:: SPRECT_5 semantic presentation
begin
theorem
:: SPRECT_5:1
for
D
being ( ( non
empty
) ( non
empty
)
set
)
for
f
being ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
D
: ( ( non
empty
) ( non
empty
)
set
) )
for
q
,
p
being ( ( ) ( )
Element
of
D
: ( ( non
empty
) ( non
empty
)
set
) ) st
q
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
in
rng
(
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
|
(
p
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
)
: ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( )
set
) holds
q
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
p
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:2
for
D
being ( ( non
empty
) ( non
empty
)
set
)
for
f
being ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
D
: ( ( non
empty
) ( non
empty
)
set
) )
for
p
,
q
being ( ( ) ( )
Element
of
D
: ( ( non
empty
) ( non
empty
)
set
) ) st
p
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
in
rng
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( )
set
) &
q
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
in
rng
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( )
set
) &
p
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
q
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
q
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
(
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
:-
p
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
)
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
(
(
q
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
)
: ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-
(
p
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
)
: ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V39
()
V43
() )
set
)
+
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V39
()
V43
() )
set
) ;
theorem
:: SPRECT_5:3
for
D
being ( ( non
empty
) ( non
empty
)
set
)
for
f
being ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
D
: ( ( non
empty
) ( non
empty
)
set
) )
for
p
,
q
being ( ( ) ( )
Element
of
D
: ( ( non
empty
) ( non
empty
)
set
) ) st
p
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
in
rng
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( )
set
) &
q
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
in
rng
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( )
set
) &
p
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
q
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
p
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
(
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-:
q
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
)
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
p
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:4
for
D
being ( ( non
empty
) ( non
empty
)
set
)
for
f
being ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
D
: ( ( non
empty
) ( non
empty
)
set
) )
for
p
,
q
being ( ( ) ( )
Element
of
D
: ( ( non
empty
) ( non
empty
)
set
) ) st
p
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
in
rng
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( )
set
) &
q
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
in
rng
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( )
set
) &
p
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
q
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
q
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
(
Rotate
(
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
p
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
(
(
q
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
)
: ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-
(
p
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
)
: ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
ext-real
V39
()
V43
() )
set
)
+
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V39
()
V43
() )
set
) ;
theorem
:: SPRECT_5:5
for
D
being ( ( non
empty
) ( non
empty
)
set
)
for
f
being ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
D
: ( ( non
empty
) ( non
empty
)
set
) )
for
p1
,
p2
,
p3
being ( ( ) ( )
Element
of
D
: ( ( non
empty
) ( non
empty
)
set
) ) st
p1
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
in
rng
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( )
set
) &
p2
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
in
rng
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( )
set
) &
p3
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
in
rng
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( )
set
) &
p1
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
p2
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
p2
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
p3
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
p2
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
(
Rotate
(
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
p1
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
p3
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
(
Rotate
(
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
p1
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:6
for
D
being ( ( non
empty
) ( non
empty
)
set
)
for
f
being ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
D
: ( ( non
empty
) ( non
empty
)
set
) )
for
p1
,
p2
,
p3
being ( ( ) ( )
Element
of
D
: ( ( non
empty
) ( non
empty
)
set
) ) st
p1
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
in
rng
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( )
set
) &
p2
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
in
rng
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( )
set
) &
p3
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
in
rng
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( )
set
) &
p1
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
p2
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
p2
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
p3
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
p2
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
(
Rotate
(
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
p1
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
p3
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
(
Rotate
(
f
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
p1
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:7
for
D
being ( ( non
empty
) ( non
empty
)
set
)
for
g
being ( (
circular
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
circular
)
FinSequence
of
D
: ( ( non
empty
) ( non
empty
)
set
) )
for
p
being ( ( ) ( )
Element
of
D
: ( ( non
empty
) ( non
empty
)
set
) ) st
p
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
in
rng
g
: ( (
circular
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
circular
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( )
set
) &
len
g
: ( (
circular
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
circular
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
>
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
p
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
..
g
: ( (
circular
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
circular
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
len
g
: ( (
circular
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
FinSequence-like
circular
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
begin
registration
let
f
be ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ;
cluster
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
FinSequence
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
/^
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
V1
()
Function-like
FinSequence-like
) (
V1
()
Function-like
FinSequence-like
)
set
)
->
V1
()
Function-like
one-to-one
FinSequence-like
;
end;
theorem
:: SPRECT_5:8
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
q
being ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) ) st 1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
q
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
q
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
in
rng
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V19
() )
set
) holds
(
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
(
Rotate
(
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ,
q
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) ) )
)
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
FinSequence
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
(
(
len
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-
(
q
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V39
()
V43
() )
set
) ;
theorem
:: SPRECT_5:9
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
p
,
q
being ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) ) st
p
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
in
rng
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V19
() )
set
) &
q
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
in
rng
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V19
() )
set
) &
p
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
q
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
p
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
(
Rotate
(
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ,
q
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) ) )
)
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
FinSequence
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
(
(
len
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
(
p
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-
(
q
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
ext-real
V39
()
V43
() )
set
) ;
theorem
:: SPRECT_5:10
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
p1
,
p2
,
p3
being ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) ) st
p1
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
in
rng
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V19
() )
set
) &
p2
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
in
rng
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V19
() )
set
) &
p3
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
in
rng
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V19
() )
set
) &
p1
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
p2
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
p2
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
p3
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
p3
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
(
Rotate
(
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ,
p2
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) ) )
)
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
FinSequence
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
p1
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
(
Rotate
(
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ,
p2
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) ) )
)
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
FinSequence
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:11
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
p1
,
p2
,
p3
being ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) ) st
p1
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
in
rng
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V19
() )
set
) &
p2
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
in
rng
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V19
() )
set
) &
p3
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
in
rng
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V19
() )
set
) &
p1
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
p2
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
p2
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
p3
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
p1
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
(
Rotate
(
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ,
p3
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) ) )
)
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
FinSequence
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
p2
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
(
Rotate
(
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ,
p3
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) ) )
)
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
FinSequence
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:12
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
p1
,
p2
,
p3
being ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) ) st
p1
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
in
rng
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V19
() )
set
) &
p2
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
in
rng
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V19
() )
set
) &
p3
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
in
rng
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V19
() )
set
) &
p1
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
p2
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
p2
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
p3
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
p1
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
(
Rotate
(
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ,
p3
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) ) )
)
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
FinSequence
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
p2
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) )
..
(
Rotate
(
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ,
p3
: ( ( ) ( )
Point
of ( ( ) ( non
empty
V19
() )
set
) ) )
)
: ( ( ) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
FinSequence
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:13
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
(
S-min
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
len
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:14
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
(
S-max
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
len
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:15
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
(
E-min
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
len
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:16
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
(
E-max
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
len
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:17
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
(
N-min
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
len
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:18
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
(
N-max
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
len
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:19
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
(
W-max
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
len
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:20
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
(
W-min
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
len
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
begin
theorem
:: SPRECT_5:21
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) st
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
W-min
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
W-min
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
W-max
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:22
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) st
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
W-min
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
W-max
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
>
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:23
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
W-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
W-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
N-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
W-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
N-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:24
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
W-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
N-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
N-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:25
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
W-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
N-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
E-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
N-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
E-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:26
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
W-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
E-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
E-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:27
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
W-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
E-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
S-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
E-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
S-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:28
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
W-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
S-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
W-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
S-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
S-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:29
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) st
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
S-max
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
S-max
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
S-min
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:30
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) st
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
S-max
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
S-min
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
>
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:31
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
S-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
S-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
W-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
S-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
W-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:32
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
S-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
W-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
W-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:33
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
S-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
W-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
N-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
W-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
N-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:34
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
S-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
N-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
N-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:35
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
S-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
N-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
E-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
N-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
E-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:36
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
S-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
E-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
S-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
E-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
E-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:37
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) st
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
E-max
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
E-max
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
E-min
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:38
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) st
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
E-max
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
E-min
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
>
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:39
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
E-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
S-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
E-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
E-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
S-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:40
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
E-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
S-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
S-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:41
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
E-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
S-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
W-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
S-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
W-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:42
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
E-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
W-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
W-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:43
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
E-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
W-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
N-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
W-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
N-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:44
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
E-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
N-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
E-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
N-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
N-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:45
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) st
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
N-max
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
N-max
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
E-max
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
N-max
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
E-max
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:46
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
N-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
E-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
E-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:47
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
N-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
E-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
S-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
E-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
S-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:48
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
N-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
S-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
S-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:49
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
N-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
S-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
W-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
S-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
W-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:50
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
N-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
W-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
W-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:51
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
N-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
N-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
W-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
W-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
N-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:52
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) st
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
E-min
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
E-min
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
S-max
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
E-min
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
S-max
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:53
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
E-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
S-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
S-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:54
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
E-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
S-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
W-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
S-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
W-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:55
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
E-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
W-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
W-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:56
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
E-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
W-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
N-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
W-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
N-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:57
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
E-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
N-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
N-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:58
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
E-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
E-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
N-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
N-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
E-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:59
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) st
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
S-min
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
S-min
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
W-min
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
S-min
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
W-min
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:60
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
S-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
W-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
W-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:61
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
S-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
W-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
N-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
W-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
N-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:62
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
S-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
N-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
N-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:63
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
S-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
N-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
E-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
N-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
E-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:64
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
S-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
E-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
E-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:65
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
S-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
S-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
E-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
E-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
S-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:66
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) st
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
W-max
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
W-max
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
N-min
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
W-max
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
N-min
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:67
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
W-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
N-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
N-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:68
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
W-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
N-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
E-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
N-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
E-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:69
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
W-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
E-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
E-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:70
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
W-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
E-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
S-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
E-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
S-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:71
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
W-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
S-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
S-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: SPRECT_5:72
for
z
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
=
W-max
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) &
W-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
<>
S-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) holds
(
S-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<
(
W-min
(
L~
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
K27
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
..
z
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
V1
()
V4
(
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
V5
( the
U1
of
(
TOP-REAL
2 : ( ( ) (
V6
()
V7
()
V8
()
V12
() non
empty
ext-real
positive
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
V161
() ) (
V47
()
V52
()
V161
() )
L15
()) : ( ( ) ( non
empty
V19
() )
set
) )
Function-like
non
constant
non
empty
V19
()
FinSequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
V6
()
V7
()
V8
()
V12
()
ext-real
V39
()
V43
() )
Element
of
NAT
: ( ( ) (
V6
()
V7
()
V8
() non
empty
)
Element
of
K27
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ;