (- (len z0)) is complex real ext-real V54() set
(((z1 + 1) * (len z0)) - (len z0)) - (z1 + 1) is complex real ext-real V54() Element of REAL
(((z1 + 1) * (len z0)) - (len z0)) + (- (z1 + 1)) is complex real ext-real V54() set
((((z1 + 1) * (len z0)) - (len z0)) - (z1 + 1)) + 2 is complex real ext-real V54() Element of REAL
(z1 + 1) * (len z0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
((z1 + 1) * (len z0)) - (len z0) is complex real ext-real V54() Element of REAL
((z1 + 1) * (len z0)) + (- (len z0)) is complex real ext-real V54() set
(((z1 + 1) * (len z0)) - (len z0)) - (z1 + 1) is complex real ext-real V54() Element of REAL
(((z1 + 1) * (len z0)) - (len z0)) + (- (z1 + 1)) is complex real ext-real V54() set
((((z1 + 1) * (len z0)) - (len z0)) - (z1 + 1)) + 2 is complex real ext-real V54() Element of REAL
(z1 + 1) * (len z0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
((z1 + 1) * (len z0)) - (len z0) is complex real ext-real V54() Element of REAL
((z1 + 1) * (len z0)) + (- (len z0)) is complex real ext-real V54() set
(((z1 + 1) * (len z0)) - (len z0)) - (z1 + 1) is complex real ext-real V54() Element of REAL
(((z1 + 1) * (len z0)) - (len z0)) + (- (z1 + 1)) is complex real ext-real V54() set
((((z1 + 1) * (len z0)) - (len z0)) - (z1 + 1)) + 2 is complex real ext-real V54() Element of REAL
0 + (len z0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
2 - (len z0) is complex real ext-real V54() Element of REAL
2 + (- (len z0)) is complex real ext-real V54() set
(2 - (len z0)) + k1 is complex real ext-real V54() Element of REAL
0 + k1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom (k | ((len k) -' 1)) is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
(k | ((len k) -' 1)) | 1 is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
Sum ((k | ((len k) -' 1)) | 1) is Element of the carrier of (Polynom-Ring c₁)
1 * (len z0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(1 * (len z0)) - (len z0) is complex real ext-real V54() Element of REAL
(1 * (len z0)) + (- (len z0)) is complex real ext-real V54() set
((1 * (len z0)) - (len z0)) - 1 is complex real ext-real V54() Element of REAL
((1 * (len z0)) - (len z0)) + (- 1) is complex real ext-real V54() set
(((1 * (len z0)) - (len z0)) - 1) + 2 is complex real ext-real V54() Element of REAL
z1 is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len z1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(k | ((len k) -' 1)) /. 1 is Element of the carrier of (Polynom-Ring c₁)
<*((k | ((len k) -' 1)) /. 1)*> is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
(k | ((len k) -' 1)) . 1 is set
k . 1 is set
1 -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,z0,(1 -' 1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . (z0,(1 -' 1)) is set
np . (1 -' 1) is Element of the carrier of c₁
(c₁,(c₁,z0,(1 -' 1)),(np . (1 -' 1))) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
np . 0 is Element of the carrier of c₁
(c₁,(c₁,z0,(1 -' 1)),(np . 0)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,z0,0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . (z0,0) is set
(c₁,(c₁,z0,0),(np . 0)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
1_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
1. c₁ is non zero Element of the carrier of c₁
the OneF of c₁ is Element of the carrier of c₁
(0_. c₁) +* (0,(1. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
(c₁,(1_. c₁),(np . 0)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
<%(np . 0)%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
1 * (len z0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(1 * (len z0)) - (len z0) is complex real ext-real V54() Element of REAL
(1 * (len z0)) + (- (len z0)) is complex real ext-real V54() set
((1 * (len z0)) - (len z0)) - 1 is complex real ext-real V54() Element of REAL
((1 * (len z0)) - (len z0)) + (- 1) is complex real ext-real V54() set
(((1 * (len z0)) - (len z0)) - 1) + 2 is complex real ext-real V54() Element of REAL
c₈ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len c₈ is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(len (k | ((len k) -' 1))) * (len z0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
((len (k | ((len k) -' 1))) * (len z0)) - (len z0) is complex real ext-real V54() Element of REAL
((len (k | ((len k) -' 1))) * (len z0)) + (- (len z0)) is complex real ext-real V54() set
(((len (k | ((len k) -' 1))) * (len z0)) - (len z0)) - (len (k | ((len k) -' 1))) is complex real ext-real V54() Element of REAL
- (len (k | ((len k) -' 1))) is complex real ext-real non positive V54() set
(((len (k | ((len k) -' 1))) * (len z0)) - (len z0)) + (- (len (k | ((len k) -' 1)))) is complex real ext-real V54() set
((((len (k | ((len k) -' 1))) * (len z0)) - (len z0)) - (len (k | ((len k) -' 1)))) + 2 is complex real ext-real V54() Element of REAL
c₈ . k1 is Element of the carrier of c₁
k . (len k) is set
np . ((len k) -' 1) is Element of the carrier of c₁
(c₁,(c₁,z0,((len k) -' 1)),(np . ((len k) -' 1))) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
c₈ + (c₁,(c₁,z0,((len k) -' 1)),(np . ((len k) -' 1))) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,(c₁,z0,((len k) -' 1)),(np . ((len k) -' 1))) . k1 is Element of the carrier of c₁
(c₈ . k1) + ((c₁,(c₁,z0,((len k) -' 1)),(np . ((len k) -' 1))) . k1) is Element of the carrier of c₁
the addF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the addF of c₁ . ((c₈ . k1),((c₁,(c₁,z0,((len k) -' 1)),(np . ((len k) -' 1))) . k1)) is Element of the carrier of c₁
(c₁,z0,((len k) -' 1)) . k1 is Element of the carrier of c₁
(np . ((len k) -' 1)) * ((c₁,z0,((len k) -' 1)) . k1) is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
the multF of c₁ . ((np . ((len k) -' 1)),((c₁,z0,((len k) -' 1)) . k1)) is Element of the carrier of c₁
k /. 1 is Element of the carrier of (Polynom-Ring c₁)
k . 1 is set
1 -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,z0,(1 -' 1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . (z0,(1 -' 1)) is set
np . (1 -' 1) is Element of the carrier of c₁
(c₁,(c₁,z0,(1 -' 1)),(np . (1 -' 1))) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
np . 0 is Element of the carrier of c₁
(c₁,(c₁,z0,(1 -' 1)),(np . 0)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,z0,0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . (z0,0) is set
(c₁,(c₁,z0,0),(np . 0)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
1_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
1. c₁ is non zero Element of the carrier of c₁
the OneF of c₁ is Element of the carrier of c₁
(0_. c₁) +* (0,(1. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
(c₁,(1_. c₁),(np . 0)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
<%(np . 0)%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0. (Polynom-Ring c₁) is zero Element of the carrier of (Polynom-Ring c₁)
the ZeroF of (Polynom-Ring c₁) is Element of the carrier of (Polynom-Ring c₁)
<*> the carrier of (Polynom-Ring c₁) is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Function-like one-to-one constant functional empty V24() V29() V31( {} ) FinSequence-like FinSubsequence-like FinSequence-membered complex real ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V54() V56() V57() V58() V59() V60() V61() V62() Function-yielding V87() FinSequence of the carrier of (Polynom-Ring c₁)
(0. (Polynom-Ring c₁)) + (k /. 1) is Element of the carrier of (Polynom-Ring c₁)
the addF of (Polynom-Ring c₁) . ((0. (Polynom-Ring c₁)),(k /. 1)) is Element of the carrier of (Polynom-Ring c₁)
(0_. c₁) + <%(np . 0)%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
sq is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() set
k | sq is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
Sum (k | sq) is Element of the carrier of (Polynom-Ring c₁)
sq -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,z0,(sq -' 1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . (z0,(sq -' 1)) is set
len (c₁,z0,(sq -' 1)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
sq + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k | (sq + 1) is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
Sum (k | (sq + 1)) is Element of the carrier of (Polynom-Ring c₁)
(sq + 1) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,z0,((sq + 1) -' 1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . (z0,((sq + 1) -' 1)) is set
len (c₁,z0,((sq + 1) -' 1)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
z1 is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len z1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
sq * (len z0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(len z0) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(sq * (len z0)) + ((len z0) -' 1) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(sq * (len z0)) - ((len z0) -' 1) is complex real ext-real V54() Element of REAL
- ((len z0) -' 1) is complex real ext-real non positive V54() set
(sq * (len z0)) + (- ((len z0) -' 1)) is complex real ext-real V54() set
(len z0) - 1 is complex real ext-real V54() Element of REAL
(len z0) + (- 1) is complex real ext-real V54() set
(sq * (len z0)) - ((len z0) - 1) is complex real ext-real V54() Element of REAL
- ((len z0) - 1) is complex real ext-real V54() set
(sq * (len z0)) + (- ((len z0) - 1)) is complex real ext-real V54() set
(sq * (len z0)) - (len z0) is complex real ext-real V54() Element of REAL
(sq * (len z0)) + (- (len z0)) is complex real ext-real V54() set
((sq * (len z0)) - (len z0)) + 1 is complex real ext-real V54() Element of REAL
(((sq * (len z0)) - (len z0)) + 1) - sq is complex real ext-real V54() Element of REAL
- sq is non empty complex real ext-real non positive negative V54() set
(((sq * (len z0)) - (len z0)) + 1) + (- sq) is complex real ext-real V54() set
(sq * (len z0)) - sq is complex real ext-real V54() Element of REAL
(sq * (len z0)) + (- sq) is complex real ext-real V54() set
((sq * (len z0)) - (len z0)) - sq is complex real ext-real V54() Element of REAL
((sq * (len z0)) - (len z0)) + (- sq) is complex real ext-real V54() set
(((sq * (len z0)) - (len z0)) - sq) + 1 is complex real ext-real V54() Element of REAL
((((sq * (len z0)) - (len z0)) - sq) + 1) + 1 is complex real ext-real V54() Element of REAL
((sq * (len z0)) - sq) + 1 is complex real ext-real V54() Element of REAL
sq - 1 is complex real ext-real V54() Element of REAL
sq + (- 1) is complex real ext-real V54() set
(sq -' 1) * (len z0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
((sq -' 1) * (len z0)) - (sq -' 1) is complex real ext-real V54() Element of REAL
- (sq -' 1) is complex real ext-real non positive V54() set
((sq -' 1) * (len z0)) + (- (sq -' 1)) is complex real ext-real V54() set
(((sq -' 1) * (len z0)) - (sq -' 1)) + 1 is complex real ext-real V54() Element of REAL
(sq - 1) * (len z0) is complex real ext-real V54() Element of REAL
((sq - 1) * (len z0)) - (sq -' 1) is complex real ext-real V54() Element of REAL
((sq - 1) * (len z0)) + (- (sq -' 1)) is complex real ext-real V54() set
(((sq - 1) * (len z0)) - (sq -' 1)) + 1 is complex real ext-real V54() Element of REAL
1 * (len z0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(sq * (len z0)) - (1 * (len z0)) is complex real ext-real V54() Element of REAL
- (1 * (len z0)) is complex real ext-real non positive V54() set
(sq * (len z0)) + (- (1 * (len z0))) is complex real ext-real V54() set
((sq * (len z0)) - (1 * (len z0))) - (sq - 1) is complex real ext-real V54() Element of REAL
- (sq - 1) is complex real ext-real V54() set
((sq * (len z0)) - (1 * (len z0))) + (- (sq - 1)) is complex real ext-real V54() set
(((sq * (len z0)) - (1 * (len z0))) - (sq - 1)) + 1 is complex real ext-real V54() Element of REAL
F2 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,z0,F2) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . (z0,F2) is set
len (c₁,z0,F2) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₈ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len c₈ is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . F2 is Element of the carrier of c₁
(c₁,(c₁,z0,F2),(np . F2)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len (c₁,(c₁,z0,F2),(np . F2)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
max ((len c₈),(len (c₁,(c₁,z0,F2),(np . F2)))) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
np . sq is set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
np . sq is set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
np . sq is set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
F1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
F2 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k /. (F2 + 1) is Element of the carrier of (Polynom-Ring c₁)
<*(k /. (F2 + 1))*> is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
(k | sq) ^ <*(k /. (F2 + 1))*> is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like non empty V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
k /. (sq + 1) is Element of the carrier of (Polynom-Ring c₁)
(Sum (k | sq)) + (k /. (sq + 1)) is Element of the carrier of (Polynom-Ring c₁)
the addF of (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁)))
K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)) is set
K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁)) is set
K27(K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁))) is set
the addF of (Polynom-Ring c₁) . ((Sum (k | sq)),(k /. (sq + 1))) is Element of the carrier of (Polynom-Ring c₁)
k . (sq + 1) is set
np . ((sq + 1) -' 1) is Element of the carrier of c₁
(c₁,(c₁,z0,((sq + 1) -' 1)),(np . ((sq + 1) -' 1))) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,(c₁,z0,((sq + 1) -' 1)),(np . F2)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
c₈ + (c₁,(c₁,z0,F2),(np . F2)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
k | (len k) is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
k | 1 is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
Sum (k | 1) is Element of the carrier of (Polynom-Ring c₁)
1 -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,z0,(1 -' 1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . (z0,(1 -' 1)) is set
len (c₁,z0,(1 -' 1)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
sq is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len sq is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k /. 1 is Element of the carrier of (Polynom-Ring c₁)
<*(k /. 1)*> is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
k . 1 is set
np . (1 -' 1) is Element of the carrier of c₁
(c₁,(c₁,z0,(1 -' 1)),(np . (1 -' 1))) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
np . 0 is Element of the carrier of c₁
(c₁,(c₁,z0,(1 -' 1)),(np . 0)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,z0,0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . (z0,0) is set
(c₁,(c₁,z0,0),(np . 0)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
1_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
1. c₁ is non zero Element of the carrier of c₁
the OneF of c₁ is Element of the carrier of c₁
(0_. c₁) +* (0,(1. c₁)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
(c₁,(1_. c₁),(np . 0)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
<%(np . 0)%> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len (1_. c₁) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
len (c₁,z0,0) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₁ is non empty non degenerated V94() left_add-cancelable right_add-cancelable right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital domRing-like V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty V19() set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
z0 is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,np,z0) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
k is Element of the carrier of c₁
eval ((c₁,np,z0),k) is Element of the carrier of c₁
eval (z0,k) is Element of the carrier of c₁
eval (np,(eval (z0,k))) is Element of the carrier of c₁
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
power c₁ is Relation-like K28( the carrier of c₁,NAT) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁))
K28( the carrier of c₁,NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of c₁,NAT), the carrier of c₁) is V24() set
K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁)) is V24() set
k1 is Relation-like NAT -defined the carrier of c₁ -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of c₁
Sum k1 is Element of the carrier of c₁
len k1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom k1 is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
Polynom-Ring c₁ is non empty left_add-cancelable right_add-cancelable right_complementable strict Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital V174() V175() V176() V177() doubleLoopStr
the carrier of (Polynom-Ring c₁) is non empty set
sq is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
Sum sq is Element of the carrier of (Polynom-Ring c₁)
len sq is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom sq is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
F2 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
sq | F2 is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
Sum (sq | F2) is Element of the carrier of (Polynom-Ring c₁)
k1 | F2 is Relation-like NAT -defined the carrier of c₁ -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of c₁
Sum (k1 | F2) is Element of the carrier of c₁
F2 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
sq | (F2 + 1) is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
Sum (sq | (F2 + 1)) is Element of the carrier of (Polynom-Ring c₁)
k1 | (F2 + 1) is Relation-like NAT -defined the carrier of c₁ -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of c₁
Sum (k1 | (F2 + 1)) is Element of the carrier of c₁
c₈ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
eval (c₈,k) is Element of the carrier of c₁
k1 /. (F2 + 1) is Element of the carrier of c₁
<*(k1 /. (F2 + 1))*> is Relation-like NAT -defined the carrier of c₁ -valued Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of c₁
(k1 | F2) ^ <*(k1 /. (F2 + 1))*> is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of c₁
sq /. (F2 + 1) is Element of the carrier of (Polynom-Ring c₁)
<*(sq /. (F2 + 1))*> is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
(sq | F2) ^ <*(sq /. (F2 + 1))*> is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like non empty V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
(Sum (sq | F2)) + (sq /. (F2 + 1)) is Element of the carrier of (Polynom-Ring c₁)
the addF of (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁)))
K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)) is set
K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁)) is set
K27(K28(K28( the carrier of (Polynom-Ring c₁), the carrier of (Polynom-Ring c₁)), the carrier of (Polynom-Ring c₁))) is set
the addF of (Polynom-Ring c₁) . ((Sum (sq | F2)),(sq /. (F2 + 1))) is Element of the carrier of (Polynom-Ring c₁)
(F2 + 1) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . ((F2 + 1) -' 1) is Element of the carrier of c₁
(power c₁) . ((eval (z0,k)),((F2 + 1) -' 1)) is Element of the carrier of c₁
(np . ((F2 + 1) -' 1)) * ((power c₁) . ((eval (z0,k)),((F2 + 1) -' 1))) is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . ((np . ((F2 + 1) -' 1)),((power c₁) . ((eval (z0,k)),((F2 + 1) -' 1)))) is Element of the carrier of c₁
k1 . (F2 + 1) is set
sq . (F2 + 1) is set
(c₁,z0,((F2 + 1) -' 1)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
power (Polynom-Ring c₁) is Relation-like K28( the carrier of (Polynom-Ring c₁),NAT) -defined the carrier of (Polynom-Ring c₁) -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)))
K28( the carrier of (Polynom-Ring c₁),NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁)) is V24() set
K27(K28(K28( the carrier of (Polynom-Ring c₁),NAT), the carrier of (Polynom-Ring c₁))) is V24() set
(power (Polynom-Ring c₁)) . (z0,((F2 + 1) -' 1)) is set
(c₁,(c₁,z0,((F2 + 1) -' 1)),(np . ((F2 + 1) -' 1))) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
np . F2 is Element of the carrier of c₁
(c₁,(c₁,z0,((F2 + 1) -' 1)),(np . F2)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,z0,F2) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(power (Polynom-Ring c₁)) . (z0,F2) is set
(c₁,(c₁,z0,F2),(np . F2)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
z1 is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
z1 + (c₁,(c₁,z0,F2),(np . F2)) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
eval (z1,k) is Element of the carrier of c₁
eval ((c₁,(c₁,z0,F2),(np . F2)),k) is Element of the carrier of c₁
(eval (z1,k)) + (eval ((c₁,(c₁,z0,F2),(np . F2)),k)) is Element of the carrier of c₁
the addF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
the addF of c₁ . ((eval (z1,k)),(eval ((c₁,(c₁,z0,F2),(np . F2)),k))) is Element of the carrier of c₁
(Sum (k1 | F2)) + (eval ((c₁,(c₁,z0,F2),(np . F2)),k)) is Element of the carrier of c₁
the addF of c₁ . ((Sum (k1 | F2)),(eval ((c₁,(c₁,z0,F2),(np . F2)),k))) is Element of the carrier of c₁
eval ((c₁,z0,F2),k) is Element of the carrier of c₁
(np . F2) * (eval ((c₁,z0,F2),k)) is Element of the carrier of c₁
the multF of c₁ . ((np . F2),(eval ((c₁,z0,F2),k))) is Element of the carrier of c₁
(Sum (k1 | F2)) + ((np . F2) * (eval ((c₁,z0,F2),k))) is Element of the carrier of c₁
the addF of c₁ . ((Sum (k1 | F2)),((np . F2) * (eval ((c₁,z0,F2),k)))) is Element of the carrier of c₁
(power c₁) . ((eval (z0,k)),F2) is Element of the carrier of c₁
(np . F2) * ((power c₁) . ((eval (z0,k)),F2)) is Element of the carrier of c₁
the multF of c₁ . ((np . F2),((power c₁) . ((eval (z0,k)),F2))) is Element of the carrier of c₁
(Sum (k1 | F2)) + ((np . F2) * ((power c₁) . ((eval (z0,k)),F2))) is Element of the carrier of c₁
the addF of c₁ . ((Sum (k1 | F2)),((np . F2) * ((power c₁) . ((eval (z0,k)),F2)))) is Element of the carrier of c₁
(np . ((F2 + 1) -' 1)) * ((power c₁) . ((eval (z0,k)),F2)) is Element of the carrier of c₁
the multF of c₁ . ((np . ((F2 + 1) -' 1)),((power c₁) . ((eval (z0,k)),F2))) is Element of the carrier of c₁
(Sum (k1 | F2)) + ((np . ((F2 + 1) -' 1)) * ((power c₁) . ((eval (z0,k)),F2))) is Element of the carrier of c₁
the addF of c₁ . ((Sum (k1 | F2)),((np . ((F2 + 1) -' 1)) * ((power c₁) . ((eval (z0,k)),F2)))) is Element of the carrier of c₁
(Sum (k1 | F2)) + (k1 /. (F2 + 1)) is Element of the carrier of c₁
the addF of c₁ . ((Sum (k1 | F2)),(k1 /. (F2 + 1))) is Element of the carrier of c₁
sq | (len sq) is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of (Polynom-Ring c₁)
k1 | (len k1) is Relation-like NAT -defined the carrier of c₁ -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of c₁
sq | 0 is Relation-like NAT -defined RAT -valued the carrier of (Polynom-Ring c₁) -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Function-like one-to-one constant functional empty V24() V29() V31( {} ) FinSequence-like FinSubsequence-like FinSequence-membered complex real ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V54() V56() V57() V58() V59() V60() V61() V62() Function-yielding V87() FinSequence of the carrier of (Polynom-Ring c₁)
Sum (sq | 0) is Element of the carrier of (Polynom-Ring c₁)
k1 | 0 is Relation-like NAT -defined RAT -valued the carrier of c₁ -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Function-like one-to-one constant functional empty V24() V29() V31( {} ) FinSequence-like FinSubsequence-like FinSequence-membered complex real ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V54() V56() V57() V58() V59() V60() V61() V62() Function-yielding V87() FinSequence of the carrier of c₁
Sum (k1 | 0) is Element of the carrier of c₁
F2 is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
eval (F2,k) is Element of the carrier of c₁
<*> the carrier of (Polynom-Ring c₁) is Relation-like NAT -defined the carrier of (Polynom-Ring c₁) -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Function-like one-to-one constant functional empty V24() V29() V31( {} ) FinSequence-like FinSubsequence-like FinSequence-membered complex real ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V54() V56() V57() V58() V59() V60() V61() V62() Function-yielding V87() FinSequence of the carrier of (Polynom-Ring c₁)
<*> the carrier of c₁ is Relation-like NAT -defined the carrier of c₁ -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Function-like one-to-one constant functional empty V24() V29() V31( {} ) FinSequence-like FinSubsequence-like FinSequence-membered complex real ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V54() V56() V57() V58() V59() V60() V61() V62() Function-yielding V87() FinSequence of the carrier of c₁
0. (Polynom-Ring c₁) is zero Element of the carrier of (Polynom-Ring c₁)
the ZeroF of (Polynom-Ring c₁) is Element of the carrier of (Polynom-Ring c₁)
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
c₁ is non empty unital doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
c₁ is non empty unital doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
c₁ is non empty unital doubleLoopStr
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
the Element of the carrier of c₁ is Element of the carrier of c₁
eval ((0_. c₁), the Element of the carrier of c₁) is Element of the carrier of c₁
c₁ is non empty unital doubleLoopStr
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
c₁ is non empty unital doubleLoopStr
the carrier of c₁ is non empty set
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support (c₁) Element of K27(K28(NAT, the carrier of c₁))
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
np is Element of the carrier of c₁
eval ((0_. c₁),np) is Element of the carrier of c₁
c₁ is non empty unital doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
0_. c₁ is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support (c₁) Element of K27(K28(NAT, the carrier of c₁))
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
NAT --> (0. c₁) is Relation-like NAT -defined the carrier of c₁ -valued T-Sequence-like Function-like constant non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
c₁ is non empty unital doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
K27( the carrier of c₁) is set
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
{ b₁ where b₁ is Element of the carrier of c₁ : (c₁,np,b₁) } is set
z0 is set
k is Element of the carrier of c₁
z0 is Element of K27( the carrier of c₁)
k is Element of the carrier of c₁
k1 is Element of the carrier of c₁
z0 is Element of K27( the carrier of c₁)
k is Element of K27( the carrier of c₁)
k1 is set
sq is Element of the carrier of c₁
k1 is set
sq is Element of the carrier of c₁
c₁ is non empty almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(len np) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . ((len np) -' 1) is Element of the carrier of c₁
z0 is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
z0 . k is Element of the carrier of c₁
np . k is Element of the carrier of c₁
(np . k) / (np . ((len np) -' 1)) is Element of the carrier of c₁
z0 is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
k is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
k1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
z0 . k1 is Element of the carrier of c₁
np . k1 is Element of the carrier of c₁
(np . k1) / (np . ((len np) -' 1)) is Element of the carrier of c₁
k . k1 is Element of the carrier of c₁
c₁ is non empty left_add-cancelable right_add-cancelable right_complementable almost_left_invertible add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital domRing-like V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,np) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
(c₁,np) . z0 is set
k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . k is Element of the carrier of c₁
(len np) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . ((len np) -' 1) is Element of the carrier of c₁
(np . k) / (np . ((len np) -' 1)) is Element of the carrier of c₁
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
(0. c₁) / (np . ((len np) -' 1)) is Element of the carrier of c₁
(np . ((len np) -' 1)) " is Element of the carrier of c₁
(0. c₁) * ((np . ((len np) -' 1)) ") is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . ((0. c₁),((np . ((len np) -' 1)) ")) is Element of the carrier of c₁
c₁ is non empty almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
1. c₁ is Element of the carrier of c₁
the OneF of c₁ is Element of the carrier of c₁
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,np) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of c₁))
(len np) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,np) . ((len np) -' 1) is Element of the carrier of c₁
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
((len np) -' 1) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . ((len np) -' 1) is Element of the carrier of c₁
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
(np . ((len np) -' 1)) / (np . ((len np) -' 1)) is Element of the carrier of c₁
(np . ((len np) -' 1)) " is Element of the carrier of c₁
(np . ((len np) -' 1)) * ((np . ((len np) -' 1)) ") is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . ((np . ((len np) -' 1)),((np . ((len np) -' 1)) ")) is Element of the carrier of c₁
c₁ is non empty non degenerated V94() left_add-cancelable right_add-cancelable right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital domRing-like V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty V19() set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,np) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len (c₁,np) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(len np) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
((len np) -' 1) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . ((len np) -' 1) is Element of the carrier of c₁
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
(np . ((len np) -' 1)) " is Element of the carrier of c₁
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
np . k is set
(c₁,np) . k is set
k1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . k1 is Element of the carrier of c₁
(np . k1) / (np . ((len np) -' 1)) is Element of the carrier of c₁
(np . k1) * ((np . ((len np) -' 1)) ") is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . ((np . k1),((np . ((len np) -' 1)) ")) is Element of the carrier of c₁
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
(c₁,np) . z0 is set
k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . k is Element of the carrier of c₁
(np . k) / (np . ((len np) -' 1)) is Element of the carrier of c₁
(0. c₁) / (np . ((len np) -' 1)) is Element of the carrier of c₁
(0. c₁) * ((np . ((len np) -' 1)) ") is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . ((0. c₁),((np . ((len np) -' 1)) ")) is Element of the carrier of c₁
c₁ is non empty non degenerated V94() left_add-cancelable right_add-cancelable right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital domRing-like V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty V19() set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,np) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(len np) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . ((len np) -' 1) is Element of the carrier of c₁
k is Element of the carrier of c₁
eval ((c₁,np),k) is Element of the carrier of c₁
eval (np,k) is Element of the carrier of c₁
(eval (np,k)) / (np . ((len np) -' 1)) is Element of the carrier of c₁
power c₁ is Relation-like K28( the carrier of c₁,NAT) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁))
K28( the carrier of c₁,NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of c₁,NAT), the carrier of c₁) is V24() set
K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁)) is V24() set
k1 is Relation-like NAT -defined the carrier of c₁ -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of c₁
Sum k1 is Element of the carrier of c₁
len k1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom k1 is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
len (c₁,np) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
sq is Relation-like NAT -defined the carrier of c₁ -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of c₁
Sum sq is Element of the carrier of c₁
len sq is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom sq is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
F2 is set
c₈ is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₈ -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . (c₈ -' 1) is Element of the carrier of c₁
(power c₁) . (k,(c₈ -' 1)) is Element of the carrier of c₁
(np . (c₈ -' 1)) * ((power c₁) . (k,(c₈ -' 1))) is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . ((np . (c₈ -' 1)),((power c₁) . (k,(c₈ -' 1)))) is Element of the carrier of c₁
k1 . F2 is set
k1 /. F2 is Element of the carrier of c₁
sq /. F2 is Element of the carrier of c₁
sq . F2 is set
(c₁,np) . (c₈ -' 1) is Element of the carrier of c₁
((c₁,np) . (c₈ -' 1)) * ((power c₁) . (k,(c₈ -' 1))) is Element of the carrier of c₁
the multF of c₁ . (((c₁,np) . (c₈ -' 1)),((power c₁) . (k,(c₈ -' 1)))) is Element of the carrier of c₁
(np . (c₈ -' 1)) / (np . ((len np) -' 1)) is Element of the carrier of c₁
((np . (c₈ -' 1)) / (np . ((len np) -' 1))) * ((power c₁) . (k,(c₈ -' 1))) is Element of the carrier of c₁
the multF of c₁ . (((np . (c₈ -' 1)) / (np . ((len np) -' 1))),((power c₁) . (k,(c₈ -' 1)))) is Element of the carrier of c₁
(np . ((len np) -' 1)) " is Element of the carrier of c₁
(np . (c₈ -' 1)) * ((np . ((len np) -' 1)) ") is Element of the carrier of c₁
the multF of c₁ . ((np . (c₈ -' 1)),((np . ((len np) -' 1)) ")) is Element of the carrier of c₁
((np . (c₈ -' 1)) * ((np . ((len np) -' 1)) ")) * ((power c₁) . (k,(c₈ -' 1))) is Element of the carrier of c₁
the multF of c₁ . (((np . (c₈ -' 1)) * ((np . ((len np) -' 1)) ")),((power c₁) . (k,(c₈ -' 1)))) is Element of the carrier of c₁
(k1 /. F2) * ((np . ((len np) -' 1)) ") is Element of the carrier of c₁
the multF of c₁ . ((k1 /. F2),((np . ((len np) -' 1)) ")) is Element of the carrier of c₁
k1 * ((np . ((len np) -' 1)) ") is Relation-like NAT -defined the carrier of c₁ -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of c₁
(eval (np,k)) * ((np . ((len np) -' 1)) ") is Element of the carrier of c₁
the multF of c₁ . ((eval (np,k)),((np . ((len np) -' 1)) ")) is Element of the carrier of c₁
c₁ is non empty non degenerated V94() left_add-cancelable right_add-cancelable right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital domRing-like V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty V19() set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,np) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(len np) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
((len np) -' 1) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . ((len np) -' 1) is Element of the carrier of c₁
0. c₁ is zero Element of the carrier of c₁
the ZeroF of c₁ is Element of the carrier of c₁
(np . ((len np) -' 1)) " is Element of the carrier of c₁
z0 is Element of the carrier of c₁
eval (np,z0) is Element of the carrier of c₁
eval ((c₁,np),z0) is Element of the carrier of c₁
(0. c₁) / (np . ((len np) -' 1)) is Element of the carrier of c₁
(0. c₁) * ((np . ((len np) -' 1)) ") is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . ((0. c₁),((np . ((len np) -' 1)) ")) is Element of the carrier of c₁
eval ((c₁,np),z0) is Element of the carrier of c₁
eval (np,z0) is Element of the carrier of c₁
(eval (np,z0)) / (np . ((len np) -' 1)) is Element of the carrier of c₁
(eval (np,z0)) * ((np . ((len np) -' 1)) ") is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . ((eval (np,z0)),((np . ((len np) -' 1)) ")) is Element of the carrier of c₁
c₁ is non empty non degenerated V94() left_add-cancelable right_add-cancelable right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital domRing-like V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty V19() set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,np) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
z0 is Element of the carrier of c₁
z0 is Element of the carrier of c₁
c₁ is non empty non degenerated V94() left_add-cancelable right_add-cancelable right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital domRing-like V174() V175() V176() V177() doubleLoopStr
the carrier of c₁ is non empty V19() set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(c₁,np) is Element of K27( the carrier of c₁)
K27( the carrier of c₁) is set
(c₁,np) is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
(c₁,(c₁,np)) is Element of K27( the carrier of c₁)
z0 is set
k is Element of the carrier of c₁
z0 is set
k is Element of the carrier of c₁
id COMPLEX is Relation-like COMPLEX -defined COMPLEX -valued Function-like one-to-one non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
c₁ is complex Element of COMPLEX
np is complex real ext-real Element of REAL
z0 is complex real ext-real Element of REAL
k is complex Element of COMPLEX
k - c₁ is complex Element of COMPLEX
- c₁ is complex set
k + (- c₁) is complex set
|.(k - c₁).| is complex real ext-real Element of REAL
(id COMPLEX) /. c₁ is complex Element of COMPLEX
(id COMPLEX) . c₁ is complex Element of COMPLEX
(id COMPLEX) /. k is complex Element of COMPLEX
(id COMPLEX) . k is complex Element of COMPLEX
((id COMPLEX) /. k) - ((id COMPLEX) /. c₁) is complex Element of COMPLEX
- ((id COMPLEX) /. c₁) is complex set
((id COMPLEX) /. k) + (- ((id COMPLEX) /. c₁)) is complex set
|.(((id COMPLEX) /. k) - ((id COMPLEX) /. c₁)).| is complex real ext-real Element of REAL
dom (id COMPLEX) is set
c₁ is complex Element of COMPLEX
COMPLEX --> c₁ is Relation-like COMPLEX -defined COMPLEX -valued Function-like constant non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
np is complex Element of COMPLEX
z0 is complex real ext-real Element of REAL
k is complex real ext-real Element of REAL
k1 is complex Element of COMPLEX
k1 - np is complex Element of COMPLEX
- np is complex set
k1 + (- np) is complex set
|.(k1 - np).| is complex real ext-real Element of REAL
(COMPLEX --> c₁) /. np is complex Element of COMPLEX
(COMPLEX --> c₁) . np is complex Element of COMPLEX
(COMPLEX --> c₁) /. k1 is complex Element of COMPLEX
(COMPLEX --> c₁) . k1 is complex Element of COMPLEX
((COMPLEX --> c₁) /. k1) - ((COMPLEX --> c₁) /. np) is complex Element of COMPLEX
- ((COMPLEX --> c₁) /. np) is complex set
((COMPLEX --> c₁) /. k1) + (- ((COMPLEX --> c₁) /. np)) is complex set
|.(((COMPLEX --> c₁) /. k1) - ((COMPLEX --> c₁) /. np)).| is complex real ext-real Element of REAL
dom (COMPLEX --> c₁) is set
c₁ is non empty unital multMagma
the carrier of c₁ is non empty set
K28( the carrier of c₁, the carrier of c₁) is set
K27(K28( the carrier of c₁, the carrier of c₁)) is set
np is Element of the carrier of c₁
power c₁ is Relation-like K28( the carrier of c₁,NAT) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁))
K28( the carrier of c₁,NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of c₁,NAT), the carrier of c₁) is V24() set
K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁)) is V24() set
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k is Relation-like the carrier of c₁ -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of c₁, the carrier of c₁))
k1 is Relation-like the carrier of c₁ -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of c₁, the carrier of c₁))
sq is Element of the carrier of c₁
k1 . sq is Element of the carrier of c₁
(power c₁) . (sq,z0) is Element of the carrier of c₁
np * ((power c₁) . (sq,z0)) is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . (np,((power c₁) . (sq,z0))) is Element of the carrier of c₁
k is Relation-like the carrier of c₁ -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of c₁, the carrier of c₁))
k1 is Relation-like the carrier of c₁ -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of c₁, the carrier of c₁))
sq is Element of the carrier of c₁
k . sq is Element of the carrier of c₁
(power c₁) . (sq,z0) is Element of the carrier of c₁
np * ((power c₁) . (sq,z0)) is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . (np,((power c₁) . (sq,z0))) is Element of the carrier of c₁
k1 . sq is Element of the carrier of c₁
c₁ is non empty unital multMagma
the carrier of c₁ is non empty set
1_ c₁ is Element of the carrier of c₁
(c₁,(1_ c₁),1) is Relation-like the carrier of c₁ -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of c₁, the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K27(K28( the carrier of c₁, the carrier of c₁)) is set
id the carrier of c₁ is Relation-like the carrier of c₁ -defined the carrier of c₁ -valued Function-like one-to-one non empty total quasi_total Element of K27(K28( the carrier of c₁, the carrier of c₁))
np is set
z0 is Element of the carrier of c₁
(c₁,(1_ c₁),1) . z0 is Element of the carrier of c₁
power c₁ is Relation-like K28( the carrier of c₁,NAT) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁))
K28( the carrier of c₁,NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of c₁,NAT), the carrier of c₁) is V24() set
K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁)) is V24() set
(power c₁) . (z0,1) is Element of the carrier of c₁
(1_ c₁) * ((power c₁) . (z0,1)) is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . ((1_ c₁),((power c₁) . (z0,1))) is Element of the carrier of c₁
(c₁,(1_ c₁),1) . np is set
dom (c₁,(1_ c₁),1) is set
(F_Complex,(1_ F_Complex),2) is Relation-like the carrier of F_Complex -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of F_Complex, the carrier of F_Complex))
K28( the carrier of F_Complex, the carrier of F_Complex) is set
K27(K28( the carrier of F_Complex, the carrier of F_Complex)) is set
(id COMPLEX) (#) (id COMPLEX) is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
np is complex Element of the carrier of F_Complex
z0 is complex Element of COMPLEX
(id COMPLEX) /. z0 is complex Element of COMPLEX
(id COMPLEX) . z0 is complex Element of COMPLEX
dom ((id COMPLEX) (#) (id COMPLEX)) is set
c₁ is Relation-like the carrier of F_Complex -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of F_Complex, the carrier of F_Complex))
c₁ . np is complex Element of the carrier of F_Complex
np * np is complex Element of the carrier of F_Complex
the multF of F_Complex is Relation-like K28( the carrier of F_Complex, the carrier of F_Complex) -defined the carrier of F_Complex -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex))
K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex) is set
K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex)) is set
the multF of F_Complex . (np,np) is complex Element of the carrier of F_Complex
K595(np,np) is complex Element of COMPLEX
(power F_Complex) . (np,2) is complex Element of the carrier of F_Complex
(1_ F_Complex) * ((power F_Complex) . (np,2)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((1_ F_Complex),((power F_Complex) . (np,2))) is complex Element of the carrier of F_Complex
K595((1_ F_Complex),((power F_Complex) . (np,2))) is complex Element of COMPLEX
c₁ is non empty unital multMagma
the carrier of c₁ is non empty set
np is Element of the carrier of c₁
(c₁,np,0) is Relation-like the carrier of c₁ -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of c₁, the carrier of c₁))
K28( the carrier of c₁, the carrier of c₁) is set
K27(K28( the carrier of c₁, the carrier of c₁)) is set
the carrier of c₁ --> np is Relation-like the carrier of c₁ -defined the carrier of c₁ -valued Function-like constant non empty total quasi_total Element of K27(K28( the carrier of c₁, the carrier of c₁))
z0 is Relation-like the carrier of c₁ -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of c₁, the carrier of c₁))
k is Element of the carrier of c₁
z0 . k is Element of the carrier of c₁
1_ c₁ is Element of the carrier of c₁
np * (1_ c₁) is Element of the carrier of c₁
the multF of c₁ is Relation-like K28( the carrier of c₁, the carrier of c₁) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁))
K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁) is set
K27(K28(K28( the carrier of c₁, the carrier of c₁), the carrier of c₁)) is set
the multF of c₁ . (np,(1_ c₁)) is Element of the carrier of c₁
power c₁ is Relation-like K28( the carrier of c₁,NAT) -defined the carrier of c₁ -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁))
K28( the carrier of c₁,NAT) is INT -valued RAT -valued V24() complex-valued ext-real-valued real-valued natural-valued set
K28(K28( the carrier of c₁,NAT), the carrier of c₁) is V24() set
K27(K28(K28( the carrier of c₁,NAT), the carrier of c₁)) is V24() set
(power c₁) . (k,0) is Element of the carrier of c₁
np * ((power c₁) . (k,0)) is Element of the carrier of c₁
the multF of c₁ . (np,((power c₁) . (k,0))) is Element of the carrier of c₁
c₁ is complex Element of the carrier of F_Complex
(F_Complex,c₁,1) is Relation-like the carrier of F_Complex -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of F_Complex, the carrier of F_Complex))
np is complex Element of COMPLEX
np (#) (id COMPLEX) is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
k is complex Element of the carrier of F_Complex
z0 is Relation-like the carrier of F_Complex -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of F_Complex, the carrier of F_Complex))
z0 . k is complex Element of the carrier of F_Complex
k1 is complex Element of COMPLEX
(id COMPLEX) . k1 is complex Element of COMPLEX
np * ((id COMPLEX) . k1) is complex Element of COMPLEX
c₁ * k is complex Element of the carrier of F_Complex
the multF of F_Complex is Relation-like K28( the carrier of F_Complex, the carrier of F_Complex) -defined the carrier of F_Complex -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex))
K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex) is set
K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex)) is set
the multF of F_Complex . (c₁,k) is complex Element of the carrier of F_Complex
K595(c₁,k) is complex Element of COMPLEX
(power F_Complex) . (k,1) is complex Element of the carrier of F_Complex
c₁ * ((power F_Complex) . (k,1)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (c₁,((power F_Complex) . (k,1))) is complex Element of the carrier of F_Complex
K595(c₁,((power F_Complex) . (k,1))) is complex Element of COMPLEX
c₁ is complex Element of the carrier of F_Complex
(F_Complex,c₁,2) is Relation-like the carrier of F_Complex -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of F_Complex, the carrier of F_Complex))
np is complex Element of COMPLEX
np (#) ((id COMPLEX) (#) (id COMPLEX)) is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
k is complex Element of the carrier of F_Complex
z0 is Relation-like the carrier of F_Complex -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of F_Complex, the carrier of F_Complex))
z0 . k is complex Element of the carrier of F_Complex
k1 is complex Element of COMPLEX
((id COMPLEX) (#) (id COMPLEX)) . k1 is complex Element of COMPLEX
np * (((id COMPLEX) (#) (id COMPLEX)) . k1) is complex Element of COMPLEX
(id COMPLEX) . k1 is complex Element of COMPLEX
((id COMPLEX) . k1) * ((id COMPLEX) . k1) is complex Element of COMPLEX
np * (((id COMPLEX) . k1) * ((id COMPLEX) . k1)) is complex Element of COMPLEX
k1 * ((id COMPLEX) . k1) is complex Element of COMPLEX
np * (k1 * ((id COMPLEX) . k1)) is complex Element of COMPLEX
k * k is complex Element of the carrier of F_Complex
the multF of F_Complex is Relation-like K28( the carrier of F_Complex, the carrier of F_Complex) -defined the carrier of F_Complex -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex))
K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex) is set
K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex)) is set
the multF of F_Complex . (k,k) is complex Element of the carrier of F_Complex
K595(k,k) is complex Element of COMPLEX
c₁ * (k * k) is complex Element of the carrier of F_Complex
the multF of F_Complex . (c₁,(k * k)) is complex Element of the carrier of F_Complex
K595(c₁,(k * k)) is complex Element of COMPLEX
(power F_Complex) . (k,2) is complex Element of the carrier of F_Complex
c₁ * ((power F_Complex) . (k,2)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (c₁,((power F_Complex) . (k,2))) is complex Element of the carrier of F_Complex
K595(c₁,((power F_Complex) . (k,2))) is complex Element of COMPLEX
c₁ is complex Element of the carrier of F_Complex
np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(F_Complex,c₁,np) is Relation-like the carrier of F_Complex -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of F_Complex, the carrier of F_Complex))
np + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(F_Complex,c₁,(np + 1)) is Relation-like the carrier of F_Complex -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of F_Complex, the carrier of F_Complex))
z0 is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
z0 (#) (id COMPLEX) is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
k1 is complex Element of the carrier of F_Complex
k is Relation-like the carrier of F_Complex -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of F_Complex, the carrier of F_Complex))
k . k1 is complex Element of the carrier of F_Complex
sq is complex Element of COMPLEX
z0 . sq is complex Element of COMPLEX
(id COMPLEX) . sq is complex Element of COMPLEX
(z0 . sq) * ((id COMPLEX) . sq) is complex Element of COMPLEX
(F_Complex,c₁,np) . k1 is complex Element of the carrier of F_Complex
((F_Complex,c₁,np) . k1) * k1 is complex Element of the carrier of F_Complex
the multF of F_Complex is Relation-like K28( the carrier of F_Complex, the carrier of F_Complex) -defined the carrier of F_Complex -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex))
K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex) is set
K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex)) is set
the multF of F_Complex . (((F_Complex,c₁,np) . k1),k1) is complex Element of the carrier of F_Complex
K595(((F_Complex,c₁,np) . k1),k1) is complex Element of COMPLEX
(power F_Complex) . (k1,np) is complex Element of the carrier of F_Complex
c₁ * ((power F_Complex) . (k1,np)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (c₁,((power F_Complex) . (k1,np))) is complex Element of the carrier of F_Complex
K595(c₁,((power F_Complex) . (k1,np))) is complex Element of COMPLEX
(c₁ * ((power F_Complex) . (k1,np))) * k1 is complex Element of the carrier of F_Complex
the multF of F_Complex . ((c₁ * ((power F_Complex) . (k1,np))),k1) is complex Element of the carrier of F_Complex
K595((c₁ * ((power F_Complex) . (k1,np))),k1) is complex Element of COMPLEX
((power F_Complex) . (k1,np)) * k1 is complex Element of the carrier of F_Complex
the multF of F_Complex . (((power F_Complex) . (k1,np)),k1) is complex Element of the carrier of F_Complex
K595(((power F_Complex) . (k1,np)),k1) is complex Element of COMPLEX
c₁ * (((power F_Complex) . (k1,np)) * k1) is complex Element of the carrier of F_Complex
the multF of F_Complex . (c₁,(((power F_Complex) . (k1,np)) * k1)) is complex Element of the carrier of F_Complex
K595(c₁,(((power F_Complex) . (k1,np)) * k1)) is complex Element of COMPLEX
(power F_Complex) . (k1,(np + 1)) is complex Element of the carrier of F_Complex
c₁ * ((power F_Complex) . (k1,(np + 1))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (c₁,((power F_Complex) . (k1,(np + 1)))) is complex Element of the carrier of F_Complex
K595(c₁,((power F_Complex) . (k1,(np + 1)))) is complex Element of COMPLEX
c₁ is complex Element of the carrier of F_Complex
np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(F_Complex,c₁,np) is Relation-like the carrier of F_Complex -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of F_Complex, the carrier of F_Complex))
np + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(F_Complex,c₁,(np + 1)) is Relation-like the carrier of F_Complex -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of F_Complex, the carrier of F_Complex))
k is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
z0 is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
k1 is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
k1 (#) (id COMPLEX) is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
(F_Complex,c₁,0) is Relation-like the carrier of F_Complex -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of F_Complex, the carrier of F_Complex))
np is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
the carrier of F_Complex --> c₁ is Relation-like the carrier of F_Complex -defined the carrier of F_Complex -valued Function-like constant non empty total quasi_total complex-valued Element of K27(K28( the carrier of F_Complex, the carrier of F_Complex))
c₁ is non empty unital right_unital well-unital left_unital doubleLoopStr
the carrier of c₁ is non empty set
K28(NAT, the carrier of c₁) is V24() set
K27(K28(NAT, the carrier of c₁)) is V24() set
K28( the carrier of c₁, the carrier of c₁) is set
K27(K28( the carrier of c₁, the carrier of c₁)) is set
np is Relation-like NAT -defined the carrier of c₁ -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of c₁))
z0 is Relation-like the carrier of c₁ -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of c₁, the carrier of c₁))
k is Relation-like the carrier of c₁ -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of c₁, the carrier of c₁))
k1 is Element of the carrier of c₁
k . k1 is Element of the carrier of c₁
eval (np,k1) is Element of the carrier of c₁
z0 is Relation-like the carrier of c₁ -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of c₁, the carrier of c₁))
k is Relation-like the carrier of c₁ -defined the carrier of c₁ -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of c₁, the carrier of c₁))
k1 is Element of the carrier of c₁
z0 . k1 is Element of the carrier of c₁
eval (np,k1) is Element of the carrier of c₁
k . k1 is Element of the carrier of c₁
K28(NAT, the carrier of F_Complex) is V24() set
K27(K28(NAT, the carrier of F_Complex)) is V24() set
Funcs (COMPLEX,COMPLEX) is functional non empty FUNCTION_DOMAIN of COMPLEX , COMPLEX
np is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of F_Complex))
(F_Complex,np) is Relation-like the carrier of F_Complex -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of F_Complex, the carrier of F_Complex))
COMPLEX --> 0c is Relation-like COMPLEX -defined COMPLEX -valued Function-like constant non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
k is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
k1 is Relation-like COMPLEX -defined COMPLEX -valued Function-like total quasi_total complex-valued Element of Funcs (COMPLEX,COMPLEX)
sq is Relation-like COMPLEX -defined COMPLEX -valued Function-like total quasi_total complex-valued Element of Funcs (COMPLEX,COMPLEX)
k1 + sq is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
K28((Funcs (COMPLEX,COMPLEX)),(Funcs (COMPLEX,COMPLEX))) is set
K28(K28((Funcs (COMPLEX,COMPLEX)),(Funcs (COMPLEX,COMPLEX))),(Funcs (COMPLEX,COMPLEX))) is set
K27(K28(K28((Funcs (COMPLEX,COMPLEX)),(Funcs (COMPLEX,COMPLEX))),(Funcs (COMPLEX,COMPLEX)))) is set
k1 is Relation-like K28((Funcs (COMPLEX,COMPLEX)),(Funcs (COMPLEX,COMPLEX))) -defined Funcs (COMPLEX,COMPLEX) -valued Function-like total quasi_total Function-yielding V87() Element of K27(K28(K28((Funcs (COMPLEX,COMPLEX)),(Funcs (COMPLEX,COMPLEX))),(Funcs (COMPLEX,COMPLEX))))
z0 is Relation-like COMPLEX -defined COMPLEX -valued Function-like total quasi_total complex-valued Element of Funcs (COMPLEX,COMPLEX)
addLoopStr(# (Funcs (COMPLEX,COMPLEX)),k1,z0 #) is strict addLoopStr
sq is non empty addLoopStr
the carrier of sq is non empty set
F2 is Element of the carrier of sq
c₈ is Element of the carrier of sq
z1 is Element of the carrier of sq
F1 is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
gc is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
F1 + gc is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
i is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
gc + i is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
F2 + c₈ is Element of the carrier of sq
the addF of sq is Relation-like K28( the carrier of sq, the carrier of sq) -defined the carrier of sq -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of sq, the carrier of sq), the carrier of sq))
K28( the carrier of sq, the carrier of sq) is set
K28(K28( the carrier of sq, the carrier of sq), the carrier of sq) is set
K27(K28(K28( the carrier of sq, the carrier of sq), the carrier of sq)) is set
the addF of sq . (F2,c₈) is Element of the carrier of sq
(F2 + c₈) + z1 is Element of the carrier of sq
the addF of sq . ((F2 + c₈),z1) is Element of the carrier of sq
k1 . ((F1 + gc),z1) is set
(F1 + gc) + i is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
F1 + (gc + i) is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
k1 . (F2,(gc + i)) is set
c₈ + z1 is Element of the carrier of sq
the addF of sq . (c₈,z1) is Element of the carrier of sq
F2 + (c₈ + z1) is Element of the carrier of sq
the addF of sq . (F2,(c₈ + z1)) is Element of the carrier of sq
F2 is Element of the carrier of sq
c₈ is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
c₈ + z0 is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
z1 is complex Element of COMPLEX
(c₈ + z0) . z1 is complex Element of COMPLEX
c₈ . z1 is complex Element of COMPLEX
z0 . z1 is complex Element of COMPLEX
(c₈ . z1) + (z0 . z1) is complex Element of COMPLEX
(c₈ . z1) + 0c is complex Element of COMPLEX
0. sq is zero Element of the carrier of sq
the ZeroF of sq is Element of the carrier of sq
F2 + (0. sq) is Element of the carrier of sq
the addF of sq . (F2,(0. sq)) is Element of the carrier of sq
F2 is Element of the carrier of sq
c₈ is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
- c₈ is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
z1 is Element of the carrier of sq
F2 + z1 is Element of the carrier of sq
the addF of sq . (F2,z1) is Element of the carrier of sq
c₈ + (- c₈) is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
F1 is complex Element of COMPLEX
(c₈ + (- c₈)) . F1 is complex Element of COMPLEX
c₈ . F1 is complex Element of COMPLEX
(- c₈) . F1 is complex Element of COMPLEX
(c₈ . F1) + ((- c₈) . F1) is complex Element of COMPLEX
- (c₈ . F1) is complex Element of COMPLEX
(c₈ . F1) + (- (c₈ . F1)) is complex Element of COMPLEX
z0 . F1 is complex Element of COMPLEX
F2 is non empty left_add-cancelable right_add-cancelable right_complementable add-associative right_zeroed V174() V175() V176() V177() addLoopStr
the carrier of F2 is non empty set
c₈ is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
c₈ -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . (c₈ -' 1) is complex Element of the carrier of F_Complex
(F_Complex,(np . (c₈ -' 1)),(c₈ -' 1)) is Relation-like the carrier of F_Complex -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of F_Complex, the carrier of F_Complex))
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
Seg (len np) is V24() V31( len np) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
z1 is Element of the carrier of F2
F1 is Element of the carrier of F2
c₈ is Relation-like NAT -defined the carrier of F2 -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F2
dom c₈ is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
len c₈ is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₈ | (len c₈) is Relation-like NAT -defined the carrier of F2 -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F2
Sum c₈ is Element of the carrier of F2
F1 is complex Element of COMPLEX
gc is complex Element of the carrier of F_Complex
eval (np,gc) is complex Element of the carrier of F_Complex
i is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
Sum i is complex Element of the carrier of F_Complex
len i is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom i is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
eg is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₈ | eg is Relation-like NAT -defined the carrier of F2 -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F2
Sum (c₈ | eg) is Element of the carrier of F2
i | eg is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
Sum (i | eg) is complex Element of the carrier of F_Complex
eg + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₈ | (eg + 1) is Relation-like NAT -defined the carrier of F2 -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F2
Sum (c₈ | (eg + 1)) is Element of the carrier of F2
i | (eg + 1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
Sum (i | (eg + 1)) is complex Element of the carrier of F_Complex
R is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
R . F1 is complex Element of COMPLEX
np . eg is complex Element of the carrier of F_Complex
(F_Complex,(np . eg),eg) is Relation-like the carrier of F_Complex -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of F_Complex, the carrier of F_Complex))
c₈ /. (eg + 1) is Element of the carrier of F2
c₈ . (eg + 1) is set
(eg + 1) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . ((eg + 1) -' 1) is complex Element of the carrier of F_Complex
(F_Complex,(np . ((eg + 1) -' 1)),((eg + 1) -' 1)) is Relation-like the carrier of F_Complex -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of F_Complex, the carrier of F_Complex))
(F_Complex,(np . eg),((eg + 1) -' 1)) is Relation-like the carrier of F_Complex -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of F_Complex, the carrier of F_Complex))
<*(c₈ . (eg + 1))*> is Relation-like NAT -defined Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like set
(c₈ | eg) ^ <*(c₈ . (eg + 1))*> is Relation-like NAT -defined Function-like non empty V24() FinSequence-like FinSubsequence-like set
<*(c₈ /. (eg + 1))*> is Relation-like NAT -defined the carrier of F2 -valued Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of F2
(c₈ | eg) ^ <*(c₈ /. (eg + 1))*> is Relation-like NAT -defined the carrier of F2 -valued Function-like non empty V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F2
(Sum (c₈ | eg)) + (c₈ /. (eg + 1)) is Element of the carrier of F2
the addF of F2 is Relation-like K28( the carrier of F2, the carrier of F2) -defined the carrier of F2 -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of F2, the carrier of F2), the carrier of F2))
K28( the carrier of F2, the carrier of F2) is set
K28(K28( the carrier of F2, the carrier of F2), the carrier of F2) is set
K27(K28(K28( the carrier of F2, the carrier of F2), the carrier of F2)) is set
the addF of F2 . ((Sum (c₈ | eg)),(c₈ /. (eg + 1))) is Element of the carrier of F2
PF is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
z is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
PF + z is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
PF . F1 is complex Element of COMPLEX
i /. (eg + 1) is complex Element of the carrier of F_Complex
i . (eg + 1) is set
(power F_Complex) . (gc,((eg + 1) -' 1)) is complex Element of the carrier of F_Complex
(np . ((eg + 1) -' 1)) * ((power F_Complex) . (gc,((eg + 1) -' 1))) is complex Element of the carrier of F_Complex
the multF of F_Complex is Relation-like K28( the carrier of F_Complex, the carrier of F_Complex) -defined the carrier of F_Complex -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex))
K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex) is set
K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex)) is set
the multF of F_Complex . ((np . ((eg + 1) -' 1)),((power F_Complex) . (gc,((eg + 1) -' 1)))) is complex Element of the carrier of F_Complex
K595((np . ((eg + 1) -' 1)),((power F_Complex) . (gc,((eg + 1) -' 1)))) is complex Element of COMPLEX
(np . eg) * ((power F_Complex) . (gc,((eg + 1) -' 1))) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((np . eg),((power F_Complex) . (gc,((eg + 1) -' 1)))) is complex Element of the carrier of F_Complex
K595((np . eg),((power F_Complex) . (gc,((eg + 1) -' 1)))) is complex Element of COMPLEX
(power F_Complex) . (gc,eg) is complex Element of the carrier of F_Complex
(np . eg) * ((power F_Complex) . (gc,eg)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((np . eg),((power F_Complex) . (gc,eg))) is complex Element of the carrier of F_Complex
K595((np . eg),((power F_Complex) . (gc,eg))) is complex Element of COMPLEX
(F_Complex,(np . eg),eg) . F1 is set
<*(i . (eg + 1))*> is Relation-like NAT -defined Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like set
(i | eg) ^ <*(i . (eg + 1))*> is Relation-like NAT -defined Function-like non empty V24() FinSequence-like FinSubsequence-like set
<*(i /. (eg + 1))*> is Relation-like NAT -defined the carrier of F_Complex -valued Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
(i | eg) ^ <*(i /. (eg + 1))*> is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
(Sum (i | eg)) + (i /. (eg + 1)) is complex Element of the carrier of F_Complex
the addF of F_Complex is Relation-like K28( the carrier of F_Complex, the carrier of F_Complex) -defined the carrier of F_Complex -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex))
the addF of F_Complex . ((Sum (i | eg)),(i /. (eg + 1))) is complex Element of the carrier of F_Complex
K593((Sum (i | eg)),(i /. (eg + 1))) is complex Element of COMPLEX
c₈ | 0 is Relation-like NAT -defined RAT -valued the carrier of F2 -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Function-like one-to-one constant functional empty V24() V29() V31( {} ) FinSequence-like FinSubsequence-like FinSequence-membered complex real ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V54() V56() V57() V58() V59() V60() V61() V62() Function-yielding V87() FinSequence of the carrier of F2
Sum (c₈ | 0) is Element of the carrier of F2
i | 0 is Relation-like NAT -defined the carrier of F_Complex -valued RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Function-like one-to-one constant functional empty V24() V29() V31( {} ) FinSequence-like FinSubsequence-like FinSequence-membered complex real ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V54() V56() V57() V58() V59() V60() V61() V62() Function-yielding V87() FinSequence of the carrier of F_Complex
Sum (i | 0) is complex Element of the carrier of F_Complex
eg is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
eg . F1 is complex Element of COMPLEX
<*> the carrier of F2 is Relation-like NAT -defined the carrier of F2 -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Function-like one-to-one constant functional empty V24() V29() V31( {} ) FinSequence-like FinSubsequence-like FinSequence-membered complex real ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V54() V56() V57() V58() V59() V60() V61() V62() Function-yielding V87() FinSequence of the carrier of F2
0. F2 is zero Element of the carrier of F2
the ZeroF of F2 is Element of the carrier of F2
Sum (c₈ | (len c₈)) is Element of the carrier of F2
z1 is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
k . F1 is complex Element of COMPLEX
i | (len i) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
Sum (i | (len i)) is complex Element of the carrier of F_Complex
z1 . F1 is complex Element of COMPLEX
F1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₈ | F1 is Relation-like NAT -defined the carrier of F2 -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F2
Sum (c₈ | F1) is Element of the carrier of F2
F1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₈ | (F1 + 1) is Relation-like NAT -defined the carrier of F2 -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F2
Sum (c₈ | (F1 + 1)) is Element of the carrier of F2
gc is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
i is Relation-like COMPLEX -defined COMPLEX -valued Function-like complex-valued Element of K27(K28(COMPLEX,COMPLEX))
c₈ /. (F1 + 1) is Element of the carrier of F2
c₈ . (F1 + 1) is set
(F1 + 1) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . ((F1 + 1) -' 1) is complex Element of the carrier of F_Complex
(F_Complex,(np . ((F1 + 1) -' 1)),((F1 + 1) -' 1)) is Relation-like the carrier of F_Complex -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of F_Complex, the carrier of F_Complex))
np . F1 is complex Element of the carrier of F_Complex
(F_Complex,(np . F1),((F1 + 1) -' 1)) is Relation-like the carrier of F_Complex -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of F_Complex, the carrier of F_Complex))
(F_Complex,(np . F1),F1) is Relation-like the carrier of F_Complex -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of F_Complex, the carrier of F_Complex))
eg is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
<*(c₈ . (F1 + 1))*> is Relation-like NAT -defined Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like set
(c₈ | F1) ^ <*(c₈ . (F1 + 1))*> is Relation-like NAT -defined Function-like non empty V24() FinSequence-like FinSubsequence-like set
<*(c₈ /. (F1 + 1))*> is Relation-like NAT -defined the carrier of F2 -valued Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of F2
(c₈ | F1) ^ <*(c₈ /. (F1 + 1))*> is Relation-like NAT -defined the carrier of F2 -valued Function-like non empty V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F2
(Sum (c₈ | F1)) + (c₈ /. (F1 + 1)) is Element of the carrier of F2
the addF of F2 is Relation-like K28( the carrier of F2, the carrier of F2) -defined the carrier of F2 -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of F2, the carrier of F2), the carrier of F2))
K28( the carrier of F2, the carrier of F2) is set
K28(K28( the carrier of F2, the carrier of F2), the carrier of F2) is set
K27(K28(K28( the carrier of F2, the carrier of F2), the carrier of F2)) is set
the addF of F2 . ((Sum (c₈ | F1)),(c₈ /. (F1 + 1))) is Element of the carrier of F2
gc + eg is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
F1 is Relation-like COMPLEX -defined COMPLEX -valued Function-like complex-valued Element of K27(K28(COMPLEX,COMPLEX))
<*> the carrier of F2 is Relation-like NAT -defined the carrier of F2 -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Function-like one-to-one constant functional empty V24() V29() V31( {} ) FinSequence-like FinSubsequence-like FinSequence-membered complex real ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V54() V56() V57() V58() V59() V60() V61() V62() Function-yielding V87() FinSequence of the carrier of F2
0. F2 is zero Element of the carrier of F2
the ZeroF of F2 is Element of the carrier of F2
c₁ is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of F_Complex))
len c₁ is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(len c₁) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₁ . ((len c₁) -' 1) is complex Element of the carrier of F_Complex
|.(c₁ . ((len c₁) -' 1)).| is complex real ext-real Element of REAL
c₁ . 0 is complex Element of the carrier of F_Complex
|.(c₁ . 0).| is complex real ext-real Element of REAL
|.(c₁ . 0).| + 1 is complex real ext-real Element of REAL
np is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len np is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom np is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
Sum np is complex real ext-real Element of REAL
K294(REAL,np,K623()) is complex real ext-real Element of REAL
(len np) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
((len np) -' 1) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np | (((len np) -' 1) + 1) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
np | ((len np) -' 1) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
np /. (((len np) -' 1) + 1) is complex real ext-real Element of REAL
<*(np /. (((len np) -' 1) + 1))*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued increasing decreasing non-decreasing non-increasing FinSequence of REAL
(np | ((len np) -' 1)) ^ <*(np /. (((len np) -' 1) + 1))*> is Relation-like NAT -defined REAL -valued Function-like non empty V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
dom (np | ((len np) -' 1)) is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(np | ((len np) -' 1)) . k is complex real ext-real Element of REAL
(np | ((len np) -' 1)) /. k is complex real ext-real Element of REAL
np /. k is complex real ext-real Element of REAL
np . k is complex real ext-real Element of REAL
k -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₁ . (k -' 1) is complex Element of the carrier of F_Complex
|.(c₁ . (k -' 1)).| is complex real ext-real Element of REAL
len (np | ((len np) -' 1)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k is complex Element of the carrier of F_Complex
|.k.| is complex real ext-real Element of REAL
eval (c₁,k) is complex Element of the carrier of F_Complex
|.(eval (c₁,k)).| is complex real ext-real Element of REAL
k1 is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
Sum k1 is complex Element of the carrier of F_Complex
len k1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom k1 is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
(len np) -' 2 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np . (((len np) -' 1) + 1) is complex real ext-real Element of REAL
Sum (np | ((len np) -' 1)) is complex real ext-real Element of REAL
K294(REAL,(np | ((len np) -' 1)),K623()) is complex real ext-real Element of REAL
(Sum (np | ((len np) -' 1))) + 1 is complex real ext-real Element of REAL
1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(1 + 1) + 0 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(np | ((len np) -' 1)) . 1 is complex real ext-real Element of REAL
(np | ((len np) -' 1)) /. 1 is complex real ext-real Element of REAL
np /. 1 is complex real ext-real Element of REAL
np . 1 is complex real ext-real Element of REAL
1 -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₁ . (1 -' 1) is complex Element of the carrier of F_Complex
|.(c₁ . (1 -' 1)).| is complex real ext-real Element of REAL
k1 | (((len np) -' 1) + 1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
k1 | ((len np) -' 1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
k1 /. (((len np) -' 1) + 1) is complex Element of the carrier of F_Complex
<*(k1 /. (((len np) -' 1) + 1))*> is Relation-like NAT -defined the carrier of F_Complex -valued Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
(k1 | ((len np) -' 1)) ^ <*(k1 /. (((len np) -' 1) + 1))*> is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
Sum (k1 | ((len np) -' 1)) is complex Element of the carrier of F_Complex
(Sum (k1 | ((len np) -' 1))) + (k1 /. (((len np) -' 1) + 1)) is complex Element of the carrier of F_Complex
the addF of F_Complex is Relation-like K28( the carrier of F_Complex, the carrier of F_Complex) -defined the carrier of F_Complex -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex))
K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex) is set
K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex)) is set
the addF of F_Complex . ((Sum (k1 | ((len np) -' 1))),(k1 /. (((len np) -' 1) + 1))) is complex Element of the carrier of F_Complex
K593((Sum (k1 | ((len np) -' 1))),(k1 /. (((len np) -' 1) + 1))) is complex Element of COMPLEX
k1 . (((len np) -' 1) + 1) is set
c₁ . ((len np) -' 1) is complex Element of the carrier of F_Complex
(power F_Complex) . (k,((len np) -' 1)) is complex Element of the carrier of F_Complex
(c₁ . ((len np) -' 1)) * ((power F_Complex) . (k,((len np) -' 1))) is complex Element of the carrier of F_Complex
the multF of F_Complex is Relation-like K28( the carrier of F_Complex, the carrier of F_Complex) -defined the carrier of F_Complex -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex))
the multF of F_Complex . ((c₁ . ((len np) -' 1)),((power F_Complex) . (k,((len np) -' 1)))) is complex Element of the carrier of F_Complex
K595((c₁ . ((len np) -' 1)),((power F_Complex) . (k,((len np) -' 1)))) is complex Element of COMPLEX
|.(k1 /. (((len np) -' 1) + 1)).| is complex real ext-real Element of REAL
|.((power F_Complex) . (k,((len np) -' 1))).| is complex real ext-real Element of REAL
1 * |.((power F_Complex) . (k,((len np) -' 1))).| is complex real ext-real Element of REAL
|.(Sum (k1 | ((len np) -' 1))).| is complex real ext-real Element of REAL
|.((power F_Complex) . (k,((len np) -' 1))).| - |.(Sum (k1 | ((len np) -' 1))).| is complex real ext-real Element of REAL
- |.(Sum (k1 | ((len np) -' 1))).| is complex real ext-real set
|.((power F_Complex) . (k,((len np) -' 1))).| + (- |.(Sum (k1 | ((len np) -' 1))).|) is complex real ext-real set
1 + 0 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(len np) - 1 is complex real ext-real V54() Element of REAL
- 1 is non empty complex real ext-real non positive negative V54() set
(len np) + (- 1) is complex real ext-real V54() set
len (k1 | ((len np) -' 1)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(np | ((len np) -' 1)) | (len (np | ((len np) -' 1))) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(k1 | ((len np) -' 1)) | (len (np | ((len np) -' 1))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
(power F_Complex) . (k,((len np) -' 2)) is complex Element of the carrier of F_Complex
|.((power F_Complex) . (k,((len np) -' 2))).| is complex real ext-real Element of REAL
(len np) - 2 is complex real ext-real V54() Element of REAL
- 2 is non empty complex real ext-real non positive negative V54() set
(len np) + (- 2) is complex real ext-real V54() set
((len np) -' 2) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
((len np) - 2) + 1 is complex real ext-real V54() Element of REAL
((power F_Complex) . (k,((len np) -' 2))) * k is complex Element of the carrier of F_Complex
the multF of F_Complex . (((power F_Complex) . (k,((len np) -' 2))),k) is complex Element of the carrier of F_Complex
K595(((power F_Complex) . (k,((len np) -' 2))),k) is complex Element of COMPLEX
|.((power F_Complex) . (k,((len np) -' 2))).| * (Sum (np | ((len np) -' 1))) is complex real ext-real Element of REAL
|.((power F_Complex) . (k,((len np) -' 1))).| - (|.((power F_Complex) . (k,((len np) -' 2))).| * (Sum (np | ((len np) -' 1)))) is complex real ext-real Element of REAL
- (|.((power F_Complex) . (k,((len np) -' 2))).| * (Sum (np | ((len np) -' 1)))) is complex real ext-real set
|.((power F_Complex) . (k,((len np) -' 1))).| + (- (|.((power F_Complex) . (k,((len np) -' 2))).| * (Sum (np | ((len np) -' 1))))) is complex real ext-real set
|.((power F_Complex) . (k,((len np) -' 2))).| * |.k.| is complex real ext-real Element of REAL
(|.((power F_Complex) . (k,((len np) -' 2))).| * |.k.|) - (|.((power F_Complex) . (k,((len np) -' 2))).| * (Sum (np | ((len np) -' 1)))) is complex real ext-real Element of REAL
(|.((power F_Complex) . (k,((len np) -' 2))).| * |.k.|) + (- (|.((power F_Complex) . (k,((len np) -' 2))).| * (Sum (np | ((len np) -' 1))))) is complex real ext-real set
|.k.| - (Sum (np | ((len np) -' 1))) is complex real ext-real Element of REAL
- (Sum (np | ((len np) -' 1))) is complex real ext-real set
|.k.| + (- (Sum (np | ((len np) -' 1)))) is complex real ext-real set
|.((power F_Complex) . (k,((len np) -' 2))).| * (|.k.| - (Sum (np | ((len np) -' 1)))) is complex real ext-real Element of REAL
dom (k1 | ((len np) -' 1)) is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
F2 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(k1 | ((len np) -' 1)) | F2 is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
Sum ((k1 | ((len np) -' 1)) | F2) is complex Element of the carrier of F_Complex
|.(Sum ((k1 | ((len np) -' 1)) | F2)).| is complex real ext-real Element of REAL
(np | ((len np) -' 1)) | F2 is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum ((np | ((len np) -' 1)) | F2) is complex real ext-real Element of REAL
K294(REAL,((np | ((len np) -' 1)) | F2),K623()) is complex real ext-real Element of REAL
(Sum ((np | ((len np) -' 1)) | F2)) * |.((power F_Complex) . (k,((len np) -' 2))).| is complex real ext-real Element of REAL
F2 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(k1 | ((len np) -' 1)) | (F2 + 1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
Sum ((k1 | ((len np) -' 1)) | (F2 + 1)) is complex Element of the carrier of F_Complex
|.(Sum ((k1 | ((len np) -' 1)) | (F2 + 1))).| is complex real ext-real Element of REAL
(np | ((len np) -' 1)) | (F2 + 1) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum ((np | ((len np) -' 1)) | (F2 + 1)) is complex real ext-real Element of REAL
K294(REAL,((np | ((len np) -' 1)) | (F2 + 1)),K623()) is complex real ext-real Element of REAL
(Sum ((np | ((len np) -' 1)) | (F2 + 1))) * |.((power F_Complex) . (k,((len np) -' 2))).| is complex real ext-real Element of REAL
(k1 | ((len np) -' 1)) /. (F2 + 1) is complex Element of the carrier of F_Complex
|.((k1 | ((len np) -' 1)) /. (F2 + 1)).| is complex real ext-real Element of REAL
|.(Sum ((k1 | ((len np) -' 1)) | F2)).| + |.((k1 | ((len np) -' 1)) /. (F2 + 1)).| is complex real ext-real Element of REAL
((Sum ((np | ((len np) -' 1)) | F2)) * |.((power F_Complex) . (k,((len np) -' 2))).|) + |.((k1 | ((len np) -' 1)) /. (F2 + 1)).| is complex real ext-real Element of REAL
|.k.| to_power F2 is complex real ext-real Element of REAL
|.k.| to_power ((len np) -' 2) is complex real ext-real set
c₁ . F2 is complex Element of the carrier of F_Complex
|.(c₁ . F2).| is complex real ext-real Element of REAL
(power F_Complex) . (k,F2) is complex Element of the carrier of F_Complex
|.((power F_Complex) . (k,F2)).| is complex real ext-real Element of REAL
<*((k1 | ((len np) -' 1)) /. (F2 + 1))*> is Relation-like NAT -defined the carrier of F_Complex -valued Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
((k1 | ((len np) -' 1)) | F2) ^ <*((k1 | ((len np) -' 1)) /. (F2 + 1))*> is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
(Sum ((k1 | ((len np) -' 1)) | F2)) + ((k1 | ((len np) -' 1)) /. (F2 + 1)) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((Sum ((k1 | ((len np) -' 1)) | F2)),((k1 | ((len np) -' 1)) /. (F2 + 1))) is complex Element of the carrier of F_Complex
K593((Sum ((k1 | ((len np) -' 1)) | F2)),((k1 | ((len np) -' 1)) /. (F2 + 1))) is complex Element of COMPLEX
(np | ((len np) -' 1)) /. (F2 + 1) is complex real ext-real Element of REAL
np /. (F2 + 1) is complex real ext-real Element of REAL
np . (F2 + 1) is complex real ext-real Element of REAL
(F2 + 1) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₁ . ((F2 + 1) -' 1) is complex Element of the carrier of F_Complex
|.(c₁ . ((F2 + 1) -' 1)).| is complex real ext-real Element of REAL
k1 /. (F2 + 1) is complex Element of the carrier of F_Complex
k1 . (F2 + 1) is set
(power F_Complex) . (k,((F2 + 1) -' 1)) is complex Element of the carrier of F_Complex
(c₁ . ((F2 + 1) -' 1)) * ((power F_Complex) . (k,((F2 + 1) -' 1))) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((c₁ . ((F2 + 1) -' 1)),((power F_Complex) . (k,((F2 + 1) -' 1)))) is complex Element of the carrier of F_Complex
K595((c₁ . ((F2 + 1) -' 1)),((power F_Complex) . (k,((F2 + 1) -' 1)))) is complex Element of COMPLEX
(c₁ . F2) * ((power F_Complex) . (k,((F2 + 1) -' 1))) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((c₁ . F2),((power F_Complex) . (k,((F2 + 1) -' 1)))) is complex Element of the carrier of F_Complex
K595((c₁ . F2),((power F_Complex) . (k,((F2 + 1) -' 1)))) is complex Element of COMPLEX
(c₁ . F2) * ((power F_Complex) . (k,F2)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((c₁ . F2),((power F_Complex) . (k,F2))) is complex Element of the carrier of F_Complex
K595((c₁ . F2),((power F_Complex) . (k,F2))) is complex Element of COMPLEX
((np | ((len np) -' 1)) /. (F2 + 1)) * |.((power F_Complex) . (k,F2)).| is complex real ext-real Element of REAL
((np | ((len np) -' 1)) /. (F2 + 1)) * |.((power F_Complex) . (k,((len np) -' 2))).| is complex real ext-real Element of REAL
((Sum ((np | ((len np) -' 1)) | F2)) * |.((power F_Complex) . (k,((len np) -' 2))).|) + (((np | ((len np) -' 1)) /. (F2 + 1)) * |.((power F_Complex) . (k,((len np) -' 2))).|) is complex real ext-real Element of REAL
<*((np | ((len np) -' 1)) /. (F2 + 1))*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued increasing decreasing non-decreasing non-increasing FinSequence of REAL
((np | ((len np) -' 1)) | F2) ^ <*((np | ((len np) -' 1)) /. (F2 + 1))*> is Relation-like NAT -defined REAL -valued Function-like non empty V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(Sum ((np | ((len np) -' 1)) | F2)) + ((np | ((len np) -' 1)) /. (F2 + 1)) is complex real ext-real Element of REAL
(k1 | ((len np) -' 1)) | 0 is Relation-like NAT -defined the carrier of F_Complex -valued RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Function-like one-to-one constant functional empty V24() V29() V31( {} ) FinSequence-like FinSubsequence-like FinSequence-membered complex real ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V54() V56() V57() V58() V59() V60() V61() V62() Function-yielding V87() FinSequence of the carrier of F_Complex
Sum ((k1 | ((len np) -' 1)) | 0) is complex Element of the carrier of F_Complex
|.(Sum ((k1 | ((len np) -' 1)) | 0)).| is complex real ext-real Element of REAL
(np | ((len np) -' 1)) | 0 is Relation-like NAT -defined REAL -valued RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Function-like one-to-one constant functional empty V24() V29() V31( {} ) FinSequence-like FinSubsequence-like FinSequence-membered complex real ext-real non positive non negative complex-valued ext-real-valued real-valued natural-valued V54() V56() V57() V58() V59() V60() V61() V62() Function-yielding V87() FinSequence of REAL
Sum ((np | ((len np) -' 1)) | 0) is complex real ext-real Element of REAL
K294(REAL,((np | ((len np) -' 1)) | 0),K623()) is complex real ext-real Element of REAL
(Sum ((np | ((len np) -' 1)) | 0)) * |.((power F_Complex) . (k,((len np) -' 2))).| is complex real ext-real Element of REAL
(Sum (np | ((len np) -' 1))) * |.((power F_Complex) . (k,((len np) -' 2))).| is complex real ext-real Element of REAL
|.((power F_Complex) . (k,((len np) -' 1))).| - ((Sum (np | ((len np) -' 1))) * |.((power F_Complex) . (k,((len np) -' 2))).|) is complex real ext-real Element of REAL
- ((Sum (np | ((len np) -' 1))) * |.((power F_Complex) . (k,((len np) -' 2))).|) is complex real ext-real set
|.((power F_Complex) . (k,((len np) -' 1))).| + (- ((Sum (np | ((len np) -' 1))) * |.((power F_Complex) . (k,((len np) -' 2))).|)) is complex real ext-real set
2 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
|.k.| to_power 1 is complex real ext-real Element of REAL
|.k.| to_power ((len np) -' 2) is complex real ext-real set
(power F_Complex) . (k,1) is complex Element of the carrier of F_Complex
|.((power F_Complex) . (k,1)).| is complex real ext-real Element of REAL
|.((power F_Complex) . (k,((len np) -' 2))).| * 1 is complex real ext-real Element of REAL
c₁ is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of F_Complex))
len c₁ is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(F_Complex,c₁) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of F_Complex))
{ H₁(b₁) where b₁ is complex Element of the carrier of F_Complex : S₁[b₁] } is set
z0 is V56() V57() V58() Element of K27(REAL)
lower_bound z0 is complex real ext-real Element of REAL
k1 is ext-real set
sq is complex Element of the carrier of F_Complex
eval ((F_Complex,c₁),sq) is complex Element of the carrier of F_Complex
|.(eval ((F_Complex,c₁),sq)).| is complex real ext-real Element of REAL
eval ((F_Complex,c₁),(0. F_Complex)) is complex Element of the carrier of F_Complex
|.(eval ((F_Complex,c₁),(0. F_Complex))).| is complex real ext-real Element of REAL
k1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
1 / (k1 + 1) is non empty complex real ext-real positive non negative Element of REAL
(k1 + 1) " is non empty complex real ext-real positive non negative set
1 * ((k1 + 1) ") is non empty complex real ext-real positive non negative set
(lower_bound z0) + (1 / (k1 + 1)) is complex real ext-real Element of REAL
sq is complex real ext-real set
F2 is complex Element of the carrier of F_Complex
eval ((F_Complex,c₁),F2) is complex Element of the carrier of F_Complex
|.(eval ((F_Complex,c₁),F2)).| is complex real ext-real Element of REAL
c₈ is complex Element of COMPLEX
k1 is Relation-like NAT -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(NAT,COMPLEX))
len (F_Complex,c₁) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
sq is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len sq is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom sq is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
Seg (len (F_Complex,c₁)) is V24() V31( len (F_Complex,c₁)) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
F2 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
sq . F2 is complex real ext-real Element of REAL
F2 -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(F_Complex,c₁) . (F2 -' 1) is complex Element of the carrier of F_Complex
|.((F_Complex,c₁) . (F2 -' 1)).| is complex real ext-real Element of REAL
(len c₁) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
((len c₁) -' 1) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₁ . ((len c₁) -' 1) is complex Element of the carrier of F_Complex
|.(c₁ . ((len c₁) -' 1)).| is complex real ext-real Element of REAL
Sum sq is complex real ext-real Element of REAL
K294(REAL,sq,K623()) is complex real ext-real Element of REAL
(Sum sq) + 1 is complex real ext-real Element of REAL
F2 is complex real ext-real Element of REAL
c₈ is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k1 . c₈ is complex Element of COMPLEX
|.(k1 . c₈).| is complex real ext-real Element of REAL
k1 . c₈ is complex Element of COMPLEX
c₈ + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
1 / (c₈ + 1) is non empty complex real ext-real positive non negative Element of REAL
(c₈ + 1) " is non empty complex real ext-real positive non negative set
1 * ((c₈ + 1) ") is non empty complex real ext-real positive non negative set
(lower_bound z0) + (1 / (c₈ + 1)) is complex real ext-real Element of REAL
z1 is complex Element of the carrier of F_Complex
eval ((F_Complex,c₁),z1) is complex Element of the carrier of F_Complex
|.(eval ((F_Complex,c₁),z1)).| is complex real ext-real Element of REAL
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(len (F_Complex,c₁)) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(F_Complex,c₁) . ((len (F_Complex,c₁)) -' 1) is complex Element of the carrier of F_Complex
|.(k1 . c₈).| is complex real ext-real Element of REAL
(F_Complex,c₁) . 0 is complex Element of the carrier of F_Complex
|.((F_Complex,c₁) . 0).| is complex real ext-real Element of REAL
|.((F_Complex,c₁) . 0).| + 1 is complex real ext-real Element of REAL
|.(k1 . c₈).| + 0 is complex real ext-real Element of REAL
F2 is Relation-like NAT -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(NAT,COMPLEX))
lim F2 is complex Element of COMPLEX
z1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
F2 . z1 is complex Element of COMPLEX
F1 is complex Element of the carrier of F_Complex
eval ((F_Complex,c₁),F1) is complex Element of the carrier of F_Complex
gc is complex Element of COMPLEX
z1 is Relation-like NAT -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(NAT,COMPLEX))
c₈ is complex Element of the carrier of F_Complex
eval ((F_Complex,c₁),c₈) is complex Element of the carrier of F_Complex
gc is complex Element of COMPLEX
i is complex Element of the carrier of F_Complex
eval ((F_Complex,c₁),i) is complex Element of the carrier of F_Complex
(F_Complex,(F_Complex,c₁)) is Relation-like the carrier of F_Complex -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28( the carrier of F_Complex, the carrier of F_Complex))
R is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
PF is complex real ext-real Element of REAL
R /. gc is complex Element of COMPLEX
R . gc is complex Element of COMPLEX
z is complex real ext-real Element of REAL
Rcons is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
Nseq is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
F2 . n is complex Element of COMPLEX
(F2 . n) - gc is complex Element of COMPLEX
- gc is complex set
(F2 . n) + (- gc) is complex set
|.((F2 . n) - gc).| is complex real ext-real Element of REAL
z1 . n is complex Element of COMPLEX
R /. (F2 . n) is complex Element of COMPLEX
R . (F2 . n) is complex Element of COMPLEX
G1n is complex Element of the carrier of F_Complex
eval ((F_Complex,c₁),G1n) is complex Element of the carrier of F_Complex
eg is complex Element of COMPLEX
(z1 . n) - eg is complex Element of COMPLEX
- eg is complex set
(z1 . n) + (- eg) is complex set
|.((z1 . n) - eg).| is complex real ext-real Element of REAL
PF is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued Element of K27(K28(COMPLEX,COMPLEX))
R is complex real ext-real Element of REAL
PF /. (lim F2) is complex Element of COMPLEX
PF . (lim F2) is complex Element of COMPLEX
z is complex real ext-real Element of REAL
Rcons is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
Nseq is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
F2 . n is complex Element of COMPLEX
(F2 . n) - (lim F2) is complex Element of COMPLEX
- (lim F2) is complex set
(F2 . n) + (- (lim F2)) is complex set
|.((F2 . n) - (lim F2)).| is complex real ext-real Element of REAL
z1 . n is complex Element of COMPLEX
PF /. (F2 . n) is complex Element of COMPLEX
PF . (F2 . n) is complex Element of COMPLEX
G1n is complex Element of the carrier of F_Complex
eval ((F_Complex,c₁),G1n) is complex Element of the carrier of F_Complex
F1 is complex Element of COMPLEX
(z1 . n) - F1 is complex Element of COMPLEX
- F1 is complex set
(z1 . n) + (- F1) is complex set
|.((z1 . n) - F1).| is complex real ext-real Element of REAL
lim z1 is complex Element of COMPLEX
R is Relation-like NAT -defined REAL -valued Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K27(K28(NAT,REAL))
eval (c₁,c₈) is complex Element of the carrier of F_Complex
|.(eval (c₁,c₈)).| is complex real ext-real Element of REAL
z is complex Element of the carrier of F_Complex
eval (c₁,z) is complex Element of the carrier of F_Complex
|.(eval (c₁,z)).| is complex real ext-real Element of REAL
eval ((F_Complex,c₁),z) is complex Element of the carrier of F_Complex
|.(eval ((F_Complex,c₁),z)).| is complex real ext-real Element of REAL
NAT --> |.(eval ((F_Complex,c₁),z)).| is Relation-like NAT -defined REAL -valued T-Sequence-like Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued bounded convergent bounded_above bounded_below Element of K27(K28(NAT,REAL))
Nseq is Relation-like NAT -defined NAT -valued Function-like non empty total quasi_total complex-valued ext-real-valued real-valued natural-valued increasing non-decreasing Element of K27(K28(NAT,NAT))
k1 * Nseq is Relation-like NAT -defined COMPLEX -valued Function-like non empty total quasi_total complex-valued subsequence of k1
n is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
F2 . n is complex Element of COMPLEX
z1 . n is complex Element of COMPLEX
G1n is complex Element of the carrier of F_Complex
eval ((F_Complex,c₁),G1n) is complex Element of the carrier of F_Complex
Nseq . n is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k1 . (Nseq . n) is complex Element of COMPLEX
(Nseq . n) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
1 / ((Nseq . n) + 1) is non empty complex real ext-real positive non negative Element of REAL
((Nseq . n) + 1) " is non empty complex real ext-real positive non negative set
1 * (((Nseq . n) + 1) ") is non empty complex real ext-real positive non negative set
(lower_bound z0) + (1 / ((Nseq . n) + 1)) is complex real ext-real Element of REAL
gNn is complex Element of the carrier of F_Complex
eval ((F_Complex,c₁),gNn) is complex Element of the carrier of F_Complex
|.(eval ((F_Complex,c₁),gNn)).| is complex real ext-real Element of REAL
n + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
1 / (n + 1) is non empty complex real ext-real positive non negative Element of REAL
(n + 1) " is non empty complex real ext-real positive non negative set
1 * ((n + 1) ") is non empty complex real ext-real positive non negative set
(lower_bound z0) + (1 / (n + 1)) is complex real ext-real Element of REAL
|.(eval ((F_Complex,c₁),gNn)).| - (1 / (n + 1)) is complex real ext-real Element of REAL
- (1 / (n + 1)) is non empty complex real ext-real non positive negative set
|.(eval ((F_Complex,c₁),gNn)).| + (- (1 / (n + 1))) is complex real ext-real set
Rcons is Relation-like NAT -defined REAL -valued Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K27(K28(NAT,REAL))
Rcons . n is complex real ext-real Element of REAL
|.z1.| is Relation-like NAT -defined REAL -valued Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K27(K28(NAT,REAL))
|.z1.| - R is Relation-like NAT -defined REAL -valued Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K27(K28(NAT,REAL))
dom (|.z1.| - R) is V56() V57() V58() V59() V60() V61() set
(|.z1.| - R) . n is complex real ext-real Element of REAL
|.z1.| . n is complex real ext-real Element of REAL
R . n is complex real ext-real Element of REAL
(|.z1.| . n) - (R . n) is complex real ext-real Element of REAL
- (R . n) is complex real ext-real set
(|.z1.| . n) + (- (R . n)) is complex real ext-real set
(|.z1.| . n) - (1 / (n + 1)) is complex real ext-real Element of REAL
(|.z1.| . n) + (- (1 / (n + 1))) is complex real ext-real set
|.(eval ((F_Complex,c₁),G1n)).| is complex real ext-real Element of REAL
|.(eval ((F_Complex,c₁),G1n)).| - (1 / (n + 1)) is complex real ext-real Element of REAL
|.(eval ((F_Complex,c₁),G1n)).| + (- (1 / (n + 1))) is complex real ext-real set
Rcons . 0 is complex real ext-real Element of REAL
lim (|.z1.| - R) is complex real ext-real Element of REAL
lim Rcons is complex real ext-real Element of REAL
lim |.z1.| is complex real ext-real Element of REAL
lim R is complex real ext-real Element of REAL
(lim |.z1.|) - (lim R) is complex real ext-real Element of REAL
- (lim R) is complex real ext-real set
(lim |.z1.|) + (- (lim R)) is complex real ext-real set
|.(lim z1).| is complex real ext-real Element of REAL
|.(lim z1).| - (lim R) is complex real ext-real Element of REAL
|.(lim z1).| + (- (lim R)) is complex real ext-real set
|.(lim z1).| - 0 is complex real ext-real Element of REAL
- 0 is complex real ext-real non positive V54() set
|.(lim z1).| + (- 0) is complex real ext-real set
|.(eval ((F_Complex,c₁),c₈)).| is complex real ext-real Element of REAL
(eval (c₁,z)) / (c₁ . ((len c₁) -' 1)) is complex Element of the carrier of F_Complex
|.((eval (c₁,z)) / (c₁ . ((len c₁) -' 1))).| is complex real ext-real Element of REAL
(eval (c₁,c₈)) / (c₁ . ((len c₁) -' 1)) is complex Element of the carrier of F_Complex
|.((eval (c₁,c₈)) / (c₁ . ((len c₁) -' 1))).| is complex real ext-real Element of REAL
|.(eval (c₁,z)).| / |.(c₁ . ((len c₁) -' 1)).| is complex real ext-real Element of REAL
|.(c₁ . ((len c₁) -' 1)).| " is complex real ext-real set
|.(eval (c₁,z)).| * (|.(c₁ . ((len c₁) -' 1)).| ") is complex real ext-real set
|.(eval (c₁,c₈)).| / |.(c₁ . ((len c₁) -' 1)).| is complex real ext-real Element of REAL
|.(eval (c₁,c₈)).| * (|.(c₁ . ((len c₁) -' 1)).| ") is complex real ext-real set
c₁ is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of F_Complex))
len c₁ is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
np is complex Element of the carrier of F_Complex
eval (c₁,np) is complex Element of the carrier of F_Complex
|.(eval (c₁,np)).| is complex real ext-real Element of REAL
(F_Complex,np,(1_ F_Complex)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(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 quasi_total finite-Support ( F_Complex ) Element of K27(K28(NAT, the carrier of F_Complex))
NAT --> (0. F_Complex) is Relation-like NAT -defined the carrier of F_Complex -valued T-Sequence-like Function-like constant non empty total quasi_total complex-valued Element of K27(K28(NAT, the carrier of F_Complex))
(0_. F_Complex) +* (0,np) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of F_Complex))
((0_. F_Complex) +* (0,np)) +* (1,(1_ F_Complex)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of F_Complex))
(F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of F_Complex))
len (F_Complex,np,(1_ F_Complex)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
len (F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
2 * (len c₁) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(2 * (len c₁)) - (len c₁) is complex real ext-real V54() Element of REAL
- (len c₁) is complex real ext-real non positive V54() set
(2 * (len c₁)) + (- (len c₁)) is complex real ext-real V54() set
((2 * (len c₁)) - (len c₁)) - 2 is complex real ext-real V54() Element of REAL
- 2 is non empty complex real ext-real non positive negative V54() set
((2 * (len c₁)) - (len c₁)) + (- 2) is complex real ext-real V54() set
(((2 * (len c₁)) - (len c₁)) - 2) + 2 is complex real ext-real V54() Element of REAL
1 - 1 is complex real ext-real V54() Element of REAL
- 1 is non empty complex real ext-real non positive negative V54() set
1 + (- 1) is complex real ext-real V54() set
(len (F_Complex,c₁,(F_Complex,np,(1_ F_Complex)))) - 1 is complex real ext-real V54() Element of REAL
(len (F_Complex,c₁,(F_Complex,np,(1_ F_Complex)))) + (- 1) is complex real ext-real V54() set
(len (F_Complex,c₁,(F_Complex,np,(1_ F_Complex)))) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k is set
k + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k is complex Element of the carrier of F_Complex
k is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
(F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k is set
k + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0 is complex Element of the carrier of F_Complex
k1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1 is complex Element of the carrier of F_Complex
((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1) is complex Element of the carrier of F_Complex
- (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)) is complex Element of the carrier of F_Complex
the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)) is complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))
k1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(len (F_Complex,c₁,(F_Complex,np,(1_ F_Complex)))) -' (k1 + 1) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
F2 is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
len F2 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom F2 is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
(k + 1) + 0 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(len (F_Complex,c₁,(F_Complex,np,(1_ F_Complex)))) - (k + 1) is complex real ext-real V54() Element of REAL
- (k + 1) is non empty complex real ext-real non positive negative V54() set
(len (F_Complex,c₁,(F_Complex,np,(1_ F_Complex)))) + (- (k + 1)) is complex real ext-real V54() set
np + (0. F_Complex) is complex Element of the carrier of F_Complex
the addF of F_Complex is Relation-like K28( the carrier of F_Complex, the carrier of F_Complex) -defined the carrier of F_Complex -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex))
K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex) is set
K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex)) is set
the addF of F_Complex . (np,(0. F_Complex)) is complex Element of the carrier of F_Complex
K593(np,(0. F_Complex)) is complex Element of COMPLEX
eval (c₁,(np + (0. F_Complex))) is complex Element of the carrier of F_Complex
eval ((F_Complex,np,(1_ F_Complex)),(0. F_Complex)) is complex Element of the carrier of F_Complex
eval (c₁,(eval ((F_Complex,np,(1_ F_Complex)),(0. F_Complex)))) is complex Element of the carrier of F_Complex
eval ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))),(0. F_Complex)) is complex Element of the carrier of F_Complex
c₈ is complex Element of the carrier of F_Complex
eval ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))),c₈) is complex Element of the carrier of F_Complex
eval ((F_Complex,np,(1_ F_Complex)),c₈) is complex Element of the carrier of F_Complex
eval (c₁,(eval ((F_Complex,np,(1_ F_Complex)),c₈))) is complex Element of the carrier of F_Complex
np + c₈ is complex Element of the carrier of F_Complex
the addF of F_Complex . (np,c₈) is complex Element of the carrier of F_Complex
K593(np,c₈) is complex Element of COMPLEX
eval (c₁,(np + c₈)) is complex Element of the carrier of F_Complex
|.(eval ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))),c₈)).| is complex real ext-real Element of REAL
|.((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0).| is complex real ext-real Element of REAL
c₈ is complex real ext-real Element of REAL
[**c₈,0**] is complex Element of the carrier of F_Complex
<i> is complex Element of COMPLEX
K286(REAL,0,1,0,1) is Relation-like {0,1} -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K27(K28({0,1},REAL))
{0,1} is V56() V57() V58() V59() V60() V61() set
K28({0,1},REAL) is complex-valued ext-real-valued real-valued set
K27(K28({0,1},REAL)) is set
0 * <i> is complex set
c₈ + (0 * <i>) is complex set
[**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)) is complex Element of the carrier of F_Complex
the multF of F_Complex is Relation-like K28( the carrier of F_Complex, the carrier of F_Complex) -defined the carrier of F_Complex -valued Function-like total quasi_total associative Element of K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex))
the multF of F_Complex . ([**c₈,0**], the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))) is complex Element of the carrier of F_Complex
K595([**c₈,0**], the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))) is complex Element of COMPLEX
eval ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))),([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)))) is complex Element of the carrier of F_Complex
F1 is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
Sum F1 is complex Element of the carrier of F_Complex
len F1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
dom F1 is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
F1 /^ (k + 1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
c₈ to_power (k + 1) is complex real ext-real Element of REAL
[**(c₈ to_power (k + 1)),0**] is complex Element of the carrier of F_Complex
(c₈ to_power (k + 1)) + (0 * <i>) is complex set
[**(c₈ to_power (k + 1)),0**] " is complex Element of the carrier of F_Complex
(F1 /^ (k + 1)) * ([**(c₈ to_power (k + 1)),0**] ") is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
dom ((F1 /^ (k + 1)) * ([**(c₈ to_power (k + 1)),0**] ")) is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
dom (F1 /^ (k + 1)) is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
Seg k is V24() V31(k) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
F1 | k is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
len (F1 | k) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
Seg (len (F1 | k)) is V24() V31( len (F1 | k)) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
dom (F1 | k) is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
gc is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(1 + 1) - 1 is complex real ext-real V54() Element of REAL
- 1 is non empty complex real ext-real non positive negative V54() set
(1 + 1) + (- 1) is complex real ext-real V54() set
gc - 1 is complex real ext-real V54() Element of REAL
gc + (- 1) is complex real ext-real V54() set
gc -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
F1 | k1 is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
(F1 | k1) /. gc is complex Element of the carrier of F_Complex
F1 /. gc is complex Element of the carrier of F_Complex
F1 . gc is set
(F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (gc -' 1) is complex Element of the carrier of F_Complex
(power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),(gc -' 1)) is complex Element of the carrier of F_Complex
((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (gc -' 1)) * ((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),(gc -' 1))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (gc -' 1)),((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),(gc -' 1)))) is complex Element of the carrier of F_Complex
K595(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (gc -' 1)),((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),(gc -' 1)))) is complex Element of COMPLEX
(0. F_Complex) * ((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),(gc -' 1))) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((0. F_Complex),((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),(gc -' 1)))) is complex Element of the carrier of F_Complex
K595((0. F_Complex),((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),(gc -' 1)))) is complex Element of COMPLEX
Sum (F1 | k) is complex Element of the carrier of F_Complex
(F1 | k1) /. 1 is complex Element of the carrier of F_Complex
F1 /. 1 is complex Element of the carrier of F_Complex
F1 . 1 is set
1 -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (1 -' 1) is complex Element of the carrier of F_Complex
(power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),(1 -' 1)) is complex Element of the carrier of F_Complex
((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (1 -' 1)) * ((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),(1 -' 1))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (1 -' 1)),((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),(1 -' 1)))) is complex Element of the carrier of F_Complex
K595(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (1 -' 1)),((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),(1 -' 1)))) is complex Element of COMPLEX
((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * ((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),(1 -' 1))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0),((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),(1 -' 1)))) is complex Element of the carrier of F_Complex
K595(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0),((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),(1 -' 1)))) is complex Element of COMPLEX
(power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),0) is complex Element of the carrier of F_Complex
((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * ((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),0)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0),((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),0))) is complex Element of the carrier of F_Complex
K595(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0),((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),0))) is complex Element of COMPLEX
((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * (1_ F_Complex) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0),(1_ F_Complex)) is complex Element of the carrier of F_Complex
K595(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0),(1_ F_Complex)) is complex Element of COMPLEX
Seg (len F1) is V24() V31( len F1) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
F1 . (k + 1) is set
F1 /. (k + 1) is complex Element of the carrier of F_Complex
Sum (F1 /^ (k + 1)) is complex Element of the carrier of F_Complex
(Sum (F1 /^ (k + 1))) / [**(c₈ to_power (k + 1)),0**] is complex Element of the carrier of F_Complex
[**(c₈ to_power (k + 1)),0**] * (Sum (F1 /^ (k + 1))) is complex Element of the carrier of F_Complex
the multF of F_Complex . ([**(c₈ to_power (k + 1)),0**],(Sum (F1 /^ (k + 1)))) is complex Element of the carrier of F_Complex
K595([**(c₈ to_power (k + 1)),0**],(Sum (F1 /^ (k + 1)))) is complex Element of COMPLEX
([**(c₈ to_power (k + 1)),0**] * (Sum (F1 /^ (k + 1)))) / [**(c₈ to_power (k + 1)),0**] is complex Element of the carrier of F_Complex
[**(c₈ to_power (k + 1)),0**] * ((Sum (F1 /^ (k + 1))) / [**(c₈ to_power (k + 1)),0**]) is complex Element of the carrier of F_Complex
the multF of F_Complex . ([**(c₈ to_power (k + 1)),0**],((Sum (F1 /^ (k + 1))) / [**(c₈ to_power (k + 1)),0**])) is complex Element of the carrier of F_Complex
K595([**(c₈ to_power (k + 1)),0**],((Sum (F1 /^ (k + 1))) / [**(c₈ to_power (k + 1)),0**])) is complex Element of COMPLEX
(k + 1) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . ((k + 1) -' 1) is complex Element of the carrier of F_Complex
(power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),((k + 1) -' 1)) is complex Element of the carrier of F_Complex
((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . ((k + 1) -' 1)) * ((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),((k + 1) -' 1))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . ((k + 1) -' 1)),((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),((k + 1) -' 1)))) is complex Element of the carrier of F_Complex
K595(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . ((k + 1) -' 1)),((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),((k + 1) -' 1)))) is complex Element of COMPLEX
((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1) * ((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),((k + 1) -' 1))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1),((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),((k + 1) -' 1)))) is complex Element of the carrier of F_Complex
K595(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1),((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),((k + 1) -' 1)))) is complex Element of COMPLEX
(power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),k1) is complex Element of the carrier of F_Complex
((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1) * ((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),k1)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1),((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),k1))) is complex Element of the carrier of F_Complex
K595(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1),((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),k1))) is complex Element of COMPLEX
(power F_Complex) . ([**c₈,0**],k1) is complex Element of the carrier of F_Complex
(power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),k1) is complex Element of the carrier of F_Complex
((power F_Complex) . ([**c₈,0**],k1)) * ((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),k1)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((power F_Complex) . ([**c₈,0**],k1)),((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),k1))) is complex Element of the carrier of F_Complex
K595(((power F_Complex) . ([**c₈,0**],k1)),((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),k1))) is complex Element of COMPLEX
((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1) * (((power F_Complex) . ([**c₈,0**],k1)) * ((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),k1))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1),(((power F_Complex) . ([**c₈,0**],k1)) * ((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),k1)))) is complex Element of the carrier of F_Complex
K595(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1),(((power F_Complex) . ([**c₈,0**],k1)) * ((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),k1)))) is complex Element of COMPLEX
((power F_Complex) . ([**c₈,0**],k1)) * (- (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((power F_Complex) . ([**c₈,0**],k1)),(- (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)))) is complex Element of the carrier of F_Complex
K595(((power F_Complex) . ([**c₈,0**],k1)),(- (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)))) is complex Element of COMPLEX
((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1) * (((power F_Complex) . ([**c₈,0**],k1)) * (- (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1),(((power F_Complex) . ([**c₈,0**],k1)) * (- (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))))) is complex Element of the carrier of F_Complex
K595(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1),(((power F_Complex) . ([**c₈,0**],k1)) * (- (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))))) is complex Element of COMPLEX
((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1) * (- (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1),(- (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)))) is complex Element of the carrier of F_Complex
K595(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1),(- (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)))) is complex Element of COMPLEX
(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1) * (- (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)))) * ((power F_Complex) . ([**c₈,0**],k1)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1) * (- (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)))),((power F_Complex) . ([**c₈,0**],k1))) is complex Element of the carrier of F_Complex
K595((((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1) * (- (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)))),((power F_Complex) . ([**c₈,0**],k1))) is complex Element of COMPLEX
- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) is complex Element of the carrier of F_Complex
(- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0)) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1) is complex Element of the carrier of F_Complex
((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1) * ((- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0)) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1),((- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0)) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))) is complex Element of the carrier of F_Complex
K595(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1),((- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0)) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))) is complex Element of COMPLEX
(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1) * ((- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0)) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))) * ((power F_Complex) . ([**c₈,0**],k1)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1) * ((- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0)) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),((power F_Complex) . ([**c₈,0**],k1))) is complex Element of the carrier of F_Complex
K595((((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1) * ((- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0)) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),((power F_Complex) . ([**c₈,0**],k1))) is complex Element of COMPLEX
((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1) * (- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1),(- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0))) is complex Element of the carrier of F_Complex
K595(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1),(- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0))) is complex Element of COMPLEX
(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1) * (- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0))) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1) is complex Element of the carrier of F_Complex
((((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1) * (- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0))) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)) * ((power F_Complex) . ([**c₈,0**],k1)) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1) * (- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0))) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),((power F_Complex) . ([**c₈,0**],k1))) is complex Element of the carrier of F_Complex
K595(((((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1) * (- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0))) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),((power F_Complex) . ([**c₈,0**],k1))) is complex Element of COMPLEX
(- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0)) * ((power F_Complex) . ([**c₈,0**],k1)) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0)),((power F_Complex) . ([**c₈,0**],k1))) is complex Element of the carrier of F_Complex
K595((- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0)),((power F_Complex) . ([**c₈,0**],k1))) is complex Element of COMPLEX
c₈ to_power k is complex real ext-real set
[**(c₈ to_power k),0**] is complex Element of the carrier of F_Complex
(c₈ to_power k) + (0 * <i>) is complex set
(- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0)) * [**(c₈ to_power k),0**] is complex Element of the carrier of F_Complex
the multF of F_Complex . ((- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0)),[**(c₈ to_power k),0**]) is complex Element of the carrier of F_Complex
K595((- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0)),[**(c₈ to_power k),0**]) is complex Element of COMPLEX
(1_ F_Complex) - [**(c₈ to_power k),0**] is complex Element of the carrier of F_Complex
- [**(c₈ to_power k),0**] is complex Element of the carrier of F_Complex
(1_ F_Complex) + (- [**(c₈ to_power k),0**]) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((1_ F_Complex),(- [**(c₈ to_power k),0**])) is complex Element of the carrier of F_Complex
K593((1_ F_Complex),(- [**(c₈ to_power k),0**])) is complex Element of COMPLEX
((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * ((1_ F_Complex) - [**(c₈ to_power k),0**]) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0),((1_ F_Complex) - [**(c₈ to_power k),0**])) is complex Element of the carrier of F_Complex
K595(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0),((1_ F_Complex) - [**(c₈ to_power k),0**])) is complex Element of COMPLEX
(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * ((1_ F_Complex) - [**(c₈ to_power k),0**])) + ([**(c₈ to_power (k + 1)),0**] * ((Sum (F1 /^ (k + 1))) / [**(c₈ to_power (k + 1)),0**])) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * ((1_ F_Complex) - [**(c₈ to_power k),0**])),([**(c₈ to_power (k + 1)),0**] * ((Sum (F1 /^ (k + 1))) / [**(c₈ to_power (k + 1)),0**]))) is complex Element of the carrier of F_Complex
K593((((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * ((1_ F_Complex) - [**(c₈ to_power k),0**])),([**(c₈ to_power (k + 1)),0**] * ((Sum (F1 /^ (k + 1))) / [**(c₈ to_power (k + 1)),0**]))) is complex Element of COMPLEX
|.((((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * ((1_ F_Complex) - [**(c₈ to_power k),0**])) + ([**(c₈ to_power (k + 1)),0**] * ((Sum (F1 /^ (k + 1))) / [**(c₈ to_power (k + 1)),0**]))).| is complex real ext-real Element of REAL
|.(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * ((1_ F_Complex) - [**(c₈ to_power k),0**])).| is complex real ext-real Element of REAL
|.([**(c₈ to_power (k + 1)),0**] * ((Sum (F1 /^ (k + 1))) / [**(c₈ to_power (k + 1)),0**])).| is complex real ext-real Element of REAL
|.(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * ((1_ F_Complex) - [**(c₈ to_power k),0**])).| + |.([**(c₈ to_power (k + 1)),0**] * ((Sum (F1 /^ (k + 1))) / [**(c₈ to_power (k + 1)),0**])).| is complex real ext-real Element of REAL
F1 | ((k + 1) -' 1) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
<*(F1 . (k + 1))*> is Relation-like NAT -defined Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like set
(F1 | ((k + 1) -' 1)) ^ <*(F1 . (k + 1))*> is Relation-like NAT -defined Function-like non empty V24() FinSequence-like FinSubsequence-like set
((F1 | ((k + 1) -' 1)) ^ <*(F1 . (k + 1))*>) ^ (F1 /^ (k + 1)) is Relation-like NAT -defined Function-like non empty V24() FinSequence-like FinSubsequence-like set
<*(F1 /. (k + 1))*> is Relation-like NAT -defined the carrier of F_Complex -valued Function-like constant non empty V19() V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
(F1 | ((k + 1) -' 1)) ^ <*(F1 /. (k + 1))*> is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty V24() FinSequence-like FinSubsequence-like FinSequence of the carrier of F_Complex
Sum ((F1 | ((k + 1) -' 1)) ^ <*(F1 /. (k + 1))*>) is complex Element of the carrier of F_Complex
(Sum ((F1 | ((k + 1) -' 1)) ^ <*(F1 /. (k + 1))*>)) + (Sum (F1 /^ (k + 1))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((Sum ((F1 | ((k + 1) -' 1)) ^ <*(F1 /. (k + 1))*>)),(Sum (F1 /^ (k + 1)))) is complex Element of the carrier of F_Complex
K593((Sum ((F1 | ((k + 1) -' 1)) ^ <*(F1 /. (k + 1))*>)),(Sum (F1 /^ (k + 1)))) is complex Element of COMPLEX
Sum (F1 | ((k + 1) -' 1)) is complex Element of the carrier of F_Complex
Sum <*(F1 /. (k + 1))*> is complex Element of the carrier of F_Complex
(Sum (F1 | ((k + 1) -' 1))) + (Sum <*(F1 /. (k + 1))*>) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((Sum (F1 | ((k + 1) -' 1))),(Sum <*(F1 /. (k + 1))*>)) is complex Element of the carrier of F_Complex
K593((Sum (F1 | ((k + 1) -' 1))),(Sum <*(F1 /. (k + 1))*>)) is complex Element of COMPLEX
((Sum (F1 | ((k + 1) -' 1))) + (Sum <*(F1 /. (k + 1))*>)) + (Sum (F1 /^ (k + 1))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((Sum (F1 | ((k + 1) -' 1))) + (Sum <*(F1 /. (k + 1))*>)),(Sum (F1 /^ (k + 1)))) is complex Element of the carrier of F_Complex
K593(((Sum (F1 | ((k + 1) -' 1))) + (Sum <*(F1 /. (k + 1))*>)),(Sum (F1 /^ (k + 1)))) is complex Element of COMPLEX
(Sum (F1 | k)) + (Sum <*(F1 /. (k + 1))*>) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((Sum (F1 | k)),(Sum <*(F1 /. (k + 1))*>)) is complex Element of the carrier of F_Complex
K593((Sum (F1 | k)),(Sum <*(F1 /. (k + 1))*>)) is complex Element of COMPLEX
((Sum (F1 | k)) + (Sum <*(F1 /. (k + 1))*>)) + (Sum (F1 /^ (k + 1))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((Sum (F1 | k)) + (Sum <*(F1 /. (k + 1))*>)),(Sum (F1 /^ (k + 1)))) is complex Element of the carrier of F_Complex
K593(((Sum (F1 | k)) + (Sum <*(F1 /. (k + 1))*>)),(Sum (F1 /^ (k + 1)))) is complex Element of COMPLEX
((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) + ((- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0)) * [**(c₈ to_power k),0**]) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0),((- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0)) * [**(c₈ to_power k),0**])) is complex Element of the carrier of F_Complex
K593(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0),((- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0)) * [**(c₈ to_power k),0**])) is complex Element of COMPLEX
(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) + ((- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0)) * [**(c₈ to_power k),0**])) + (Sum (F1 /^ (k + 1))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) + ((- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0)) * [**(c₈ to_power k),0**])),(Sum (F1 /^ (k + 1)))) is complex Element of the carrier of F_Complex
K593((((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) + ((- ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0)) * [**(c₈ to_power k),0**])),(Sum (F1 /^ (k + 1)))) is complex Element of COMPLEX
((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * [**(c₈ to_power k),0**] is complex Element of the carrier of F_Complex
the multF of F_Complex . (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0),[**(c₈ to_power k),0**]) is complex Element of the carrier of F_Complex
K595(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0),[**(c₈ to_power k),0**]) is complex Element of COMPLEX
- (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * [**(c₈ to_power k),0**]) is complex Element of the carrier of F_Complex
((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) + (- (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * [**(c₈ to_power k),0**])) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0),(- (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * [**(c₈ to_power k),0**]))) is complex Element of the carrier of F_Complex
K593(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0),(- (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * [**(c₈ to_power k),0**]))) is complex Element of COMPLEX
(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) + (- (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * [**(c₈ to_power k),0**]))) + (Sum (F1 /^ (k + 1))) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) + (- (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * [**(c₈ to_power k),0**]))),(Sum (F1 /^ (k + 1)))) is complex Element of the carrier of F_Complex
K593((((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) + (- (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * [**(c₈ to_power k),0**]))),(Sum (F1 /^ (k + 1)))) is complex Element of COMPLEX
(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * (1_ F_Complex)) - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * [**(c₈ to_power k),0**]) is complex Element of the carrier of F_Complex
(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * (1_ F_Complex)) + (- (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * [**(c₈ to_power k),0**])) is complex Element of the carrier of F_Complex
the addF of F_Complex . ((((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * (1_ F_Complex)),(- (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * [**(c₈ to_power k),0**]))) is complex Element of the carrier of F_Complex
K593((((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * (1_ F_Complex)),(- (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * [**(c₈ to_power k),0**]))) is complex Element of COMPLEX
((((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * (1_ F_Complex)) - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * [**(c₈ to_power k),0**])) + (Sum (F1 /^ (k + 1))) is complex Element of the carrier of F_Complex
the addF of F_Complex . (((((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * (1_ F_Complex)) - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * [**(c₈ to_power k),0**])),(Sum (F1 /^ (k + 1)))) is complex Element of the carrier of F_Complex
K593(((((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * (1_ F_Complex)) - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) * [**(c₈ to_power k),0**])),(Sum (F1 /^ (k + 1)))) is complex Element of COMPLEX
|.((1_ F_Complex) - [**(c₈ to_power k),0**]).| is complex real ext-real Element of REAL
|.((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0).| * |.((1_ F_Complex) - [**(c₈ to_power k),0**]).| is complex real ext-real Element of REAL
(|.((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0).| * |.((1_ F_Complex) - [**(c₈ to_power k),0**]).|) + |.([**(c₈ to_power (k + 1)),0**] * ((Sum (F1 /^ (k + 1))) / [**(c₈ to_power (k + 1)),0**])).| is complex real ext-real Element of REAL
|.[**(c₈ to_power (k + 1)),0**].| is complex real ext-real Element of REAL
|.((Sum (F1 /^ (k + 1))) / [**(c₈ to_power (k + 1)),0**]).| is complex real ext-real Element of REAL
|.[**(c₈ to_power (k + 1)),0**].| * |.((Sum (F1 /^ (k + 1))) / [**(c₈ to_power (k + 1)),0**]).| is complex real ext-real Element of REAL
(|.((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0).| * |.((1_ F_Complex) - [**(c₈ to_power k),0**]).|) + (|.[**(c₈ to_power (k + 1)),0**].| * |.((Sum (F1 /^ (k + 1))) / [**(c₈ to_power (k + 1)),0**]).|) is complex real ext-real Element of REAL
c₈ to_power k1 is complex real ext-real Element of REAL
0 + (c₈ to_power k1) is complex real ext-real Element of REAL
1 - (c₈ to_power k) is complex real ext-real Element of REAL
- (c₈ to_power k) is complex real ext-real set
1 + (- (c₈ to_power k)) is complex real ext-real set
(((F1 /^ (k + 1)) * ([**(c₈ to_power (k + 1)),0**] "))) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len (((F1 /^ (k + 1)) * ([**(c₈ to_power (k + 1)),0**] "))) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
len ((F1 /^ (k + 1)) * ([**(c₈ to_power (k + 1)),0**] ")) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
len (F1 /^ (k + 1)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(len F1) - (k + 1) is complex real ext-real V54() Element of REAL
(len F1) + (- (k + 1)) is complex real ext-real V54() set
(F2) is Relation-like NAT -defined REAL -valued Function-like V24() FinSequence-like FinSubsequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len (F2) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
i is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(k + 1) + i is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
((k + 1) + i) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
k + i is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
(k + i) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V24() V29() complex real ext-real positive non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
((k + i) + 1) - 1 is complex real ext-real V54() Element of REAL
((k + i) + 1) + (- 1) is complex real ext-real V54() set
dom (((F1 /^ (k + 1)) * ([**(c₈ to_power (k + 1)),0**] "))) is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
Seg (len (((F1 /^ (k + 1)) * ([**(c₈ to_power (k + 1)),0**] ")))) is V24() V31( len (((F1 /^ (k + 1)) * ([**(c₈ to_power (k + 1)),0**] ")))) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
i - 1 is complex real ext-real V54() Element of REAL
i + (- 1) is complex real ext-real V54() set
i -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
c₈ to_power (i -' 1) is complex real ext-real set
c₈ to_power (i - 1) is complex real ext-real Element of REAL
c₈ to_power (k + i) is complex real ext-real Element of REAL
(k + i) - (k + 1) is complex real ext-real V54() Element of REAL
(k + i) + (- (k + 1)) is complex real ext-real V54() set
Seg (len ((F1 /^ (k + 1)) * ([**(c₈ to_power (k + 1)),0**] "))) is V24() V31( len ((F1 /^ (k + 1)) * ([**(c₈ to_power (k + 1)),0**] "))) V56() V57() V58() V59() V60() V61() Element of K27(NAT)
(F1 /^ (k + 1)) /. i is complex Element of the carrier of F_Complex
(F1 /^ (k + 1)) . i is set
F1 . ((k + 1) + i) is set
(F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (((k + 1) + i) -' 1) is complex Element of the carrier of F_Complex
(power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),(((k + 1) + i) -' 1)) is complex Element of the carrier of F_Complex
((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (((k + 1) + i) -' 1)) * ((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),(((k + 1) + i) -' 1))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (((k + 1) + i) -' 1)),((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),(((k + 1) + i) -' 1)))) is complex Element of the carrier of F_Complex
K595(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (((k + 1) + i) -' 1)),((power F_Complex) . (([**c₈,0**] * the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1))),(((k + 1) + i) -' 1)))) is complex Element of COMPLEX
(F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (k + i) is complex Element of the carrier of F_Complex
(power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i)) is complex Element of the carrier of F_Complex
(power F_Complex) . ([**c₈,0**],(k + i)) is complex Element of the carrier of F_Complex
((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i))) * ((power F_Complex) . ([**c₈,0**],(k + i))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i))),((power F_Complex) . ([**c₈,0**],(k + i)))) is complex Element of the carrier of F_Complex
K595(((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i))),((power F_Complex) . ([**c₈,0**],(k + i)))) is complex Element of COMPLEX
((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (k + i)) * (((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i))) * ((power F_Complex) . ([**c₈,0**],(k + i)))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (k + i)),(((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i))) * ((power F_Complex) . ([**c₈,0**],(k + i))))) is complex Element of the carrier of F_Complex
K595(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (k + i)),(((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i))) * ((power F_Complex) . ([**c₈,0**],(k + i))))) is complex Element of COMPLEX
((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (k + i)) * ((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i))) is complex Element of the carrier of F_Complex
the multF of F_Complex . (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (k + i)),((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i)))) is complex Element of the carrier of F_Complex
K595(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (k + i)),((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i)))) is complex Element of COMPLEX
(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (k + i)) * ((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i)))) * ((power F_Complex) . ([**c₈,0**],(k + i))) is complex Element of the carrier of F_Complex
the multF of F_Complex . ((((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (k + i)) * ((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i)))),((power F_Complex) . ([**c₈,0**],(k + i)))) is complex Element of the carrier of F_Complex
K595((((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (k + i)) * ((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i)))),((power F_Complex) . ([**c₈,0**],(k + i)))) is complex Element of COMPLEX
dom (F2) is V56() V57() V58() V59() V60() V61() Element of K27(NAT)
(((F1 /^ (k + 1)) * ([**(c₈ to_power (k + 1)),0**] "))) . i is complex real ext-real Element of REAL
(((F1 /^ (k + 1)) * ([**(c₈ to_power (k + 1)),0**] "))) /. i is complex real ext-real Element of REAL
((F1 /^ (k + 1)) * ([**(c₈ to_power (k + 1)),0**] ")) /. i is complex Element of the carrier of F_Complex
|.(((F1 /^ (k + 1)) * ([**(c₈ to_power (k + 1)),0**] ")) /. i).| is complex real ext-real Element of REAL
((F1 /^ (k + 1)) /. i) * ([**(c₈ to_power (k + 1)),0**] ") is complex Element of the carrier of F_Complex
the multF of F_Complex . (((F1 /^ (k + 1)) /. i),([**(c₈ to_power (k + 1)),0**] ")) is complex Element of the carrier of F_Complex
K595(((F1 /^ (k + 1)) /. i),([**(c₈ to_power (k + 1)),0**] ")) is complex Element of COMPLEX
|.(((F1 /^ (k + 1)) /. i) * ([**(c₈ to_power (k + 1)),0**] ")).| is complex real ext-real Element of REAL
|.((F1 /^ (k + 1)) /. i).| is complex real ext-real Element of REAL
|.([**(c₈ to_power (k + 1)),0**] ").| is complex real ext-real Element of REAL
|.((F1 /^ (k + 1)) /. i).| * |.([**(c₈ to_power (k + 1)),0**] ").| is complex real ext-real Element of REAL
|.((((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (k + i)) * ((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i)))) * ((power F_Complex) . ([**c₈,0**],(k + i)))).| is complex real ext-real Element of REAL
abs (c₈ to_power (k + 1)) is complex real ext-real Element of REAL
(abs (c₈ to_power (k + 1))) " is complex real ext-real Element of REAL
|.((((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (k + i)) * ((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i)))) * ((power F_Complex) . ([**c₈,0**],(k + i)))).| * ((abs (c₈ to_power (k + 1))) ") is complex real ext-real Element of REAL
|.(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (k + i)) * ((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i)))).| is complex real ext-real Element of REAL
|.((power F_Complex) . ([**c₈,0**],(k + i))).| is complex real ext-real Element of REAL
|.(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (k + i)) * ((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i)))).| * |.((power F_Complex) . ([**c₈,0**],(k + i))).| is complex real ext-real Element of REAL
(|.(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (k + i)) * ((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i)))).| * |.((power F_Complex) . ([**c₈,0**],(k + i))).|) * ((abs (c₈ to_power (k + 1))) ") is complex real ext-real Element of REAL
[**(c₈ to_power (k + i)),0**] is complex Element of the carrier of F_Complex
(c₈ to_power (k + i)) + (0 * <i>) is complex set
|.[**(c₈ to_power (k + i)),0**].| is complex real ext-real Element of REAL
|.(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (k + i)) * ((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i)))).| * |.[**(c₈ to_power (k + i)),0**].| is complex real ext-real Element of REAL
(|.(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (k + i)) * ((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i)))).| * |.[**(c₈ to_power (k + i)),0**].|) * ((abs (c₈ to_power (k + 1))) ") is complex real ext-real Element of REAL
|.(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (k + i)) * ((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i)))).| * (c₈ to_power (k + i)) is complex real ext-real Element of REAL
(|.(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (k + i)) * ((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i)))).| * (c₈ to_power (k + i))) * ((abs (c₈ to_power (k + 1))) ") is complex real ext-real Element of REAL
(c₈ to_power (k + 1)) " is complex real ext-real Element of REAL
(|.(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (k + i)) * ((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i)))).| * (c₈ to_power (k + i))) * ((c₈ to_power (k + 1)) ") is complex real ext-real Element of REAL
(c₈ to_power (k + i)) * ((c₈ to_power (k + 1)) ") is complex real ext-real Element of REAL
|.(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (k + i)) * ((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i)))).| * ((c₈ to_power (k + i)) * ((c₈ to_power (k + 1)) ")) is complex real ext-real Element of REAL
(c₈ to_power (k + i)) / (c₈ to_power (k + 1)) is complex real ext-real Element of REAL
(c₈ to_power (k + 1)) " is complex real ext-real set
(c₈ to_power (k + i)) * ((c₈ to_power (k + 1)) ") is complex real ext-real set
|.(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (k + i)) * ((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i)))).| * ((c₈ to_power (k + i)) / (c₈ to_power (k + 1))) is complex real ext-real Element of REAL
|.(((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . (k + i)) * ((power F_Complex) . ( the complex CRoot of k1, - (((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0) / ((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . k1)),(k + i)))).| * (c₈ to_power (i - 1)) is complex real ext-real Element of REAL
F2 . i is set
F2 /. i is complex Element of the carrier of F_Complex
|.(F2 /. i).| is complex real ext-real Element of REAL
(F2) /. i is complex real ext-real Element of REAL
(F2) . i is complex real ext-real Element of REAL
Sum (((F1 /^ (k + 1)) * ([**(c₈ to_power (k + 1)),0**] "))) is complex real ext-real Element of REAL
K294(REAL,(((F1 /^ (k + 1)) * ([**(c₈ to_power (k + 1)),0**] "))),K623()) is complex real ext-real Element of REAL
Sum (F2) is complex real ext-real Element of REAL
K294(REAL,(F2),K623()) is complex real ext-real Element of REAL
[**1,0**] is complex Element of the carrier of F_Complex
1 + (0 * <i>) is complex set
[**1,0**] - [**(c₈ to_power k),0**] is complex Element of the carrier of F_Complex
[**1,0**] + (- [**(c₈ to_power k),0**]) is complex Element of the carrier of F_Complex
the addF of F_Complex . ([**1,0**],(- [**(c₈ to_power k),0**])) is complex Element of the carrier of F_Complex
K593([**1,0**],(- [**(c₈ to_power k),0**])) is complex Element of COMPLEX
|.([**1,0**] - [**(c₈ to_power k),0**]).| is complex real ext-real Element of REAL
1 - (c₈ to_power k1) is complex real ext-real Element of REAL
- (c₈ to_power k1) is complex real ext-real set
1 + (- (c₈ to_power k1)) is complex real ext-real set
0 - 0 is complex real ext-real V54() Element of REAL
- 0 is complex real ext-real non positive V54() set
0 + (- 0) is complex real ext-real V54() set
[**(1 - (c₈ to_power k1)),(0 - 0)**] is complex Element of the carrier of F_Complex
(0 - 0) * <i> is complex set
(1 - (c₈ to_power k1)) + ((0 - 0) * <i>) is complex set
|.[**(1 - (c₈ to_power k1)),(0 - 0)**].| is complex real ext-real Element of REAL
|.((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0).| * 1 is complex real ext-real Element of REAL
|.((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0).| * (1 - (c₈ to_power k)) is complex real ext-real Element of REAL
(|.((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0).| * 1) - (|.((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0).| * (1 - (c₈ to_power k))) is complex real ext-real Element of REAL
- (|.((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0).| * (1 - (c₈ to_power k))) is complex real ext-real set
(|.((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0).| * 1) + (- (|.((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0).| * (1 - (c₈ to_power k)))) is complex real ext-real set
|.((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0).| * (c₈ to_power k) is complex real ext-real Element of REAL
(c₈ to_power (k + 1)) * |.((Sum (F1 /^ (k + 1))) / [**(c₈ to_power (k + 1)),0**]).| is complex real ext-real Element of REAL
(|.((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0).| * (c₈ to_power k)) / (c₈ to_power k) is complex real ext-real Element of REAL
(c₈ to_power k) " is complex real ext-real set
(|.((F_Complex,c₁,(F_Complex,np,(1_ F_Complex))) . 0).| * (c₈ to_power k)) * ((c₈ to_power k) ") is complex real ext-real set
((c₈ to_power (k + 1)) * |.((Sum (F1 /^ (k + 1))) / [**(c₈ to_power (k + 1)),0**]).|) / (c₈ to_power k) is complex real ext-real Element of REAL
((c₈ to_power (k + 1)) * |.((Sum (F1 /^ (k + 1))) / [**(c₈ to_power (k + 1)),0**]).|) * ((c₈ to_power k) ") is complex real ext-real set
(c₈ to_power (k + 1)) / (c₈ to_power k) is complex real ext-real Element of REAL
(c₈ to_power (k + 1)) * ((c₈ to_power k) ") is complex real ext-real set
((c₈ to_power (k + 1)) / (c₈ to_power k)) * |.((Sum (F1 /^ (k + 1))) / [**(c₈ to_power (k + 1)),0**]).| is complex real ext-real Element of REAL
(k + 1) - k is complex real ext-real V54() Element of REAL
- k is complex real ext-real non positive V54() set
(k + 1) + (- k) is complex real ext-real V54() set
c₈ to_power ((k + 1) - k) is complex real ext-real Element of REAL
(c₈ to_power ((k + 1) - k)) * |.((Sum (F1 /^ (k + 1))) / [**(c₈ to_power (k + 1)),0**]).| is complex real ext-real Element of REAL
c₈ * |.((Sum (F1 /^ (k + 1))) / [**(c₈ to_power (k + 1)),0**]).| is complex real ext-real Element of REAL
(Sum (F1 /^ (k + 1))) * ([**(c₈ to_power (k + 1)),0**] ") is complex Element of the carrier of F_Complex
the multF of F_Complex . ((Sum (F1 /^ (k + 1))),([**(c₈ to_power (k + 1)),0**] ")) is complex Element of the carrier of F_Complex
K595((Sum (F1 /^ (k + 1))),([**(c₈ to_power (k + 1)),0**] ")) is complex Element of COMPLEX
Sum ((F1 /^ (k + 1)) * ([**(c₈ to_power (k + 1)),0**] ")) is complex Element of the carrier of F_Complex
c₈ * (Sum (F2)) is complex real ext-real Element of REAL
c₈ is complex Element of the carrier of F_Complex
(F_Complex,c₁) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(NAT, the carrier of F_Complex))
(len c₁) -' 1 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
2 - 1 is complex real ext-real V54() Element of REAL
- 1 is non empty complex real ext-real non positive negative V54() set
2 + (- 1) is complex real ext-real V54() set
len (F_Complex,c₁) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
z0 is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() set
(F_Complex,c₁) . z0 is set
(F_Complex,c₁) . 0 is complex Element of the carrier of F_Complex
(F_Complex,((F_Complex,c₁) . 0),(1_ F_Complex)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(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 quasi_total finite-Support ( F_Complex ) Element of K27(K28(NAT, the carrier of F_Complex))
NAT --> (0. F_Complex) is Relation-like NAT -defined the carrier of F_Complex -valued T-Sequence-like Function-like constant non empty total quasi_total complex-valued Element of K27(K28(NAT, the carrier of F_Complex))
(0_. F_Complex) +* (0,((F_Complex,c₁) . 0)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of F_Complex))
((0_. F_Complex) +* (0,((F_Complex,c₁) . 0))) +* (1,(1_ F_Complex)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of F_Complex))
(F_Complex,((F_Complex,c₁) . 0),(1_ F_Complex)) . z0 is set
(F_Complex,c₁) . z0 is set
(F_Complex,c₁) . 0 is complex Element of the carrier of F_Complex
(F_Complex,((F_Complex,c₁) . 0),(1_ F_Complex)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(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 quasi_total finite-Support ( F_Complex ) Element of K27(K28(NAT, the carrier of F_Complex))
NAT --> (0. F_Complex) is Relation-like NAT -defined the carrier of F_Complex -valued T-Sequence-like Function-like constant non empty total quasi_total complex-valued Element of K27(K28(NAT, the carrier of F_Complex))
(0_. F_Complex) +* (0,((F_Complex,c₁) . 0)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of F_Complex))
((0_. F_Complex) +* (0,((F_Complex,c₁) . 0))) +* (1,(1_ F_Complex)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of F_Complex))
(F_Complex,((F_Complex,c₁) . 0),(1_ F_Complex)) . z0 is set
(F_Complex,c₁) . 0 is complex Element of the carrier of F_Complex
(F_Complex,((F_Complex,c₁) . 0),(1_ F_Complex)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(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 quasi_total finite-Support ( F_Complex ) Element of K27(K28(NAT, the carrier of F_Complex))
NAT --> (0. F_Complex) is Relation-like NAT -defined the carrier of F_Complex -valued T-Sequence-like Function-like constant non empty total quasi_total complex-valued Element of K27(K28(NAT, the carrier of F_Complex))
(0_. F_Complex) +* (0,((F_Complex,c₁) . 0)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of F_Complex))
((0_. F_Complex) +* (0,((F_Complex,c₁) . 0))) +* (1,(1_ F_Complex)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of F_Complex))
(F_Complex,c₁) . 0 is complex Element of the carrier of F_Complex
(F_Complex,((F_Complex,c₁) . 0),(1_ F_Complex)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total quasi_total finite-Support Element of K27(K28(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 quasi_total finite-Support ( F_Complex ) Element of K27(K28(NAT, the carrier of F_Complex))
NAT --> (0. F_Complex) is Relation-like NAT -defined the carrier of F_Complex -valued T-Sequence-like Function-like constant non empty total quasi_total complex-valued Element of K27(K28(NAT, the carrier of F_Complex))
(0_. F_Complex) +* (0,((F_Complex,c₁) . 0)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of F_Complex))
((0_. F_Complex) +* (0,((F_Complex,c₁) . 0))) +* (1,(1_ F_Complex)) is Relation-like NAT -defined the carrier of F_Complex -valued Function-like non empty total quasi_total Element of K27(K28(NAT, the carrier of F_Complex))
len (F_Complex,((F_Complex,c₁) . 0),(1_ F_Complex)) is epsilon-transitive epsilon-connected ordinal natural V24() V29() complex real ext-real non negative V54() V55() V56() V57() V58() V59() V60() V61() Element of NAT
- ((F_Complex,c₁) . 0) is complex Element of the carrier of F_Complex
z0 is complex Element of the carrier of F_Complex
eval ((F_Complex,c₁),z0) is complex Element of the carrier of F_Complex
((F_Complex,c₁) . 0) + z0 is complex Element of the carrier of F_Complex
the addF of F_Complex is Relation-like K28( the carrier of F_Complex, the carrier of F_Complex) -defined the carrier of F_Complex -valued Function-like total quasi_total Element of K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex))
K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex) is set
K27(K28(K28( the carrier of F_Complex, the carrier of F_Complex), the carrier of F_Complex)) is set
the addF of F_Complex . (((F_Complex,c₁) . 0),z0) is complex Element of the carrier of F_Complex
K593(((F_Complex,c₁) . 0),z0) is complex Element of COMPLEX
z0 is complex Element of the carrier of F_Complex