:: PRGCOR_1 semantic presentation
begin
theorem
:: PRGCOR_1:1
for
n
,
m
,
k
being ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-'
(
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-'
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: PRGCOR_1:2
for
n
,
k
being ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) st
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
>
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
mod
(
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
*
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
>=
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
(
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
mod
(
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
*
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
mod
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
(
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
mod
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
mod
(
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
*
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) ;
theorem
:: PRGCOR_1:3
for
n
,
k
being ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) st
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
>
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
mod
(
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
*
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
>=
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
div
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
(
(
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
div
(
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
*
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
*
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: PRGCOR_1:4
for
n
,
k
being ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) st
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
>
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
mod
(
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
*
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
mod
(
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
*
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
mod
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: PRGCOR_1:5
for
n
,
k
being ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) st
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
>
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
mod
(
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
*
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
div
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
(
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
div
(
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
*
k
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
*
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: PRGCOR_1:6
for
m
,
n
being ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) st
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
>
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
ex
i
being ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) st
( ( for
k2
being ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) st
k2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
i
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
*
(
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
|^
k2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) &
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
*
(
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
|^
i
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
>
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) ;
theorem
:: PRGCOR_1:7
for
i
being ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
for
f
being ( (
V16
()
Function-like
FinSequence-like
) (
V16
()
Function-like
FinSequence-like
)
FinSequence
) st 1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) &
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
<=
len
f
: ( (
V16
()
Function-like
FinSequence-like
) (
V16
()
Function-like
FinSequence-like
)
FinSequence
) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
in
dom
f
: ( (
V16
()
Function-like
FinSequence-like
) (
V16
()
Function-like
FinSequence-like
)
FinSequence
) : ( ( ) ( )
Element
of
K11
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
definition
let
n
,
m
be ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) ;
assume
that
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
>=
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
and
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
>
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
func
idiv1_prg
(
n
,
m
)
->
( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
means
:: PRGCOR_1:def 1
ex
sm
,
sn
,
pn
being ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) st
(
len
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
set
) &
len
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
set
) &
len
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
set
) & (
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) implies
it
: ( (
V13
() ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
set
)
=
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) & ( not
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) implies (
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) & ex
i
being ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) st
( 1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) &
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
<=
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) & ( for
k
being ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) st 1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) &
k
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
<
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) holds
(
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
k
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
(
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
k
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
*
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) & not
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
k
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
>
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) ) &
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
(
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
*
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) &
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
>
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) & ( for
j
being ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) st 1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) &
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
<=
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) holds
( (
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
>=
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) implies (
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
(
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) &
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
(
(
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
*
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) ) ) & ( not
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
>=
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) implies (
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) &
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
(
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
*
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) ) ) ) ) &
it
: ( (
V13
() ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
set
)
=
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) ) ) ) );
end;
theorem
:: PRGCOR_1:8
for
n
,
m
being ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) st
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
>=
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
for
sm
,
sn
,
pn
being ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
for
i
being ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) st
len
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) &
len
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) &
len
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) & ( not
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
<
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) implies (
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) & 1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) &
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
<=
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) & ( for
k
being ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) st 1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) &
k
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
<
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) holds
(
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
k
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
(
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
k
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
*
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) & not
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
k
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
>
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) ) ) &
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
(
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
*
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) &
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
>
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) &
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) & ( for
j
being ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) st 1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) &
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
<=
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) holds
( (
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
>=
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) implies (
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
(
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) &
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
(
(
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
*
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) ) ) & ( not
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
>=
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) implies (
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) &
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
(
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
*
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) ) ) ) ) &
idiv1_prg
(
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) ,
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) ) : ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
=
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) ) ) holds
(
len
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) &
len
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) &
len
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) & (
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
<
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) implies
idiv1_prg
(
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) ,
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) ) : ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
=
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) & ( not
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
<
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) implies ( 1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
in
dom
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K11
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) & 1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) &
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
<=
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) & ( for
k
being ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) st 1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) &
k
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
<
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) holds
(
k
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
in
dom
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K11
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
k
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
in
dom
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K11
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
k
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
(
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
k
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
*
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) & not
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
k
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
>
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) ) ) &
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
in
dom
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K11
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
in
dom
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K11
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
(
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
*
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) &
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
>
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) &
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
in
dom
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K11
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
in
dom
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K11
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) & ( for
j
being ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) st 1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) &
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
<=
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) holds
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
in
dom
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K11
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
in
dom
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K11
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) & (
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
>=
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) implies (
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
in
dom
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K11
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
in
dom
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K11
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
(
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) &
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
in
dom
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K11
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
in
dom
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K11
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
(
(
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
*
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) ) ) & ( not
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
>=
sm
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) implies (
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
in
dom
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K11
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
in
dom
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K11
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
sn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) &
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
in
dom
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K11
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
in
dom
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K11
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
(
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
(
(
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
+
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
(
j
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
)
: ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
*
2 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) ) ) ) ) & 1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
in
dom
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K11
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
idiv1_prg
(
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) ,
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) ) : ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
=
pn
: ( ( ) (
V16
()
V19
(
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V20
(
INT
: ( ( ) ( )
set
) )
Function-like
FinSequence-like
)
FinSequence
of
INT
: ( ( ) ( )
set
) )
.
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) ) ) ) ;
theorem
:: PRGCOR_1:9
for
n
,
m
being ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) st
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
>
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
idiv1_prg
(
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
=
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
div
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: PRGCOR_1:10
for
n
,
m
being ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) st
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
>=
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
>
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
idiv1_prg
(
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) ,
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) ) : ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
=
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
div
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
set
) ;
theorem
:: PRGCOR_1:11
for
n
,
m
being ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
for
n2
,
m2
being ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
( (
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
=
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
n2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) &
m2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) implies (
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
div
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
set
)
=
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
n2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
div
m2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) ) & (
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
>=
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
>
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
n2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) &
m2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) implies
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
div
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
set
)
=
n2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
div
m2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) & (
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
>=
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
<
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
n2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) &
m2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
-
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( (
V14
() ) (
ext-real
V14
()
V15
()
integer
)
set
) implies ( (
m2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
*
(
n2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
div
m2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
n2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) implies
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
div
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
set
)
=
-
(
n2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
div
m2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
V14
() ) (
ext-real
non
positive
V14
()
V15
()
integer
)
set
) ) & (
m2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
*
(
n2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
div
m2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<>
n2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) implies
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
div
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
set
)
=
(
-
(
n2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
div
m2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V14
() ) (
ext-real
non
positive
V14
()
V15
()
integer
)
set
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
positive
negative
V4
()
V14
()
V15
()
integer
)
set
) ) ) ) & (
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
<
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
>
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
n2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
-
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( (
V14
() ) (
ext-real
V14
()
V15
()
integer
)
set
) &
m2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) implies ( (
m2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
*
(
n2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
div
m2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
n2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) implies
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
div
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
set
)
=
-
(
n2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
div
m2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
V14
() ) (
ext-real
non
positive
V14
()
V15
()
integer
)
set
) ) & (
m2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
*
(
n2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
div
m2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<>
n2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) implies
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
div
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
set
)
=
(
-
(
n2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
div
m2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V14
() ) (
ext-real
non
positive
V14
()
V15
()
integer
)
set
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
positive
negative
V4
()
V14
()
V15
()
integer
)
set
) ) ) ) & (
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
<
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
<
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
n2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
-
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( (
V14
() ) (
ext-real
V14
()
V15
()
integer
)
set
) &
m2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
-
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( (
V14
() ) (
ext-real
V14
()
V15
()
integer
)
set
) implies
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
div
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
set
)
=
n2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
div
m2
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) ) ;
definition
let
n
,
m
be ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) ;
func
idiv_prg
(
n
,
m
)
->
( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
means
:: PRGCOR_1:def 2
ex
i
being ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) st
( (
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) implies
it
: ( (
V13
() ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
set
)
=
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) & ( not
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) implies ( (
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
>=
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
>
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) implies
it
: ( (
V13
() ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
set
)
=
idiv1_prg
(
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) ) & ( ( not
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
>=
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) or not
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
>
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) implies ( (
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
>=
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) implies (
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
=
idiv1_prg
(
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
-
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V14
() ) (
ext-real
non
positive
V14
()
V15
()
integer
)
set
) ) : ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) & (
(
-
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V14
() ) (
ext-real
non
positive
V14
()
V15
()
integer
)
set
)
*
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) implies
it
: ( (
V13
() ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
set
)
=
-
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( (
V14
() ) (
ext-real
V14
()
V15
()
integer
)
set
) ) & (
(
-
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V14
() ) (
ext-real
non
positive
V14
()
V15
()
integer
)
set
)
*
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
<>
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) implies
it
: ( (
V13
() ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
set
)
=
(
-
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( (
V14
() ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) ) ) ) & ( ( not
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
>=
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) or not
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) implies ( (
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
>
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) implies (
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
=
idiv1_prg
(
(
-
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V14
() ) (
ext-real
non
positive
V14
()
V15
()
integer
)
set
) ,
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) & (
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
*
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
=
-
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
V14
() ) (
ext-real
non
positive
V14
()
V15
()
integer
)
set
) implies
it
: ( (
V13
() ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
set
)
=
-
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( (
V14
() ) (
ext-real
V14
()
V15
()
integer
)
set
) ) & (
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
*
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
)
<>
-
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
V14
() ) (
ext-real
non
positive
V14
()
V15
()
integer
)
set
) implies
it
: ( (
V13
() ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
set
)
=
(
-
i
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
)
: ( (
V14
() ) (
ext-real
V14
()
V15
()
integer
)
set
)
-
1 : ( ( ) (
ext-real
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V14
()
V15
()
integer
)
set
) ) ) ) & ( ( not
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) or not
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
>
0
: ( ( ) (
ext-real
non
positive
non
negative
V4
()
V7
()
V8
()
V9
()
V11
()
V12
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) implies
it
: ( (
V13
() ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
set
)
=
idiv1_prg
(
(
-
n
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V14
() ) (
ext-real
non
positive
V14
()
V15
()
integer
)
set
) ,
(
-
m
: ( ( ) (
ext-real
non
negative
V7
()
V8
()
V9
()
V13
()
V14
()
V15
()
integer
)
Element
of
NAT
: ( ( ) (
V4
()
V7
()
V8
()
V9
() )
Element
of
K11
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V14
() ) (
ext-real
non
positive
V14
()
V15
()
integer
)
set
) ) : ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) ) ) ) ) ) ) ) );
end;
theorem
:: PRGCOR_1:12
for
n
,
m
being ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) holds
idiv_prg
(
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) ,
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) ) : ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
=
n
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
)
div
m
: ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
Integer
) : ( (
integer
) (
ext-real
V14
()
V15
()
integer
)
set
) ;