begin
theorem
for
A,
B being ( ( ) ( )
set ) st ( for
x being ( ( ) ( )
set ) st
x : ( ( ) ( )
set )
in A : ( ( ) ( )
set ) holds
ex
K being ( ( ) ( )
set ) st
(
K : ( ( ) ( )
set )
c= B : ( ( ) ( )
set ) &
x : ( ( ) ( )
set )
c= union K : ( ( ) ( )
set ) : ( ( ) ( )
set ) ) ) holds
union A : ( ( ) ( )
set ) : ( ( ) ( )
set )
c= union B : ( ( ) ( )
set ) : ( ( ) ( )
set ) ;
begin
theorem
for
m,
i,
a,
b being ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
for
D being ( ( non
empty ) ( non
empty )
Subset of ) st 2 : ( ( ) ( non
empty ordinal natural V14()
real V16()
ext-real positive non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
<= m : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) &
m : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
< len (Gauge (D : ( ( non empty ) ( non empty ) Subset of ) ,i : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V18() non
empty-yielding V21(
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
V22(
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) )
Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column )
FinSequence of
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) ) : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) & 1 : ( ( ) ( non
empty ordinal natural V14()
real V16()
ext-real positive non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
<= a : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) &
a : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
<= len (Gauge (D : ( ( non empty ) ( non empty ) Subset of ) ,i : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V18() non
empty-yielding V21(
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
V22(
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) )
Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column )
FinSequence of
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) ) : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) & 1 : ( ( ) ( non
empty ordinal natural V14()
real V16()
ext-real positive non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
<= b : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) &
b : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
<= len (Gauge (D : ( ( non empty ) ( non empty ) Subset of ) ,(i : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V18() non
empty-yielding V21(
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
V22(
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) )
Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column )
FinSequence of
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) ) : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) holds
((Gauge (D : ( ( non empty ) ( non empty ) Subset of ) ,i : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V18() non empty-yielding V21( NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) V22(K354( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) ) : ( ( ) ( ) M17( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column ) FinSequence of K354( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) ) : ( ( ) ( ) M17( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) )) ) * (m : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ,a : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V38(2 : ( ( ) ( non
empty ordinal natural V14()
real V16()
ext-real positive non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V95() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )
`1 : ( ( ) (
V14()
real ext-real )
Element of
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) )
= ((Gauge (D : ( ( non empty ) ( non empty ) Subset of ) ,(i : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V18() non empty-yielding V21( NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) V22(K354( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) ) : ( ( ) ( ) M17( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column ) FinSequence of K354( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) ) : ( ( ) ( ) M17( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) )) ) * (((2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) * m : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() even ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) -' 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ,b : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V38(2 : ( ( ) ( non
empty ordinal natural V14()
real V16()
ext-real positive non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V95() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )
`1 : ( ( ) (
V14()
real ext-real )
Element of
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) ;
theorem
for
n,
i,
a,
b being ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
for
D being ( ( non
empty ) ( non
empty )
Subset of ) st 2 : ( ( ) ( non
empty ordinal natural V14()
real V16()
ext-real positive non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
<= n : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) &
n : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
< len (Gauge (D : ( ( non empty ) ( non empty ) Subset of ) ,i : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V18() non
empty-yielding V21(
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
V22(
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) )
Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column )
FinSequence of
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) ) : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) & 1 : ( ( ) ( non
empty ordinal natural V14()
real V16()
ext-real positive non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
<= a : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) &
a : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
<= len (Gauge (D : ( ( non empty ) ( non empty ) Subset of ) ,i : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V18() non
empty-yielding V21(
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
V22(
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) )
Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column )
FinSequence of
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) ) : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) & 1 : ( ( ) ( non
empty ordinal natural V14()
real V16()
ext-real positive non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
<= b : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) &
b : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
<= len (Gauge (D : ( ( non empty ) ( non empty ) Subset of ) ,(i : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V18() non
empty-yielding V21(
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
V22(
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) )
Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column )
FinSequence of
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) ) : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) holds
((Gauge (D : ( ( non empty ) ( non empty ) Subset of ) ,i : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V18() non empty-yielding V21( NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) V22(K354( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) ) : ( ( ) ( ) M17( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column ) FinSequence of K354( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) ) : ( ( ) ( ) M17( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) )) ) * (a : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ,n : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V38(2 : ( ( ) ( non
empty ordinal natural V14()
real V16()
ext-real positive non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V95() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )
`2 : ( ( ) (
V14()
real ext-real )
Element of
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) )
= ((Gauge (D : ( ( non empty ) ( non empty ) Subset of ) ,(i : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V18() non empty-yielding V21( NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) V22(K354( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) ) : ( ( ) ( ) M17( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column ) FinSequence of K354( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) ) : ( ( ) ( ) M17( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) )) ) * (b : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ,((2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) * n : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() even ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) -' 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V38(2 : ( ( ) ( non
empty ordinal natural V14()
real V16()
ext-real positive non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V95() )
Element of the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )
`2 : ( ( ) (
V14()
real ext-real )
Element of
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) ;
theorem
for
m,
i,
n being ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
for
D being ( (
compact non
horizontal non
vertical ) ( non
empty compact non
horizontal non
vertical )
Subset of ) st 2 : ( ( ) ( non
empty ordinal natural V14()
real V16()
ext-real positive non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
<= m : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) &
m : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
+ 1 : ( ( ) ( non
empty ordinal natural V14()
real V16()
ext-real positive non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( non
empty ordinal natural V14()
real V16()
ext-real positive non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
< len (Gauge (D : ( ( compact non horizontal non vertical ) ( non empty compact non horizontal non vertical ) Subset of ) ,i : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V18() non
empty-yielding V21(
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
V22(
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) )
Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) ) : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) & 2 : ( ( ) ( non
empty ordinal natural V14()
real V16()
ext-real positive non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
<= n : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) &
n : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
+ 1 : ( ( ) ( non
empty ordinal natural V14()
real V16()
ext-real positive non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( non
empty ordinal natural V14()
real V16()
ext-real positive non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
< len (Gauge (D : ( ( compact non horizontal non vertical ) ( non empty compact non horizontal non vertical ) Subset of ) ,i : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V18() non
empty-yielding V21(
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
V22(
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) )
Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) ) : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) holds
cell (
(Gauge (D : ( ( compact non horizontal non vertical ) ( non empty compact non horizontal non vertical ) Subset of ) ,i : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V18() non
empty-yielding V21(
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
V22(
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) )
Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) ) ,
m : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) ,
n : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) ( )
Element of
K10( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
= (((cell ((Gauge (D : ( ( compact non horizontal non vertical ) ( non empty compact non horizontal non vertical ) Subset of ) ,(i : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V18() non empty-yielding V21( NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) V22(K354( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) ) : ( ( ) ( ) M17( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K354( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) ) : ( ( ) ( ) M17( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) )) ) ,((2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) * m : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() even ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) -' 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ,((2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) * n : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() even ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) -' 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K10( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) \/ (cell ((Gauge (D : ( ( compact non horizontal non vertical ) ( non empty compact non horizontal non vertical ) Subset of ) ,(i : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V18() non empty-yielding V21( NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) V22(K354( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) ) : ( ( ) ( ) M17( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K354( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) ) : ( ( ) ( ) M17( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) )) ) ,((2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) * m : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() even ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) -' 1 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ,((2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) * n : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() even ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) -' 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K10( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) Element of K10( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) \/ (cell ((Gauge (D : ( ( compact non horizontal non vertical ) ( non empty compact non horizontal non vertical ) Subset of ) ,(i : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V18() non empty-yielding V21( NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) V22(K354( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) ) : ( ( ) ( ) M17( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K354( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) ) : ( ( ) ( ) M17( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) )) ) ,((2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) * m : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() even ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) -' 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ,((2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) * n : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() even ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) -' 1 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K10( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( )
Element of
K10( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
\/ (cell ((Gauge (D : ( ( compact non horizontal non vertical ) ( non empty compact non horizontal non vertical ) Subset of ) ,(i : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V18() non empty-yielding V21( NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) V22(K354( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) ) : ( ( ) ( ) M17( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K354( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) ) : ( ( ) ( ) M17( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) )) ) ,((2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) * m : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() even ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) -' 1 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ,((2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) * n : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() even ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) -' 1 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( )
Element of
K10( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
Element of
K10( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) ;
theorem
for
m,
i,
n being ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
for
D being ( (
compact non
horizontal non
vertical ) ( non
empty compact non
horizontal non
vertical )
Subset of )
for
k being ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) st 2 : ( ( ) ( non
empty ordinal natural V14()
real V16()
ext-real positive non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
<= m : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) &
m : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
+ 1 : ( ( ) ( non
empty ordinal natural V14()
real V16()
ext-real positive non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( non
empty ordinal natural V14()
real V16()
ext-real positive non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
< len (Gauge (D : ( ( compact non horizontal non vertical ) ( non empty compact non horizontal non vertical ) Subset of ) ,i : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V18() non
empty-yielding V21(
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
V22(
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) )
Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) ) : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) & 2 : ( ( ) ( non
empty ordinal natural V14()
real V16()
ext-real positive non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
<= n : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) &
n : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
+ 1 : ( ( ) ( non
empty ordinal natural V14()
real V16()
ext-real positive non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) ( non
empty ordinal natural V14()
real V16()
ext-real positive non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
< len (Gauge (D : ( ( compact non horizontal non vertical ) ( non empty compact non horizontal non vertical ) Subset of ) ,i : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V18() non
empty-yielding V21(
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
V22(
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) )
Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) ) : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) holds
cell (
(Gauge (D : ( ( compact non horizontal non vertical ) ( non empty compact non horizontal non vertical ) Subset of ) ,i : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V18() non
empty-yielding V21(
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) )
V22(
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) )
Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K354( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
M17( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) )) ) ,
m : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) ,
n : ( ( ) (
ordinal natural V14()
real V16()
ext-real non
negative V103()
V104()
V105()
V106()
V107()
V108()
V109() )
Element of
NAT : ( ( ) (
V104()
V105()
V106()
V107()
V108()
V109()
V110() )
Element of
K10(
REAL : ( ( ) (
V104()
V105()
V106()
V110() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) ( )
Element of
K10( the
U1 of
(TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V142()
V167()
V168()
V169()
V170()
V171()
V172()
V173()
strict )
RLTopStruct ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
= union { (cell ((Gauge (D : ( ( compact non horizontal non vertical ) ( non empty compact non horizontal non vertical ) Subset of ) ,(i : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) + k : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V18() non empty-yielding V21( NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) V22(K354( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) ) : ( ( ) ( ) M17( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K354( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) ) : ( ( ) ( ) M17( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) )) ) ,a : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ,b : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K10( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V142() V167() V168() V169() V170() V171() V172() V173() strict ) RLTopStruct ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) where a, b is ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) : ( (((2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) |^ k : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) * m : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) - (2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) |^ (k : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() even ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V14() real V16() ext-real ) Element of REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) + 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V14() real V16() ext-real ) Element of REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) <= a : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) & a : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) <= (((2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) |^ k : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) * m : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) - (2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) |^ k : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V14() real V16() ext-real ) Element of REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) + 1 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V14() real V16() ext-real ) Element of REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) & (((2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) |^ k : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) * n : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) - (2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) |^ (k : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() even ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V14() real V16() ext-real ) Element of REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) + 2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V14() real V16() ext-real ) Element of REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) <= b : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) & b : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) <= (((2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) |^ k : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) * n : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) - (2 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) |^ k : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ordinal natural V14() real V16() ext-real non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V14() real V16() ext-real ) Element of REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) + 1 : ( ( ) ( non empty ordinal natural V14() real V16() ext-real positive non negative V103() V104() V105() V106() V107() V108() V109() ) Element of NAT : ( ( ) ( V104() V105() V106() V107() V108() V109() V110() ) Element of K10(REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V14() real V16() ext-real ) Element of REAL : ( ( ) ( V104() V105() V106() V110() ) set ) ) ) } : ( ( ) ( )
set ) ;