begin
theorem
for
s,
s1 being ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence) st
s : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
= s1 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
(#) s1 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence) : ( (
V21() ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Element of
K6(
K7(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V33()
V34()
V35() )
set ) ) : ( ( ) ( )
set ) ) holds
for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) holds
(Partial_Sums s : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Element of
K6(
K7(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V33()
V34()
V35() )
set ) ) : ( ( ) ( )
set ) )
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
>= 0 : ( ( ) (
V1()
ordinal natural V11()
real ext-real non
positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) ;
theorem
for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
for
s being ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence) st ( for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) holds
(
s : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
> 0 : ( ( ) (
V1()
ordinal natural V11()
real ext-real non
positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) &
s : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
> s : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. (n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) - 1 : ( ( ) ( V1() ordinal natural V11() real ext-real positive non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) ) holds
(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() ordinal natural V11() real ext-real positive non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V1()
ordinal natural V11()
real ext-real positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
* (s : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) . (n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() ordinal natural V11() real ext-real positive non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V1() ordinal natural V11() real ext-real positive non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
> (Partial_Sums s : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Element of
K6(
K7(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V33()
V34()
V35() )
set ) ) : ( ( ) ( )
set ) )
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ;
theorem
for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
for
s being ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence) st ( for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) holds
(
s : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
> 0 : ( ( ) (
V1()
ordinal natural V11()
real ext-real non
positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) &
s : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
>= s : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. (n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) - 1 : ( ( ) ( V1() ordinal natural V11() real ext-real positive non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) ) holds
(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() ordinal natural V11() real ext-real positive non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V1()
ordinal natural V11()
real ext-real positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
* (s : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) . (n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() ordinal natural V11() real ext-real positive non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V1() ordinal natural V11() real ext-real positive non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
>= (Partial_Sums s : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Element of
K6(
K7(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V33()
V34()
V35() )
set ) ) : ( ( ) ( )
set ) )
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ;
theorem
for
s,
s1,
s2 being ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence) st
s : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
= s1 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
(#) s2 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence) : ( (
V21() ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Element of
K6(
K7(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V33()
V34()
V35() )
set ) ) : ( ( ) ( )
set ) ) & ( for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) holds
(
s1 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
>= 0 : ( ( ) (
V1()
ordinal natural V11()
real ext-real non
positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) &
s2 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
>= 0 : ( ( ) (
V1()
ordinal natural V11()
real ext-real non
positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) ) ) holds
for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) holds
(Partial_Sums s : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Element of
K6(
K7(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V33()
V34()
V35() )
set ) ) : ( ( ) ( )
set ) )
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
<= ((Partial_Sums s1 : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Element of K6(K7(NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( V33() V34() V35() ) set ) ) : ( ( ) ( ) set ) ) . n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
* ((Partial_Sums s2 : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Element of K6(K7(NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( V33() V34() V35() ) set ) ) : ( ( ) ( ) set ) ) . n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ;
theorem
for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
for
s,
s1,
s2 being ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence) st
s : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
= s1 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
(#) s2 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence) : ( (
V21() ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Element of
K6(
K7(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V33()
V34()
V35() )
set ) ) : ( ( ) ( )
set ) ) & ( for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) holds
(
s1 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
< 0 : ( ( ) (
V1()
ordinal natural V11()
real ext-real non
positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) &
s2 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
< 0 : ( ( ) (
V1()
ordinal natural V11()
real ext-real non
positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) ) ) holds
(Partial_Sums s : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Element of
K6(
K7(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V33()
V34()
V35() )
set ) ) : ( ( ) ( )
set ) )
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
<= ((Partial_Sums s1 : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Element of K6(K7(NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( V33() V34() V35() ) set ) ) : ( ( ) ( ) set ) ) . n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
* ((Partial_Sums s2 : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Element of K6(K7(NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( V33() V34() V35() ) set ) ) : ( ( ) ( ) set ) ) . n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ;
theorem
for
s being ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) holds
abs ((Partial_Sums s : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Element of K6(K7(NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( V33() V34() V35() ) set ) ) : ( ( ) ( ) set ) ) . n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V11()
real ext-real non
negative )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
<= (Partial_Sums (abs s : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( ( V21() ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Element of K6(K7(NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( V33() V34() V35() ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Element of
K6(
K7(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V33()
V34()
V35() )
set ) ) : ( ( ) ( )
set ) )
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ;
theorem
for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
for
s being ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence) holds
(Partial_Sums s : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Element of
K6(
K7(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V33()
V34()
V35() )
set ) ) : ( ( ) ( )
set ) )
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
<= (Partial_Sums (abs s : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( ( V21() ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Element of K6(K7(NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( V33() V34() V35() ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Element of
K6(
K7(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V33()
V34()
V35() )
set ) ) : ( ( ) ( )
set ) )
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ;
theorem
for
s being ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence) st ( for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) holds
(
s : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
> 0 : ( ( ) (
V1()
ordinal natural V11()
real ext-real non
positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) &
s : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
< 1 : ( ( ) (
V1()
ordinal natural V11()
real ext-real positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) ) ) holds
for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) holds
(
(Partial_Product s : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
> 0 : ( ( ) (
V1()
ordinal natural V11()
real ext-real non
positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) &
(Partial_Product s : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
< 1 : ( ( ) (
V1()
ordinal natural V11()
real ext-real positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) ) ;
theorem
for
s1,
s2 being ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence) st ( for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) holds
(
s1 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
>= 0 : ( ( ) (
V1()
ordinal natural V11()
real ext-real non
positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) &
s2 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
>= 0 : ( ( ) (
V1()
ordinal natural V11()
real ext-real non
positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) ) ) holds
for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) holds
((Partial_Product s1 : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) . n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
+ ((Partial_Product s2 : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) . n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
<= (Partial_Product (s1 : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) + s2 : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Element of K6(K7(NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( V33() V34() V35() ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ;
theorem
for
s1,
s being ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence) st ( for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) holds
(
s1 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
= 1 : ( ( ) (
V1()
ordinal natural V11()
real ext-real positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
+ (s : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) . n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) &
s : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
> - 1 : ( ( ) (
V1()
ordinal natural V11()
real ext-real positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V1()
V11()
real ext-real non
positive negative )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) &
s : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
< 0 : ( ( ) (
V1()
ordinal natural V11()
real ext-real non
positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) ) ) holds
for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) holds 1 : ( ( ) (
V1()
ordinal natural V11()
real ext-real positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
+ ((Partial_Sums s : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Element of K6(K7(NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( V33() V34() V35() ) set ) ) : ( ( ) ( ) set ) ) . n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
<= (Partial_Product s1 : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ;
theorem
for
s1,
s being ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence) st ( for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) holds
(
s1 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
= 1 : ( ( ) (
V1()
ordinal natural V11()
real ext-real positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
+ (s : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) . n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) &
s : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
>= 0 : ( ( ) (
V1()
ordinal natural V11()
real ext-real non
positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) ) ) holds
for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) holds 1 : ( ( ) (
V1()
ordinal natural V11()
real ext-real positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
+ ((Partial_Sums s : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Element of K6(K7(NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( V33() V34() V35() ) set ) ) : ( ( ) ( ) set ) ) . n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
<= (Partial_Product s1 : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ;
theorem
for
s3,
s1,
s2,
s4,
s5 being ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence) st
s3 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
= s1 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
(#) s2 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence) : ( (
V21() ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Element of
K6(
K7(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V33()
V34()
V35() )
set ) ) : ( ( ) ( )
set ) ) &
s4 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
= s1 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
(#) s1 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence) : ( (
V21() ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Element of
K6(
K7(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V33()
V34()
V35() )
set ) ) : ( ( ) ( )
set ) ) &
s5 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
= s2 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
(#) s2 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence) : ( (
V21() ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Element of
K6(
K7(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V33()
V34()
V35() )
set ) ) : ( ( ) ( )
set ) ) holds
for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) holds
((Partial_Sums s3 : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Element of K6(K7(NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( V33() V34() V35() ) set ) ) : ( ( ) ( ) set ) ) . n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
^2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
<= ((Partial_Sums s4 : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Element of K6(K7(NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( V33() V34() V35() ) set ) ) : ( ( ) ( ) set ) ) . n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
* ((Partial_Sums s5 : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Element of K6(K7(NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( V33() V34() V35() ) set ) ) : ( ( ) ( ) set ) ) . n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ;
theorem
for
s4,
s1,
s5,
s2,
s3 being ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence) st
s4 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
= s1 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
(#) s1 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence) : ( (
V21() ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Element of
K6(
K7(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V33()
V34()
V35() )
set ) ) : ( ( ) ( )
set ) ) &
s5 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
= s2 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
(#) s2 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence) : ( (
V21() ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Element of
K6(
K7(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V33()
V34()
V35() )
set ) ) : ( ( ) ( )
set ) ) & ( for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) holds
(
s1 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
>= 0 : ( ( ) (
V1()
ordinal natural V11()
real ext-real non
positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) &
s2 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
>= 0 : ( ( ) (
V1()
ordinal natural V11()
real ext-real non
positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) &
s3 : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
= ((s1 : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) . n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) + (s2 : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) . n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
^2 : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) ) holds
for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) holds
sqrt ((Partial_Sums s3 : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Element of K6(K7(NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( V33() V34() V35() ) set ) ) : ( ( ) ( ) set ) ) . n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
<= (sqrt ((Partial_Sums s4 : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Element of K6(K7(NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( V33() V34() V35() ) set ) ) : ( ( ) ( ) set ) ) . n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
+ (sqrt ((Partial_Sums s5 : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Element of K6(K7(NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ,REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( V33() V34() V35() ) set ) ) : ( ( ) ( ) set ) ) . n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ;
theorem
for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
for
s being ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence) st ( for
n being ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) holds
(
s : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
> 0 : ( ( ) (
V1()
ordinal natural V11()
real ext-real non
positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) &
s : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
>= s : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Real_Sequence)
. (n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) - 1 : ( ( ) ( V1() ordinal natural V11() real ext-real positive non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) ) holds
(Partial_Sums s : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( (
V21()
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ) (
V16()
V19(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V20(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V21()
V26(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
V30(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
V33()
V34()
V35() )
Element of
K6(
K7(
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ,
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V33()
V34()
V35() )
set ) ) : ( ( ) ( )
set ) )
. n : ( ( ) (
ordinal natural V11()
real ext-real non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) )
>= (n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() ordinal natural V11() real ext-real positive non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) (
V1()
ordinal natural V11()
real ext-real positive non
negative V43()
V56()
V57()
V58()
V59()
V60()
V61()
V62() )
Element of
NAT : ( ( ) (
V57()
V58()
V59()
V60()
V61()
V62()
V63() )
Element of
K6(
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) ( )
set ) ) )
* ((n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() ordinal natural V11() real ext-real positive non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V1() ordinal natural V11() real ext-real positive non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) -root ((Partial_Product s : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) ) : ( ( V21() V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) ( V16() V19( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V20( REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V21() V26( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) V30( NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) , REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) V33() V34() V35() ) Real_Sequence) . n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V56() V57() V58() V59() V60() V61() V62() ) Element of NAT : ( ( ) ( V57() V58() V59() V60() V61() V62() V63() ) Element of K6(REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V1() V45() V57() V58() V59() V63() ) set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) (
V1()
V45()
V57()
V58()
V59()
V63() )
set ) ) ;